FATIGUE HANDBOOK Offshore Steel Structures
Edited by A. Almar-Naess
I B
TAPIR 1985
Editorial Committee Jan R. Getz Professor, MARINTEK, Trondheim, Chairman of Committee. A. Alrnar-Naess Professor, Norges tekniske hogskole, Trondheim. Carl A. Carlsen Dr.ing., Senior Principal Surveyor, Det norske Veritas, Oslo. Kristian Haslum Sivilingenior, MAROTEC A/S, Oslo. Torgeir Moan Professor, Dr-ing., Norges tekniske hogskole, Trondheim. Per Tenge M-Sc., Chief Surveyor, Det norske Veritas, Oslo. Harold S. Tyler B.Sc. (M.E.), Principal Metallurgical and Corrosion Engineer, Phillips Petroleum Company Norway, Stavanger. Authors A. Alrnar-Naess Professor, Norges tekniske hogskole, Trondheim. Hiikan Andersson M.Sc., Structural Analyst, VERITEC, Oslo Einar Bardal Professor, Dr.ing., SINTEF, Trondheim. Stig Berge Professor, Dr .ing., Norges tekniske hogskole, Trondheim. Knut Engesvik Dr.ing., Senior Research Engineer, SINTEF, Trondheim. StAle Fines Sivilingenior, Senior Engineer, A.S VERITEC, Oslo. M.B. Gibstein M.Sc., Senior Principal Engineer, A.S VERITEC, Oslo. Per J. Haagensen M.Sc.A., Senior Research Engineer, SINTEF, Trondheim. Agnar Karlsen Sivilingenior, Principal Surveyor, Det norske Veritas, Oslo. Jon Lereim M.Eng., Principal Surveyor, Det norske Veritas, Oslo. Inge Lotsberg Dr .ing., Principal Engineer, A.S VERITEC, Oslo. Torgeir Moan Professor, Dr.ing., Norges tekniske hogskole, Trondheim. Einar T. Moe M.Sc., Senior Project Engineer, A.S VERITEC, Oslo. Stephen Slatcher M.A., Ph.D., Research Engineer, A.S VERITAS RESEARCH, Oslo. Stig Wastberg Ph.D., Principal Engineer, A.S VERITEC, Oslo.
PREFACE
Soon after oil and gas exploration and production began in the North Sea in the 19603, it became apparent that the steel structure design developed for offshore activities in the Gulf of Mexico was not adequate when transferred to the more rigorous North Sea environment. In particular, fatigue cracks evolved as a result of wave action during the severe winter storms. There were no serious accidents, but it was evident that there was a great need for better understanding of the fatigue phenomenon so that safer structures could be built. In Norway, a vigorous effort to collect wave, wind and current data, and to develop methods for calculating static and dynamic response in offshore structures started in the early 1970's. A corresponding, but less intensive activity to determine fatigue capacity of materials and welded joints in air and sea water, was initiated some years later, However, everyone concerned recognized that a much greater effort was needed to keep up with the rapidly developing construction work in progress in the North Sea. In 1977, concerned materials scientists at SINTEF and Det norske Veritas prepared a 5 year program for intensified research on fatigue of offshore steel structures. This was approved by the Royal Norwegian Council for Scientific and Industrial Research in 1979. In 1981, it became the National 5 Year Program for Fatigue of Offshore Steel Structures. The stated objective of the program: Establishing a more reliable basis for design of welded marine structures with respect to fatigue, thus contributing to an improved and better defined safety level for such structures, and developing a basic understanding of mechanisms and conditions governing the fatigue life of steel structures. A steering committee was named with responsibility for the organization and execution of the program. Present members are: Bjom Lian, Statoil, Chairman A. Almar-Naess, Norges tekniske hogskole Einar Horn, Det norske Veritas Per Tenge, Det norske Veritas Harold S. Tyler, Phillips Petroleum Company Norway.
During 1981-1985, research work was performed in laboratories at Norges tekniske hogskole, SINTEF, and Det norske Veritas. This work generally followed the original program at a total cost of about 25 million Nkr. The main contributors to the program are the Norwegian Council for Scientific and Industrial Research and Phillips Petroleum Company Norway. Supplementary funding is coming from Statoil, Oljedirektoratet, Norsk Hydro A/S, and Kvaerner Industrier A/S. Close cooperation was established with similar programs organized by the European Coal and Steel Community and National programs within the Community. In order to satisfy the objective of the program, it is important that results are available to engineering industries, oil companies and certifying authorities without delay, and in a form that can be understood and utilized by those responsible for the different stages in engineering, design, fabrication and service of offshore structures. Therefore, this book was written as one of the projects within the program. A six member committee with Mr. Kristian Haslum as editor drafted the outline and gave the initial instructions to the authors. At the final stage of the book, the editorial work was undertaken by Professor A. Almar-Niess. It is intended that the book should cover the most important subjects related to fatigue of steel structures, to an extent and depth which will give the reader a correct understanding of the main problems, and enable transfer of knowledge into practical design. Examples of calculation of fatigue stresses and fatigue lives have been included to illustrate the text. Much of the editorial work has been to coordinate the eleven chapters so that the different topics are dealt with in a logical order without unnecessary recurrences, and with nomenclature and symbols that are essentially consistent. In this, the editor has been only partially successful. The editorial work has been a joint effort between the authors, Mrs. Vera AlmarNaess, who has composed the book and corrected the proofs, Mr. Per Molde and Mr. Ingar Graneggen, who have drawn the figures, and myself. I want to thank them all for a rewarding cooperation. I would also like to acknowledge the positive connection with Professor Jan R. Getz, chairman of the drafting committee, and Mr. Nils Ostlyng, director of Tapir. Trondheim May 1985 A. Alrnar-Naess
CONTENTS 1
OVERVIEW OF OFFSHORE STEEL STRUCTURES. . . . . . . . . . . . . . . . . . 1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Types of offshore steel structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.1 System layouts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.2 Joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2 Design requirements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.2.1 General remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.2.2 Loads and load effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.2.3 Ultimate strength design check. . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.2.4 Fatigue design check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.2.5 Progressive failure design check . . . . . . . . . . . . . . . . . . . . . . . . . 18 1.3 Practical implications of design criteria . . . . . . . . . . . . . . . . . . . . . . . . . 19 1.3.1 Semi-submersibles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 1.3.2 Tension leg platforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 1.3.3 Jackets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .22 1.4 Lessons learned from fatigue failures. . . . . . . . . . . . . . . . . . . . . . . . . . . 23 1.4.1 General remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 1.4.2 Fatigue failures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 1.4.3 Implications of service failures . . . . . . . . . . . . . . . . . . . . . . . . . . 32 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .35
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LOADS ON OCEAN STRUCTURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 List of symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 2.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 2.2 Stochastic processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 2.3 Dynamic effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 2.3.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 2.3.2 Single-degree-of-freedom system . . . . . . . . . . . . . . . . . . . . . . . . 48 2.3.3 Physical properties used for dynamic analysis . . . . . . . . . . . . . . . . 50 2.3.4 Natural frequencies of common structural elements . . . . . . . . . . . . 52 2.4 Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 2.4.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 2.4.2 Regularwaves. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 2.4.3 Irregular waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 2.4.4 Long-term wave statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
Contents Hydrodynamic forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 2.5.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 2.5.2 Loads on small-volume bodies - Morison's equation . . . . . . . . . . . 63 2.5.3 Loads on large-volume bodies . . . . . . . . . . . . . . . . . . . . . . . . . . 66 2.5.4 Deterministic calculation of response to hydrodynamic loads. . . . . . 69 2.5.5 Spectral method for calculation of response to hydrodynamic loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 2.5.6 Slamming. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 2.5.7 Vortex-induced oscillations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 2.6 Long-term stress range distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 2.6.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 2.6.2 Deterministic approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 2.6.3 Stochastic approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 2.6.4 Simplified long-term distribution . . . . . . . . . . . . . . . . . . . . . . . . 87 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 2.5
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FRACTURE MECHANICS AS A TOOL IN FATIGUE ANALYSIS . . . . . . . 91 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 3.1 Fundamentals of fracture mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 3.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 3.1.2 Analytical basis of LEFM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 3.1.3 Evaluation of stress intensity factors . . . . . . . . . . . . . . . . . . . . . . 98 3.2 Fracture mechanics applied to fatigue problems . . . . . . . . . . . . . . . . . . . 113 3.2.1 Estimation of crack growth . . . . . . . . . . . . . . . . . . . . . . . . . . . .113 3.2.2 Estimation of fatigue life . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 3.2.3 Fracture mechanics applied in the calculation of SN-curves . . . . . . . 130 3.3 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 Appendix 3 .A. Conversion tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 Appendix 3.B. General references . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .143 Appendix 3.C. A small compendium of stress intensity factors . . . . . . . . . . . . . 144 Two-dimensional edge crack problems . . . . . . . . . . . . . . . . . . . 144 Elliptical cracks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
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BASIC FATIGUE PROPERTIES OF WELDED JOINTS. . . . . . . . . . . . . . . - 1 5 7 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 List of symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 4.1 Basic fatigue mechanisms and characteristics . . . . . . . . . . . . . . . . . . . . . . 159 4.1.1 Fatigue initiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .160 4.1.2 Crack growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 4.1.3 Final failure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .168 4.1.4 Characteristics of fatigue failures . . . . . . . . . . . . . . . . . . . . . . . . 168 4.1.5 Fatigue capacity assessment. . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 4.2 Constant amplitude SN testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .176 4.2.1 SN testing versus crack growth testing . . . . . . . . . . . . . . . . . . . . .176
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Contents 4.2.2 Basic concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 4.2.3 TypesofSNtests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182 4.2.4 Fatigue failure criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 4.2.5 Fatigue limit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 4.2.6 Real structures versus test specimens. . . . . . . . . . . . . . . . . . . . . . 187 4.3 Cyclic strain and material response . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 4.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 4.3.2 Monotonic stress and strain . . . . . . . . . . . . . . . . . . . . . . . . . . . .189 4.3.3 Cyclic stress and strain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 4.3.4 Cyclic stress and strain resistance . . . . . . . . . . . . . . . . . . . . . . . . 192 4.3.5 Fatigue of notched members . . . . . . . . . . . . . . . . . . . . . . . . . . . 194 4.4 Variable amplitude loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196 4.4.1 Characterization of fatigue loading . . . . . . . . . . . . . . . . . . . . . . . 196 4.4.2 Cycle counting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 4.4.3 Load spectra. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 4.5 Cumulative damage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .208 4.5.1 The Miner summation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .208 4.5.2 Equivalent stress range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210 4.5.3 Stress interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 4.6 Fatigue of welded joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212 4.6.1. Crack initiation versus crack growth . . . . . . . . . . . . . . . . . . . . . . 212 4.6.2 SN-curve - low cycle and lugh cycle fatigue . . . . . . . . . . . . . . . . . 214 4.6.3 The effect of geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .215 4.6.4. Residual stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 4.6.5 Material properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 4.7 SN data for welded joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 4.7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 4.7.2 Classification of SN data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 4.7.3 Assessment of design SN-curves . . . . . . . . . . . . . . . . . . . . . . . . . 227 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 5
SIGNIFICANCE OF DEFECTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 5.2 Classification of defects according to origin . . . . . . . . . . . . . . . . . . . . . . 237 5.2.1 Fabrication defects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238 5.2.2 In-senice defects. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .241 5.3 Other faults in fusion welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242 5.4 Statistical description of weld quality . . . . . . . . . . . . . . . . . . . . . . . . . . 244 5.5 Non-destructive inspection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247 5.5.1 Non-destructive inspection methods . . . . . . . . . . . . . . . . . . . . . .247 5.5.2 Nondestructive inspection reliability . . . . . . . . . . . . . . . . . . . . . 249 5.6 Assessment of defects. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252 5.6.1 Fitness-for-purpose approach . . . . . . . . . . . . . . . . . . . . . . . . . . 252 5.6.2 Defect severity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258 IX-
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IMPROVING THE FATIGUE STRENGTH OF WELDED JOINTS . . . . . . . . 259 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .259 6.1.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 6.1.2 The potential for improving fatigue strength . . . . . . . . . . . . . . . . . 260 6.1.3 Improvement methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262 6.2 Weld geometry modification and defect removal methods . . . . . . . . . . . . . 264 6.2.1 Grinding techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264 6.2.2 Weld toe remelting methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 266 6.2.3 Improved welding techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . 270 6.3 Residual stress methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .273 6.3.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 6.3.2 Hammer peening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 6.3.3 Shot peening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275 6.4 Combination of improvement methods . . . . . . . . . . . . . . . . . . . . . . . . . 276 6.5 Test on large scale components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276 6.6 Comparison of improvement methods . . . . . . . . . . . . . . . . . . . . . . . . . . 278 6.7 Cost of improvement methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282 6.8 Applying improvement methods to offshore structures . . . . . . . . . . . . . . .283 6.8.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283 6.8.2 Effects of size and stress distribution in improved joints . . . . . . . . . 283 6.8.3 Inspection criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285 6.9 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .285 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286
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EFFECTS OF MARINE ENVIRONMENT AND CATHODIC PROTECTION ON FATIGUE OF STRUCTURAL STEELS . . . . . . . . . . . . . . . . . . . . . . . . 291 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291 7.1 Qualitative presentation of effects. mechanisms and important factors. . . . . 291 7.2 Effects of corrosion and cathodic protection on experimentally determined SNdata . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294 7.2.1 Plain specimens and different types and qualities of welded joints . . . 294 7.2.2 Significance of environmental factors and corrosion protection measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296 7.2.3 Significance of loading variables and materials properties . . . . . . . . 299 7.3 Effects of corrosion and cathodic protection on crack growth . . . . . . . . . . 300 7.3.1 Different effects at different levels of crack growth . . . . . . . . . . . . 300 7.3.2 Significance of loading variables and materials properties . . . . . . . . 301 7.3.3 Significance of environmental factors . . . . . . . . . . . . . . . . . . . . . 302 7.4 Prediction of effects of corrosion and cathodic protection on fatigue life by means of crack growth data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .304 7.5 Design guide-lines, British proposal . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308 7.6 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .309
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2 ! 3 -3Y 9
9
FATIGUE OF TUBULAR JOINTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .313 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .313 . Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .313 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314 8.2 Types of tubular joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .-315 8.3 Simple welded tubular joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318 8.3.1 Definitions and symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .318 8.3.2 Definition of the hot spot stress, and stress and strain concentration factors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320 8.3.3 Methods for stress analysis of tubular joints . . . . . . . . . . . . . . . . . 326 8.3.4 Stress concentration factors. . . . . . . . . . . . . . . . . . . . . . . . . . . . 333 8.3.5 Fatigue testing, experimental results and establishment of SN-curves 339 8.3.6 Joint design and fabrication. . . . . . . . . . . . . . . . . . . . . . . . . . . . 345 8.3.7 Procedurg for fatigue evaluation of tubular joints . . . . . . . . . . . . .346 8.3.8 In-senice experience. Repair . . . . . . . . . . . . . . . . . . . . . . . . . . . 348 8.3.9 Fracture mechanics analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . .349 8.4 Heavy duty joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349 8.4.1 Overlapping joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 350 8.4.2 Complex joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .353 8.4.3 Cast steel nodes (CSN) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359 . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360 Appendix A: Parametric formulas for stress concentration factors. . . . . . . . . . . . 363 UNSTABLE FRACTURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .371 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371 . 9.1 Failure modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .371 . 9.2 Modes of unstable fracture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372 9.3 Toughness parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374 9.3.1 Charpy toughness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .374 9.3.2 Fracture mechanics parameters to characterise unstable fracture . . . -375 9.4 Fracture toughness (KIC and CTOD) testing . . . . . . . . . . . . . . . . . . . . . . 376 . 9.4.1 KIC testing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377 9.4.2 CTOD testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .380 9.5 Application of fracture mechanics to unstable fracture . . . . . . . . . . . . . . .382 9.5.1 The stress intensity factor approach . . . . . . . . . . . . . . . . . . . . . . 382 9.5.2 The CTOD design curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 386 9.5.3 The R6 failure assessment diagram . . . . . . . . . . . . . . . . . . . . . . .389 9.5.4 Stress concentrations and residual stresses . . . . . . . . . . . . . . . . . . 393 9.6 Factors affecting fracture toughness . . . . . . . . . . . . . . . . . . . . . . . . . . .396 . 9.6.1 Thickness. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 396 9.6.2 Temperature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397 9.6.3 Strain rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .398 9.6.4 Metallurgy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .401 .
Contents
10 FATIGUE LIFE CALCULATIONS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .405 10.1 Importance of fatigue life estimation at the design stage . . . . . . . . . . . . . . 405 10.2 Prediction of fatigue life by use of SN data and the Miner-Palmgren approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 406 10.2.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .406 10.2.2 Closed form fatigue life equations. . . . . . . . . . . . . . . . . . . . . . . . 409 10.2.3 Calculation of equivalent stress range . . . . . . . . . . . . . . . . . . . . .413 10.2.4 Stresses to be considered . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415 10.2.5 SN-curves and joint classifications . . . . . . . . . . . . . . . . . . . . . . .421 10.3 Prediction of crack propagation by use of da/dN-AK curves . . . . . . . . . . . 422 10.3.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .422 10.3.2 Constant amplitude loading . . . . . . . . . . . . . . . . . . . . . . . . . . . .423 10.3.3 Variable amplitude loading . . . . . . . . . . . . . . . . . . . . . . . . . . . .425 10.3.4 Geometry functions and crack growth integrals . . . . . . . . . . . . . . . 425 10.4 Sensitivity and uncertainty analysis of fatigue life . . . . . . . . . . . . . . . . . . 427 10.4.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .427 10.4.2 Load calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .428 10.4.3 Stress calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 429 10.4.4 SN data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431 10.4.5 Fabrication tolerances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .433 10.4.6 Cumulative damage hypothesis. . . . . . . . . . . . . . . . . . . . . . . . . . 434 10.4.7 Probability of failure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434 10.5 Design formats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .437 10.5.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .437 10.5.2 Allowable stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 438 10.5.3 Allowable cumulative damage ratio . . . . . . . . . . . . . . . . . . . . . . . 440 10.5.4 Comments on the design formats . . . . . . . . . . . . . . . . . . . . . . . .443 10.6 Allowable stress format for pre-engineering design check . . . . . . . . . . . . . 443 10.6.1 Design chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .443 10.6.2 Considerations on the Weibull parameter h . . . . . . . . . . . . . . . . . . 445 10.7 Considerations on yield strength and relieving of residual stresses . . . . . . . . 447 10.7.1 Yield strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 447 10.7.2 Post weld heat treatment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 447 10.8 Example 9 . Redesigning of cross joint in a loading buoy . Discussion on the choice of SN-curve and possible use of stress relief heat treatment . . . . . . . 448 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 456
. . 459 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 459 11.1 The various codes on fatigue requirements . . . . . . . . . . . . . . . . . . . . . . .459 11.2 Fatigue design regulations based on fatigue strength tests . . . . . . . . . . . . . 462 11.2.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 462 11.2.2 Stresses to be considered . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .462 11.2.3 SN-curves and joint classifications . . . . . . . . . . . . . . . . . . . . . . . 463
11 FATIGUE IN BUILDING CODES . BACKGROUND AND APPLICATIONS
Contents 11.2.4 Thickness effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465 11.2.5 Fatigue failure criteria inherent the SN-curves. . . . . . . . . . . . . . . . 468 11.3 Stress concentration factors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 468 11.4 Examples of fatigue design based on fatigue strength tests . . . . . . . . . . . . . 468 11.5 Fatigue design regulations based on crack growth rate tests and fracture mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .481 11.5.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .481 11.5.2 Crack growth parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481 1 1 -5.3 Crack growth calculation for butt welds, cruciform joints and tubular joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 482 11.6 Examples of crack growth calculation based on crack growth rate tests and fracture mechanics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 492 11.7 Fatigue failure criteria in connection with repair of defects . . . . . . . . . . . . 495 11.8 Notes on damages and methods for making repairs . . . . . . . . . . . . . . . . . . 496 11.8.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 496 11.8.2 Repair and reinforcing methods . . . . . . . . . . . . . . . . . . . . . . . . . 497 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 500 Appendix A. Joint classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 502
SUBJECT INDEX. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513
CHAPTER 1
OVERVIEW OF OFFSHORE STEEL STRUCTURES Torgeir Moan Norges tekniske hsgskole, Trondheirn
ABSTRACT The main features of various types of offshore steel structures are outlined. Their construction and fabrication are discussed in relation to their fatigue strength. Design requirements for offshore platforms are reviewed, with emphasis on those concerned with structural integrity. The practical implications of design requirements are shown, with a semi-submersible being used as the principal example. In particular, the factors that determine the relative importance of the fatigue design criterion have been discussed. Lessons learnt from service failures of structures are used to illustrate how fatigue failures may be avoided by proper design, fabrication and operation. 1.1
TYPES OF OFFSHORE STEEL STRUCTURES
1.1.1 System layouts Fig. 1.1 shows typical floating and bottom supported offshore platforms. All these structures are made of steel, except the one in Fig. 1 . l e, which is a concrete platform with a steel deck. Semi-submersibles, or column-stabilized units differ radically in appearance from traditional vessels. They have a platform or deck area that might be square, rectangular or triangular in general configuration. This platform is supported by columns connected to large underwater displacement hulls, or it is mounted on large vertical caissons. The basic purpose of this design
Section 1.1.1
Fig. 1.1 Selected offshore structures. a) Semi-submersible platform; b) Tension leg platform; c) Buoytype platform; d) Jack-up; e) Gravity platform; f') Jacket; g) Steel tripod; h) Articulated tower; i) Guyed tower.
Section 1.1.1
t--I- I t ?
Section 1.1.1 is to reduce the effects of wave forces by locating the major buoyancy members beneath the surface and therewith the wave action. Sufficient stability is provided by the columns. Their operation displacement ranges from 15 00030 000 metric tons. The ratio between minimum (transit) and maximum displacement is 112 - 213. Several semi-submersible designs have the basic features displayed in Fig. 1.1 a - b, with a deck supported by two rows of columns, each connected to a "longitudinal" pontoon. The slender bracing arrangement varies. Semi-submersibles are commonly used in exploratory drilling, but also serve as production units in "marginal" oil fields. The buoytype platform in Fig. I . 1c is self-explanatory. Floating platforms are kept on location either by a conventional spread mooring, or a taut mooring system or a dynamic positioning system. Up to now spread mooring systems consisting of 6-12 lines with anchors at the ends have been used. The tension leg platform, Fig. 1.1b, is a semi-submersible type platform with buoyancy that exceeds its weight, and hence causes a pretension force in the vertical cables. The first tension leg production platform was installed in the Hutton field in the summer of 1984. The jack-up is characterized by 3-4 (or more) legs that can be lowered to serve as bottom support, see Fig. 1.ld. The main platform deck will thus be raised out of the water on location during drilling. However, the deck unit is watertight and has buoyancy and stability to serve as a transport unit with elevated legs during ocean or field transit. The legs may be pipes perforated with holes, or a truss-work. The jack-up is commonly used as a drilling plat form. A (concrete) gravity platform essentially consists of a large cellular caisson supporting 3-4 towers with a deck on the top, see Fig. 1.1 e. To date, the upper part of the superstructure has been exclusively a steel grillage, built of plate girders or as a truss-work, the main reason being the desire for low self-weight during tow-out. This makes it possible to install more equipment before tow-out, and thus reduce the offshore installation time. The basic concept of the gravity platform is to attain stability in the permanent location without special piling. The jacket or "template" platform is a truss-work tower consisting of tubular members with a deck on the top and piles into the sea-bed, see Fig. 1.1 f. The deck loads (and environmental loads) are transferred to the foundation through the legs, of which there may be 4 to 16. The legs are stiffened by a bracing, w h c h will also carry resultant horizontal forces. Most of the some 2500 jackets in the world are located in shallow waters. There are only about 50 in water depths over 100 meters.
Section 1.1.1 Smaller jackets are transported to the field location on a barge and lifted into position by a crane. Heavier jackets are towed self-floating and positioned by a weight-buoyancy system. The large legs on one broad-side of the jacket, illustrated in Fig. 1.1 f, served as buoyancy volume during towout. The installation phase is sensitive to the weather, and several weeks may elapse before the structure is safely pinned to the sea-bed. As an alternative to the conventional truss-work platform, steel or concrete tripod platforms have been suggested for deep water applications, Fig. 1.1 g. The use of inclined legs makes the global transfer of wave loads to the seafloor very effective, mainly by axial forces. The articulated tower shown in Fig. 1.l h, consists of a deck, a buoyancy chamber and a load bearing truss-work structure linked to the sea-bed by a joint. Alternative structural layouts are envisaged. So far, this type of platform has been used as loading buoys, but its potential as a production platform is being investigated. The guyed tower in Fig. 1.1i is a truss-work tower resting on a spud can (or piles) and is moored by some 20-24 pre-tensioned cables. A buoyancy chamber located below the mean water level may be used to relieve the spud can or piles of some of the vertical loads. The first guyed tower has been successfully installed in the Lena field of the Gulf of Mexico.
T-joint
Y -joint
K-joint D T joint
Heavy wall can joint
Fig. 1.2 Simple tubular welded joints. a) Simple plane joints; b) Multiplane joints.
Section 1.1.2
1.1.2 Joints Offshore steel structures are commonly composed of thin tubular members because their closed sections provide buoyancy and high torsional rigidity, minimum surface for painting and corrosion attack, simplicity of shape and pleasing appearance. In submerged parts of the structures, circular tubes are preferred because they result in smaller hydrodynamic forces than members with square cross-sections. However, fabrication is easier for the latter type. Above the splash-zone, hollow rectangular sections or other sectional shapes may be used.
Colu shell I
I
I
I
a)
I
Fig. 1.3 Welded joints of circular tubular members.
Section 1.1.2 Possible ringstiffener/bulkhead
Fig. 1.4 Transition components for a) small diameter tubes and b) large diameter tubes. Possible vertical T-shape stiffeners are not shown.
Welded
Cast
Fig. 1.5 Difference in layout of a) welded and b) cast tubular joints. Fig. 1.2 a shows typical configurations of tubular joints for members lying in one plane. In Fig. 1.2 b more complex three dimensional situations are displayed. Depending on the relative diameters of the members and their plate thicknesses, stiffening of the joint may be used. The simplest form of stiffening is to increase the plate thicknesses in the joint area. Other possi-
Section 1.1.2
Fig. 1.6 Various types of welded joints. a) Between tubes with rectangular cross sections, b) and c) between plates, d) attachment welds. bilities include the use of internal bulkheads and stiffeners as shown in Fig. 1.3. Fig. 1.3 a shows a layout applicable when members of very different sizes are to be joined. Fabricating joints with internal stiffeners obviously requires a minimum space and thus a minimum diameter of the tubes. Sometimes, a transition component is introduced between the member and the joint itself. This may be done to increase the diameter or t o change
Section 1.2.1 the cross-sectional shape as shown in Fig. 1.4 a. Ring-stiffeners may be introduced at the juncture between the circular tube and the transition component. Cast joints may be used instead of joints built-up by welding, Fig. 1.5. The advantage is that the geometry may be smoothly shaped to keep stress concentrations low. In the connection between the column and pontoon in Fig. 1.3 b, a cast piece was used to reduce stress concentrations and avoid welds in the highly stressed region. However, costs and proneness to brittle fracture are disadvantages that should be considered. Rectangular members may be joined as shown in Fig. 1.6 a, possibly with internal stiffening. Such joints tend to be planar joints or complex joints in planes which make right angles to each other. Members having equal widths and lying in one plane can be effectively joined as shown in Fig. 1.6a. Joints between rectangular tubes may offer advantages with respect to analysis and fabrication. Various joints between plates are shown in Fig. 1.6b and c. Other structural details may have to be introduced in offshore structures for different reasons. Holes for penetrating pipes, water drainage, attachment of anodes, etc. are examples of such details, Fig. 1.6 d. 1.2
DESIGN REQUIREMENTS
1.2.1 General remarks In general, a structure is designed so as to serve its function with an adequate safety and economy. For instance, the main layout (pontoons, columns, deck) of a floating platform as shown in Fig. 1.7 used in drilling operations, is determined by the requirement for a stable platform having a large deckload capacity combined with limited motions, sufficient mobility and overall strength. To fulfill most effectively the requirements of structural strength, it may be necessary to introduce bracings or other members. The local layout, i.e. the plate thicknesses, use of brackets etc. and materials, are determined on the basis of strength, fabrication and inspection, and maintenance requirements. Strength criteria refer to failure modes such as rupture by overloading, or to fatigue failure of individual structural components or by the progressive failure of the system. Rupture may occur as an unstable fracture or a ductile buckling.
Section 1.2.1
Fig. 1.7 Semi-submersible drilling plat form. Unstable fracture, which reveals itself as a fishbone pattern (Fig. 1.8a), is primarily avoided by proper selection of material qualities, depending upon ambient temperature, plate thickness and triaxiality of the stress pattern (Refs. / 1/, 120. A ductile collapse occurs by excessive yielding or buckling (Fig. 1.8 b) under a single extreme load. A fatigue failure is caused by the cumulative effect of many load cycles (Fig. 4.8). The region surrounding the origin of the fatigue fracture has a smooth, silky appearance. As the crack progresses, the texture becomes rougher. Careful examination of this smooth part frequently reveals concentric rings or beach marks around the fracture nucleus. On a microscopic level, lines corresponding to each load cycle or group of cycles may be observed (Fig. 4.8). Design criteria for ductile collapse and fatigue may be stated more explicitly in terms of stresses (load effects) caused by the external loads on one hand and the capacity of the structural components on the other. Before stating these criteria, a brief description of loads and load effects is provided. A full discussion is given in Chapter 2.
Section 1.2.2
Fig. 1.8 Appearance of overload failures. a) Unstable fracture surface (Ref. 131); b) Ductile collapse of a cylinder (Ref. 141). 1.2.2 Loads and load effects Loads on platforms mainly consist of two categories:
-
-
Functional loads due to steel weight, ballast, deck loads, and the reaction forces: Buoyancy for floating platforms, and foundation reactions for fixed ones. These loads are quasi-static (slowly varying over time). Environmental loads due to waves, currents and wind. The corresponding reaction forces are primarily inertia forces due to the dynamic wave and wind forces, mooring forces due to steady currents together with wind forces for floating platforms, and foundation reactions for fixed platforms.
Section 1.2.2 The forces and stresses due to external loads are commonly determined by separately calculating their local and global effects. For instance, the effect of the distributed hydrostatic pressure on the pontoon plate, stiffeners and frames of the semi-submersible in Fig. 1.7 are determined by considering the direct pressure on the pontoon plates. In addition, the hydrostatic pressure yields a resultant load per unit length of the pontoons , i.e. the buoyancy, which will balance the own weight of the platform. The global behaviour of most types of platforms, such as semi-submersibles and jackets is determined by using a frame model of the platform. The functional loads are directly applied t o the frame. The wave (and wind) loads fluctuate in a stochastic manner. However, experience has shown that the extreme effects (stresses, forces) due to waves can be determined accurately enough by the so-called design wave method. The wave forces are then determined with the platform in a regular extreme wave of appropriate length and height. In practice, several design wave load conditions (wave height/-length, direction) have to be applied to obtain the maximum forces and stresses in each member or joint. Fig. 1.9 a shows how the stress may vary at a weld joint in an offshore structure. In welded structures it is the stress reversal o r stress range, Ao, that causes the crack to grow. Normally, the effect of the sequence of the reversals is not accounted for. Therefore, the stress history in Fig. 1.9 a may be represented by the number of cycles, ni associated with each stress range interval [noi; Aoi + A(Ao)] in a time period T, as shown in Fig. 1.9 b. If the time period is long e.g. several years, a probability density function fA,(Ao) may be defined on the basis of relative frequency and information of the type given in Fig. 1.9 b.
Time
Stress r a n g e
Fig. 1.9 Fatigue load effects. a) Stress history; b) Frequency of stress ranges.
Ao
Section 1.2.3
where No is the number of stress cycles in the period T. For many marine structures, fA,(AO) can be closely represented by the Weibull distribution:
= the scale parameter where: h = Aoo /[ lnNo 1'' Aoo = expected maximum stress range in the period T p = the shape parameter
(1.3)
0 is a good indicator for the relative importance of the stresses inducing fatigue and those inducing overload in the structure. This is because P indicates the relative magnitude between the stress occurring once in the lifetime of the structure and stresses occurring, say, lo4 times within the same life. The Weibull distribution Eq. (1.2) has been generally verified, but the parameters p and h (or Aoo) have yet to be determined. For a wide class of semi-submersible platforms, P varies in the range 1.0 to 1.2. If Aoo is determined conservatively by a design wave approach, 0 can be assumed equal to 1.0. Hence, when the extreme wave load effect, i.e. the stress oo, at a weld joint has been determined as mentioned above, the extreme stress range Aoo is obtained as 2u0. The value of the shape parameter 0 is further discussed in Sec. 10.6.2. More information regarding P and Auo is available in Refs. /5/and / 6 / . 1.2.3 Ultimate strength design check As previously indicated, the occurrence of unstable fracture due to overloads is avoided by proper selection of material properties, weld layout, welding procedures etc. Criteria for ultimate ductile failure are usually expressed by a load effect Q, in terms of a stress resultant or stress, due to the various types of loads, and the associated strength R of the structural component. The characteristic strength, R,, is required to be greater than the characteristic load effect, Q,, by a certain safety factor 7
Section 1-2.4 The characteristic value of the strength R, is determined as a value which R will exceed in 95-98% of the cases. Characteristic values of the functional loads are specified values, and characteristic values of environmental loads correspond to an occurrence on the average once every 100 years. The safety factor y is introduced to ensure that failure does not occur too frequently, due to the inherent uncertainties in Q, and R,. For, e.g. a brace in axial tension or compression, the design check in terms of stresses, is simply (Ref. / 1/) :
where o, and o,, are the load effect (axial stress due to external loads) and the strength, respectively. For tensile stresses o,, = Re (yield strength). For compressive stresses o,, decreases with increasing slenderness ratio, A, due to buckling. Here, h is L/ri, where L and ri are the buckling length of the brace and radius of inertia of its cross section, respectively. In many cases a more general design check than Eq. (1.4) must be applied. For instance, when a brace is subjected to both axial stresses due to an axial force (0,) and bending moments (ab), the design check for a semisubmersible drilling platform may be stated as (Ref. /I/):
k
o,
+ ob < Y1 Re -
where k = Re/oUa
The stresses o, and ob are obtained for an extreme load condition, i.e. by a design wave approach. For production platforms, slightly different formats for design checks are applied (Ref. 121).
1.2.4 Fatigue design check The fatigue phenomenon. Fatigue fracture goes through three stages: initiation, slow growth, and onset of unstable fracture, see Refs. 171 and 181. Fatigue cracks usually originate at the surface. Once a crack is initiated, it grows slowly as the stress cycles are repeated, even if the stress level is below yield. In offshore structures the cyclic stress variations are primarily caused by waves and wind loading. When the crack size becomes critical, an unstable fracture occurs. In welded structures fatigue cracks almost always start at a weld defect, and the growth period accounts for more than 90 percent of the fatigue life. The crack growth depends on the stress conditions at the crack tip as further discussed in Secs, 3.2 and 4.1. The crack grows when opened by tensile stresses. Under a compressive loading the two surfaces may be forced into
Section 1.2.4
b V)
E
*-'
v,
V)
-
-
:
R
e
v e
Fig. 1.10 a) Stress variation due to external loading.
Time
b) Stress variation due to external loading and extreme residual stresses.
contact and can then transmit forces without activating the notch at the crack tip. It is still a matter of discussion whether a compressive stress (i.e. below the time axis in Fig. 1.10a) should be considered to contribute to the fatigue damage. In the presence of residual tensile stresses it is the combined stresses due t o fabrication and external loads that matter. Residual stresses adjacent to welds are commonly assumed to be tensile and amount to yield stress level. In the case of a one dimensional stress condition, the yield stress represents the upper limit of stress, and a constant amplitude loading will then result in stress variations adjacent to a weld, as shown in Fig. 1.10 b. In this case Ao will be the significant parameter to describe the time variation of the stress. In weldments with careful stress relief treatment and in cast nodes where initiation will contribute to the fatigue life, the mean stress om may also be a fatigue load parameter. The fatigue crack propagates in a direction normal to the maximum principal (tensile) stress. This has been observed by comparing fractured structures and calculated stress distributions. Fatigue crack growth follows different laws depending upon the level of the stress reversals. We therefore distinguish between:
-
low-stress, high-cycle fatigue - high-stress, low-cycle fatigue
Fatigue failures that occur after only 1O4 to lo5 cycles are usually denoted low-cycle. The endurance in high-cycle fatigue is usually several millions cycles. Since only the latter phenomenon has been of real concern in offshore platforms t o date, this section will be concerned with high-cycle fatigue.
Section 1.2.4 The fatigue capacity of a welded joint subjected to constant amplitude uniaxial loading, is expressed in terms of an SN diagram. For welded structures the SN-curve is independent of the yield strength. This is because welded joints contain crack-type defects and the fatigue life consists of crack growth, which is independent of the yield strength. The crack growth depends on the very local cyclic stress at the crack tip. Hence, fatigue is governed by the geometry, especially any change in the geometry which introduces a concentration of the stress flow. The geometrical effects associated with the weld profile and inevitable weld defects are normally accounted for in the SN (capacity) data. Other geometrical effects should be considered in the calculation of local stress ranges, see Fig. 1.1 1. The effect of geometry on the local stress is further discussed in Secs. 4.6.3 and 10.2.4, and in Chapter 8 for tubular joints.
Plate
a)
Ring I stiffen-
LA
b
Plate thickness
A-A
LA
A -A
Crack o r undercut
c)
Fig. 1.11 Stress concentrations due to macroscopic changes of geometry. Order of magnitude of concentrator: a) Plate widthlmember diameter; b) Fraction of plate widthlstiffener height; c) Plate thickness.
Section 1.2.4
Failure criterion - variable amplitude loading. The failure criterion is commonly expressed by the Miner-Palmgren hypothesis as
where the cumulative damage, D, is determined on the basis of the number of cycles, ni, in the local stress range interval between Aoi and A U ~ +Ni~ .is the number of cycles to failure at stress range A u ~ +according ~ , ~ to the SN-curve. S is a constant of magnitude between 0.5 and 1.O.
Design check. The fatigue design check may be performed with a different degree of refinement, namely : 1. Judgement, more or less qualitative, based on experience. 2. Calculation of acceptable fatigue life based on the SN Miner-Palmgren approach. 3. Fracture mechanics analysis. As discussed earlier, the first approach should be used with caution, if it is not supported by significant quantitative experience from similar cases. Underestimation of the fatigue hazard has led to several accidents. The second method may be expressed as:
Bearing in mind the uncertainties in the factors involved in Eq. (1.8), the acceptable cumulative damage A is chosen as a value smaller than 6 to ensure an adequate margin of safety. Eq. (1.8) may be approximated by assuming that ni is represented by Eqs. (1.1 a) and (1.2) and by using an SN-curve of the form
The result for the damage:
where No is the number of cycles in the design life of the structure (e.g. 20 or 50 years), Aao is the expected maximum value of the stress range in the design lifetime, and I'( ) is the gamma function. Clearly, Eq. ( 1.lo) is based on approximations and should be used with caution.
Section 1.2.5 The format expressed by Eq. (1 .lo) may be reformulated as
which resembles Eqs. (1.5) and (1.6) for the ultimate limit state (ULS) check. The principal differences are that Eq. (1 .l Oa) refers to an extreme stress range due to wave and wind loading, while Eqs. (1.5) and (1.6) involve extreme stresses due to functional as well as environmental loads. Furthermore, Eqs. (1.5) and (1.6) refer t o nominal stresses in braces due to beam theory while the stress range in Eq. (1 .lOa) includes the magnification due to local changes in the geometry. Finally it is noted that Oo will depend on the shape parameter, p, of the distribution of stress-ranges, and hence the total load history. As in the ULS check, a characteristic value of Ni is applied in Eq. (1.9). Usually, SN-curves corresponding to a probability of 97.5% of survival are used. ni in Eq. (1.8) is taken as the expected long-term distribution. The value of A is chosen such that the probability of failure due to the uncertainties of ni and Ni in Eq. (1.8) is acceptably small. In practice, A lies between 0.1 and 1.0. The third approach by fracture mechanics may be viewed as a refinement in the determination of Ni in Eq. (1 3). 1.2.5 Progressive failure design check
Progressive failure may develop after a local damage if the structure has little reserve strength. The initial damage may be ductile collapse due to collision or other abnormal loads; or it may be a fracture due to fabrication faults, or a fatigue fracture. Since it can obviously take some time before such damage is detected and repaired, the structure ought to survive a certain period of time in the damaged state. The philosophy applied by e.g . the Norwegian Petroleum Directorate (NPD), Ref. 121, for production platforms is that system failure should not occur due to local damage. The design check is accomplished by assuming a certain degree of damage, as specified in the code, and primarily applying an ULS type criterion to check that there is adequate strength to resist the loads acting on the structure in the damaged condition. The loads used in the residual strength check depend upon the anticipated time to repair. As repairs are often only possible in the summer, the structure should survive a winter storm. The NPD specifies environmental loads that occur once in 100 years. However, the required safety factors are less than in the ordinary ultimate strength check and generally equal to 1.O.
Section 1.3.1 The "Alexander L. Kielland" accident initiated progressive strength criteria for semi-submersibles and other mobile platforms classified by Det norske Veritas. Semi-submersibles are hence required to have adequate reserve strength after the failure of any one brace. In this case environmental loads with an annual occurrence and a safety factor of 1.2 are applied. PRACTICAL IMPLICATIONS OF DESIGN CRITERIA
1.3
In this section the influence of fatigue criteria on layout, dimensions, local detailing of structural components and on materials selection will be discussed. 1.3.1 Semi-submersibles
In the design of semi-submersible platforms for exploratory drilling operations in the North Sea (Fig. 1.7), the overall layout is determined on the basis of requirements to floatability/stability, limited motion and strength for resisting progressive failure. The scantlings of the deck, columns and pontoons are governed by ultimate strength criteria. For the braces the situation is different as fatigue criteria may be important. The procedure will normally be first to determine the plate thickness of the braces so that the ultimate strength requirement in Eq. (1.6) is fulfilled, and thereafter check for fatigue. The typical locations investigated, by applying formulas like Eq. ( 1.1O), are :
-
-
-
the brace to column connections possible transitions in cross-section properties longitudinal or transversal stiffeners on the braces cut-outs for equipment, port holes etc. attachments for equipment
If the fatigue criterion is not satisfied, one or more of the following remedies may be applied :
-
change of overall layout to reduce the fatigue loading increase of overall plate thickness in the brace or at areas with high local stresses, or introduction of stiffeners make the local geometry more smooth, e.g. by applying: brackets at hard points fully penetrated welds rather than fillet welds grinding butt welds and the toes of fillet welds
Section 1.3.1 Deck ?
I
0
/
-
Column
- -
A - W a v e length
I
I
Fig. 1.12 Semi-submersible platform subjected to a regular beam wave. To illustrate that the overall layout may have an important effect on the fatigue loads and hence the susceptibility to fatigue cracking, consider the platform shown in Fig. 1.12. Extreme waves occurring once in 100 years, may be 30 m high, and about 400 m long with a wave period of 16 s. Waves that induce fatigue occur more frequently, and have lengths of 100 m to 220 m and periods of 8 to 12 s. The extreme stresses in platforms do not necessarily occur for extreme waves, hence, the condition shown in Fig. 1.12 can often be the most critical for the horizontal braces in semi-submersible plat forms. The length of the wave in Fig. 1.12 is 100 m, and occurs quite frequently, so in this case the amplitude of the stresses, occurring many thousand times, will not be very much less than the one occurring once during the lifetime. Therefore, the fatigue criteria rather than ultimate strength criteria will dominate for these braces. However, the significant change of main dimensions required to achieve reduced fatigue loads introduces other disadvantages, e.g. regarding the strength of the deck. This approach is therefore practised rarely in semisubmersibles, though in other types of platforms, such as jackets, the choice of layout to limit fatigue loads is of more interest (Ref. 191). If it is assumed that an increase in plate thickness affects the nominal stress level and not the stress concentration, then an increase in plate thickness by a factor of a will reduce the fatigue damage, D, by a factor a-0.75m, where m lies between 3 and 5. Hence doubling the plate thickness, results in a D which is between 20% and 8% of the reference value. The reduction will be greater if the possible effect of increased plate thickness on the stress concentration is considered. If larger plate thicknesses are introduced for
Section 1.3.1 fatigue reasons, it is also natural to use steel with a lower yield strength, Re. This is because the fatigue strength does not depend upon the yield strength, and the ultimate strength criterion, Eq. (1.6), will be satisfied by a lower Re when o, and ob are reduced by increased thicknesses. Also, steels with lower yield strengths usually have better weldability. The extra steel weight in braces does not represent a serious penalty because their centre of gravity is low. However, increased thicknesses themselves may cause weldability problems, and imply more costly fit-up, welding and welding procedures. By smoothing the geometry as shown in Fig. 1.13, the stress concentration factors (SCF's) are reduced. A reduction of SCF to SCFIa implies a reduction of the fatigue damage from D to D/am. According to recent fatigue codes (Ref. /8/), grinding of the weld toe implies a reduction of D by about 50%. However, grinding should preferably not be used as a design measure but rather kept as a last resort of improvement after fabrication when for any reason tlus would be necessary. Such a
G r o u n d flush
Im l m proved
l m proved
l m proved
M l m proved
Improved
P l a t e a i s continuous through p l a t e b
Fig. 1.13 Improvement of fatigue life by changes of geometry. a) Butt weld, b) fillet weld, c) plates, d) plane plates in a 3-D joint.
Section 1.3.1 measure might be accepted by the authorities, but the benefit might not make up for the costs. Different methods for improving the fatigue strength of welded joints are discussed in Chapter 6. When fatigue requirements, with A in Eq. (1.8) equal to 1.O, are imposed on braces in actual semi-submersibles which have been designed to fulfill ULS requirements, the results have been increases of plate thicknesses by as much as 50%, local smoothing of brace-column connections by brackets and cut-outs (Fig. 1-13), and improvements of the weld geometry and quality. As the requirements have been tightened recently, changes on existing platforms have also been undertaken, obviously at much higher costs than when implemented during the initial design and fabrication.
1.3.2 Tension leg platforms For tension leg platforms (Fig. 1.1 b), fatigue criteria in particular may influence the layout and scantlings relating to the pontoon-column connections. In the Hutton platform in the North Sea, fatigue requirements with A in Eq. (1.8) equal to 1.O, were governing for in-board sections of the column shell and the pontoon (Ref. /lo/). As in the case of semi-submersibles, it was found that relatively short waves, with periods of 10 to 12 s, were equally important as the extreme 100 year wave of greater length. The fatigue criterion led to a 10% increase of steel weight of a hull designed according ULS criteria. In addition, fatigue considerations implied careful design of geometrical transition areas and weld connections together with restrictive fabrication procedures and control. A special design feature that evolved from the fatigue analysis was the introduction of a cast steel transition piece as shown in Fig. 1.3 b. The objectives of this were to :
-
improve the stress concentration - move critical welds away from the hot spots - solve the geometrical problem of tapering the curved pontoon to the column shell. - improve the SN weld class in the area The cast joint improved the fatigue life by a factor of 9 compared t o a conventional welded joint. 1.3-3 Jackets
In the design of the Mau jacket platform offshore New Zealand (Ref. 11I/), the fatigue criterion was found to increase the weight of the jacket by about 4%.
Section 1-4.1 For North Sea jackets in up to 180 m water depths, such as the Murchison jacket (Ref. /12/), fatigue governs plate thicknesses in some joints. For most platforms in the Gulf of Mexico, fatigue criteria are not governing because the wave climate is dominated by rarely occurring hurricanes, which induce large extreme loads, but few stress reversals. However, for the Cognac platform in 300 m of water, fatigue had some influence on the design of some tubular joints due to dynamic magnification of the response (Ref. 191). In the first two cases mentioned above, the A in Eq. (1.8) was set equal to 1 .O, in the latter to 0.5. If A is reduced to 0.1 for joints where fatigue is governing, then the plate thickness must be increased by 30-50%. Increasing the thickness may cause fabrication problems and stiffeners may have to be used.
1.4
LESSONS LEARNED FROM FATIGUE FAILURES
1.4.1 General remarks
We learn more from failures than successes. The phenomenon which is today known as fatigue was itself discovered prior to 1850 by observing railway axles failing without apparent cause. The understanding of the phenomenon was brought a big step forward by Wohler's intensive and systematic studies in the 1850's. Many times afterwards the fatigue phenomenon has been more or less rediscovered for various types of structures, i.e. bridges, ships, aircraft and offshore platforms. In the popular literature, Kipling was presumably the first to exploit the dramatic possibilities of fatigue. In "Bread Upon the Waters" in 1895 he described how the Grotkau lost a propellor due to a fatigue crack in the tailshaft. Kipling went out of fashion, but public interest in fatigue was reviewed in 1948 by Nevi1 Shute's "No Highway", a few years before the three Comet aeroplane disasters, which were initiated by fatigue cracks. We can still learn from fatigue failures. For instance, the appearance of the crack surface may provide information about the rate of crack propagation. On the microscopic level the distance between striations, which are marks set up by each load cycle, may give such insight. In case of variable amplitude loading, beach marks on the crack surface may also give clues to the load history and crack propagation rate. Another source of information is the location of crack initiation, which may be roughly determined from the beach mark pattern (Fig. 4.8). Both the shape and size of the weld defect initiating the crack and the surrounding geometry may contribute to the understanding of how the failure has been affected by factors relating to design and fabrication.
Section 1.4.2 Only in relatively few cases has the physical cause of the failure, e.g., the type of cracking (hydrogen induced, lamellar tearing, fatigue, stress corrosion, brittle fracture) been determined. This information can only be revealed when there is access to the fracture surface. The crack appearance on the plate surface does not even allow judgement as to whether the crack is fatigue or otherwise. Where it is possible for repairs to be effected in situ, failures are frequently not removed from the installation for investigation, so that either no specific cause is recorded, or where the cause is stated, its veracity must be open to question. In certain cases, removal of the failed parts for investigation may enhance the existing hazard or create a new one. In any case, establishing the causes of failures frequently requires quite extensive and laborous investigations in competent laboratories, together with reanalyses of fatigue loading etc. Some case histories and more general experiences regarding fatigue failures are briefly described in the following section. 1.4.2 Fatigue failures
Semi-submersibles and jack-ups. An early example of fatigue damage occurred in the original "Sedco 135", a triangular semi-submersible drilling rig, illustrated in Fig. 1.14 a, which began working in the Gulf of Mexico in 1965. By the end of 1967 fatigue failures were experienced in an aft horizontal brace in the same type of rigs operating in the North Sea, the South China Sea, the Canadian Pacific Ocean, and offshore Australia. The North Sea case is particularly illustrative, because the axial stress in the failed horizontal member was recorded during the few months before failure. The stress concentration factor measured on the prototype was 4.7 for the critical cylinder-to-flare knuckle transition. A cumulative fatigue damage calculation using curve X in AWS Code Dl .l-72 yields a Miner-Palmgren damage ratio of 2.18 for the North Sea platform (Ref. 1131). By using the mean value of more recent SN data, the expected damage ratio is found to be nearly an order of magnitude less than shown in Ref. 1131. Recognizing the scatter in fatigue life estimates, the above results imply a reasonable correlation between calculated and actual performance. However, abnormal weld defects or other deficiencies may also have contributed to the failure. This failure occurred in 1967 in a platform designed a few years earlier, at a time when fatigue design checks were not routine, and also before the severity of the fatigue loading of the North Sea was fully recognized. Other examples of occurrences of cracks which were published early, appear in Refs. / 141 and / 151.
Section 1.4.2 In May 1979 the jack-up drilling rig "Ranger I" (Fig. 1.14b) collapsed in the Gulf of Mexico (Ref. /16/). The accident occurred because a crack initiated and propagated in the aft leglstiffener weld and stiffenerlmat fillet weld. The cracks were coincident with the leg/mat bulkhead and structural bulkheads. This suggests that considerable rigidity in this region resulted in stress concentration. The approximately 500 mm long fatigue crack apparently developed at position 270' and to a lesser degree at position 90° in the course of the lifetime of the structure, and led to the collapse of the leg, with the subsequent falling down of the aft deck, and bending and separation of the forward legs. Crack indications were also observed near the same locations on the forward legs. The fatigue crack already existed when the platform entered a shipyard for repairs three months before the accident, but remained undetected. The rules of the Classification Society involved, were amended subsequent to the accident, demanding non-destructive testing of critical connections of support legs at periodic intervals. In March 1980 the accomodation platform "Alexander L. Kielland" (Fig. 1.14 c) with 2 12 men onboard capsized in the North Sea (Ref. 1171). The primary reason for the accident was the failure of a brace mainly due to a fatigue crack starting from a hydrophone support, followed by a rapid, unstable fracture. The fillet welds between the hydrophone support and the brace had a poor shape. Inspections had been performed during fabrication as well as during operation without discovering the 70 mm long cracks present already at the time of fabrication. Fatigue life calculations have been carried out based on Miner's rule as well as on the Paris equation, and the fatigue life of the brace could be verified within reasonable limits of uncertainty. Fracture mechanics analysis showed that the crack growth in the brace had accelerated very quickly from the initial stage. With a through-thickness crack of about 30 mm length, the remaining life of the brace was found to be less than one year. Cracks were observed at hydrophone supports in other rigs of similar design during inspections after the accident. The failure of this brace was rapidly followed by the failure of other braces supporting column D. The subsequent loss of column D led to flooding and capsizing within 20 min. It is noted that also the design of this platform was conceived in the 1960's when fatigue design checks were not as routinely done as they are today. However, when the actual platform was built in 1975-76, the general practice in the offshore industry regarding fatigue design check was different. But no fatigue checks had been made for "Alexander L. Kielland". Besides the above cases, where members actually parted, several cases of
Section 1.4.2
/I Forward
69
A f t horizontal
,Plate
o f brace D 6
\
marks
Drainage /hole
rnm
-
F i l l e t weld
Fig. 1.14 Mobile platforms suffering fatigue failures. a) "Sedco 135" (Ref. 1131); c) "Alexander L. Kielland" (Ref. 1171).
Section 1.4.2
F r a c t u r e i n a f t leg
- m a t connection
Fig. 1.14 b) "Ranger I" (Ref. /16/). cracks have been detected in semi-submersible and jack-up platforms (Refs. /18/ and /19/). Most cracks have been repaired without further examination and circulation of information. For instance, Lloyds' list contains only one of the many cracks detected at brace-leg connections, manholes etc. during the extraordinary surveys carried out especially on rigs in the North Sea after the "Alexander L. Kielland" accident. This incident was, however, widely published in the press. There are incidents that ought to have been reported and investigated, but were not. For instance, it is known that in a number of semi-submersibles, weld failures were so extensive that the safe operation of the rig was in jeopardy (Ref. / 181).
Section 1.4.2 Jackets. A case of partial failure of a fixed offshore platform in the North Sea is reported by Harrison (Ref. 1201). A plan view of the platform, a tubular structure with four legs joined by sundry tubular bracing members, is illustrated in Fig. 1.15 a. The failure involved the complete failure of three joints between the diagonal bracing and the main legs situated at a level approximately 0.6 m below the lowest astronomical tide level. Fig. 1.15 a shows the location of the fractures and cracks. At corners A8, A9 and B9, the 300 mm dia. 12 mm thick bracing tubes were completely detached from the legs, the failures having occurred through the bracing tubes and initiated at the toes of the tube-to-leg welds. At corner B8 the fracture had occurred in the leg material so that a disc of the leg had come off with the bracing. Cracks were also found at the crossing points of the diagonal members initiating at the toes of the welds. The welds between the bracing tubes and the legs were nominally full penetration welds made from the outside and built up with external fillets of about 10 mm leg length. Observations of the fracture surfaces revealed that the fractures were initiated at the outside circumference at the weld toe, by low stress-high cycle bending in the vertical plane. Underestimation of vertical wave loads seems to be a cause of the failure. Unusually large amount of marine growth surrounding the members, which had not been accounted for, was the main underlying cause. The marine growth amounted to 200 mm at the time of failure, so that the original 300 mm dia. bracing tubes were increased t o 700 mm. Taking the marine growth into account, the fatigue life was calculated t o 4.5-5.5 years. Ref. /2 1/ reports recent Findings of fatigue cracks at two levels (-6 m, - 20 m) in the horizontal conductor frame of an eight-leg platform in 110 m water depth, Fig. 1.15 b. Two reasons were found for the premature appearance of these cracks: Firstly horizontal wave forces had been fully considered in the original design but only limited allowance had been made for vertical forces, which were now found to be significant. Secondly, the original analysis used low stress concentration factors. A reanalysis was performed based on the new SN T-curve proposed by DOE for tubular joints, and up-to-date knowledge about loads and stress concentration factors. Good correlation was obtained for many of the cracked joints. Other incidents of fatigue crack propagation are referred to in general terms, for instance, in Refs. 1181 and 1231. Because these cases have been investigated less, our knowledge is incomplete and yields little information for the present purpose. The files of the Norwegian Petroleum Directorate reveal that 163
..,
a---Aeue--m,.aes.
--
I"'
"-
".-
A
--
"
--e"""w"+m*
Section 1.4.2 Fracture
Fracture plane
C
\
= Crack
.-------. -------------
-
Crack
.-------. ------------
Fig. 1.15 Jackets suffering fatigue damage. a) Horizontal truss-work of West Sole jacket (Ref. 1201); b) Horizontal conductor frame in eight leg platform (horizontal plane) (Ref. 1211); c) Typical cracked tubular joint.
cracks, fairly evenly distributed over the water depth, were detected in 27 North Sea jackets in the four-year period 1980-83. The actual number of cracks may be greater, as only 5-10% of the nodes are inspected in a four to five years cyclus. The cause of the cracks is hard to judge, but they are most
Section 1.4.2 likely due to fabrication defects. Most cracks were found to be non-propagating. In another survey (Ref. 1231) only 3 out of 33 cracks were reported to propagate. Also, most cracks are shallow and are easily repaired by grinding. Finally, most cracks affect secondary structures, such as the conductor frame in Fig. 1.15 b. A particular case worth noting is of a crack that was initiated and grew from a sharp dent caused by collision. In another case, a severe offset and poor weld between components which were assembled offshore, led rapidly to failure. Finally it is observed that malfunction of the corrosion protection system may lead to reduced plate thicknesses, and hence increased crack growth, or accelerated crack growth due to corrosion-fatigue. Such malfunctions of impressed current corrosion protection systems have been experienced (Refs. 1231 and 1241).
Other structures. Fatigue failure experiences in other structures such as ships, bridges, towers, etc., may provide useful insight into the fatigue problem for offshore platforms. Due to the greater structural redundancy in ships, fatigue damage has generally less severe consequences than in offshore structures. However, the economical losses may be considerable. It has been found that fatigue cracks are a dominating type of damage in ships, the total number being larger in oil tankers than in other types of ships (Ref. 1251). A very interesting survey of damages in large tankers is given in Ref.
1261, where types and frequency of damages are related to hull areas and types of constructional details. Most damages occur in the midship part. Cracks in brackets, at bulkheads and at notches dominate, see Fig. 1.16 a. No case was found where a crack could be related to an internal weld defect, although a rather large number of internal planar defects had been found by NDT. The cause of the surface defects observed was bad workmanship, which in many cases could be traced back to difficult working conditions for the welders (bad access). In some cases poorly designed structural details with excessive stress concentration had been the cause of cracking. Most cracks were initiated at structural discontinuities. Improvement in design practice had reduced the earlier experienced rate of such cracks. Another extensive investigation by the American Ship Structure Committee is reported in Ref. 1271. Over a long period Commission XI11 of the Int. Institute of Welding
Section 1.4.2
Longitudinal stiffener,
i
h, Cracks
I\. Side shell
Fig. 1.16 Cracks in ship details. a) Longitudinal-transverse stiffener connection, b) bracket in transverse frame. has collected information about fatigue failures in welded structures and their interpretation. Conclusions are drawn in Ref. 1281. The major part of failures are initiated at details of classes F, F2 and G according to Ref. 171. Details concerned are amongst others butt welds with backing bars, transverse and longitudinal fillet welded attachments, and load carrying transverse fillet welds. Incorrect design dominates as a primary reason, although other reasons such as bad workmanship and unexpected sources of fatigue loading may contribute to the failure. In particular, vortex shedding induced by a moving fluid has caused cyclic loading, and hence fatigue damage in bridges, offshore platforms, etc. Attention is drawn to the very high frequency involved. Fatigue failures can therefore occur, even if the damaging conditions are experienced only for short periods during either fabrication or delivery. It is further worth mentioning that fatigue cracks are rarely reported to start from internal weld defects. Several cases of fatigue failures in bridges are presented in Ref. 1291. A primary cause seems to be secondary stresses due to local bending, which have not been designed for. Large fabrication defects or cracks make up the next largest category of cracked members and components. Cracks occurring in planes parallel to the tensile stresses considered in the design, may not be
Section 1.4.3 detrimental to the performance of the structure, provided they are discovered and repaired before turning perpendicular to the tensile stresses produced by the loads on the structure. In several cases the defect was due to poor quality welds which were produced before non-destructive test methods were well developed. A large number of these cracks occurred because the component was considered a secondary member or attachment, so no weld quality criteria were established, nor were nondestructive test requirements imposed on the weldment . For some bridges an increased traffic intensity also increased the failure likelihood. 1.4.3 Implications of service failures
Design precautions. Fatigue crack growth especially occurs when the loading is predominantly dynamic, local stresses are relatively high, high-strength steels are applied, and when crack-type fabrication defects are likely. In some situations the design check may easily be overlooked, even if one or more of these factors are present. Some examples of such situations will be mentioned in the following. For instance, it should be noted that fatigue damage may be accumulated in temporary phases of the platform, such as during towing. In fact some components may be more stressed in temporary phases than in the in-service condition. Vortex-shedding phenomena may especially lead t o significant fatigue loads. Fatigue may occur even in components which are not introduced in the structure for strength purposes, such as installation lugs etc. Cracks may grow even in areas where the stresses due to the external loading are predominantly compressive, due to the presence of tensile residual stresses. Fatigue depends critically on stress concentrations, and every effort should be made to make geometrical transitions smooth and locate welds outside the areas of the highest stress concentrations. Use of cast components may facilitate this objective. Fillet welds have often been the cause of fatigue failures because of underdimensioning of the throat thickness, and improper weld shapes. The local geometry (alignment of plates, shape of weld profiles, size of weld defects) depends to a large extent on the execution of fabrication. The designer should have a realistic understanding of geometrical tolerances and the use of them in the design calculations and specifications for fabrication, see Fig. 1.17.
-
-
Section 1.4.3
Unrealistic
t I
v
Realistic
r
Unrealistic
Stiffener
Unrealistic
Realistic
%
Stiffener Gap
'plate
Section A-A
Realistic
Section A-A
Fig. 1.17 Geometric tolerances. a) Plate connection, b) stiffened plate.
It is important t o limit the susceptibility to cracking during fabrication and afterwards, including lamellar tearing, by specification of adequate materials properties and fabrication procedures, to achieve good weldability. Choice of a simple layout is important because it simplifies the fabrication and inspection, and thus reduces the probability of defects. In some cases the design check is done simply by copying previous design practice. However, great caution should be exercised when this practice is employed, since environmental conditions, material qualities, fatigue accept criteria etc. may differ, compared with previous cases. The designer should not focuse just on the direct satisfaction of the design criteria, but should consider other factors that could affect the fatigue risk indirectly. For instance, choice of layout is important for the access during fabrication. Good access is a necessary condition to avoid welding defects, as shown in Fig..l .l8. Also, overhead welding is more difficult and prone to faults than downhand or horizontal welding. Obviously access is also necessary to accomplish inspection. It is especially noted that some regulations and codes for fatigue design include fatigue acceptance criteria, which are dependent upon accessibility. Specification of fatigue prone areas which should be scrutinized during inspection, constitutes a part of the design documentation.
Section 1.4.3
J
Stiffener
Fig. 1.18 Difficult access for the welding stick may increase the susceptibility to welding defects. a) Steel-plated structure; b) Tubular joint. Fabrication precautions. Clearly, the fabrication should closely follow the specifications. However, brackets and stiffeners are sometimes chosen with more material than specified at the ends, because it might ease fabrication by reducing the welding deformations (Fig. 1.19). Such liberty in interpretation of the specifications might have a significant effect on the stress concentrations, and is not recommended. Stiffener
Fig. 1.19 Deviation between a) specified and b) as-fabricated details.
The design specifications do not define all the factors that influence the fatigue strength. For instance, start-stop positions of welds are decided during fabrication. As weld defects frequently occur at start-stop points, they should be located outside areas with high dynamic stresses as far as possible. In general, the quality of workmanship plays an important role for the fatigue life.
Chapter 1. References Precautions during operation. During operation the main aspect of fracture control involves reliable detection of cracks, judgement of their significance and the decision to repair. The time to failure of a cracked structure must be assessed by a fracture mechanics approach, or by experimental investigations. Repair of any damage must be carefully planned with due consideration of possible defects and stress concentrations. Repair welds, particularly when made under water or in other difficult circumstances, are unlikely to be better than those that have failed. Repaired cracked welds often fail again after a relatively short period. Sometimes some form of reinforcement is applied, but this often has the effect of moving the point of failure from one location to another.
REFERENCES 1. "Rules for Classification of Mobile Offshore Units", Det norske Veritas, Oslo, 1981. 2. "Regulations for the structural design of fixed structures on the Norwegian Continental Shelf' (with guidance notes), Norwegian Petroleum Directorate, Stavanger,
1984. 3. "The Alexander L. Kielland Accident", NOU report 1981:11, (in Norwegian with English summary), Oslo, 19 8 1. 4. Cottrill, A.: "Crumpled Frigg Jacket Begins to Recover its Lost Buoyancy': Offshore Engineer, May 1975.
5. Marshall, P.W.and Luyties, W.H. : "Allowable stresses for fatigue design", Proc. BOSS Conf., MIT, 1982. 6. Odland, J.: "Response and Strength Analysis of Jack-up Platforms", Norwegian Maritime Research, Vol. 10, No. 4,1982.
7. Gurney, T.R.: "Fatigue of Welded Structures", Cambridge University Press, Cambridge, 1979. 8. "Guidance on Design and Construction", 1977, with Amendment No. 8, Fatigue, Department of Energy, London, 1984. 9. Kinra, R.K. and Marshall, P.W. : "Fatigue Analysis of the Cognac Platform", Paper No. 3378, Proc. Offshore Technology Conference, 1979.
Chapter 1 . References 10. Ellis, N.: "Hutton Tension Leg Platform. Structural Design and Configuration", Proc. "Ocean Structural Dynamics Symposium", September 8.-10. 1982. 1 1. Kallaby, J. and Price, J.B.: "Evaluation of Fatigue Considerations in the Design of Framed Offshore Structures", Paper No. 2609, Proc. Offshore Technology Conference, 1976. 12. Hallam, M.G. et al.: "Dynamic .and Fatigue Analysis of Murchison Tower Structure", Paper No. 3163, Proc. Offshore Technology Conf., 1978. 13. Marshall, P.W. : "Basic Considerations for Tubular Joint Design in Offshore Construction", Int. Conference on Welding in Offshore Construction, The Welding Institute, Newcastle, 26-28 February 1974. 14. "Stricken rigs highlight checking weaknesses", Offshore Engineer, March 1975. 15 . "Mobile platform, SPM repairs completed for Argyll Field", Ocean Industry, June 1978, p. 63. 16. U.S. Coast Guard Marine Casuality Report No. USCG 16732193621, May 1981. 17. Moan, T. et al.: "Analysis of the fatigue failure of the Alexander L. Kielland", ASME Winter Annual Meeting, November 1981. 18. Burgoyne, J.H. et al.: "Offshore Safety", Report of the Committee, HMSO, March 1980. 19. Carlsen, C.A. et al.: "Lessons Learned from Failure and Damage of Offshore Structures", 8th ISSC, Gdansk, 1982.
20. Harrison, J.D. : "Partial Failure of a Fixed Offshore Platform", Int. Inst. of Welding, Doc. XIII-708-73, 1973. 2 1. Green M.B. : "Experience with Fatigue Analysis and Inspection Results", Paper No. 4524, Proc. Offshore Technology Conference, 1983.
22. "Safety and Offshore Oil", Committee on Assessment of Safety of OCS Activities et al., National Research Council, National Academy Press, Washington D.C., 1981. 23. Sollie, T.:
"Safety and Quality Assurance of Fixed Offshore Installations. In-service Experiences and Prospects after some 10 Years of Involvement", 6th European Maintenance Congress, Oslo, June 1982.
Chapter 1 . References 24. "Repairs to North Sea Offshore Structures - a Review", UEG Report UR 21, London, 1983. 25. Petershagen, H.G. et al.: "Report of Committee 111.1",8th ISSC, Gdansk, 1982. 26. Kjellander, S. and Persson, B.: "Hull damages further investigation and significance of weld defect", (in Swedish), STU-report 76-3948 and 77-4205, March 1980.
-
27. Jordan, C.R. and Knight, L.T.: "Further survey of in-service performance of structural details", Ship Structure Committee Report No. 294,1980. 28. Harrison, J.D.: "Lessons from Service Fatigue Failures", The Welding Institute Research Bulletin, Vol. 21 .,March 1980.
29. Fisher, J.W.: "Fatigue and Fracture in Steel Bridges. Case Studies". John Wiley & Sons, New York, 1984.
CHAPTER 2
LOADS ON OCEAN STRUCTURES StAle Fines A.S VERITEC, Oslo
ABSTRACT The theory of stochastic processes is extensively used for the description of waves and the associated structural response, and is briefly summed up. Also some elements of the theory of dynamic systems are discussed, since dynamic amplification of the structural response of offshore structures may be significant. The theory of regular and irregular waves and the hydrodynamic forces on offshore structures caused by the waves are described, using the deterministic as well as the stochastic approach. Finally the different methods for arriving at a long time distribution of stress ranges are discussed and illustrated by examples taken from elements of offshore structures.
LIST OF SYMBOLS
-
-
-
-
-
cross-sectional area water particle acceleration amplitude damping coefficient drag coefficient inertia coefficient added mass coefficient parameter in Weibull distribution of individual wave heights diameter parameter .in Weibull distribution of individual wave heights water depth
List of symbols
DAF - dynamic amplification factor modules of elasticity expected value of x force frequency acceleration of gravity individual wave height parameter in the Weibull distribution of significant wave heights parameter in the Weibull distribution of significant wave heights significant wave height moment of inertia spring stiffness Keulegan-Carpenter number stability parameter surface roughness height wave number wave length member length mass mass per unit length n'th order spectral moment cumulative probability distribution of the parameter x probability density distribution of the parameter x autocorrelation function Reynold's number Strouhal's number energy spectrum individual wave period peak period zero-upcrossing period transfer function
time volume water particle velocity reduced velocity stochastic process stochastic process vertical distance from still water level, positive upwards parameter of the JONSWAP wave spectrum
Section 2.1 parameter of the JONSWAP wave spectrum parameter in the Weibull distribution of significant wave heights logarithmic decrement of structural damping spectral width parameter parameter, relating wave heights and stress ranges water surface elevation kinematic viscosity of water damping ratio density of water standard deviation stress stress range time interval phase angle angular frequency peak angular frequency natural angular frequency
2.1 GENERAL
An offshore structure will be subjected to a number of loads during its lifetime. These loads may be categorized as: Permanent loads, which are gravity loads that will not be removed, such as the weight of the structure, weight of pennanent ballast and equipment and external hydrostatic pressure of permanent nature. Live loads, which are loads associated with the operation and normal use of the structure, such as stored materials, equipment and liquids, operation of cranes, helicopters and fendering and mooring of vessels. Deformation loads, which are associated with imposed deformation, such as prestressing and temperature. Environmental loads, which are loads due to wind, waves, current, ice, snow, earthquake and other environmental actions. All loads that are varying in magnitude and/or direction will cause stress variations in the structure and may lead to fatigue damage. The live loads and the environmental loads are especially important in this connection. The live loads may be the dominating contributors to fatigue damage for equipment like cranes etc ., whereas the environmental loads, and the wave loads in particular, are dominating for the main part of the load carrying structure.
Section 2.1 The aim of this chapter is to present methods that may be used to calculate the long-term distribution of stresses induced by wave and current loading. This distribution may then be used to estimate the fatigue life as discussed elsewhere in this book. The calculation procedures that are followed in practical cases may vary in detail. In general the method will depend on the type of structure, the accuracy required, the wave and current data available and the computer facilities and software at hand. The present chapter aims at presenting the general calculation principles rather than all details of the various methods. The calculation usually includes the following steps: Step 1. Establishment of long-term statistics of waves and currents, i.e. description of how the waves and currents are assumed to vary throughout the lifetime of the structure. Step 2. Representation of these distributions by sets of defined wave and current conditions with associated probabilities of occurence. Step 3. For each of the defined environmental conditions: Calculation of external hydrodynamic loads acting on each member of the structure considered. Step 4. For each of the defined environmental conditions: Calculation of internal cross-sectional forces and stresses due to the external loads established in step 3. This calculation is normally based on elastic theory . Step 5. Etablishrnent of long-term distributions of stresses based on the results of step 4 and the probabilities of occurence of each environmental condition. The waves and the associated structural response have a stochastic (non-deterministic) nature. The theory of stochastic processes is therefore extensively used for their description. A basic knowledge of the theory will be helpful to anyone dealing with this subject. The theory is therefore briefly discussed in Section 2.2. The natural frequencies of many offshore structures are so close to the frequencies of the environmental loads that the dynamic amplification of the structural response can be significant. Some elements of the theory of dynamic systems are therefore presented in Section 2.3.
Section 2.2
2.2 STOCHASTIC PROCESSES The theory of stochastic processes is treated in a number of textbooks, see for instance Refs. / 11, /2/ and 131. Some basic elements of the theory are given in the following.
Fig. 2.1 Time history of a stochastic process. The basic nature of a stochastic process may be understood by considering the time history of such a process, as shown in Fig. 2.1. The value of the process at time t is denoted by x(t). The value of x at any chosen time t = to cannot be precisely predicted, we may, however, be able to find the probability that x(to) will be within certain limits. As we are unable to describe the process precisely as a function of time (as we can for a deterministic process) we instead describe the process by its statistical properties, e.g. mean value, -standard deviation etc. A process is said to be stationary if these statistical properties do not vary with time. Many processes may be considered as stationary provided the time interval in question is short enough. The sea surface elevation, for example, is normally considered to be stationary within time intervals of three to six hours. Only stationary stochastic processes are considered in the following. The probability density function of x, p(x) is given by: p(x) dx = prob(x < x(t) < (x + dx)) The cumulative distribution function is given by: X
P(x) = 1p(x) dx -00
The expected value of the process is given by:
Section 2.2 The expected value is equal to the mean value of the process. In some cases, the co-ordinate system can be chosen so that the mean value is zero. The sea surface variation about the mean water level is an example. A zero mean value is assumed in the following. The autocorrelation function is defined as: R,(T) = E[x(t) x(t
+r)]
where T is a freely chosen time interval. When the mean value is equal to zero, the autocorrelation function for T = 0 is equal t o the variance of the process:
ox is the standard deviation of the process. The one-sided spectral density or energy spectrum is related to the autocorrelation by sX(w)=
1
00
J R ~ ( T )e- i o r , d r
-00
(2.6)
where w is angular frequency. A stationary stochastic process may be considered as being composed of infinitely many harmonic components, each with different frequency. The energy of a harmonic wave is proportional to the square of its amplitude. The energy spectrum shows how this energy is distributed on the various frequency bands, Fig. 2.2.
Fig. 2.2 A stochastic process x(t) and its energy spectrum S(w). The spectrum shows how the energy of the process is distributed on the various frequency bands. The energy within a band Ac;,is equal to that of a sine wave with amplitude ai.
Section 2.2
The moments of the energy spectrum are defined as:
The zero order moment gives the area under the spectral curve. This represents the total energy of the process. The zero order moment is also equal
to the variance of the process: mo = ox2
(2.8)
The spectral width parameter is defined by: -I
It varies between zero and one. When E is close to zero, the spectrum is narrow and a time history of the process is relatively smooth and regular, Fig. 2.3. When E is close to one, the spectrum is broad and a time history is more irregular in shape. Broad band
Fig. 2.3 Probability density of maxima. A broad band process has many local maxima and minima. The maxima (amplitudes) are Rice distributed. A narrow band process has no local maxima. All maxima are positive
and follow the Rayleigh distribution.
Many of the processes encountered in engineering may be assumed to be Gaussian with zero mean. The ,. probability density function is then
Section 2.2 The amplitudes of this process are distributed according to the Rice distribution with the following probability density function:
The corresponding cumulative probability function is :
where the error function erf(x) is defined as
For E = 0 the density distribution of the amplitudes may be written ,,
This is the Rayleigh distribution. It is a good approximation to the Rice distribution for small values of E and is much used due to its simple formula. The corresponding cumulative distribution function is:
The average zero crossing period of a narrow-band process may be approximated by
The most probable highest of N successive peaks is then given by
Section 2.2 In many engineering problems we encounter linear systems, i.e. systems where the relation between the input or exitation x(t) and the output or response y(t) is described by a linear differential equation with constant coefficients. An example of such a system may be the wave loading on an offshore structure, where the ocean wave forces may be regarded as the exitation and the stresses in a point of the structure as the response. It was mentioned above that a stochastic process could be considered as being composed of infinitely many harmonic components. If one such component of the exitation process is given by (real part understood)
then the component of the response process at the same frequency is given by
T(u) is the transfer function. From Eq. (2.19) we see that the exitation and response components are proportional. If we consider the above example with wave forces and stresses, the system will be linear if Hooke's law is valid, but non-linear if plastic effects are significant. It was mentioned above that the value of the energy spectrum at a given frequency was proportional to the square of the amplitude of the harmonic component at that frequency. Eq. (2.19) above shows that the amplitudes of the exitation and the response are related through the transfer function. The energy spectrum of the response process is thus given by (Fig. 2.4)
We will often be primarily interested in some specific properties of the response process, e.g. the most probably largest value within a given time interval or the distribution of response amplitudes. The procedure below can then be followed.
-
-
Establish the energy spectrum of the exitation process. Find the transfer function of the system, for example by calculating the response to harmonic exit ation (Eq. (2.1 9)). Calculate the energy spectrum of the response (Eq. (2.20)). Calculate the desired properties of the response process by use of - (2.17).
Eqs. (2.7)
Section 2.3.1
Fig. 2.4
2.3
-
2.3.2
The transfer function T(w) relates the exitation spectrum S,(o) and the response spectrum Sy(w). Sy(w) = T(w) 2 S,(w).
I
I
DYNAMIC EFFECTS
2.3.1 General
Dynamic loading is loading which varies appreciably with time, such as wave loading. The response of structures t o dynamic loading is generally dependent not only on the magnitude of the loading but also on the time history of the loading . Many load-time histories are irregular, i.e. they are stochastic processes. It was mentioned in the preceding section that such processes could be considered as composed of infinitely many harmonic components. Provided that the relation between the acting loads and the corresponding structural response is linear, the response to each loading component can be considered separately. The response of structures subjected to random loading can thus be found by studying the response to harmonic loading. The theory of dynamic analysis is treated in a number of textbooks, e.g. Refs./3/,/4/and/5/, and is outside the scope of this book. The basic formulas for a single-degree-of-freedom system (SDOF system) are given in the following. Although a detailed analysis of most structures requires a much more complex dynamic model, an SDOF model may be used for simplified calculations in many cases. 2 -3-2 Single-degree-of-freedom system
A SDOF system consists of a mass, a linear spring and a viscous damper, Fig. 2.5. Consider first a system consisting only of a mass and a spring. The spring produces a force
Section 2.3.2
Force
Fig. 2.5
Single-degree-of-freedom system. K = spring stiffness, M = mass, C = viscous damping.
The behaviour of the system when no external forces are acting is described by M a y = -K.y (2.22)
A solution to this equation is
where C 1 and C2 are constants and the system
WN
is the natural angular frequency of
The natural period is given by
The viscous damper produces a force which is proportional to the velocity and directed against it:
FD = -C
9
(2.26)
Incorporating this force in the above equations would have modified the natural period, but for most offshore structures the damping is so small that its effect on the natural frequency can be neglected.
Section 2.3.3 The damping is normally expressed in terms of the demping ratio
where C , is the critical damping, given by
c c =2
, / R
Assume that an external force
x = a, * c o s o t is acting on the system. The behaviour of the system is then described by
The solution to this equation is
The amplitude (displacement) of the response is given by -ax DAF ay K
where DAF is the dynamic amplification factor
DAF = J(1 -522)2
where
1
+ (2.E
a=" ON
The phase angle between the exitation (applied force) and the response (displacement) is
Eqs. (2.33) and (2.34) are plotted in Figs 2.6 and 2.7. 2.3.3 Physical properties used for dynamic analysis
Mass. In addition to the structural mass one must also consider the added mass for submerged or partly submerged bodies. The added mass represent hydrodynamic forces acting on the body from the surrounding water, and for most practical purposes one can model this effect as a certain amount of water that is fixed t o the body and thus has to follow its motions. The added mass is discussed in more detail in Sec. 2.5.
Section 2.3.3
Fig. 2.6 The dynamic amplification factor (DAF) as a function of w/wN. WN = natural frequency, = damping ratio.
Fig. 2.7 The phase angle @ is the phase lag between the exitation x(t) and the response y(t). O N = natural frequency, 5 = damping ratio.
Damping. The damping types of major significance for offshore structures are structural damping, hydrodynamic damping and, for bottom-founded structures, soil damping. The structural damping is due to internal damping in the structural material, and to friction and slippage in structural joints. The hydrodynamic damping is of two types: One is due to the formation of surface waves (radiation damping) and the other to viscous effects. The soil damping is due to the formation of waves in the ground and to internal damping in the soil.
Section 2.3.4
2.3.4 Natural frequencies of common structural elements The natural frequency of some common structural elements is given by WN
= 2 ~ f N- = a~
where: EI 1 m aN
* dme1T rad/s
(2.35)
= the bending stiffness of the section = the length of the beam
of the beam = a numerical constant, see Fig. 2.8.
= the mass per unit length
Cantilever or "clamped-free" beam =
3.52
a,=
I?=
a,
a
a1
Sinlply supported or "hinged-hinged" beam
"Free-free" bean1 or floating ship
a l = 22.0 a2 = 61.7 a3 = 121.0 a4 = 200.0 as = 298.2
a2
$c-
a3
a,
a
9.87
"Clamped-clamped'' beam has same frequencies as "free-free"
a , = 22.0
"Claniped-hinged" beam may be considered as half a "clamped-clamped" beam for even
Fig. 2.8 The value of the numerical constant a~ in Eq. (2.35) for some common structural elements.
Section 2.4.1 - 2.4.2 2.4
WAVES
2.4.1 General Two different methods are commonly used t o describe ocean waves. The sea may be regarded as composed of discrete o r individual waves, each described by its height H and period T (Fig. 2.9) (discrete wave method). Alternatively, the sea may be described in terms of the statistical properties of the sea surface elevation (stochastic method). In both methods, the calculation of wave kinematics is based on regular wave theory.
Fig. 2.9 A time history of the irregular sea surface. TI ,T2,. . ., T5 are individual wave periods. H I , H z , . . ., H 5 are individual wave heights. 2.4.2 Regular waves
Fig. 2.10 Regular waves. H = wave height from crest to trough, L = wave length, d = water depth, SWL = still water level, q = free water sur-
face profile. Regular waves are a train of two-dimensional periodic waves which may be divided into individual waves of identical form. The most important parameters for description of regular waves are given in Fig. 2.10. The simplest description of the wave form is given by the linear wave theory (AIRY wave theory), by which the surface profile is given by a sine function
Section 2 -4.2 where:
2n/T = angular frequency T = wave period k = 27rlL = wave number ~ c= ,
The wave kinematics beneath a linear wave are given by Eqs. (2.37) through (2.43) below. Due to the simplicity of these equations, the theory is well suited for simplified calculations. The linear wave theory is also a building stone in the description of irregular waves (Sec. 2.4.3). The water particle motion is illustrated in Fig. 2.1 1.
Surfuce profile
Wave length
Water particle velocity horizontal =H a) component 2
. fl . T=+f 1 . cos(wt) L cosh(2n d/L)
vertical w=-H . g * T b, component 2 L
.
sinhl2n(zkd)/L1 cosh(2n d/L)
(2.39)
sin(~t)
(2.40)
- g o n * H . co~h[2n(z+d)/L_I.~~~(,~) L c o s h ( 2 ~ d/L)
(2.41)
Water particle acceleration horizontal
a) component ax b)
vertical az = component
x
R
L
H
. 5inh[?n(z + d)/LI . cos(wt) cosh(2n d/L)
Su bsurjace pressure
H = wave height L = wave length T = wave period d = water depth k = wave number
g = acceleration of gravity z = distance t o water particle from SWL, positive upwards w = angular frequency p = density of water 7 = water surface elevation
(2.42)
Section 2.4.3
SWL
I
I
d
I
Fig. 2.11 Particle orbits according to linear wave theory.
A number of wave theories have been developed in addition to the linear. The Stoke wave theories, the Cnoidal wave theories, the stream function wave theory and the solitary wave theory are commonly used for design purposes (Refs./6/,/7/). The range of application of the various theories is shown in Fig. 2.1 2.
TI' CJY
0.003
depth waves 0.003
0.03
~ 8 J ~ ~ 0.3
d
p Fig. 2.12. The area of validity of various wave theories (Ref. 171). 2.4.3 Irregular waves A real sea does not possess the regular characteristics of a regular wave, but has an irregular form as shown in Fig. 2.9. The wave periods of such a seastate are defined as the time between successive upcrossings through still
Section 2.4.3 water level, whereas the wave heights are defined as the difference between maxima and minima values within the wave periods. In a short time interval (hours), the statistical properties of the seastate may be considered t o be constant, and the sea is termed stationary. The theory of stationary stochastic processes (Sec. 2.2) is used to describe such a seastate. The following terms are used in the description:
-
The zero upcrossing period T, (average wave period) is the average value of the wave periods as defined by Fig. 2.9.
- The significant wave height Hs is the average of the highest third of the wave heights as defined by Fig. 2.9.
-
The wave spectrum S(w) is the energy spectrum of the sea surface elevation.
Wave spectra can be obtained by analyses of recorded wave-time histories. For design purposes the model wave spectra are normally used, which are analytical expressions describing the spectral shape. The spectra are then described by statistical parameters like Hs and T,. A number of such spectra have been developed. The most commonly used in the North Sea are: The Pierson-Moskowitz (PM) spectrum defined by
S(o)
2
= Hs
T,
1 8r2
- (-
w.TZ -5 ) 27~
1 ueTz-4 exp [- - ( ---) ] 7~ 27~
(2.44)
The JONSWAP spectrum, defined by (=W , - 1 ) 2
The parameters a, up and 7 are functions of Hs and T,, as shown in Table 2.1. The peak angular frequency up is the frequency at maximum value of S(o). The PM spectrum is applicable to a fully developed sea, i.e. when the growth of waves is not limited by the size of the generation area. This will be the case for the major part of the time in the North Sea. Thus the PM spectrum may be used for most fatigue analyses. The JONSWAP spectrum applies when the growth of the waves is limited by the size of the generation area. This is the case for extreme wave conditions in the North Sea. The PM and JONSWAP spectra are illustrated in Figs. 2.13 and 2.14.
Table 2.1 The parameters of the JONSWAP spectrum as functions of Hs and T, (Ref. 181).
Significant wave height (m)
'02. is/
2.02.49
2.52.99
3.03.49
3.53.99
4.04.49
4.5499
5.05.49
- - . --
5.5599
.-
6.06.49
6.56.99
7.07.49
-
7.57.99
.
8.0849
8.58.99
-.-.-
HS (m) 9.09.49
9.59.99
10.0- 10.510.49 10.99
11.0- 11.5- 12.0- 12.5 11.49 11.99 12.49 12.99 - - -- --
13013.49
13.5 13.99
- .. -
14.0- 14514.49 14.99
-
4.05.490 5.970 6.330 6.600 6.890 4.99 0.0138 0.0201 0.0277 0.0359 0.0485
0.1800 0,1810 0.1820 0.1830 0.1850
--.
.
.---
. . -. . ..
.- -.--.
5.04.130 4.910 5.400 5.770 6.070 6290 6.490 6.680 6.830 6.960 5.99 0.0064 0.0094 0.0129 0.0171 0.0219 0.0267 0.0323 0.0390 0.0455 0.0523
.--
-- -
--- -
1
-
-- -- ---
-. - --.-
0.1440 0.1460 0.1470 0,1480 0.1490 0.1490 0.1490 0.1500 0.1500 0.1500
-
.- ..
~~
---
- .-.- -
-
- - - ..
--
-
-.. .
-
I
-2
-
---
6.01.260 3.370 4.280 4 . m 5.210 5.530 5.770 5.840 6.170 6.320 6.490 6.610 6.730 6.870 6.960 6.99 0.0036 0.0051 0.0069 0.0092 0.0113 0.0142 0.0170 0.0180 0.0239 0.0274 0.0323 0.0363 0.0410 0.0475 0.0523
0,1110 0.1200 0.1220 0.1240 0.1240 0.1250 0.1250 0.1260 0.1260 0.1260 0.1270 0.1270 0.1270 0.1280 0.1280 .
-
1.090 1.650 3.620 4.240 4.690 5.040 5.280 5.490 5.540 5.870 6.020 6.150 6.300 6.410 6.510 6 . W 6.690 6.770 6.880 6.960 0.0032 0.0042 0.0055 0.0067 0.0083 0.0102 /0.0119 0.0138 0.0143 0.0185 0.0210 0.0235 0.0269 0.0299 0.0329 0.0359 0.0394 0.0427 0 . M O 0.0520 0.0960 0.0980 0.1050 0.1060 0.1070 0.108010.1080 0.1080 0.1090 0.1090 0.1090 0.1090 0.1100 0.1100 0.1100 0.1100 0.1100 0.1100 0.1110 0.1110
7.07.99 8.08.99
1.210 1.960 3.460 4.040 4.460 4.800 5.020 5.220 5.440 5.590 5.730 5.850 5.960 6.110 6.210 6.300 6.380 6.470 6.540 6.610 6.680 6750 6840 0.0035 0.0044 0.0052 0.0062 0.0074 0.0088 0.0100 0.0114 0.0133 0.0148 0.0165 0.0182 0.0199 0.0227 0.0248 0.0269 0.0290 0.0316 0.0339 0.0363 0.0390 0.0419 0.0460 0.0850 0.0880 0.0920 0.0930 0.0940 0.0950 0.0950 0.0950 0.0960 0.0960 0.0960 0.0960 0.0960 0.0970 0.0970 0.0970 0.0970 0.0970 0.0970 0.0970 0.0970 0.0970 0.0980
9.09.99
1.000 1.230 1.770 3.230 3.810 4.230 4.480 4.770 4.960 5.120 5.330 5.470 5.580 5.690 5.800 5.890 5.980 6.110 6.190 6.270 6.340 6.410 0.0029 0.0036 0.0043 0.0050 0.0058 0.0067 0.0075 0.0087 0.0097 0.0107 0.0123 0.0136 0.0147 0.0160 0.0175 0.0188 0.0202 0.0227 0.0244 0.0261 0.0280 0.0299 0.0750 0.0760 0.0780 0.0820 0.0830 0.0840 0.0840 0.0850 0.0850 0.0850 0.0850 0.0860 0.0860 0.0860 0.0860 0.0860 0.0860 0.0870 0.0870 0.0870 0.0870 0.0870
--.
11
I
10.0 10.99
--
1
12.0. 12.99 -
13.0 13.99 14.014.99
-
1.020 1.230 1.560 2.700 3.220 3.650 4.230 4.440 4.710 4.870 5.010 5.150 5.260 5.420 5.540 5.640 5.730 5.810 5880 5960 0.0030 0.0036 0.0041 0.0047 0.0050 0.0055 0.0067 0.0074 0.0084 0.0092 0.0100 0.0109 0.0117 0.0132 0.0143 0.0154 0.0165 0.0176 0.0186 0.0199 0.0680 0.0690 0.0700 0.0730 0.0740 0.0750 0.0760 0.0760 0.0770 0.0770 0.0770 0.0770 0.0770 0.0780 0.0780 .00780 0.0780 0.0780 0.0780 0.0780
..
11.011.99
-
- -- -. ---
-. --.
1.010 1.180 1.450 1.920 2.930 3.500 3.910 4.130 4.380 4.580 4.730 4.870 4.970 5.110 5.230 5.360 5.480 5.540 0.0029 0.0035 0.0040 0.0044 0.0048 0.0053 0.0660 0.0064 0.0070 0.0079 0.0085 0.0092 0.0098 0.0106 0.0114 0.0126 0.0136 0.0143 0.0620 0.0630 0.0640 0.0650 0.0670 0.0680 0.0690 0.0690 0.0700 0.0700 0.0700 0.0700 0.0700 0.0700 0.0700 0.0700 0.0710 0.0710 1.260 1.540 2.050 3.020 3.450 3.760 4.000 4.270 4.420 4.550 4.650 4.810 4.950 5.090 0.0036 0.0041 0.0045 0.0048 0.0052 0.0057 0.0061 0.0068 0.0073 0.0078 0.0082 0.0090 0.0099 0.0105 0.0580 0.0590 0.0600 0.0620 0.0630 0.0830 0.0640 0.0640 0.0640 0.0640 0.0640 0.0650 0.0650 0.0650
-
y First number: Second number: a Thud number: fp
1.040 1.140 1.320 1.680 2.150 2.830 3.360 3.710 3.920 4.100 4.250 4.300 4440 0.0030 0.0034 0.0038 0.0043 0.0045 0.0047 0.0051 0.0056 00060 0.0064 0.0068 0.0070 0.0073 0.0530 0.0540 0.0540 0.0550 0.0560 0.0570 0.0580 0.0580 0.0590 0 . 0 5 ~0.0590 0,0590 0.0580 1.190 1.290 1.570 2.030 2.670 3.120 3.440 3.650 3.780 0.0035 0.0037 0.0042 0.0045 0.0047 0.0048 0.0052 0.0055 0.0067 0.0500 0.0500 0.0510 0.0520 0.0530 0.0536 0.0540 00540 0.0550
15.015.99 I
1
2.900 0 0048 0 0500
Section 2.4.3
Fig. 2.14 JONSWAP wave spectra. Fig. 2.13 Pierson-Moskowitz wave spectra. Hs = 1 0 m , T, = 10s. - - - - - - Hs = 8 m , T z = 9.5 S.
The spectral moments are defined as (Eqs. (2.7), (2.8)) 00
m, = J w n *S ( o ) dm
(2.46)
0
Specifically, the zero order moment
represents the total wave energy of the seastate. In a stationary seastate, the sea surface is normally taken to be Gaussian distributed with zero mean and a variance o2 = mo. If the wave spectrum is assumed to be narrow-banded, the wave amplitudes will follow the Rayleigh distribution, see Sec. 2.2. It can then be shown
Section 2.4.4 that also the wave height will follow the Rayleigh distribution The probability density function of wave heights following the Rayleigh distribution (Eq. (2.14)) is thus given by
The cumulative distribution of wave heights is correspondingly
P(H) = 1 - exp [- ( l21 2& Still assuming the wave heights to be Rayleigh distributed, we have: For the significant wave height
For the zero upcrossing wave period
For the most probable largest value of N wave heights
2.4.4 Long-term wave statistics
As mentioned in 2.4.3, the statistical properties of the sea are assumed to be constant within a short time interval and the parameters Hs and Tz may be used to describe a seastate. The duration of a seastate is normally taken as 3 hours. A long-term observation of the sea may be performed by recording the parameters Hs and T,. Typically, the sea surface is observed for 20 minutes each third hour, and Hs and T, are estimated for each observation period. This may be done from the observed wave record directly using the definitions of Hs and Tz given in 2.4.3 (zero crossing analysis) or by calculating the wave spectrum and applying Eqs. (2.50) and (2.5 1). The pairs of observed Hs and Tz values thus obtained may be divided into classes and the probability of each pair written in a matrix as shown by Table 2.2. This is called a wave scatter diagram. Also, the cumulative distribution of longterm significant wave heights may be found from the observations. This distribution is normally well described by the Weibull distribution
Q ,Hc and y are the parameters of the distribution.
Section 2.4.4 Table 2.2 Scatter matrix representative for the Central North Sea. PROBABILITY I N PARTS P E R THOUSAND
I
,
0
1
2
3
4
5
6
7
8
9
10
11
12
AVERAGE Z E R O UPCROSSING P E R I O D , T, (s)
The distribution gives a straight line if plottet on a Weibull probability paper. The distribution shown by Fig. 2.15 is representative for the distribution of significant wave heights in the Central North Sea. Assuming that the significant wave height is Weibull distributed with Ho = 0 and that the individual wave heights in a seastate are Rayleigh distributed, it can be shown that the long-term distribution of individual wave heights also follows a Weibull distribution:
where C and D are functions of y, and Hc and y are parameters in the longterm distribution of significant wave heights. The relation between y, C and D is given in Table 2.3.
e(+hs>k.
'
9I ,//,
I L
I 2
t
I -
b
>ti5
L
Q
CtL)
-
, -
H 10
z
3 ,
Section 2.4.4
Fig. 2.15 Long-term distribution of significant wave heights Hs representative for Central North Sea. Weibull parameters:y = 1.49, Hc = 2.7, H, = 0. Table 2.3 Parameters of the Weibull distribution of individual wave heights.
Section 2.4.4 The number of waves exceeding a given individual wave height in one year is given by
where No is the total number of waves in one year. The above equation is shown by Fig. 2.16.
Fig. 2.16 (left) Wave exceedance diagram showing the number of waves exceeding a given wave height in one year.
Fig. 2.1 7 (right) Simplified long-term exceedance diagram distribution of wave is the 100 year wave height. Nl is the numheights. Hl Z 8.72 for North Sea ber of waves in 100 years. Log Nl conditions. The directional distribution of waves may be represented by a set of long-term distributions of waves, each representing a sector of wave approach directions.
A useful approximation to the long-term distribution of individual wave heights may be obtained by setting D = 1.0 and H, = H l o O/(ln N1 o ) in Eq. (2.55). HI is the most probable largest wave in 100 years and N l o 0 is the total number of waves in 100 years. This gives for the number of waves N exceeding a wave height H (Fig. 2.17) log N H = H, (1 ) log N10 0
Section 2.5.1 - 2.5.2
2.5
HYDRODYNAMIC FORCES
2.5.1 General Three wave force regimes are normally identified. These are termed the drag, the inertia and the diffraction regimes. Flow separation and viscous effects are of major significance in the drag regime. In the diffraction regime, the incident wave undergoes significant diffraction or scattering, whereas flow separation is of minor significance. In the inertia regime neither flow separation nor diffraction are dominating. Offshore structures are grouped according to the nature of the acting wave forces. Small-volume bodies are bodies for which drag and inertia forces are dominating, whereas large-volume bodies are bodies for which diffraction effects are significant. Examples of large-volume bodies are ships and the caissons of concrete gravity plat forms. Examples of small-volume bodies are jacket structures and the shafts of concrete gravity platforms. 2.5.2 Loads on small-volume bodies - Morison's equation
The hydrodynamic forces on structures in the drag and inertia regimes are normally calculated by Morison's equation. Normally, Morison's equation is applicable when the wave length L is more than five times the diameter of the structural member D. The hydrodynamic force per unit length on a body expressed by Morison's equation is: Froude-Krylov
added mass force
drag force
force
where: A A, a
-
C ,
-
a,
-
-
CD v,
-
D
-
p
-
is the cross-sectional area of the body is a reference area is the component of the water particle acceleration normal to the member axis is the added mass coefficient is the relative acceleration between water particle and member normal to member axis is the drag coefficient is the water particle velocity relative to the member normal to the member axis is the diameter of the member exposed to the sea is the density of seawater.
Section 2.5.2 The Froude-Krylov force is the sum of the hydrodynamic pressures acting on the surface of the body, not including the pressure disturbance due to the presence of the body. This latter effect is included by the added mass force. The term p C, A, is called the added mass. It is often considered as an amount of water that is "fixed" to the member. This is not a correct interpretation of the phenomenon, although it may serve to give an understanding of the nature of the acting forces. The added mass force is due t o the relative acceleration between the water and the body. In general it is dependent on the flow conditions and the location of the body. The added mass is wave-frequency-dependent for bodies at or close to the surface, whereas it is independent of frequency for deeply submerged bodies provided their dimensions are small relative to the wave length. The drag force is the viscous force acting o n the body. The sum of the Froude-Krylov force and the added mass force is called the inertia force. For a fixed body, a, = a and v, = v. If we set A, = A, we may write
The inertia coefficient is defined as
For three-dimensional cases, the equation is written
where F is the force, V is the volume of the body, and A is the cross-sectional area of the body. The coefficients CM and CD are generally dependent on the shape of the body, the flow conditions and the body surface roughness. Circular cylinders. For a circular cylinder, CM and CD are found to be functions of the following nondimensional parameters: v, D Reynolds number Re = v
v, T Keulegan-Carpenter number KC = -
D
Surface roughness = k/D
Section 2.5.2 where: v, v
T k
-
-
is the maximum wave-induced velocity is the kinematic viscosity of water, = 1.1 1 x 10-6 m2 /s is the wave period is the surface roughness height. For North Sea conditions a range of roughnesses from 0.005 m to 0.05 m may be appropriate, depending on the precautions taken to reduce the growth.
Inertia and drag coefficients should preferably be found by testing in full scale or model scale. Full-scale testing is difficult to perform, expecially in waves, and it is difficult to obtain the relevant conditions in a model. Thus, there are still large uncertainties associated with the values of the coefficients.
Fig. 2.18 The drag coefficient CD of circular cylinders in steady flow. Re = Reynolds number, D = cylinder diameter, k = roughness height. Ref. / 191. In steady flow the drag coefficient is a function of Re and k/D only, see Fig. 2.18. Drag coefficients obtained from full-scale tests in waves, are shown in Fig. 2.19. The results show considerable scatter. The mean curve indicated by a dotted line may be used in design. However, the designer should try to consult the latest research work available. The inertia coefficient has a theoretical value of 2.0 based on potential flow theory. Full scale and model tests have given lower values. However, it is common design practice to use the theoretical value of 2.0.
Section 2.5.3
Mean C D
KC
--
Fig. 2.19 Drag coefficient CD as a function of KC. Full-scale test data, Ref. 11 11.
Non-circular shapes. Drag and inertia coefficients of sharp-angeled bodies are normally taken t o be independent of Re. Drag coefficients for members of various cross-sectional shapes are given in Fig. 2.20. The added mass per unit length for various members is given in Fig. 2.21, and Fig. 2.22 gives the added mass of some three-dimensional bodies. 2.5.3 Loads on large-volume bodies When the body is not small compared to the wave length, the incident wave generally undergoes scattering or diffraction. This effect is normally considered to be significant when the cross-sectional diameter of the body is larger than one fifth of the wave length. The viscous wave forces acting on such structures, i.e. the drag forces, are normally of little significance. In this case the calculation of wave forces may be based on the potential flow theory. This theory describes the flow kinematics of an ideal fluid, i.e. a fluid without shear stresses. The pressure at every point of the structure is calculated and the wave force is found by integrating the pressure over the surface of the structure. This normally requires the use of numerical methods programmed in a computer. An analytical solution, i.e. the McCamy and Fuchs theory, is available for vertical cylinders standing on the bottom and penetrating the surface. The inertia force term in Morison's equation is calculated, using the equivalent inertia coefficient in Fig. 2.23.
Section 2.5.3
-+'m[-l 01 I Sect~onshape
CD 2.0
0 .
i - 0 . 1 7 0.6
-'
-[-I I.
= 0.33 0.5
D
a
2.0
-0
1.5
Fig. 2.20 Drag coefficients of cylinders of infinite length, Ref. 1101. SHAPE
-1
ADDED MASS PER U N I T LENGTH MOTION ll+-2b-i
CIRCLE
2 pnc
. 1 T
bELLIPSE
9ab2
c . )
--
a/b
RECTANGLE
2a
2b
4 DIAMOND
I, I-BEAM
2
PmJ
0' REGULAR P L Y
... ...
a/b 1.00pna2 1.14
10 5 2
1.36
2 1 0.5 0.2
0.85 0.76 0.67 0.61
-
n = 3 4
1.21
" "
1 0.5 0.2 0.1
1.51pna2 1.70 " 1.98 " 2.23 "
(Wendel 1950)
"
"
"
(Wendel1950)
c
0.654 qaz 0.787 1.000
M
(Wendel 1950)
n SIDED
Fig. 2.21 Added mass per unit length of cylinder, Ref. / 1 11.
SPHERE
4
ELLIPSOID OF
0nR3
k
q
(Wendel 1950)
pnb3
REVOLUTION
-;u-I FLOATING CYLINDER
h
(Sarpkaya 1960, Yu 1945)
( B a i 1977)
FLOATING RECTANGLE
(Sarpkaya 1960)
4 -
1 .o 1.2 1.6 2.0 2.4 2.8 3.6
( B a i 1977, Flagg a n d NemMn 1
Fig. 2.22 Added mass of three-dimensional bodies, Ref. / 1 11.
Section 2.5.4
Fig. 2.23 McCamy and Fuchs theory for a vertical circular cylinder standing
on the bottom and penetrating the free surface.
2.5.4 Deterministic calculation of response to hydrodynamic loads In a deterministic calculation of hydrodynamic loading, the structure is loaded with a regular wave described by the wave height H, the wave period T and a suitable wave theory. A design current may be included. The direction of the current is normally assumed to be in the direction of wave propagation, and the velocities due to wave and current are added vectorially. The calculation of hydrodynamic forces is performed according to the methods described in 2.5 -2 or 2.5.3, whichever is applicable. Depending on the nature of the relation between wave height and response, various methods may be used to find the variation of the hydrodynamic force and the associated response throughout the wave cycle. When the relation between the wave height and the response is strongly non-linear, the response-time history may be defined by calculating the response for various positions of the wave relative to the structure (Fig. 2.24). The number of positions chosen depends on the required accuracy. For structures where the relations between wave height and response are linear, e.g. large volume structures, a simplified method may be used. The response-time history at a given point in the structure may then be assumed to vary as a harmonic function, and the wave surface elevation is expressed by the linear wave theory
The response, .y(t), is calculated for two positions in the wave, defined by t = to and t = to + T/4. The response may then be expressed as
Section 2.5.5
Fig. 2.24 Calculation of the response for various positions of the wave relative to the structure. q(t) = wave surface elevation, y(t) = structural response.
where
The method may also be used when the relation between the wave height and response is non-linear, provided a linearization is carried out. This is done in the same manner as described for stochastic analysis, cf. Sec. 2.5.5. 2.5.5 Spectral method for calculation of response to hydrodynamic loading The spectral method applies the theory of stochastic processes for calculation of the response to hydrodynamic loading, see Section 2.2. For a particular seastate, the spectrum of a response variable is found by combining the wave spectrum with the transfer function relating the wave amplitude t o the amplitude of the response, Eq. (2.20). By integrating the response spectrum, the variance of the response and the spectral moments can be calculated. These calculations will normally be performed numerically. Particular care must be taken to ensure that the frequency grid used for the integration of the response spectrum is appropriate. Furthermore, attention should be given to the selection of integration points in the vicinity of any irregularities in the response spectrum to ensure that an accurate integration is achieved. Having established the response spectrum, the various statistical properties of the response, such as probability distribution of response amplitudes and maximum probable response, can be calculated using the formulas given in Sec. 2.2.
Section 2.5.5 The transfer functions can be found by two different methods: The regular wave approach and the time history simulation method. Regular wave approach. The value of the transfer function at frequency w may be found by calculating the response due to a simple harmonic wave with height H and period T = 27rlw. The transfer function value is then the ratio between the response amplitude and the wave amplitude, see Eq. (2.19). This procedure is repeated for a number of frequencies thus yielding a number of points on the transfer function. The spacing between the points should be sufficiently small to ensure that the transfer function is adequately described. The above procedure implies the assumption that there is a linear relation between the wave height and the response for a given wave period. This is generally not true. Non-linearities can be introduced due to various effects, the most significant being the non-linear drag term in Morison's equation. A linearization must therefore be carried out.
The drag term may be written as
FD = KD ~ ( t ) ( ~ ( t () where We consider a regular component of the water particle velocity, (Eq. (2.40)): v(t) = vo sin(wt)
(2.65)
If the drag term is expanded in a Fourier series and higher order terms are neglected, we obtain (Fig. 2.25)
Nonlinear
force
Fig. 2.25 The non-linear drag force in harmonic waves and various linearization techniques.
Section 2.5.5 The above linearization renders the same energy dissipation per wave cycle as the non-linear force. It is recommended when dynamic effects are significant. If it is required that the maximum non-linear drag force shall be equal t o the maximum linearized force, we get
FD(t) = KD vo ~ ( t ) The stochastic linearization is obtained by assuming that the particle velocity at a given point is normally distributed and finding the function that minimized the mean square approximation error to the non-linear drag force :
FD(t) = KD
J$ uv
~(t)
where a, is the standard deviation of the water particle velocity. In all the linearization techniques mentioned above, the transfer functions obtained will be functions of the wave height used for the calculation. It is thus essential that an appropriate wave height is used when calculating the linearized transfer functions.
Time history simulation. An alternative method of stochastic analysis is t o calculate the structural response to a time history of the hydrodynamic forces. The distribution of response amplitudes may then be found from statistical analysis of the time history of the response. Time histories of the wave-induced velocities and accelerations may be constructed from the wave spectrum by use of linear wave theory and the Montecarlo simulation technique, see e.g. Ref. 1121. The hydrodynamic forces are calculated at discrete time steps and the structural response at each time step is calculated by use of a numerical integration procedure, see Ref. /13/ and 1141. A time history of the response is thus obtained. The distribution of response amplitudes within the seastate considered may then be obtained by a counting of the amplitudes directly from the time history, e.g. by use of the rainflow technique (Ref. / 1 51) or similar procedures. Alternatively, the response spectrum may be calculated and if found t o be narrowbanded, the distribution of response amplitudes are found by use of Eq. (2.15). The advantage of the time history simulation technique is that all non-linearities may be taken into account in a proper manner. However, the calculation of the transfer function by Equation (2.20) also involves a linearization process which is basically appropriate only for the seastate for which the simulation was done.
Section 2.5.6 - 2.5.7
2.5.6 Slamming Members in the splash zone will be hit by the rising surface when a wave passes. This will cause an impact force, called slamming,on horizontal members, as their whole length may be hit by the wave surface simultaneously. The slamming force per unit length may be calculated as
where : Cs = the slamming coefficient vs = the velocity of the water surface. It is usually taken as the vertical particle velocity at the time of the impact. As the slamming force is impulsive, dynamic amplification must be considered when calculating the response. Ref. 1161 recommends the following values for horizontal circular cylinders fixed at both ends: Slamming coefficient : C, = 3.0 Dynamic amplification factor: 1.5 for ends and 2.0 for midspan .The member will respond with a dampened oscillation to each slam. Ref. 1171 recommends that each slam is associated with 20 linearly decaying oscillations. It also states that only waves with propagation directions + l o degrees to the normal of the member axis need be considered.
2.5.7 Vor tex-induced oscillations
A structure with a bluff trailing edge sheds vortices in a subsonic flow. Periodic forces are generated in the structure as the vortices are shed alternately from each side of the structure. The oscillating forces can cause large amplitude oscillations and thus high stresses in elastic structures. This phenomenon is a major problem for submerged parts of risers and conductors and also for antennas, stacks, etc. exposed to wind. The vortex shedding frequency is: v f" = s t 5 where: St = the Strouhal number v = the flow velocity normal to the member axis D = the member diameter The Strouhal number is in the range of 0.12-0.14 for sharp edged members and approximately 0.2 for circular cylinders.
Section 2.5.7 Large amplitude resonant oscillations may occur when the frequency of vortex shedding is close t o the natural frequency f N . This is expressed by the reduced velocity
The nature of the oxcillations is complex and model or full-scale tests are normally needed to determine the response of a particular structural configuration. Vortex induced oscillations occur in several regions of the reduced velocity. Ref. 1181 recommends the following calculation procedure for circular members in a uniform current: 1.0 < vR < 3.5 :
The cylinder oscillates in the direction of the flow (in-line oscillations).
3.5 < vR < 10:
The cylinder oscillates in the direction normal to the flow (cross-flow oscillations).
The amplitude of oscillation is a function of the stability parameter Ks :
where: m = mass per unit length, including added mass 6 = logarithmic decrement of structural damping = 2 .rr $, p = fluid density D = cylinder diameter The relation between Ks and the maximum oscillation amplitude is given by Figs. ( 2 . 2 6 ) and ( 2 . 2 7 ) . The cylinder oscillates with its natural frequency. Large amplitude oscillations of sharp-edged members in steady flow have been observed when vR > 5. The effect of vortex shedding in waves is not well known, and no generally recommended design procedure is available at present. EXAMPLE 1:Vortex-induced oscillations of a free span of a pipeline. A submarine pipeline with a 25 m long free span (Fig. (2.28)) may undergo vortex-induced oscillations due to the presence of a bottom current. The steel pipeline has a concrete coating and is carrying oil. Calculate the stress range in the pipe produced by the oscillations.
Section 2.5.7
-First instability r e g i o n , V R < 2.2
In-iine
motion
I
Second instability r e g i o n , V R > 2.2
Fig. 2.26 Max. amplitude of in-line motion, Ref. 1181.
For a simply supported beam in fitst mode, is equal to 1.16. For a cantilever beam in fist and second mode, the 7-value is equal to 1.31 and 1 .SO respectively.
4
I
I
I
1
Fig. 2.28 Free span of a pipeline.
I
I
Fig. 2.27 Max. amplitude of crossflow motion, Ref. / 181.
Section 2.5.7 Characteristics of the pipeline: Steel pipe
Outer diameter = 0.273 m Wall thickness = 0.015 m Moment of inertia = 1.02
m4
Concrete coating
Thickness Density
= 0.005 m = 3000 kg/m3
Oil
Density
= 800 kg/m3
Based on the above data, the following values have been calculated: Total pipeline diameter Mass of steel pipe Mass of concrete coating Mass of internal oil Added mass
Df = 0.283 m m, = 96.1 kg/m m, = 12.7 kg/m m, = 37.0 kg/m ma = 64.5 kg/m
The added mass is taken equal to the mass of the water displaced by the pipeline, i.e. the added mass coefficient is 1.O. Total mass:
So Eution. The pipeline is assumed t o be simply supported at both ends. The first natural frequency is calculated as (Eq. (2.35))
Substituting the values above, and taking E = 2.1 10'
~ / mwe~ get ,
The reduced velocity determines the current velocity at which oscillations will occur: v VR = f, * D In-line oscillations, 1 . instability region: 1.0 < vR < 2.2
*
0.23 m/s < v < 0.5 m/s
In-line oscillations, 2. instability region: 2.2 < v, < 3.5 =+ 0.50 m/s < v < 0.79 m/s Cross-flow oscillations: 3.5 < vR * 0.79 m/s < v
Section 2.5.7 The oscillation amplitude is a function of the stability parameter Ks (Eq. (2.72)). Substituting 6 = 0.05 and p = 1025 kg/m3, we get
Figs 2.26 and 2.27 give the maximum oscillation amplitudes as functions of Ks : In-line oscillations. 1. region:
A = 0.13 Df
In-line oscillations, 2. region:
A = 0.16 Df
Cross-flow oscillations:
A = l.lO*r*Df
The mode-shape parameter y is taken as 1.16 according to Fig. 2.27. The following expression is used for relating the stress amplitude at the center of the span and the oscillation amplitude (Fig. 2.29):
Fig. 2.29 Moment corresponding to assumed mode-shape. This gives the following maximum stresses: In-line, 1. region: om, In-line, 2. region: om, Cross-flow :
om,
=
20 MPa for 0.23 mls < v < 0.50 m/s
=
25 MPa for 0.5 m/s < v < 0.79 m/s
= 200 MPa for 0.79 m/s
The stress ranges may be taken as Ao = 2o,, The span will oscillate with its natural frequency for all types of oscillation. The number of oscillations per hour is therefore: N1 hour = 3600 0.80 = 2880.
Section 2.6.1
2.6
-
2.6.2
LONG-TERM STRESS RANGE DISTRIBUTION
2.6.1 General This section outlines three different methods for arriving at a long-term distribution of stress ranges:
-
Deterministic analysis Stochastic analysis Simplified analysis
A deterministic analysis is based on a relatively simple description of the environmental data and the associated loads. Non-linear wave heightstress relations are easily taken into account and the calculation procedure is easy to follow. It should be used with great care when dynamic amplification is significant, as this effect is difficult to account for in a proper manner. A stochastic analysis requires a more complex description of the environmental data and loads, and a more detailed knowledge of these phenomena is required. Non-linear effects are not so easily taken into account as in a deterministic analysis. A time history simulation may be performed, but this may be very expensive for complex structures. Dynamic effects are taken care of more properly in a stochastic analysis than in a deterrninistic analysis. A simplified analysis based on a simple description of both the environmental data and the associated response, may be a valuable tool in the early design phase.
2.6.2 Deterministic approach A deterministic approach to calculate the long-term stress distribution is based on the deterministic method of wave force calculation given in Sec. 2.5.4. It involves the following steps: i) Selection of major wave directions. A few wave directions, typically 4-8, are selected for analysis. The total number of waves is distributed between these major directions. Major wave propagation directions should be included, as well as directions causing high stresses in major structural elements. Advantage may be taken of structural symmetry, as identical waves propagating in opposite directions may cause equal stress ranges in many structures.
Section 2.6.2 ii) Establishment of long-term distributions of waves. For each wave direction considered, a long-term distribution of wave heights must be established, such that the total number of waves reaching the structure during the time considered is the sum of the waves from the directions considered. For a given direction the long-term distribution of wave heights is represented by a set of regular waves, which adequately describes the directional long-term wave distribution. Special care should be taken to properly describe the range of wave heights which gives the highest contribution to the fatigue damage. The wave period to be associated with a given wave height is normally taken as the most probable period for that wave height. iii) Calculation of stress ranges. For each wave thus identified (direction-height-period), the stress range is calculated, using one of the methods given in Sec. 2.5.4. If the stress range is found by placing the wave at various positions relative to the structure (Fig. 2.24), the positions should be chosen with great care in order to estimate the maximum and minimum stresses and the resulting stress range as accurately as possible. iiii) Establish stress distribution. The long-term stress distribution for each wave direction is established using a methodology as shown in Fig. 2.30.
Fig. 2.30 Calculation of a stress range exceedance diagram from a wave height exceedance diagram. Aoi is the stress range induced in a given wave direction by wave height Hi. Log N
79
Section 2.6.2
EXAMPLE 2 : Long-term distribution of stresses in a riser span, deterministic analysis.
Fig. 2.3 1 Jacket platform with riser clamped t o the platform leg. The span between -1 5.0 m and -25.0 m is considered in Example 2. Consider a riser clamped to the leg of a jacket platform (Fig. 2.3 1). The longterm distribution of stress ranges at the center of the span is wanted. As the only aim of this example is to show the principles of the calculation, we introduce the following simplifying assumptions:
-
-
-
The span is considered as fixed in both ends. Wave kinematics are calculated by the linear wave theory. All waves are assumed t o approach from one direction.
The span has the following characteristics : Length Riser outer diameter Riser wall thickness Moment of inertia
1 = 10m D = 0.27 m t = 0.0 15 m I = 9 . 8 . 1 0 ' ~ m4
Solution. According to Eq. (2.35) the first natural period of the span, fN1, is calculated to 0.17 s, which is low enough t o make dynamic amplification insignificant (cf. Fig. 2.7).
Section 2.6.2 The wave force intensity is denoted F(z). The moment at the center of the span (z = -20 m) is given by
and the maximum bending stress at the center of the span
The linear wave theory gives the same maximum wave force in both directions, thus: -M .D A a = 20,,I The wave data are given by the wave diagram in Fig. 2.16 for individual wave heights with Hc = 2.7, Ho = 0 and y = 1.49. Each height used in the analysis must be associated with a wave period. This is taken as the most probable wave period for the given wave height. For North Sea conditions, the following relation may be used :
The long-term distribution of individual wave heights is given by Eq. (234) -
L'nc
where Hc = 2.7 and C and D are respectively 0.462 and 0.928 for y = 1.49, cf. Table 2.3.
%!I
ii A
The number of waves exceeding a wave height H per year is given by N = No[l -PL(H)]
> -0
where No is the total number of waves in one year, taken as NO = 106.72. The following waves are now selected for analysis:
H = 3.0m H = 5.0m H = 7.0m H = 9.0m H = 11.0m H = 15.0 m H = 20.0 m
T = 7.2 s T = 8.7s T = 9.8 s T = 10.8 s T = 11.7s T = 13.1 s T = 14.6 s
log N = 5.74 log N = 5.14 log N = 4.57 log N = 4.00 log N = 3.45 log N = 2.35 log N = 1.OO
t d
Section 2.6.2 The wave forces are calculated by Morison's equation (Eq. (2.5 7)) , n * a~ ~ F = -1* p 0 C D * D * $ + p e C M --• 2 4 The coefficients CD and CM are taken as 1.0 and 2.0, respectively. As an example, consider the wave: H = 1 1.0 m, T = 11-7 s. The angular frequency is
Applying linear wave theory (Fig. 2.1 I), the wave number k is given by (Eq. (2.38))
where g = 9.8 1 m/s2 and the water depth d is LOO m. The equation is solved numerically, giving k = 0.0296 m-' Setting x = 0 at the center of the riser, the horizontal wave-induced water particle velocity is given by (Eq. (2.39))
and the horizontal wave-induced acceleration (Eq. (2.4 1))
When linear wave theory is used, one can simplify the calculations by separating drag and inertia forces. The moment due to the drag forces alone is given
yielding
MD ( a t ) = MD , , sin2 ( a t ) = 4596 sin2( a t ) (Nm) The moment due to inertia forces is calculated in the same manner:
Section 2.6.2 yielding MI(mt)= MI,
-cos(wt)= 1306*cos(wt)(Nm)
The total moment: M(wt) = MDm,
sin2 ( a t ) + M I ,
Maximum value of M(at) occurs for
cos(wt)
dM(wf)= 0, whichgives (Fig. 2.32) d ( 4
The maximum moment is thus:
, M
= 4596 sin28 1.BO
+ 1306
cos 8 1.go = 4689 Nm
and the resulting stress range:
Ao= M -
0
I
D=
4689 9.8 1 o
.
-~
0.27 = 12.9 MPa
sin* [at)
Fig. 2.32 Drag force FD ,inertia force FI and total force F, Example 2.
The procedure above is repeated for all waves selected for the analysis. For each wave height analysed, the corresponding number of waves exceeding that height is found by Eq. (2.56) or Fig. 2.1 6. Since the calculation procedure implies a unique relation between wave heights and stress ranges, the number of exceeding stress ranges is found in a similar manner. The final results are shown in Fig. 2.33.
Section 2.6.3
0
2
4
6
LogN
Fig. 2.33 Deterministic analysis of long-term distribution of stress ranges, Example 2. Left: Number of cycles (N) exceeding given wave heights, forces and stress ranges in one year. Right: Stress range exceedance diagram, one year. 2.6.3 Stochastic approach A stochastic approach for calculating the long-term distribution of stress
ranges is based on the stochastic methods of wave force calculation described in Sec. 2.5.5. It involves the following steps: i)
Selection of major wave directions. The same considerations as discussed for the deterministic analysis should be made.
ii) For each direction select a number of seastates which adequately
describes the long-term distribution of waves. Associate a duration to each seastate. iii) For each seastate calculate the short-term distribution of stress ranges using the methods described in Sec. 2.5.5. iiii) Combine the results for all seastates in order to find the long-term distribution of stress ranges. EXAMPLE 3: Short-term distribution of stresses in a riser span, stochastic analysis. As explained above, steps iii) and iiii), calculation of the long-term distribution of stress ranges is done by combining the short-term distributions for a number of seastates. The calculation below shows how a short-term distribution is obtained.
Section 2.6.3 The same riser span is considered as in Example 2. The short-term distribution of stress ranges within a given seastate is wanted. The same assumptions as used in the above example will be applied. Solution. The seastate is described by: Hs = 5 m, Tz = 7.5 s, duration = 3 hours.
A Pierson-Moskowitz wave spectrum is assumed, Eq. (2.44) :
The first step in the analysis is to establish the transfer function relating wave heights and stresses. This is done by calculating the stresses for a set of regular waves with different periods. The calculation is performed in the same manner as in the deterministic analysis. The transfer function for a given wave period is then calculated according to Eq. (2.19). As mentioned in Sec. 2.5.5, the relation between wave heights and wave forces is non-linear due to the drag term, and the calculated transfer function is thus a function of the wave heights used. We have for the most probable wave period for a given wave height, as explained in Example 2 :
For periods higher than 16 seconds, the formula gives wave heights higher than the 100 year wave height (= 29 m). The wave height 29 m is thus used for all periods longer than 16 seconds. The transfer function may be expressed by
where a,,,(w)
is the maximum stress caused by the wave at frequency w .
Consider again the wave H = 11 m, T = 11.7 s, w = 0.539. In the deterministic analysis we found that M,
(w = 0.539) = 4698 Nm, a,,
(w = 0.539) = 6.9 MPa.
Section 2.6.3 The transfer function is thus
The procedure is repeated for a set of wave periods within the range 3-25 seconds. The result is shown in Fig. 2.34.
Fig. 2.34 Transfer function relating stress and wave surface elevation. This transfer function is now combined with the wave spectrum defined previously in order to obtain a stress spectrum for each seastate, Eq. (2.20): So(4 =
( T(w) l2
S?)(W)
The stress spectral moments are found by numerical integration of Eqs. (2.47) and (2.48) :
00
m2 = J w2 ~ , ( w ) dw = 35.74 1 -(MPa 0
2
S
The average stress cycle period is thus, Eq. (2.1 6)
and the number of cycles within the seastate
The stress spectrum obtained is narrow-banded and the Rayleigh distribution
Section 2.6.4 is used to describe the stress amplitudes. The probability of an arbitrary amplitude exceeding a level o l is thus, Eq. (2.1 5) n
2.6.4 Simplified long-term distribution
A simplified long-term distribution of stress ranges may be obtained from the simplified wave height distribution, Fig. 2.17, and a general knowledge of the relation between wave height and response for the considered structure. The wave height H is given by Eq. (2.56): log N H = Hloo (1 1 log N1oo The relation between wave height and stress range is assumed to be of the form Aa= C * H ~
(2.73)
The long-term distribution of stress ranges may then be expressed as log N )K Aa = Aaloo (1 log N1oo where Auloo is the stress range induced by the 100 year wave. The value of the parameter K is dependent on the type of structure and the environmental conditions (wave height - wave period relation). For North Sea conditions, the following values may be appropriate: Jacket structures Concrete gravity structures Semi-submersibles
1.6 < K < 1.8 1.3 < K < 1.6 ~ . O < K < 1.3
The above method should be used with care. The choice of the parameter K should preferably be based on the. results of a detailed analysis performed for a similar structure. This may be done by a curve-fitting procedure whereby Eq. (2.74) is fitted to the known distribution. EXAMPLE 4: Long-term distribution of stresses in a platform, simplified analysis. Consider a semi-submersible platform as shown in Fig. 2.35. An analysis of the stresses induced by the 100 year wave has been performed and resulted in a stress range Aaloo = 80 MPa. A preliminary estimate of the long-term
Section 2.6.4
JOINT
Fig. 2.35 Semi-submersible platform. distribution of the stress ranges in the indicated welded joint is wanted for a first evaluation of fatigue damage. Solution. The platform is intended to operate in the North Sea. The mean wave period is assumed to be 6 seconds, i.e. the number of waves in 100 years is:
The stress ranges are assumed to follow Eq. (2.74): log N )K log N1oo where N is the number of stress cycles exceeding Ao. Previous analyses have shown that K = 0.9 is a reasonable value. We therefore get for the long-term stress distribution ACJ= Aaloo (1
-
log N)o9 n o = s o - ( 1 ---8.72 Note that a lower value of the parameter stressranges. A'
K
will result in generally higher
Chapter 2. References REFERENCES
1. Newland, D.E. : "Random Vibrations and Spectral Analysis", Longman, London, 1975. 2. Bendat, J.S. and Piersol, A.G. : "Random Data: Analysis and Measurement Procedures", Wiley-Interscience, 1971. 3. Langen, I. og Sigbjsrnsson, R.: "Dynamisk Analyse av Konstruksjoner", TAPIR, Trondheirn, 1979.
4. Clough, R.W. and Penzien, J. : "Dynamics of Structures", McGraw-Hill, 1975.
5. Meirowich, L. : "Elements of Vibration Analysis", McGraw-Hill, New York, 1975. 6. Skjellbreia, L. and Hendrikson, J.: "Fifth Order Gravity Wave Theory", Proc. Seventh Conference on Coastal Engineering, The Hague, 1961, pp. 184-196. 7. Dean, R.G.: "Evaluation and Development of Water Wave Theories for Engineering Application", Vols. I and 11. U.S. Army, Coastal Eng. Research Center, 1974. 8. Houmb, O.G. and Overvik, T.: "Parameterization of wave spectra and long term joint distribution of wave height and period". Proc. Conference on Behaviour of Offshore Structures, Trondheim, 1976.
9. Heideman, J .C., Olsen, O.A. and Johansson, P.I. : "Local Wave Force Coefficients", Civil Engineering in the Oceans IV, ASCE, 1979, pp. 684-699. 10. "Dynamics of Marine Structures", CIRIA Report UR 8, London, 1977. 11. Sarpkaya, T. and Isaacson, M.: "Mechanics of Wave Forces on Offshore Structures", Van Nostrand Reinhold Co., New York, 1981. 12. Harnrnersley, J . and Handscomb, P.: "Monte Carlo Methods", Methuen, London, 1964. 13. Houbolt, J.C.: "A Recurrence Matrix Solution for the Dynamic Response of Elastic Aircraft", J. Aeronaut. Science, Vol. 17, 1950.
14. Newmark, N.M. : "A Method of Computation for Structural Dynamics", J . Eng. Mechanics Div., Vol. 85, ASCE, 1959. 15. Dijk, G.M.: "Statistical Load Data Processing", National Aerospace Laboratory, Amsterdam, 1971.
Chapter 2. References 16. Det norske Veritas: "Rules for the design, construction and inspection of offshore structures", Appendix B, 1977. 17. Det norske Veritas : "Rules for the design, construction and inspection of offshore structures", Appendix C, 1977. 18. Det norske Veritas : "Rules for submarine pipeline systems", Appendix A, 1977.
19. British Standard CP3. Code of basic data for the design of buildings. British Standard Institution, London 1972.
CHAPTER 3
FRACTURE MECHANICS AS A TOOL IN FATIGUE ANALYSIS Knut Engesvik
SINTEF,Trondheirn
ABSTRACT This chapter deals with the basic theory of fracture mechanics with emphasis on its application in fatigue analysis. The fundamentals of fracture mechanics are presented. The relationship between the stress intensity range and crack growth is used to evaluate the development of cracks under variable loading. This approach is related to ordinary SN-curves.
NOMENCLATURE General rule Random variables are denoted by capital letters, while their realizations are denoted by the corresponding small letters. Operators and special notations E( - expectation operator e - within (the interval) Symbols The symbols are generally explained where they first appear. The most frequent symbols and their meaning are listed below. Roman letters: - crack depth, minor half axis of semielliptical crack, a half crack length of through crack a,
-
critical a
Chapter 3. Nomenclature af
-
final a initial a crack aspect ratio (shape) crack growth rate major half axis of semielliptical crack constant, crack growth coefficient Young's modulus probability density function (pdf') of X basic crack shape factor stress gradient factor front free surface factors finite thickness factor finite width factor total correction factor energy release rate influence function Rice's J-integral stress intensity factor mode I stress intensity factor mode I1 stress intensity factor mode 111stress intensity factor critical stress intensity factor elastic stress concentration factor stress intensity factor range threshold stress intensity factor range weld leg length crack growth exponent crack growth exponent, number of cycles number of cycles t o failure initiation part of Nf propagation part of Nf polar coordinate crack tip plastic zone size radius, stress ratio; R = omin/omaX plate thickness plate thickness plate width
Chapter 3. Nomenclature Greek letters:
P
r( 8
v
g P (7
-
-
-
-
o(x) Oc amax Omin OX ,OY,OZOY
Ao Affeq
4
7XY TXZ 7Y Z
4
-
-
-
-
empirical constant gamma function polar coordinate, weld flank angle, parameter in Weibull distribution Poisson's ratio parameter in Weibull distribution radius, notch tip radius, weld toe radius nominal normal stress crack surface stress distribution critical stress maximum stress minimum stress normal stresses referred to a specified coordinate system monotonic, uniaxial yield stress stress range equivalent stress range constant amplitude fatigue limit shear stress in X-Y-plane shear stress in X-Z-plane shear stress in Y-Z-plane angle
Abbreviations: CA - constant amplitude COD - crack opening displacement EPFM elastic-plastic fracture mechanics fcg - fatigue crack growth IF - influence function LEFM - linear-elastic fracture mechanics SCF - stress concentration factor
-
Section 3.1 .1 3.1
FUNDAMENTALS OF FRACTURE MECHANICS
3.1 .1 Introduction
Fracture mechanics seeks to define the local conditions of stress and strain around a crack, in terms of the global parameters of loads, geometry, etc., under which the crack will extend (Fig. 3 .I).
Local
-
condltlons
magnitude and d i s t r i b u t i o n of stresses/strains
G l o b a l conditions
- material properties - geometry; - e x t e r n a l - crack (shape, size) - Loading i.e. n o m i n a l s t r e s s
-
Fig. 3.1 Linear-elastic fracture mechanics linking global conditions with local crack-tip response. Various approaches have been employed in the analysis of fracture problems, leading t o the introduction of various fracture mechanics parameters, e.g. G, J, COD, K - all being interrelated. The most popular among these parameters has been the stress intensity factor, K . In fact, a fundamental principle of linear-elastic fracture mechanics is that the stress field ahead of a .sharp crack can be characterized in terms of this single parameter, K. Fracture mechanics can be subdivided into two general categories, namely linear-elastic (LEFM) and elastic-plastic (EPFM). This section will be restricted to LEFM, its analytical basis and the practical evaluation of the stress intensity factor.
,1
.. -
-4
-
,
\
-
~ttr Icclrrt
(rlr
-
Section 3.1.2
3.1.2 Analytical basis of LEFM
Crack tip stress field The basis of LEFM is an analysis of the elastic stress field at the tip of a crack. A crack in a solid can be stressed in three different modes, as illustrated in Fig. 3.2. The superposition of the three modes describes the general case of cracking. Mode I is technically the most important, as it is the most common mode, particularly in fatigue.
I
mode I opening mode
mode I1 s l i d i n g mode
mode111 t e a r i n g mode
Fig. 3.2 The three modes of cracking. Now, consider a through thickness sharp crack in a linear elastic isotropic body subjected to mode I loading. Such a two-dimensional crack is shown schematically in Fig. 3.3. An arbitrary stress element in the vicinity of the crack tip with coordinates r and 8 relative to the crack tip and crack plane is also shown. The stresses and displacements at any point near the crack tip can be derived, using theory of elasticity and complex stress functions. The elastic stresses near the crack tip (r/a -4 1) for the mode I case are as follows:
r x =~f
i
8 sin 8 cos3 8 cos 2 2
uz = TXZ = TYZ = 0 for plane stress
+ oy]
uz
= v[ox
Txz
= Tyz= 0
for plane strain
(3.1 d)
Section 3.1-.2 d
Fig. 3.3
Schematic illustration of the elastic stress-field distribution near the tip of a crack (Mode I deformation).
where:
K = KI = mode I stress intensity factor
= polar coordinates, as shown in Fig. 3.3 r, 8 v = Poisson's ratio Similar expressions exist for the other modes. It is seen that the crack tip stress field is singular, with singularity of the type r-1'2 . This is a common feature of the crack tip stress field, regardless of mode of deformation. Strictly speaking the stresses are defined by a series of terms involving r and 8 , but close to the crack tip (i.e. for r a) only the first (i.e. singular) term is significant since the others involve higher-order terms in r.
+
The stress intensity factor concept From Eqs. (4.1 a-c) it is seen that the elastic stresses close t o the crack tip depend on r, 8 and K only. It is also noted that the distribution of stresses around the crack tip depends only on the values of r and 8, while their magnitude at any given position (r, 8) depends only on K. Thus, the distributions of stresses at the crack tip are invariant with respect t o loading and geometry. The effect of these global parameters are incorporated in K. Hence, the whole stress field at the crack tip is known, when K is known.
noCclz.
-
$OI"~Y.
Section 3.1.2
It is important to realize that the value of K is not dependent on the material or on the coordinates r and 8. However, it depends on external load, external geometry, and crack geometry (size and shape). Hence, K provides a link between the very localized crack tip response and the more global conditions (Fig. 3.1 ). It also follows that combinations of external load, external geometry and crack geometry resulting in the same K, yield identical stress fields in the crack tip region, i.e. the same local response. This representation of the stress field around a crack tip by the stress intensity factor is a basic concept of fracture mechanics. An obvious advantage of the fracture mechanics approach to fatigue is the ability to incorporate the pertinent external loading variables (alternating stress and loading configuration) and geometry factors (flaw size, -shape, and component geometry) into a single-term parameter, such that data (e.g. for crack growth) are applicable to a wide variety of loading and geometry configurations other than those from which they were initially obtained. This allows a correlation of test results from different specimen geometries, and also a correlation between e.g. test results and service failures. K should not be confused with the elastic stress concentration factor Kt, which is the ratio of the maximum stress to the nominal stress at a notch. Hence, Kt is a scaling factor for the nominal stress, while K acts as a scaling factor for the crack tip stress field. For this reason, K is called a stress field parameter. Furthermore, Kt is a descriptive parameter relative to notches (stress concentrations), while K characterizes conditions at cracks (stress singularities). Kt is-incapableof treating cracks, as Kt=-, regardless of external loading and geometry, i.e. it is incapable of discriminating between the various loading and geometry configurations influencing the crack-tip response. The numerical value of Kt depends on the type of loading (i.e. tension, bending) and external geometry (including notch geometry), while the value of K depends on the loading (type and level), external geometry, crack geometry (size and shape) and mode of crack displacement. K used without a mode subscript I, I1 or I11 normally refers to mode I.
-
'-I<
F
Limitations of LEFM
LEFM is based on a linear-elastic analysis of the stresses at the crack tip, and inherently takes no account of plasticity. Hence, LEFM is not strictly correct as r + 0.Since infinite stresses cannot exist in a physical body, and as ductile materials will always show some plasticity at the tip of a crack, the elastic solution (Eq. 3 .l) should be modified to account for crack tip plasticity.
Section 3.1.3 In general, crack tip plasticity can be assessed, and the effect taken into account through a correction term. If, however, the plastic zone size (rp) at the crack tip is small relative to local geometry (for example, rp/t and rp/a
Section 3.1.3 I1 of Ref. /4/), Sih (Vol. I of Ref. 151) and Kobayashi 171. Numerical methods have also been reported recently /8/. In practical problems, structural geometries and loadings are often so complex that the available stress intensity factor solutions are inadequate. Evaluation of the stress intensity factor for the actual problem using standard methods may be prohibitively expensive in both time and money. Thus there is a need to develop simpler methods which will be cheap and easy to use even if less accurate than most standard methods. Many simple methods have been suggested, and their relative merits are discussed in 191. In the following, some techniques for obtaining approximate engineering estimates are treated. Tables for the conversion of units related to stress and stress intensity are given in Appendix 3 .A.
&perpositton methods Superposition is probably the most common and simplest technique in use for obtaining stress intensity factors. Complex (load-geometry) configurations are considered to be a combination of a number of separate simpler configurations with separate boundary conditions and which have known stress intensity factors. The stress intensity factors for the simple configurations are then added to obtain the required solution. Errors from using superposition can arise when the complex configuration being analysed cannot be precisely built up from configurations with known stress intensity factors. An illustration of the use of this technique is shown in Fig. 3.4 191.
a
b
Fig. 3.4 Superposition of stress intensity factors.
c
Section 3.1.3 The stress intensity factor for the configuration shown in Fig. 3.4a, is the sum of the stress intensity factors for the two simpler configurations shown in Figs. 3.4b and 3 . 4 ~ . Another important application of superposition, the analysis of pinloaded lugs is shown in Fig. 3.5. By using the procedure shown, opening mode stress intensity factors for non-symmetrical loadings can be found by adding the more easily obtainable results for simpler symmetrical loadings.
Fig. 3.5 Superposition for a pin-loaded hole with radial cracks. The stress intensity factor for a crack in a loaded body may be determined by considering the crack to be in an unloaded body with applied tractions on the crack surface only (Fig. 3.6). These surface tractions are equal in magnitude but opposite in sign to those evaluated along the line of the crack site in the uncracked configuration. This method of determining stress intensity factors is important in the use of the influence function method (See later section). Thus, application of the principle of superposition leads to an important result about the equivalence o f stress intensity factors resulting from external loading o n a body and those resulting from internal tractions on the crack surface. When employing superposition, it is important to be aware of the particular restrictions pertaining to the superposition of stress intensity factors. 1) The stress intensity factors to be superposed must correspond to the same mode of crack deformation (I, I1 or 111).
Section 3.1.3 Load
Stress f r e e crack (a1
S t r e s s over crock site=cj(x)
Crack surface tractions=-d(x)
(b)
(c
>
Fig. 3.6 Superposition showing the equivalence of K(K, = Kc) for general loading and crack surface tractions; a) initial cracked configuration; b) uncracked configuration; c) initial configuration with applied loading removed. E.g. components that contain cracks may be subjected to one or more different types of mode I loads such as uniform tensile loads, concentrated tensile loads, or bending loads. The stress-field distributions in the vicinity of the crack tip that is subjected to these loads are identical and are represented by Eqs. (3.1 a-f). Consequently, the total stress-intensity factor can be obtained by algebraically adding the stress-intensity factors that correspond to each load. However, some components may be subjected to loads that correspond to various modes of deformation. Because the stress-field distributions in the vicinity of a crack are different for different modes of deforrnation (Section 3.1.2), the stress-intensity factors for different modes of deformation cannot be added. Under these loading conditions, the total energyrelease rate, G, rather than the stress-intensity factor, can be calculated by algebraically adding the energy-release rate for the various modes of deformation.
Section 3.1.3 2) Problems with compressive forces/stresses. Although stresses may be combined linearly, even when the loading over a portion of the crack length tends to close the crack, the stress intensity factors cannot without further restrictions. This breakdown of the linear superposition occurs since stress singularities, and therefore stress intensity factors, do not exist for crack closing forces. Stress intensity factors of cracks can be superimposed for loads that either tend to open or to close the crack along the entire crack front only if the combined loading state opens the crack along the entire periphery. Thus, the crack surfaces in the final configuration must be separated along their entire length, although there may be some overlap of the crack surface, or K1 may be negative, in some of the ancillary configurations. If overlap does occur in an ancillary configuration, it must be ignored in evaluating the ancillary stress intensity factor, otherwise the results of the superposition will be invalid. 3) Boundary problems. A configuration containing a crack may have several boundaries, e.g. holes, other cracks or sheet edges, which influence the stress intensity factor. Using the method of superposition a solution is obtained by separating the configuration into a number of ancillary configurations, which have known solutions. Each ancillary configuration will often contain only one boundary, which interacts with the crack. The interaction of several boundaries is usually neglected in the compounded solution /9, 101, and thus is a source to error. Errors due to neglecting boundary - boundary interactions depend on: - nearness/closeness of boundaries, - boundary shape, - number of boundaries. E.g. consider the configurations shown in Figs. 3.7 - 3.9. These represent widely different boundary effects, namely a pair of boundaries of infinite, finite or zero radius of curvature in the path of the crack. Consider again the configuration shown in Fig. 3.7. Figure 3.10 shows the appropriate ancillary configurations. Comparison of Figs. 3.7 and 3.1 0 shows that we require c = b and d = b, + e. Studies of configurations as the above, show that: - The errors of the compounded solution increases with increasing crack length, i.e. as the crack tip approaches the boundaries. - At a fixed crack length errors tend to increase with increasing boundary radius, i.e. boundaries with large radii of curvature will have an effect over a larger distance than boundaries with small radii of curvature.
Section 3.1.3
Fig. 3.7 Eccentric crack in a finite width sheet subjected to a uniaxial tensile stress.
Fig. 3.8
Crack between two holes in an infinite sheet subjected to a uniaxial tensile stress.
Fig. 3.9
Three collinear cracks in an infinite sheet subjected to a uniaxial tensile stress.
Section 3.1.3
Fig. 3.10
-
Crack near the edge of a half plane subjected to a uniform tensile stress; ancillary configuration for Fig. 3.7 (d 2 c).
Errors increase with the number of boundaries. E.g. increasing the number of collinear cracks in Fig. 3.9 would increase the solution error.
The basic compounding equation for calculating the resultant stress intensity factor K,, neglecting boundary interactions might be expressed as:
where K, is the stress intensity factor for a crack in the presence of a single boundary B,, and K is the stress intensity factor in the absence of all boundaries. This compounding technique has been extensively used on aerospace problems. However, the methodology has general applicability and potential for providing engineering estimates of K for complex configurations. The technique has been used in very local as well as more global applications, e.g. to cracks in stiffened sheets /11/. This might be of interest in the assessment of residual strength in a structure, and closely related to considerations on inspection and structural reliability.
The influence function method Considerable effort in analytical fracture mechanics is devoted to the computation of K for complex stress/geometry combinations of actual cracked structures. Traditional approaches have been to use literature solutions or to obtain numerical solutions of K with a finite element or boundary-integral equation model of the cracked structure. There are inadequacies in both of these approaches for a large class of problems. Literature solutions lack generality, while repeated two or three-dimensional numerical stress analyses of
Section 3.1.3
cracked idealizations are costly, time-consuming and subject to errors due to poor program performance or user inexperience. To reduce errors and minimize cost, a method involving the use of influence coefficients or influence functions (h) to compute K has been shown to provide a viable alternative for many geometries. The influence function (IF) method has also been labeled the weight function or Green's function method. This method of determining stress intensity factors is applicable to a wide variety of problems, and has been used for two- as well as three-dimensional elastic crack problems 1121. Fig. 3.1 1 illustrates the elastic superposition principle which is the basis of the IF method. The superposition reduces the K solution of an arbitrary crack problem to the solution of:
1) the problem without the crack (i.e. uncracked problem), and 2) a crack problem in which only the crack face is pressurized so as to cancel the uncracked stresses ( o(x) in Fig. 3.1 1) that would exist across the crack locus in the absence of the crack. Influence functions are used to solve this second, pressurized crack problem. To solve the pressurized crack problem, and hence the original problem, consider the differential load o(x)dx (assuming constant thickness), which causes a differential increment of K given by
so that the stress intensity factor is given by K = LdK(x) = $ h(x,geo.)o(x)dx
(3.4)
La
where La is the straight crack face boundary parallel to the x axis. h( ) is the influence function. Equivalent forms can be written for KI, KII and KIII. Thus, the methodology consists of the following steps: 1) The reduction of the actual problem into two (or more) simpler problems, i.e. employing elastic superposition of (loadlgeometry) configurations (See Section on "Superposition methods").
2) Determination and specification of the uncracked stress field, i.e. the distribution of stress along the crack site in the uncracked body, which is a non-singular elasticity problem. 3) Obtaining the appropriate influence function for the actual (i.e. the pressurized) crack problem.
Section 3.1.3
(Tensile stress on c r a c k f a c e
(Compressive L o a d i n g on a c t u a l crack face)
d
Fig. 3.1 1 The reduction of a problem into two simpler problems, ( 1) and (2) for computations of stress intensity factor. An influence function h is simply the K value arising from a unit point load at some position, usually on the crack face. Thus h is independent of loading, and depends only on the crack face position and structural geometry. The influence function can be accurately obtained from relatively simple loading conditions and applied t o complex stress fields. Sources of influence functions are found in e.g. 11, 2, 31. Methods of computing influence functions are treated in e.g. 16, 12, 131. Some exact and approximate influence functions are given in / 121.
Section 3.1.3 The influence function method is exact providing that the correct influence function is used. However, it is often possible to construct approximate influence functions, so avoiding the need to use more time-consuming and costly methods.
4 ) Integration according to Eq. (3.4). Thus, once the uncracked stress field and the influence function are known, obtaining a stress intensity factor is reduced to a simple summation procedure which can be done numerically, graphically or analytically depending on the form of the influence function. The reader is reminded of the restrictions pertaining to the superposition of stress intensity factors (See Section on "Superposition methods"). E.g. for cracks in residual stress fields care must be taken to ensure that the crack surfaces are separated along their entire length. If they are not, crack surface contact conditions must be included in the influence function. Thus, one can see that the major advantage of the IF method is the markedly reduced amount of stress analysis. Once h has been determined for a geometry, K can be calculated for any crack size and shape from the "uncracked" stress field. Through the use of elastic superposition, the IF method properly accounts for stress redistribution as the crack dimensions increase due to propagation through the structure. Thus, there is no need to include the crack explicitly in the stress analysis for each crack size. To illustrate the utility of Eq. (3.4), consider the center-cracked plate under symmetric loading shown in Fig. 3.12. For the case of uniform stress of an infinite plate (a/b + O ) , the stress intensity factor is given by
where a is the half crack length and uo is the applied uniform stress. It has been shown 1121 that, for any symmetric stress field, o(x) = o(-x), the influence function for the infinite plate is given by 1 0 < x < a defines -La 2
Eqs. (3.4) and (3.6) reduce to Eq. (3.5) for the case of constant o(x) = oO. Thus, we see by example that the IF method can correctly quantify the crack-induced redistribution of the uncracked elastic stress field.
Section 3.1.3
Fig. 3.1 2 Center-cracked plate under symmetric stress.
A practical hybrid method
Introduction This method is basically an influence function - and a superposition method. It employs available solutions for two- and three-dimensional crack problems. From these the influence of different factors affecting K are separated and used to "compose" an estimate of K in an actual case 114-20/. General expression for K K may be conveniently expressed as: K= o 6 . F where :
F = FE*FS'FT*FW*FG
FE = FS = FT = FW = FG =
basic crack shape factor front face factor back face or finite thickness factor finite width factor stress gradient factor
Section 3.1.3
The basic crack shape factor - FE. This factor takes into account the effect of crack front curvature, i.e. crack shape. A good approximation is obtained through the expression:
which pertains to point A in Fig. 3.1 6.
The front free surface correction factor - FS . This factor accounts for a free surface at the "mouth" of the crack (Fig. 3.13), and depends on: - crack opening stress distribution (Fig. 3.14) (Fig. 3.14,.15) - free surface shape crack shape - position on crack front
-
The influence of crack shape might be approximated as:
which pertains to point A in Fig. 3.16. FS might be estimated as:
Fs = Fb fS where :
F i = FS(o(x),B)
from Fig. 3.14.
The finite thickness correction factor - FT . This factor (also called "the back free surface correction factor") accounts for the effect of a finite plate thickness, i.e. a free surface ahead of the crack front (Fig. 3.13b and c). It dependson:
-
-
-
crack geometry (size, shape) bending conditions (free, restrained) during cracking crack opening stress distribution position on crack front
Approximate values of FT are given in Fig. 3.16.
The finite width correction factor - FW. This factor accounts for a free surface ahead of the crack front of a through crack (Fig. 3.13a). The following expression yields a good approximation of this effect :
Section 3.1.3
I
a)
"Through"
crack
I
b)
"Edge" crack
I
C)
1
"Surfacen crack
Fig. 3.13 Plate cross-section with various crack geometries. Free surfaces and related correction factors.
Section 3.1.3
Fig. 3.1 4 Influence of free surface shape (Fig. 3.15) and crack stress distribution on FS.
Fig. 3.1 5 Free surface shape parameters.
Section 3.1.3
Section 3.2.1
The stress gradient correction factor - FG. This factor (also called "the geometry correction factor") accounts for nonuniform crack opening stresses, i.e. stress field gradients at the crack locus. The gradients may be due to e.g. non-uniform applied stress (such as bending) or stress concentration caused by detail geometry. This stress gradient should not be confused with that which occurs at the crack tip. FG represents a more global condition than the crack tip, but may account for a local stress distribution, which is not acknowledged by a strength of materials analysis. Estimates of the gradient effect on K might be extracted from known solutions to crack problems / 14, 151. Some approximate expressions for FG pertaining to welded joints are given in Section 3.2.1 .
3.2
FRACTURE MECHANICS APPLIED TO FATIGUE PROBLEMS
=Ji
#Wbm%a ef crack growth
Introduction Numerous relations for predicting the growth rate (da/dN) have been proposed. These may be divided in two main categories, i.e. theoretical and semiempirical "laws". The theoretical laws might be further grouped according to the different approaches employed in developing them. Many attempts have been made to deduce a law of fatigue crack growth (fcg) theoretically, but none of the proposed expressions has a general applicability. It is anticipated that such an expression will be a complicated one if it is to have general validity. For the technical problem of fcg the simple knowledge that da/dN is a function of AK will often be sufficient. Therefore, the crack propagation relationship is more often deduced from test data. Semi-empirical laws might be viewed as empirical fitting to available data, and each is legitimate insofar as it represents the data. As to the use of such relations, the questions will always be:
-
are the data on which the relation is based of relevance, i.e. do the material and testing conditions represent reality?
-
is the precision of fit sufficient for the purpose for which the law will be used?
Broek /21/ concludes that there is little basis for arguments about the usefulness of the various empirical expressions proposed. The scatter in
Section 3.2.1 actual data implies that many empirical expressions may have certain merits, i.e each one may be found reasonably satisfactory in a limited region or for limited sets of data. Therefore no particular expression for da/dN vs AK will have significant advantages over another. A best polynomial fit may be the most suitable in view of computer processing. Crack growth rate relations
Fig. 3.17 shows a schematic crack growth rate curve, with three distinct regions indicated, i.e. the well-known threshold-, intermediate-, and failure regions. I
I
"TWO-STAGE"
MECH.
CONT. MECH. I
Log
Fig. 3.17
aK
Schematic crack growth rate curve showing sigmoidal variation of fatigue crack propagation rate da/dN with the alternating stress intensity (AK). A&h is the threshold stress intensity for crack growth, and Kc the stress intensity at final failure (terminal K).
Section 3.2.1 Some of the most common crack growth relationships are given in the following, together with comments indicating how they adapt to the general sigmoidal shape of the crack growth rate curve (Fig. 3.17). Region B :
-,
\JJ
Regions A and B : dN
= C~AK* - A K ~ )
Regions B and C - R-effect explicitly accounted for:
Regions A, B and C - R-effect explicitly accounted for:
The relationship (3.1 8) is particularly useful in the absence of available crack growth data. In the above expressions: da/dN= crack growth rate, i.e. crack growth per cycle AK = stress intensity factor range = 4C ( 3 .F AKth = threshold-value of AK = critical value of K, triggering fast fracture Kc R = stress ratio = omin/omax = Kmin/I
Section 3.2.1
The Paris' equation The simplest relation, in mathematical terms, is the Paris-equation (Eq. (3.1 3)), where C and m are "constants" for a particular material and particular testing conditions. This equation provides an adequate description of the behaviour only for the mid-range (i.e. region B) of growth rates (typically 10*-10-~ mmlcycle). The complete variation of da/dN with AK is more complicated , being roughly sigrnoidal in form (log-log plot), and bounded at extremes by values of AKth and Kc (Fig. 3.17). Since K incorporates the various geometrical factors (e.g. joint- and crack-geometry), Eq. (3.13) may be regarded as a law of crack propagation relevant to any geometry of cracked body provided factors not related to AK, such as material and environment, correspond t o the C and m values applied. For purpose of integration, limits t o the AK regime over which this equation can operate, must be set at the threshold and final fracture conditions, and regions A and C assumed to be vertical (Fig. 3.1 8).
Crack
growth
None I
Log
A K
Fig. 3.1 8 Idealized crack growth rate curve.
It is observed that the Paris-equation is conservative in region A, and non-conservative in region C . Usually, most of the fatigue life is spent propagating cracks in regions A and B. Very little fatigue life is left when a crack
Section 3.2.1 enters region C. Thus, the Paris-relation will in general yield conservative results, i.e. computed life < actuallreal fatigue life. In such a simple relation as Eq. (3.13), only the primary parameter aK is explicitly taken into account. All the secondary parameters (e.g. materid properties, frequency, mean st= and R, environment) enter the computations implicitly through the constants C and m . Fatigue crack growth is influenced by so many uncontrollable factors that a large scatter has to be expected in practice. This is also observed on plots of da/dN vs AK, as they exhibit a wide scatter band. Several attempts have been made to find an empirical relationship between C and m. In general, the proposed relations are of the kind:
where A and B are constants for the particular type of material. Experimental results on steels tested in air at R * 0, confirm that log C and m are linearly related in plane strain fcg. Gurney 1291 analysed several published crack propagation results and found as a best fit relationship (considering results for structural - and high strength steels together):
Stress concentrations and stress intensities for welded joints
*/
Some results are available for calculation of stress concentrations and stress intensities of welded joints. They may be used to obtain:
-
an approximate solution, where this is sufficient a first estimate, pending a more elaborate and accurate analysis a fairly accurate solution, if the actual case resembles closely one of the underlying cases.
Some of the published results are given in the following. Transverse butt welds. With the overfill in the shape of a circular arc, and W = T (Fig. 3.19), the corresponding value of the stress gradient factor FG for a crack initiating at the weld toe is 1301:
where: (next page)
Section 3.2.1
Fig. 3.1 9 Transverse butt weld with circular arc overfill. q = log (1 1.584 - 0.0588 $)/log (200) @ = obtuse toe angle (degrees)
This equation is reasonably valid over the range 135O < 4 < 180". Transverse load-carrying fillet welds. The value of AK for a crack at the weld root of a cruciform joint may be expressed as /3 1/ : Ao(A, + A,&)&-= W 2 w AK = (3.22) 22 1
+
+--T
where: w = II T/2 (Fig. 3.20) Ao = nominal stress range in the main (longitudinal) plates 2a = length of internal weld root crack
Restrictions : 0.2 < Q/T < 1.2 0 < a/w < 0.7
9 FI-
Weld t o e c r a c k
Weld r o o t c r a c k
Fig. 3.20 Transverse load-carrying fillet welds.
Section 3.2.1
Transverse non-load-carrying fillet welds (Fig. 3.211.
Fig. 3.21 Transverse non-load-carrying fillet welds.
For alTG0.05 1301:
where: Q T t a
= weld leg length
= thickness of main plate = thickness of attachment plate = crack depth = t/T k = 1 -0- log Pllog 4.49 q = 0.054p + 0.2255
For 0.05 < a < 0.325 it can be assumed that there is a linear relation T between log FG and log (2a/T) passing through FG = 1 .O at a/T = 0.325, and the value of FG from Eq. (3.25) at a/T = 0.05. An approximate formula for predicting FG automatically is 116,171:
where: (next page)
Section 3.2.1
FG = stress gradient correction factor (Section 3.1.3) SCF = elastic stress concentration factor at the weld toe a = non-dimensionalized crack length (a/T or a/W) d = stress gradient correction factor decay coefficient q = stress gradient correction factor decay exponent The constants in the decay function (Eq. 3.26) are given in Table 3.1.
Table 3.1 Constants for the FG decay function. Weld detail
d
Typical stiffener geometry ) / 161
0.3602
0.2487
/ 161
0.1473
0.4348
1.158
0.6051
Average cover plate detail
)
Typical gusset plate geometry 2, / 17/ 1) a = a/Tf
(Figs. 3.22,3.23)
2) a = a / W f
(Fig.3.24)
9
Another rapid, but more precise method of obtaining FG is treated in 116, 171.
I
a . Section
I
b.Plan
view
Fig. 3.22 Detail geometry for transverse stiffener.
Section 3.2.1
T
F i [ l e t weld
Cover p l a t e F Lange
I-Fat
igu
crack
a Section
d
I b . P l a n view
Fig. 3.23 Detail geometry for cover plate.
Groove weld
W,/2
Point of t r a n s i t ion tangency
Flange
Symne t r y
d
' Web
Fig. 3.24 Detail geometry for gusset plate.
From Eq. (3.26) it is seen that FG = SCF (= Kt)
(3 -27)
when: a = a = O i.e. at the surface. This has general validity. Thus, knowledge of the SCF provides important information about K close to the surface. Hence, to obtain a first estimate of K, by employing the FGdecay-function in Eq. (3.26), an estimate of the SCF is needed. Ref. 116, 171suggest the following equations:
Section 3.2.1 Stiffeners: (Fig. 3 -22) SCF = 1.621 log (A) + 3.963 Tf
Cover Plates: (Fig. 3.23)
T SCF = -3.539 log (K) + 1.981 log (A) + 5.798 Tf Tf
1161 (3.29)
Gusset plates: (Fig. 3.24)
SCF = -1.115 log(&)
wf
0.1384 log
+ 0.5370log(L) + wf
(s) + (a) + w 0.2848
f
T
0.6801
1171 (3.30)
Tf
where: Tf = TCp = Tgp = Wf = Wgp = Q = R =
L
flange thickness cover plate thickness gusset plate thickness flange width gusset plate width weld leg size radius of circular transition at end of groove-welded gusset plate = attachment length
In evaluating FG at welded structural details, the crack is usually taken to be the through (or edge-) type (a/2c = 0). However, it is worthwhile noting that FG varies with crack shape, and in welded joints the shape is often different from that of a straight crack. Hence, Fig. 3.25 has been developed using through and circular crack Green's functions for a crack in an infinite solid. This figure shows that the values for FG diverge as the stress decay becomes more rapid. The limiting ratio, Y, for a concentrated load at the crack origin is estimated t o be 0.548. This number represents twice the deviation from 1.0 recorded between the uniform and linear stress cases. Hence, FG related to a straight crack front yields conservative (too high) K-values, compared with FG for a curved front. The crack shape significantly influences K (Section 3.1.3), and thus the fatigue life. Therefore, the fatigue designer employing fracture mechanics techniques should seek for relevant shape relations. In order to predict cyclic changes in crack shape, the shape of the surface crack is modelled with a finite number of degrees of freedom. Most often a semi-elliptical shape is
Section 3.2.1 Through crack
Crack shape
Embedded penny shaped
Ratio
Y
Stress distribution
1
1.o
a
5. r
1 .ooo
1 .ooo
1 .ooo
0.363
0.281
0.774
rn
b Fig. 3.25
0. 548
Comparison of stress gradient correction factors FG for various crack shapes and stress distributions 11 81.
assumed, described by the half-axis ratio, or the aspect ratio a/2c. Predictions of the (a/2c)-evolution during crack growth might be done empirically or theoretically. Empirical a-c-relations may be based on measurements on the fractured surface of welded joints (without parameterization of the influencing factors). Some of the published crack shape relations are given in the following. These are valid only for the specific welded joint considered, i.e. with the actual geometry, loading, material, and welding method. However, lacking relevant data they provide easy-to-use practical information, if
available for a case similar to the actual case. Gusset specimens (Fig. 3.26) 4a lower bound 20a a < 1 mm 20aoe3 a > 1 mm Stiffener specimens (Fig. 3.2 1) 2c = 2.59
[mml
upper bound
Section 3.2.2
Fig. 3.26 Gusset specimen. (Stiffener specimens cont .)
+
2c = -0.27 6.34a a < 3 mm a/2cxO aZ3mm
i
2.8a
lower bound
12 a
upper bound
3.2.2 Estimation of fatigue life Crack initiation One might generally subdivide the fatigue life in a crack initiation period (Ni) and a crack growth period (Np), ending with failure, i.e.
As is further discussed in Chapter 4, the crack initiation period in welded joints, that are not stress relieved, usually occupies a small part of the total life, and is often neglected. In most cases it leads to small errors only, in the conservative direction.
Cmck propagation Having the means of determining the crack growth rate (Section 3.2.1), one is able to make various estimates concerning crack growth, e.g. the time or number of cycles required to grow a crack from one size to another:
Section 3.2.2
This may be required when the structure is in service. E.g. a crack may be detected and reported through the in-service inspection programme, and decisions have to be taken whether this crack should be stopped, or allowed to grow further, with due consideration to the actual material specification, loading conditions, repair possibilities, and costs.
The crack propagation part of the fatigue life may be expressed as:
where : ai = initial crack length (depth) af = final (critical) crack length (depth) By inserting the relevant expressions for crack growth rate and stress intensity, one is able to obtain an estimate of the fatigue crack propagation life. Thus, by employing Eqs. (3.7,3.13) :
L
.
*. --- - -------------------.I Constant terms need not be included in the integration, i.e.: &>
For constant amplitude loading, the integrand is further reduced, i.e.:
In the case of a very simple F-function the above integral may be evaluated analytically, but generally numerical integration must be employed. In cases where F does not depend on a (which are the exceptions), Eq. (3.41) may be written as:
Section 3.2.2
This integral is easily evaluated analytically, i.e. :
Thus, for this simple case one obtains the following closed-form expression for the constant amplitude fatigue (crack propagation) life:
whenm # 2. For structural steels and aluminium alloys 2 < rn < 6. For welded steel joints 2.5 5 m 54.5. Thus, if ai 4 af, an approximate estimate of the constant amplitude fatigue life is: 1-m/2
ai
Np " c Aom rmI2
(3.45)
P (m/2 - 1)
- , > ;-r ,. If the failure condition is brittle fracture, the critical crack length may be estimated from Eq. (3.7): Kmax - Omax * * F & ,
-? .
which reads at failure:
and hence the critical crack length:
Remarks concerning fatigue life computations Some words of warning to the novice within fatigue calculations, whether based on fracture mechanics or not. The "correct" or "exact answers don 't exist. Results from deterministic fatigue calculations, as treated above, are meaningful in a qualitative and relative sense, but must be used with care and judgement when interpreted in an absolute sense. This is partly due to the numerous uncertainties involved in a fatigue life computation, i.e. uncertainties/weaknesses in the fatigue model, uncertainties linked with input "
Section 3.2.2 (material, loading and geometry) parameters due to e.g. lack or scarcity of data, and - last but not least : the uncertainty incurred when trying to predict - in a deterministic manner - an outcome of highly random nature. One vital question might be: 'What is the prediction accuracy?'This naturally depends on the computational accuracy, the accuracy of the fatigue model, and the relevance and quality of input data. (Garbage in - garbage out!) However, even if model - and statistical uncertainties were removed, how to tackle randomness in a deterministic calculation?
-
A "worst case"dpproach might lead to extremely conservative results (with unknown reliability). A 'ymean-value'y-approach, i.e. employing mean values of the input parameters, generally yields a fatigue life different from the mean fatigue life.
In view of the above, it is of vital importance to bear in mind the random nature of fatigue, and the many uncertainties involved, when working with fatigue life computations.
Variable amplitude loading adds complexity to the problem of predicting fatigue life; i.e. the definition of load/stress cycles - through cycle counting methods (Chapter 4), and sequence or interaction effects (Chapter 4). The most common approaches to the problem are given in the following. Cy cle-by-cycle approach.
Crack length after n cycles:
Crack length increment (i.e. crack growth) in cycle "j":
where: ai = initial crack length Cj = interaction coefficient, with value pertaining to cycle "j" = constant amplitude crack growth rate. (a) d N ~ ~
Thus, the interaction coefficient modifies the constant amplitude growth rate to account for interaction, i.e. acceleration or retardation. Most existing interaction models are retardation models. There is no proof that
Section 3.2.2 these models in general improve a fatigue life prediction. Hence, before taking the step of including interaction in the computations, one should give close consideration t o the stress history (irregularity factor, frequency and sign of "overload" stress peaks, etc.), to decide whether significant interactions are likely or not. Besides, neglecting retardation gives conservative results, while accounting for retardation but not for acceleration might yield nonconservative results.
Equivalent constant amplitude stress range approach. In this approach a variable amplitude stress history is represented by an equivalent constant amplitude stress range (Chapter 4) that causes the same amount of fatigue damage, i.e. crack growth. This equivalent stress range may be expressed as (Fig. 3.27a):
interval
Fig. 3.27 Stress range distribution (a) and histogram (b).
Section 3.2.2
(3.5 1) or as (Fig. 3.27b):
where: fA2(Ao) = probability density function of stress range (Ao) fi = frequency of occurrence of stress range "i" (Aoi) k = number of histogram class intervals ni = number of cycles within interval "i" NT = total number of cycles Aoi = midpoint of histogram interval "i" p = empirical or calibration constant Special cases:
p = 3 -+ RMC (root-mean-cube) stress range
/3 = 2 -+ RMS (root-meansquare) stress range fi = m = Slope of the crack growth equation + no
interaction
a =C(AK)~
dN
Interaction may be taken into account by adjusting P.
-
It is pointed out (Chapter 4) that: /3 = m is in effect a Miner-approach, in that crack growth increments are added linearly, with no account of interaction. the approach has no sound theoretical basis, but is a very practical empirical approach.
It is common practice to assume that the stress range Ao is Weibull distributed, i.e.:
where:
E=
shape parameter of the distribution 0 = scale parameter of the distribution
The n'th moment of this distribution might be expressed as:
Section 3.2.3 where: r ( ) = gamma-function Thus, AU,,
= {eo r ( i
+ p/g)
e { r ( i + pig)
=
The r-function may be approximated by simpler functions. The following expression is a functional fit to the I'-function in the argument range x c (3 .-6 .) ; r(x) r 0.0076 exp (1.60 x ) + 1.26
(3.5 6)
and hence an approximate expression is:
Ao,,
%
0
(0.0076 exp {1.6 x ) + 1.26)ltP
(3.57)
where: x = 1 + PI,$. i
\
\, *
t d
2
"'
I
'
*
3.2.3 Fracture mechanics applied in the calculation of SN-curves The Paris-equation for crack growth rate (Eq. 3.1 3) may be transformed to the equation of an SN-curve through a simple integration. Thus, Eq. (3.41) may be reformulated as:
where I is the integral in Eq. (3.4 1). This further yields:
and
The integral I depends on geometry (i.e. external- and crack-geometry), and is only weakly dependent on stress through the critical crack size. This influence is insignificant when af >> ai. Further, if initiation is absent or insignificant, then Nf = Np and :
which is the equation of an SN-curve in the high-cycle region (N 5 lo4).
Section 3.2.3
III
// Kmar=K c (a) $-curve m
log C
-
/
/
/
,/
I log
AK
Log ad
(b) SN-curve
Log a 6
I
Fig.3.28 Relationship between
aand SN-curves. dN
Section 3.2.3 Equation (3.59) yields the following expressions:
where: m, C = exponent and coefficient in Paris' equation.
The close relationship between crack growth rate curves and SN-curves is shown in Fig. 3.28 and Table 3.2.
Table 3.2 Comparison of da/dN- and SN-curves. I
Region
da/dN-curve
SN-curve
I
Threshold region (No - or intermittent growth)
Fatigue limit region (Infinite life)
I1
Intermediate region (Regular striation growth. Paris' eq .)
Finite life region (Intermediate - and high-cycle region)
111
Failure region (Fast fracture or yielding)
Lo w-cycle or static failure region
Section 3.3
T
nrc 1
3.3 EXAMPLES
~ Sn R stress fleld. Consider a crack extending through a tensile residual stress field (equal to yield stress oy) under uniform tension, as shown in the figure. When a 4 by Eq. (C. 1) in Appendix 3 .C yields: . # b ~of f&~ #36 c
tttt Res i dua 1 stress
When a > b, from Eqs. (3.C. 1) and (3 .C.3) :
K = 1.122 ofia
+ $(oy-o)
where F(b/a) is given by Eq. (3.C.3).
*fla(sin-':)*
F():
Section 3.3
Example 2
-
Estimation o f stress intensity factor related to a crack in a transverse butt welded joint. A crack is detected at the toe of the joint. Estimate K!
Data: i) Geometry.. . .
- T = 20mm
due t o specified requirement, 8 < 30' = 180'- @ - a = 1.0mm - assumed crack shape, a/2c = 0.25 - axial load, amax = 350 N/mm2
-
ii) Loading
... .
K = o*@*FSaFT*FE*FG a/T= 1/20 = 0.05,+FT = 1.0 FE = { I + 4.5945(0.25)1.65 }*.' = 0.82 q = log (1 1.584 - 0.0588 150)/log 200 = 0.19 , . / -, FG = (5120)-'*I9 = 1.30 fs = 1 - 0.16(0.25) = 0.96 ~k = 1.04 Fs = 1.04 0.96= 1.0 KT = 350 4-0 1.0 1.0 0.82 1.30
Eqs. (3.7) and (3.8) Fig. 3.16 Eq. (3.9) Eq. (3.2 1) Eq. (3.21) Eq. (3.10) Fig. 3.14 Eq. (3.1 1) Eqs. (3.7) and (3.8)
-
Example 3 Cracking in transverse stiffener weld. Estimate K for a surface crack with depth 3 mm. Data: i) Geometry
. . . . - T = 40 mm - assumed weld flank angle, 8 = 45"
-
ii) Loading
... .
weld leg length, II = 20 mm - a = 3mm - axial load, omax = 300 N/mm2
Section 3.3
+
SCF= 1.62 1 log(20/40) 3.963 = 3.5 Eq. (3.28) FG = 3.5 { 1 + 0.3602-' (3/40)OS2 13 Eq. (3.26), Table 3.1 = 1.41 2c = 2.59 (3)OSg4 = 7.32 mm Eq. (3.33) += a/2c = 3/7.32 = 0.41 FE = { l 4.5945 (0.41)"~ }.'5 = 0.70 Eq.(3.9) fs = 1-0.16*(0.41)= 0.93 Eq. (3.10) F; = 0.98 Fig. 3.14 FS = 0.98 0.93 = 0.91 Eq. (3.1 1) a/T = 3/40, -+ FT = 1.0 Fig. 3.16 KI = a - - * 0 . 9 1 - 1 . 0 - 0 . 7 0 - 1 . 4 1 Eqs.(3.7)and(3.8) = 2.76 a = 829 ~ m m - ' .=~ 26.2 M P a r m -
' r1
+
VB! Let us assume that a very wide SAE 1020 plate is subjected to a constant amplitude uniaxial cyclic loading that produce nominal stresses varying from omax = 200 MPa to omin = -50 MPa. ,---6t; What fatigue life would be attained if an initial through the thickness edge crack were no greater than 0.5 mm in length? Kc = 104 MPafi. Before we can solve this problem, several questions must be answered. Namely, - What is the applicable stress intensity factor expression for this component and loading? - What crack growth rate equation should be used?
Section 3.3
- How do we integrate this equation? - What value of AK will cause fracture?
-
Does corrosion or temperature play an important part?
Let us assume that corrosive environment is not involved, and that room temperature prevails. The Paris crack growth rate equation (Eq. 3.13) is often a reasonable expression for region B (Fig. 3.1 7) crack growth behaviour. Integration of the Paris equation involves numerical methods unless F from Eq. (3.7) is independent of crack length. In an infinite plate with a single edge crack loaded in uniform tension, F is constant and equal to 1.12. This is approximately correct for a finite plate as long as the crack length does not exceed about 10% of the width.
which is above threshold levels and hence the Paris equation is applicable.
The final crack length can be obtained by setting Kmax at fracture equal to Kc, i.e.: Eq. (3.48)
Constant amplitude fatigue life:
-
1 1
1
I
A.
A
'
, N~
= (-0.5)
0.068)-~.~ - (0.0005)-~'~ :6.9 10-I 2 ) ( 2 0 0 ) ~ (n)1.5 ( I . I 213
Eq. (3.44)
= 189 000 cycles
(m = 3 , C = 6.9 lo-'
m / ( ~ ~ a J m ) ~, ,a = 200 MPa,
i.e. neglecting the negative
of the stress cycle,
)
Now let us assume that the fracture toughness Kc were incorrect by a factor or divisor of 2, that is, Kc = 208 MPa T r nor 52 MPa Jm. The final fracture length from Eq. (3.48) would result in af = 270 mm and 17 mm, respectively, and the corresponding fatigue life Nf from Eq. (3.44) in 198 000 and 17 1 000 cycles. Thus increasing or decreasing the fracture toughness by a factor of 2 caused an increase or decrease in the final crack length by a factor of 4, respectively. However, the corresponding changes in fatigue crack growth life were less than 10%. If the initial crack length ai were 2.5 mm, the life would be only 7.5 000 cycles, instead of 189 000 cycles for the original problem with ai = 0.5 mm.
Section 3.3 These calculations illustrate the importance of minimizing initial flaw or crack lengths to increase fatigue life, and that appreciable changes in fracture toughness will alter final crack lengths, but produce small effects on fatigue lives. Thus, Eq. (3.45) for a very long crack yields:
i.e. about 9% longer life than estimated above. High fracture toughness in fatigue design, however, is still very desirable because larger crack lengths are easier to detect by inspection.
s.
-
Consider a joint of the type in Example 3. How many fatigue loading cycles can the joint endure without getting a "through crack", i.e. a crack that completely penetrates the main plate? Data: i) Geometry
. . . . - plate thickness, T = 20 mm
- weld leg length, R = 10 mm -
ii) Material iii) Loading
weld flank angle, 8 = 45 degr.
- initial crack depth, ai = 0.1 5 mm . . . . - Paris eq. parameter, m = 3 . . . . - axia1,Ao = 2 0 0 ~ l m r n ~
C(Paris'eq.)= (1.315.10-')
2 8 . 3 1 ~=~5.8. 10-l2
B = 45 degr., -+ F: = 0.98 SCF = 1.62 1 log (10120) 3.963 = 3.5
+
Eq. (3.20) Fig. 3.14 Eq. (3.28)
The computations are tabulated on the next pages. The fatigue life integral I is evaluated numerically (Simpson). This computation is too rough for general use, but shows the method.
Section 3.3
a (mm)
a/T
a/2c
fS
FS
FT
a/2c from Eq. (3.33)
fs FT FE FG
>> >> >> >>
Eq.(3.10) Fig. 3.16 Eq. (3.9) Eq. (3.26) and Table 3.1
FE
; ,-I'-.-
I =
'
+
+
+ + +
0.5 0.5 0.5 0.5 0.5 0.5
.
--
+ +
169.575 (200)3
.
a;
Chapter 3. References
7_A-
(240 + 65) (65 + 33) 8.4)(33 (8.4 5.5) (5.5 + 2.5) (2.5 +0.78)-
Np = 5.8 10-17
,
-L,-.-.
-
.
lo3 lo3 lo3 lo3 lo3 10'
.nl.5
(0.5 - 0.15) (1 .O - 0.5) (3.0 - 1.0) (5.0 - 3.0) (10.0-5.0) (20.0-10.0)
lo-' lo-' loe3
Eqs. (3.40) and (3.58)
lo-'
= 656 325 cycles
Eq. (3.41)
REFERENCES 1. Tada, H., Paris, P.C. and Irwin, G.R.:
The Stress Analysis of Cracks Handbook, Del Research Corporation Hellertown, ,Pennsylvania,1973. 2. Rooke, D.P. and Cartwright, D.J.: Compendium of Stress Intensity Factors, London, HMSO, 1976. 3. Sih. G.C.:
Handbook of Stress Intensity Factors, Bethlehem, Pennsylvania, Lehigh University, 1973. 4. Liebowitz, H. (Ed.): Fracture (in 7 volumes). Academic Press, New York, 1968-70. 5. Sih, G.C. (Ed.):
Mechanics of Fracture (in 6 volumes). Noordhoff, Leyden, 1973. 6. Cartwright, D.J. and Rooke, D.P.: "Evaluation of stress intensity factors", J. Strain Analysis, Vol. 10, No. 4, 1975, pp. 217-224. 7. Kobayashi, A.S. : Experimental Techniques in Fracture Mechanics. SESA, Connecticut, 1973.
Chapter 3. References
8. Luxmore, A.R. and Owen, D.R.J. (Ed.): Proc. Int. Conf. Numer. Methods Frac. Mech., Swansea, 1978. Luxmore, A.R. and Owen, D.R.J. (Ed .): Proc. Second Int. Conf. Numer. Methods Frac. Mech., Swansea, 1980. 9. Rooke, DP., Baratta, F.I. and Cartwright, D.J.: "Simple Methods of Determining Stress Intensity Factors", Engng. Fract. Mech., Vol. 14,1981, pp. 397-426. 10. Cartwright, D.J. and Rooke, D.P. : "Approximate Stress Intensity Factors Compounded from Known Solutions", Engng. Fract. Mech., Vol6,1974, pp. 563-571. 11. Rooke, D.P. and Cartwright, D.J. : "The Compounding Method Applied to Cracks in Stiffened Sheets", Engng. Fract. Mech., Vol. 8,1976, pp. 567-573. 12. Besuner ,P.M. : "The Influence Function Method for Fracture Mechanics and Residual Fatigue Life Analysis of Cracked Components under Complex Stress Fields", Nuclear Engng. and Design, Vol. 43, No. 1,1977, pp. 115-154. 13. Labbens, R., Pellissier-Tanon, A. and Heliot, J. : "Practical Method for Calculating Stress Intensity Factors through Weight Functions", Mechanics of Crack Growth, ASTM STP 590,1976, pp. 368-384. 14. Engesvik, K.M. : Analysis of Uncertainties in The Fatigue Capacity of Welded Joints, Dr. ing. dissertation, Division of Marine Structures, The University of Trondheim, The Norwe'gian Institute of Technology, Trondheim, 1981. 15. Albrecht, P. and Yarnada, K. : "Rapid Calculation of Stress Intensity Factors", Journal of the Struct. Div., ASCE, Proc. Paper 12742, Vol. 103, No. ST2,1977, pp. 377-389. 16. Zettlemoyer, N. and Fisher, J.W.: "Stress Gradient Correction Factor for Stress Intensity at Welded Stiffeners and Cover Plates", Welding Research Supplement, Vol. 56, No. 12, 1977, pp. 3934 - 398-s. 17. Zettlemoyer, N. and Fisher, J.W. : "Stress Gradient Correction Factor for Stress Intensity at Welded Gusset Plates", Welding Research Supplement, Vol. 57, No. 2,1978, pp. 57-s - 62-s. 18. Zettlemoyer, N. and Fisher, J.W. : "Stress Gradient and Crack Shape Effects on Stress Intensity at Welded Details", Welding Research Supplement, Vol. 57, No. 8,1978, pp. 246-s 250-s.
-
19. Maddox, S.J.: "An analysis of fatigue cracks in fillet welded joints", Int. Journ. Fracture, Vol. 11, No. 2, 1975, pp. 221-243.
Chapter 3. References 20. Newman, Jr. J.C.: "A Review and Assessment of the Stress-Intensity Factors for Surface Cracks", Part-Through Crack Fatigue Life Prediction, ASTM STP 687.1979, pp. 16-42. 2 1. Broek, D. : Elementary Engineering Fracture Mechanics, Noordhoff Int. Publ., 1974. 22. Paris, P. and Erdogan, F.: "A Critical Analysis of Crack Propagation Lawsy', Journ. Basic Engng., Dec. 1963, pp. 528-534. 23. Klesnil, M. and Lukas, P.: "Influence of Strength and Stress History on Growth and Stabilisation of Fatigue Cracks", Engng. Fract. Mech., Vol. 4,1972, pp. 77-92. 24. Forman, R.G., Kearney, V.E. and Engle, R.M.: "Numerical Analysis of Crack Propagation in Cyclic-Loaded Structures", J. Basic Engng., 89,1967, pp. 459-464. 25. Erdogan, F. and Ratwani, M. : Int. Journ. Fract. Mech., 6,1970, p. 379. 26. Hartman, A. and Schijve, J. : Engng. Fract. Mech., 1,1970, p. 615. 27. Schiitz, W. : "Procedures for the prediction of fatigue life of tubular joints", Int. Conf. on Steel in Marine Structures, Paris, 1981, pp. 254-308. 28. Austen, I.M. and Walker, E.F.: Research Report PT/6795/8/77/A. 29. Gurney, T.R.: An Analysis of Some Fatigue Crack Propagation Data for Steel Subjected to Pulsating Tension Loading, Report 5911978/E, The Welding Institute, March, 1978. 30. Gurney, T.R.: Fatigue of Welded Structures, 2nd ed., Cambridge Univ. Press, 1979. 3 1. Frank, K.H. and Fisher, J .W. : "Fatigue Strength of Fillet Welded Cruciform Joints", Journal of the Structural Division, Vol. 105, No. ST9,1979, pp. 1727- 1740. 32. Yarnada, K. and Hirt, M.A.: "Fatigue Crack Propagation from Fillet Weld Toes", Journ. Struct. Div., ASCE, Vol. 108, No. ST7, July 1982, pp. 1526-1540. 33. Albrecht,P.: Fatigue Strength of Welded Beams with Stiffeners, Ph.D. dissertation, Lehigh Univ., 1972.
Appendix 3 .A 34. Rolfe, S.T. and Barsom, J.M.: Fracture and Fatigue Control in Structures. Applications of Fracture Mechanics, Prentice-Hall, Inc., 1977. 35. Lawrence, Jr. F.V., Mattos, R.J., Higashida, Y. and Burk, J.D.: "Estimating the Fatigue Crack Initiation Life of Welds'', Fatigue Testing of Weldments, ASTM STP 648,1978, pp. 134-158.
36. Tada, H. and Irwin, G.R.: "K-value Analysis for Cracks in Bridge Structures", (Rough draft review copy), Fritz Engineering Lab. Rept. No. 399.1, June 1975.
APPENDIX 3.A
CONVERSION TABLES
Stress in tensity factor
MPa 6
ksifi
M P a 6
ksifi
1
0.9101
3 1.623
3.223 5
1.0988
1
34.747
3.5420
~ m r n - ~ " 0.03 1623
0.028780
kp mm-3'2 0.3 1022
0.28233
~ m m - ~ kp ' ~ mm-3'2
1
0.10194
9.8067
1 A
Stress
MPa
ksi
MPa
ksi
N/mm2
1
0.1449
1
0.1019
6.9033
0.7037
6.904
1
kp/mm2
N/mm2
1
0.1449
1
0.1019
kp/mm2
9 3067
1.421 1
9 24067
1
Appendix 3 .C
Fig. 3.C.19.
Fig. 3.C.20. The stress intensity factors are given by the following formulas
Where : a. When the local in-plane transverse displacement near the cracked section is not restrained Fig. 3 .C. 1 9.
(Better than 2%for any a/w.) b. When the local transverse displacement is also restrained (Fig. 3.C.20).
2w (Exact)
(3.C. 15)
Appendix 3 .C
(Better than 0.5% for any a/w.)
(C-3) Concentrated splitting forces (Green's function), Fig. 3 .C. 18.
Fig. 3.C.18.
(Better than 2% for any b/a and a/w.)
It should be noted that the solutions illustrated above are valid only when the displacement of the strip is free from constraint. In actual structures, any connected structural member is under constraints imposed by the connections. When a crack occurs in a certain component, its compliance increases and load and deformation are redistributed between members. Thus, the boundary condition is not displacement-free but displacement-limited. (C-4) Examples of displacement constrained strip with a single edge crack are given in Figs. 3.C.19, 3.C.20. The inplane transverse displacement at infinity is restrained.
Appendix 3.C (C-I) Uniform tension, Figs. 3 .C. 1 5 , 3 .C. 1 6 .
Fig. 3.C.15.
-
d
d
A
I
a
,
-
C
-
a
W
i
Fig. 3.C.16.
F(a/w) = J2-w aa
tan-aa 2w
0.752 + 2.02a + 0.37(1- ~ i n x ) ~
w
COS-
2w
na 2w
(Better than 0.5%for any alw.)
(C-2) Uniform bending, Fig. 3 .C. 1 7. d
-6
Fig. 3.C.17.
-6
(3.C. 1 1)
Appendix 3.C
(3.C. 10)
(Much better than 5%; better than 2% for S 2 0.5.) When b = 0
+ 0.03S2+ 0.89S3 F(0,S) = 1.10- 0.60ss3/2 (Better than 2% for any S.)
C. An edge crack in a long strip, Fig. 3.C.14.
Fig. 3.C.14. Stress intensity factor solutions are known for various loading conditions for this geometry. Only approximate formulas and their accuracies are given for several basic cases. For more information se /I/, pp. 2.10-2.2 1 and 2.25-2.29.
Appendix 3.C
(B-2) Linearly varying stress (in-plane bending), Fig. 3 .C. 1 2.
Fig. 3 .C. 1 2.
(Better than 1% for any S.)
(B-3) Concentrated splitting forces (Green's function), Fig. 3 .C.13.
Fig. 3.C.13.
Appendix 3 .C
Fig. 3.C.10. is relatively small, the solutions for the configuration shown in Fig. 3.C.10 may be of some value for estimating stress intensity factors.
(B-1 ) Uniform normal stress, Fig. 3 .C. 1 1.
Fig. 3.C.11.
(Better than 1% for any S.)
Appendix 3.C
Fig. 3.C.8.
within 4% accuracy. For the example shown in Fig. 3 .C.8, K is estimated at
K
1.122
0,6+ 1.255 K,
(3 .C.7)
and the accuracy improves as o o / o increases. (Even when o0 = 0, accuracy is within 476.) Although this method applies to the case where the stress distribution changes its sign over the crack length, the accuracy is not expected to be as good.
B. An edge crack in half-plane (free boundary consists of two straight lines), Fig. 3.C.10. In welded structures or components, surface cracks often initiate in the residual stress zone near the welding as shown in Fig. 3.C.9. When the crack
c Crack
Fig. 3.C.9.
Appendix 3.C
Fig. 3.C.6. entire crack.) A complicated, more rigorous analysis may not be justified.
4. When a more accurate value is desirable, K estimate is improved by separating non-uniform stress into uniform stress and non-uniform stress as shown in Fig. 3 .C.8. From Equations (3 .C. 1) through (3 .C.4), the ranges of free surface correction factors K / K , for various non-uniform stress distributions are known (Fig. 3.C.7) and the values at the middle of the range are
Fig. 3.C.7.
Appendix 3 .C
(A-4) Concentrated splitting forces (Green 's function), Fig. 3 .C.5.
Fig. 3 .C.5. 2P K= -
6
1
,hi -
b E 1.30 0.30 FG)
F (b3 (better than 2% for any b/a)
(3.C.4)
(-b-) 3/2
F(b/a) is the free surface correction factor. Note: 1. For any non-uniform stress distributions, stress intensity factors are obtained by integration of Equation (3.C.4). 2. Equation (3.C.4) shows that the correction factor for a single free surface
for any normal stress distribution as long as the normal stress has the same sign over the entire crack length.
K, is the solution for the infinite plane with geometry and loading configuration reflected across the free boundary, Fig. 3 .C.6. For the infinite plane problem, the exact Green's function is known (in Eq. (3.C.4), F(b/a) = 1) and K, calculations are considerably simpler. 3. In engineering practice, when only the rough idea with acceptable accuracy will suffice, one can simply estimate K as without causing substantial error. The error is never beyond 15% and usually much less. (When the normal stress has the same sign over the
Appendix 3.C (A-2) Linearly varying stress (in-plane bending), Fig. 3 .C.3.
Fig. 3 .C.3.
K = 0.439 o f i =
-
(accurate)
1.210 (1 - +) o f i
The factor representing free surface influences is 1.2 10. (A-3) Partially distributed constant pressure, Fig. 3 C.4.
Fig. 3.C.4.
K = 2 o+ 7T
(sin-'
b -)" 1.30 -0.18 F(T)
b 5/2 (T)
(better than 2% for any b/a)
F(b/a) is the free surface correction factor.
(3.C.3)
APPENDIX 3.C
A SMALL COMPENDIUM OF STRESS INTENSITY FACTORS (From "K-value analysis for cracks in bridge structures", by Tada and Irwin 1361.)
3 .C.l Two-dimensional edge crack problems
When surface cracks have a large surface length-todepth ratio, solutions for two-dimensional edge crack problems provide approximate stress intensity factors for the region near the deepest crack edge. A. An edge crack in half-plane (straight free boundary) (Fig. 3 .C. 1)
Fig. 3.C.1. Stress intensity factors for various loading conditions are known for this geometry. Only approximate formulas and their estimated accuracies will be presented for several basic stress distributions. For more information see / 1/ pp. 8.1-8.8.
(A-1) Uniform tension, Fig. 3 .C.2.
Fig. 3 .C.2.
K = 1.122-ov7iT
(accurate)
The factor representing free surface influence is 1.122.
(3.C.1)
Appendix 3 .B APPENDIX 3B
GENERAL REFERENCES
Textbooks Knott, J.F.: Fundamentals of Fracture Mechanics, Butterworth & Co (Publishers) Ltd., 1973.
Frost, N.E., Marsh, K.J. and Pook. L.P.: Metal Fatigue, Clarendon Press, Oxford, 1974. Broek, D. : Elementary Engineering Fracture Mechanics, Noordhoff Int. Publ., 1974. Rolfe, S.T. and Barsom, J.M.: Fracture and Fatigue Control in Structures. Applications of Fracture Mechanics, Prentice-Hall, Inc., 1977. Gurney, T.R. : Fatigue of Welded Structures, 2nd ed., Cambridge Univ. Press, 1979 Hellan, K. : Bruddmekanikk, Tapir, Trondheirn, 1979 (in Norwegian). Cherepanov, G.P. : Mechanics of Brittle Fracture, McGraw-Hill Inc., 1979. Fuchs, H.O. and Stephens, R.I.: Metal Fatigue in Engineering, John Wiley & Sons, Inc., 1980. Parker, A.P. : The Mechanics of Fracture and Fatigue, W. & F.N. Spon Ltd, 1981.
Journals
-
-
-
Engineering Fracture Mechanics Fatigue of Engineering Materials and Structures International Journal of Fatigue International Journal of Fracture Journal of Applied Mechanics, ASME Journal of Strain Analysis Journal of the Structural Division, ASCE Metal Construction
Appendix 3.C Equation (3 .C. 14) is 12 to 30 percent larger than Equation (3.C. 15). When the strip has attachments such as stiffeners, Equation (3.C.15) is expected t o give reasonable estimates for stress intensity factors. An edge crack in the flange plate of a beam is a typical example in practical structures. 3.C.2 Elliptical cracks
Completely embedded crack
Approximate influence function (i.e. stress intensity at boundary point A corresponding t o the parametric angle @, due to unit splitting forces applied at point B (Figs. 3.C.21,3.C.22)):
+- .*.R
h# = h&,y,afiA) where:
= nw2 , Q2
J a T
(3.C.16) (1-k2 - C O S ~ # ) ~ . ~ ~
$ = angle (Fig. 3 .C.2 1)
R,r,R= lengths (Fig. 3 C.22) k2 = 1 - ( a / ~ ) ~ a2 = ( ( ~ / a + ) ~( y / ~ ) ~ x,y = coordinates for point B
itting ces P=l
B
Fig. 3.C.21.
Fig. 3.C.22.
When # = 0 and 7r/2, Eq. (3 .C. 16) specializes to: hj(a,c,x,~)=
6 nl.s
where: (next page)
*
Q;
.C
Appendix 3.C j = 1 , 2 corresponds to Q, = n/2 , O . r = (x2 y2 )Oa5 C = la)^ (y/cl2 )-' - 1)0-5= { a - 2 - 1 }0-5
+
+
Thus, approximate stress intensity factors are obtained as:
The influences of free surfaces might be taken into account through correction factors. Eq. (3.C.16) is exact for k = 0 (a = c), and the loss of accuracy for moderate increases of k is expected to be relatively small. Numerical integration trials and comparisons with known solutions indicate that Eq. (3 .C. 16) yields an upper bound estimate of K. The accuracy (within +(5-lo)%) is best when q5 is close to ~ / 2 .
CHAPTER 4
BASIC FATIGUE PROPERTIES OF WELDED JOINTS Stig Berge Norges tekniske hsgskole, Trondheim
ABSTRACT The purpose of this chapter is to give a basic understanding of the fatigue properties of metals in general and of welded steels specifically. The following topics are discussed : - Basic fatigue mechanisms, characteristics of fatigue failures, and methodologies for fatigue strength assessment. - Constant amplitude (SN) testing, types of tests, test specimen vs. structural behaviour in fatigue loading. - Cyclic strain and material response, total strain response to fatigue loading. - Variable amplitude loading, cycle counting methods, load spectra. - Cumulative damage, the Miner summation, equivalent stress range. - Fatigue of welded joints, effects of geometry, residual stresses, material properties. - SN data for welded joints, classification of joint types, statistical analysis of SN data, assessment of design curves.
LIST OF SYMBOLS Unless otherwise indicated, symbols in this chapter are according to the following standards, cf. Annual Book of ASTM Standards Part 10: E6 -81 Methods of Mechanical Testing E206-72 (1979) Fatigue Testing and the Statistical Analysis of Fatigue Data E5 13-74 (1980) Constant-Amplitude Low-Cycle Fatigue Testing E6 16-8 1 Fracture Testing
Chapter 4. List of symbols elongation at fracture (ISO/DIS 82-1 972) cross sectional area of unstressed specimen cross sectional area at fracture crack length fatigue strength exponent crack growth rate parameter fatigue ductility exponent modulus of elasticity engineering strain irregularity factor stress intensity factor fracture toughness plain strain fracture toughness fatigue notch factor stress intensity maximum in one cycle stress intensity minimum in one cycle elastic or theoretical stress concentration factor range of stress intensity in one cycle threshold stress intensity range for crack growth gauge length of unstressed specimen increment of gauge length crack growth exponent fatigue life, number of cycles to failure number of stress cycles endured number of cycles with same stress range load at fracture fatigue notch sensitivity stress ratio = omin/oma = Kmin/Kmax notch root radius nominal stress stress amplitude variable component of stress equivalent stress range fatigue limit mean stress steady component of stress maximum stress in one cycle minimum stress in one cycle
Section 4.1 fatigue strength at N cycles yield tensile stress ultimate tensile stress range of stress, stress range maximum stress range in a load history reduction of area at fracture (ISO/DIS 82-1972) true strain, based on actual (strained) cross section elastic strain strain at fracture, fracture ductility in monotonic loading fatigue ductility coefficient plastic strain total strain strain range in one cycle elastic strain range in one cycle plastic strain range in one cycle spectral shape parameter true stress, based on actual (strained) cross section stress at fracture in monotonic loading fatigue strength coefficient maximum stress in one cycle minimum stress in one cycle monotonic yield stress cyclic yield stress stress range in one cycle effective stress range
4.1 BASIC FATIGUE MECHANISMS AND CHARACTERISTICS Fatigue may be defined as a process of cycle by cycle accumulation of damage in a material undergoing fluctuating stresses and strains. A significant feature of fatigue is that the load is not large enough to cause immediate failure. Instead, failure occurs after a certain number of load fluctuations have been experienced, i.e. after the accumulated damage has reached a critical level. In fatigue, the most important load effect parameter is the fluctuating component of stress or strain, commonly referred to as stress or strain range, defined as the difference between a load peak and the subsequent valley. The mean or peak levels of loading are of relatively minor importance as compared to the range of stress.
Section 4.1.1 A fatigue process will go through several stages, from the initial state of the material t o final fracture, each stage characterized by the nature of the fatigue process. For a smooth or notched (machined) component of a metallic material, the stages are commonly denoted
Stage I: Initiation or crack nucleation Stage 11: Crack growth Stage 111: Final failure A brief discussion of these stages will be given, with emphasis on the phenomenological aspects. 4.1.1 Fatigue initiation
Fatigue initiation is a process of cumulative plastic strain. The development of plastic strain is associated with dislocation mobility, which is greater at a free surface than in the bulk of the material. Hence, fatigue initiation is in general a surface phenomenon. Only in rare cases, for example at the interface between the carburized layer and the core of case hardened steels, have fatigue cracks been observed to initiate in the interior of a material. The term "surface" in the context of fatigue initiation refers to exterior as well as interior surfaces. An embedded weld defect, for example, represents a free surface where fatigue initiation may take place in the same way as on an exterior surface. Fatigue initiation is linked to microscopic material behaviour. Under cyclic strain, the macroscopic plastic deformation in each cycle will cancel out, cf. Fig. 4.1. Microscopically, however, defects produced in the lattice structure by the cycling will accumulate, leading t o a progressive fatigue damage.
Fig. 4.1 Cyclic stress-strain response in a metallic material (schematic).
Section 4.1.2 In crystalline materials, plastic deformation, or slip, takes place in preferred directions and along preferred crystallographic planes. Microscopic slip may occur in single grains at stresses below the general yield stress of the material. Due to oxidation of the newly created free surfaces and hardening of the strained material, reversed slip tends to take place on neighbouring slip planes. The cumulative effect of this process is to cause a cyclic weakening of the material, giving rise to a band of concentrated slip, a so-called persistent slip band which develops by localized plastic flow into extrusions and intrusions on the surface (Fig. 4.2).
Fig. 4.2 The development of persistent slip bands, extrusions and intrusions by cyclic slip.
An intrusion is clearly a nucleus of a crack, which may develop into what is commonly denoted Stage I crack growth. In Stage I, crack growth takes place on cry~tallographicslip planes, in a shear mode. This implies that in this stage, cracks are of subgrain size, and oriented 45' to the maximum principal stress direction. No rational theory seems to exist for the crack initiation and Stage I crack growth. Commonly these two stages are denoted "initiation", or "crack nucleation", and characterized through material parameters relating macroscopic stress and strain to initiation life, cf. Section 4.3.
4.1.2 Crack growth After initiation and Stage I crack growth, the crack will in general change mode and the growth direction will become perpendicular to the largest principal cyclic stress. (There are exceptions, for example torsional fatigue of cylindrical bars, where cracks may grow in shear modes.) In this stage, the maximum principal stress, and not the shear stress, will be the driving force.
Section 4.1.2 As has been discussed in detail Sec. 3.2.1, the stress and strain fields in the vicinity of a sharp crack under essentially elastic conditions is uniquely characterized through a single parameter, the stress intensity factor K, which is a function of the applied load (or nominal stress), crack length and shape, and external geometry. Assuming the crack growth increment in a load cycle to be a function of stresses and strains at the crack tip, then crack growth rates should correlate to the range of the stress intensity factor AK. This has indeed proved to be a valid assumption, and the general crack growth rates for Mode I cracks in metals are as shown in Fig. 4.3.
/
R e g i o n 111 UnstabLe fracture
R e g i o n 11 Stable crack
Region I Inltlation threshold
*Kt h
Log A K
Fig. 4.3 Crack growth rate curve showing the three regions discussed in the text.
The virtue of this discovery is that it allows for fatigue crack growth life calculations of any geometry, provided a crack growth rate curve for the particular material has been established by simple specimen tests. The details of such analyses are discussed in Secs. 3.2.2, 3.3, 10.3 and 1 1.5. The sigmoidal shape of the crack growth curve in Fig. 4.3 suggests a subdivision into three regions. In Region I, the crack growth rate goes asymptotically to zero as AK approaches a threshold value AKth. This means that for stress intensities below AKth there is no crack growth, i.e. there is a fatigue limit. The threshold effect is believed to be caused by a complicated synergism of processes which leads to crack blocking for small stress intensities. Corrosion deposits in the crack, surface oxidation, fracture surface microroughness, and residual plastic strains from the crack tip zone are believed to be important mechanisms contributing t o the threshold. The threshold level depends on stress parameters like mean stress, residual stresses, and stress interaction (stress memory) effects. Environmental effects are also very important. Sea water submersion, particularly under cathodic protection
Section 4.1.2 conditions, tends to increase the threshold level, most probably through crack blocking by corrosion products or by calcarious deposits. This is further discussed in Sec. 7.3
c
lo5,
10
20
50
K)O
AMPLITUDE OF STRESS INTENSITY FACTOR AK12 kglrnrf?''
c
lo9,
10
20
50
100
AMPLITUDE OF STRESS INTENSITY FACTOR A K / 2 kglmm)i7
Fig. 4.4 Crack growth rate as a function of stress ratio for two high tensile steels (Ref. 171). Typical threshold data for a high-tensile steel in constant amplitude loading are shown in Fig. 4.4. For partly negative stresses, the growth rates seem to follow the range of the positive part of the cycle
AK,ff = K,,
AK - 1 -R
where
This indicates that the negative part of the load cycle is nondamaging. It is generally assumed that crack closure is responsible for this effect. For R > 0,i.e. tensile stresses, the threshold effects cannot be explained by simple concepts.
Section 4.1 -2 A popular form of the crack growth relation in the threshold region is
In this formula, the threshold value AKth is t o be inserted appropriate to the mean stress and other parameters of importance. For welded joints, in which residual stresses tend t o prevail over any applied mean stress, this formula has proved t o be sufficient for many types of analysis. Region I1 crack growth follows a power law, the so-called Paris-Erdogan crack growth law,
This part of the curve is the basis of most finite life fatigue analyses of welded joints, cf. Secs. 3.2.1, 10.3 and 11.5. As indicated in Fig. 4.4, Region I1 crack growth rates at stress ratios R > 0.4 are relatively insensitive to mean stress. For R < 0, i.e. partly negative stresses, the growth rates are seen t o follow the range of the positive part of the cycle, cf. Eq. (4.1). This indicates that the negative part of the cycle is non-damaging, as would be anticipated if crack closure occurs for negative stresses. The description of the mean stress independency for R > 0.4 is valid only in non-corrosive environments. In sea water with cathodic protection, particularly with high strength steels, high mean stresses may cause an acceleration of crack growth rates which is quite significant, cf. Sec. 7.3. Region I1 crack growth rates for steels are remarkably insensitive to material properties. In Fig. 4.5 are shown mean curves for three different generic classes of steels: ferritic-pearlitic, martensitic, and austenitic stainless. The difference between these three mean curves is of the same order of magnitude as the inherent scatter in crack growth data (Ref. /8/). In Fig. 4.6 are shown data for different structural steels: plate material, heat-affected zone, and weld metal. No significant difference is seen between the different materials (Ref. 191). A similar trend has been found for aluminium alloys. In fact, crack growth data for structural aluminium alloys and steel may be brought on a common basis by the equation
Section 4.1.2 AK,
10
I
15 I
k s l K
X)
25
RANGE OF STRESS INTENSITY FACTOR .AK Nmm-
Fig. 4.5 Crack growth rate curves for three different classes of steels (Ref. 181).
f
Fig. 4.6 Crack growth rates for various types of weld metal, plate, and heat-affected zones in structural steels (Ref. 191).
This means that the stress which gives equal fatigue crack growth rates in these two materials, is three times larger in steel than in aluminium. From this fact, and from fatigue testing of aluminium weldments, fatigue design rules for welded aluminium structures have been assessed by simply taking the design SNsurves for corresponding welds in steel and divide the stresses by three (Ref. /lo/). This corresponds to the ratio of specific weight between steel and aluminium, which indicates that in terms of weight-saving, aluminium has no advantage over steel in fatigue design of welded structures. Region I11 crack growth is exhibiting a rapidly increasing growth rate towards "infinity", i.e. ductile tearing and/or brittle fracture. Using concepts of linear-elastic fracture mechanics (which for most engineering materials is strictly not valid in this range), instability occurs when
Section 4.1.2
This has led to the conception of parametric crack growth laws covering Region 111, like the Forman's equation, which is much used in aircraft design,
The material constants C and m in Eq. (4.8) are not necessarily equal t o those of Eqs. (4.3) and (4.4). Crack growth in Region I11 is of minor importance for marine structures design. The reason for this is that if Region I11 crack growth becomes important, the cycle rate and the load spectra for most marine structures is such that final fracture will be imminent. Exceptions to this would be structures with a low natural frequency, causing large peak loads with a very low probability of occurrence. Functional loads may also have the same characteristics. The sigmoidal shape of the crack growth curves leads to considerable complications in fracture mechanics calculations, even if simplified parametric equations are used in order to describe the different regions. A commonly used engineering approximation is shown in Fig. 4.7. Region I1 crack growth by the Paris-Erdogan formula (Eq. (4.4)) is assumed, and the threshold is approximated by a cut-off. The cut-off model is conservative in the threshold region, and the deviation from a more accurate model is in many cases negligible in relation to the uncertainty associated with an assessment of the threshold. In many cases this uncertainty is so great that practical calculations are performed with a straight-line extrapolation of the Region I1 crack growth curve as shown in Fig. 4.7. With this "engineering crack growth curve", fracture mechanics calculations become much simplified.
log A K
Fig. 4.7 Actual da/dN curve (solid) and two approximations for the threshold region commonly applied in engineering calculations.
Section 4.1.2 In summary, for most engineering purposes, a crack growth law of the Paris-Erdogan type (Eq. (4.4)) is appropriate. Fatigue crack growth rates of structural steels in air seem to fall within a common scatterband. Threshold effects need to be considered for each case, taking into account residual stresses and mean stresses in particular. Typical values of C, m, and AKth are given in Table 4.la-b. The influence of sea water environments and of cathodic protection is discussed in detail in Chapter 7. Table 4.la Fatigue crack parameters C and m (Eq. (4.4)) for C-Mn structural steels BS 4360 Grade 50 or similar, in air. C ( 2 - ) (MPa flm)m
m
7.1 10-l2 5.32 1 0 " ~ 5.9 lo-'*
3.0 2.53 3.15
2.8 10-l1
2.65
3.9 10-l2 5.2 10'12 9.5 lo-'*
3.1 3.0 3.0
Validity R>0.0 R > 0.0 RZO.O AK < 22 M P a 6 R Z 0.0 AK > 22 M P a d E R > 0.0 R=O R=O
Comments
Ref.
Mean values Upper bound
42 42
Mean values
43
Mean values
43
Mean values Mean values Upper bound
44 9 9
Table 4 . l b Fatigue crack growth thresholds compiled in Ref. 1451. Air data.
AKth (MPaJm) R = 0.0
R = 0.8
8.2 7.8 12.3 7.7 12.5 8.2
3 .O 3 .O 3.7
3.3 2.5 2.6
Material
Sy (MPa) 309 232
:ii
399 479
Mild steel Mild steel
1
Medium carbon steels ASTM A 533 B
Section 4.1.3
- 4.1.4
4.1.3 Final failure If a fatigue failure in a load-carrying member is allowed to progress, final failure will inevitably take place at some stage of crack growth (disregarding other types of limit states which may have been reached before final failure). Final failure may occur by basically three mechanisms: brittle fracture, ductile fracture, and plastic collapse, depending on the toughness of the material, temperature, loading rate, plate thickness, and constraint. A discussion of these topics is given in Chapter 9. In a fatigue life assessment, final failure represents the end of the fatigue life, commonly defined by SN tests or by a maximum tolerable defect size in crack growth calculations.
4.1.4 Characteristics of fatigue failures In this section, characteristics of fatigue failures will be discussed with reference to typical details of welded offshore structures. In Fig. 4.8 are shown the fracture surfaces from fatigue failure of an offshore structure (Ref. 11 11). Two features are to be noted, typical of high cycle fatigue of offshore structures:
- The material has undergone only minor plastic strain, i.e. the strains have been essentially elastic.
- The fracture surface is smooth, with characteristic beachmarks reflecting the variations in load intensity through interchanging periods of storms and calmer weather. By microscopic examination, striations representing single cycle advancements of the crack tip may also be observed. In high-cycle fatigue, however, it is not possible to associate these striations with cycle-by-cycle crack growth, due to the fact that crack growth does not occur simultaneously along the crack front. On a certain location, the crack may advance in one cycle, and then be arrested during the subsequent cycle(s) while the crack grows in other locations along the crack front. The da/dN rate measured experimentally is thus a measure of an average crack growth rate along the crack front. Only in special cases, generally with large growth rates in ductile and very homogeneous materials, may growth rates be inferred from cycleby-cycle striations. In engineering steels, the crack advances partly by ductile mechanisms, partly by cleavage of individual grains, and striations are in general difficult t o observe except in areas of large crack growth rates (Fig. 4.9).
Section 4.1.4
Fig. 4.8 Fracture surfaces showing beachmarks resulting from a variable amplitude load history. Crack growth direction from bottom to top (Ref. / 1 11).
Fig. 4.9 Striations on the fracture surface shown in Fig. 4.8 (Ref. / I I/).
Section 4.1.4 For a design engineer, the development of crack length vs. time in a fatigue failure is an important aspect, with bearing on defect significance, quality control, inspection strategy, and redundancy requirements. Features of fatigue failures may be illustrated by examples. Crack growth through the plate thickness in a plane weld is illustrated in Fig. 4.10. An initial toe defect of 0.05 mm has been assumed, typical of manual welds. The feature to be noted is the extremely rapid acceleration of growth after the crack has reached a length of some few millimeters. This is typical for crack growth in plane unstiffened structures, where cracks will tend to advance with a straight crack front (small aspect ratio). The acceleration of crack growth is then reflecting the power-law growth of Eq. (4.4).
Fig. 4.10 Fatigue crack growth from the toe of a cruciform joint, as obtained by computer simulation.
A similar behaviour is seen for cracks growing from cut-outs in unstiffened structures. A special case are cut-outs in tubular braces, Figs. 4.1 1 and 4.12. Even though the crack is growing away from a stress concentrator, the growth rate accelerates rapidly after the crack has reached a length of some few millimeters. The reason for this is that the cut-out itself may be regarded as part of the crack when a > d/ 10. In fracture mechanics terms:
Section 4.1 -4
Fig. 4.1 1 (left): Crack growth from a cut-out. A short crack will sense the hot spot stress at the cut-out as a homogeneous field. A long crack will sense the average stress, but with the cut+ut as a part of the crack, leading to an accelerated crack growth rate, cf. Fig. 4.12. Fig. 4.1 2 (right): Crack growth from a circular cut-out in a tubular brace (Ref. 1111). K 1 K~
s
(n a)'/*
K1S*[n-(a+d/2)]"~
for a/d
0.1
foralds0.1
leading to a crack growth behaviour as shown. A consequence of this is that for the geometries in Figs. 4.10 and 4.1 1, any engineering size weld defect will have a very detrimental effect on fatigue life. Moreover, the time to failure after the crack has reached a detectable size may be too short for inspection routines to be reliable. Therefore, a sudden loss of load-carrying capacity of single members should be considered in the design of fatigue loaded structures. For stiffened members the progress of crack growth is somewhat different. In Fig. 4.13, a crack growing in a stiffened plate is shown. In this case, redistribution of stresses to the stiffeners will take place during crack growth. The net effect is a reduction in stress intensity, and a retardation of growth
Section 4.1.4
Fig. 4.13 Fatigue loaded stiffened plate (a) and stress intensity factor for a crack growing perpendicular to the stringers (b). Crack growth rate (c) and crack length (d). Also shown in Fig. (d) is crack growth for an unstiffened plate. rate when the crack tip approaches a stiffener. This general effect of stiffening and load shedding is one reason why fatigue cracks may be tolerated in ship structures to an extent which is not allowed in tubular offshore structures. Tubular joints are a category of welded joints which warrant a closer consideration. Unstiffened tubular joints feature large stress concentrations and a very complicated stress distribution with large gradients, Fig. 4.14. In this case, contrary to the case of a cut-out, the stress intensity of a crack growing out of the hot spot region will not increase. The crack growth rate will therefore be fairly constant throughout a large part of the fatigue life. A typical crack length vs. time history for a tubular joint is shown in Fig. 4.15. From initial microscopic defects along the weld at the weld toe or
Section 4.1.4
Fig. 4.14 Circumferential stress in a tubular T-joint in axial loading. I I Region 111 I (circumI ferentlal I growth) I I I I I I 1
I
I I
0
0.2
0.4
Fraction of
tubular
0.6 joint
0.8
I
I I I I I I I I I I I I I
1.0
life
Fig. 4.15 Fatigue crack growth in a tubular joint (schematic). interpass locations, the crack will initially tend to grow in a circumferential direction under the influence of the very local stress concentration created by the weld profile. In this stage, the through-thickness growth will be limited. In the next stage, the crack will grow in a through-thickness direction, with a nearly constant growth rate, reflecting the gradual decrease in effective stress as the crack grows out of the hot spot region. The last stage is the circumferential growth of a through-thickness crack. In this stage, the crack will be intolerably large from an ultimate strength point of view. Crack growth in tubular joints are further discussed in Sec. 8.3.5.
Section 4.1.5 The purpose of these examples is to demonstrate that damage accumulation over time in a fatigue failure is strongly dependent on the type of structure or the structural element. This fact has implications on defect tolerance criteria, inspection strategy, and design philosophy for different structures and different parts of a given structure. The essential parameter to be monitored is crack length, and for a refined study the appropriate design method should be based on the principles of fracture mechanics. 4.1.5 Fatigue capacity assessment
The assessment of fatigue capacity in design of structures may follow several routes, depending on the type of structure, type of loading, etc. In general, a distinction can be made between four different methodologies: i) ii) iii) iv)
Prototype or component testing SN-curves Crack growth rate curves and fracture mechanics Cyclic strain
These methodologies will be discussed briefly in relation to marine structures. Prototype testing.
Prototype or component testing is the most direct way of assessing fatigue strength for a particular structure or structural component. The method is in common use in the automotive industry, in the design of for example crankshafts, bearing pins, etc. Also in the aircraft industry, pro totype testing is a standard technique, even in full scale testing of entire aircraft structures. Prototype testing is very expensive, and is cost-effective only for fatigue critical structures, and/or structures which are produced in large series. Moreover, the fabrication procedure and load conditions need to be well defined, otherwise the inherent uncertainties in the test conditions may invalidate the findings of the testing. Obviously, prototype testing is not feasible for welded offshore structures, except for selected components of novel design or in new applications. Examples are cast tubular joints and tendons for tension-leg platforms. Even in these cases, the test programs have generated data more of a comparative nature, with reference to standard components or materials tested under the same (simplified) conditions, rather than prototype lives under realistic loading and environmental conditions.
SN-curves. An SN-curve is a plot of fatigue life versus stress. The stress parameter, which
Section 4.1.5 for welded joints is the stress range, is normally plotted as the ordinate. Fatigue life is generally defined as the number of cycles to failure. Most SN plots are based on constant amplitude loading, in which case the parameters of stress and fatigue life are easily defined. Variable amplitude data may also be plotted on an SN format. As will be discussed in Sections 4.4 and 4.5, stress and fatigue life in variable amplitude loading may be defined in various ways. Fatigue cracks in welded structures will be confined to the welded joints or to flame cut edges. Only in very rare cases will fatigue cracks be initiated in plain rolled material. The reason for this should be obvious: The welds provide notches and initial defects which even in the most optimized designs will give a much lower fatigue strength than the adjacent plain material. The appropriate SN-curves for welded structures are therefore SN-curves for welded joints, including flame cut edges. Exceptions to this rule are cast or forged components which are welded into the structure. In such cases, stress raisers in the cast or forged part may be such that cracks will initiate from plain material surface rather than from the adjacent weld, e.g. cast tubular joints. The design will then be based on an SN-curve for the plain material, with an (elastic) stress concentration factor for the detail in question. In some codes, generally not of the latest developments, this last approach is applied to welded joints as well. The fatigue strength of each joint is based on a fatigue notch factor relative to plain material. This notch factor is empirical, and takes into account the geometric, metallurgical, and other factors which may have an influence on the fatigue strength of welds. The method has several weaknesses, and is not applied in recent codes. Crack growth rate curves and fracture mechanics. Fatigue of welded joints is mainly a crack growth phenomenon. Fracture mechanics may thus be used in order to calculate the growth, and thereby to give assessments of fatigue lives, cf. Sec. 3.2.1. A direct design calculation by fracture mechanics for a given weld is, however, not feasible. The reason for this is that there are many uncertainties in the calculation procedure, particularly linked to the initial stages of crack growth, like size of initial defects, crack growth for short cracks, and threshold effects. Due to this, absolute calculations of endurance can rarely be trusted as such. In comparative studies, however, the initiation problem may be eliminated. One is then limited to a study of cases in which the initiation conditions are identical. By choosing suitable values for the initial crack
Section 4.2.1 length, the calculated endurances can be brought into accord with experimental values by calibration. Provided the initiation conditions remain unchanged, fracture mechanics can then be used for calculating the influence of different parameters (geometrical, environmental, etc.) on the endurance. In this sense, fracture mechanics has been used extensively as a research tool, employed in order to generalize experimental data. For assessment of the significance of defects, the situation is more in favour of fracture mechanics analysis. Engineering defects, i.e. defects which can be found by non-destructive testing techniques, are generally so large that linear-elastic fracture mechanics with a crack growth power law works reasonably well. Cyclic strain. The cyclic strain approach was originally developed for machined smooth or lightly notched components in which fatigue life is dominated by a crack initiation period. The method is of limited use in the design of welded structures, in which fatigue life is dominated by crack growth. It may be used in low cycle fatigue assessments of structures where functional loads may cause plastic strains (ship structures, crane pedestals, pipelines during laying operations, etc.).
4.2
CONSTANT AMPLITUDE SN TESTING
4.2.1
SN testing versus crack growth testing
SN testing and crack growth testing may be viewed as two different approaches t o fatigue. In crack growth testing, material parameters are obtained, characterizing fatigue crack growth as a material property in a given environment. In SN testing, fatigue life of a specimen, a component, or a structure is determined under given conditions of stress and environment. In many cases, particularly with machined (non-welded) specimens, the outcome of an SN test is taken as life to crack initiation. However, crack growth is an important, sometimes dominating phase of fatigue life. This is particularly true for welded joints, where crack growth in fact occupies a major part of the fatigue life. SN testing and crack growth testing may thus be viewed as complimentary methods, which can be brought on a common basis by fracture mechanics analysis. In this section, the SN test approach will be discussed, leaving fracture mechanics to Chapter 3 .
Section 4.2.2
4.2.2 Basic concepts All practical fatigue theories contain empirical parameters which may account for qualities like material properties, surface condition, geometry, stress state, effect of environment, etc. This means that in order to apply a certain theory to a specific design case, experimental calibration is a prerequisite. The basic fatigue test is the constant amplitude SN test. In this test, a specimen is subjected t o cyclic constant amplitude loading till failure. In this respect loading may be force, strain, or displacement controlled. For most applications of interest t o structural engineers, the loading is a constant amplitude stress.
Fig. 4.16 Definition of terms relating to SN testing. The prime parameter of the loading is the stress amplitude S,, or stress range S, (cf. Fig. 4.16). Besides, the mean level of stress Sm is of interest, often denoted by the stress ratio
R, S, and S, are interrelated through
Typical load histories in SN testing are shown in Fig. 4.17. Note the singularity in the stress ratio for pulsating compression stresses. In certain codes, stress ratio is defined differently in order to avoid this problem. In an SN test, several identical specimens are usually tested at different stress or strain ranges, in order to obtain an SN-curve as shown in Fig. 4.18. Usually, either the mean level or the stress ratio is kept constant in one test series. The general effect of the stress ratio is shown in Fig. 4.19. High ratios tend to reduce the fatigue life at a given stress range. It is t o be noted that testing with Sm = const. or R = const. will in general give different SN-curves.
Section 4.2.2
''I1
I
P u l s a t i ng tension
Pulsating compression
Compressioncompression
Alternating
Tensiontension
Fig. 4.1 7 Different types of loading applied in SN testing.
Fig. 4.18 SN-curves for sharply notched specimens of mild steel and aluminium (Ref. / 121).
As indicated in Fig. 4.20, testing at S, = const. and tensile (which is a normal test condition), will give an increased stress ratio as the stress range is lowered. This will tend to reduce the fatigue life, and the comparative SN-curves will be as indicated in Fig. 4.20. Offshore structures in general will experience a constant mean load. Most fatigue experiments, however, are traditionally performed at a constant stress ratio, with 0 < R < 0.5. (R = 0.0-0.1 is a particularly popular test
Section 4.2.2
10 log N
Fig. 4 .19 SN-curves for a notched high tensile stainless steel (18 Cr at varying stress ratios (Ref. / 131).
- 9 Ni)
condition). Hence, SN data from such tests may be unconservative at low stresses when applied to offshore structures. The difference is disregarded in most applications. Several models have been proposed for the effect of mean stress, based on the limiting stress concept. The limiting stress for any material is of, the true fracture stress in monotonic tension. SN testing is normally monitored in terms of a nominal or engineering stress. Hence, the ultimate stress S, or the yield stress Sy is used as the limiting stress. Adding the mean stress S, and an alternating stress S,, this sum cannot exceed the limiting stress
In the Haigh type diagram of Fig. 4.21, this amounts to a straight line, which limits the allowable combinations of S, and S,. Outside the allowable region, the material would break during the first one quarter of a cycle, and cyclic stresses are of course not possible. This idealized description of the combined effect of S, and ,S is valid only under monotonic loading. In fatigue, Eq. (4.12) will be distorted by the cumulative effects of cyclic loading, which in general will cause a change in material properties. Empirical formulas have been established, based on
Section 4.2.2
Log N
Fig. 4.20 The difference between R = const. and S, = const. testing, and the influence on the SN-curve (schematic).
Fig. 4.21 The Haigh diagram showing allowable combinations of stress amplitude and mean stress.
Section 4.2.2
Fig. 4.22 The Modified Goodman, Gerber, and Soderberg relations for the effect of mean stress on fatigue strength for N = lo7 cycles, with data for a high tensile stainless steel (Ref. 1131). the same simple idea as displayed in Fig. 4.2 1. In Fig. 4.22 are shown three commonly used expressions in the Haigh diagram. The limiting point on the alternating stress axis is the stress Sa,N at a given fatigue life under reversed loading (S, = 0 or R = -1). The lines are drawn for a given fatigue life and exhibit empirical combinations of stresses S, and S, which will give that life.
srn su
Modified Goodman relation: S, = S a , ~ (-l -) Gerber relation : Soderberg relation:
None of the models are generally valid, as they are based on experimental data obtained under different conditions. Moreover, the concept of using monotonic tensile properties in defining fatigue strength is fundarnentally wrong. As will be discussed in Section 4.3, the stress-strain relation of materials may be very different under cyclic loading as compared to monotonic strain, thus invalidating the concept of S,, and S, as material parameters in fatigue.
Section 4.2.3
Fig. 4.23 The data shown in Fig. 21 plotted in a Smith diagram for N = 1o7 cycles.
A more practical version of the same diagram is obtained through the Smith diagram (Fig. 4.23). Here, S,, and Smi, for a certain fatigue life are shown in the same diagram, giving a pictorial impression of the allowable cyclic stress range for a given fatigue life.
4.2.3 Types of SN tests In this section, various types of SN tests are described, and the relation of such data to fatigue design is discussed. SN testing of plain materials. A basic fatigue test for material characterization is the SN test of plain material. Specimens are usually smooth cylindrical or hour-glass shaped as shown in Fig. 4.24, and loaded axially or in bending. The influence of the surface finish on the fatigue properties is minimized through standardized machining procedures. The test is thus a test of the basic fatigue strength of the material in terms of engineering stress. In applications of the data, any effects of surface treatment like residual stresses, work-hardening, heat cycling, surface roughness etc. different from the conditions of the test, must be accounted for.
Section 4.2.3
Fig. 4.24 Typical specimens for fatigue testing of plain material in predominantly elastic loading (ASTM E 466-82 Constant Amplitude Axial Fatigue Tests of Metallic Materials). In this type of test, most of the fatigue life is spent in the crack initiation stage. After crack initiation, the remaining fatigue life is relatively short. An SN plot will have a general form as shown in Fig. 4.1 8. SN data of this form are not very useful in design. One reason is the sensitivity to surface conditions as mentioned above. Another fact t o bear in mind is that fatigue cracks usually are initiated in areas of local stress concentrations, and that stress gradients and stress concentrations are important parameters in fatigue. Stress gradients define the volume of stressed material, which will be different in bending as compared to tension. Stress concentrations raise the stress level, usually by a geometry dependent factor which may be non-linear due to local yielding as shown in Fig. 4.25.
SN testing of welded joints. In a welded structure, the welds will constitute weak links with regard to fatigue strength. Plain material data of fatigue strength are not very useful
Section 4.2.3
Axia1,elastic
Notched,axial, elastic
Bending,elast ic
Notched,axial,Local yielding
Fig. 4.25 Specimens loaded to the same nominal stress but with different geometries and loading conditions will in general give different fatigue response, due to effects of stress gradients and of local yielding. for this problem. Fatigue design of welded structures is therefore based on SN data obtained with realistic welded specimens. Typical test configurations and data are shown in Fig. 4.26. The statistical analysis and conversion of such data into design criteria is described and discussed in Sec. 4.7.
o
I 1 o5
I
1 o6
Fracture
I
1 o7
I
Io 8 log N
Fig. 4.26 Typical specimens and SN data for welded joints (Ref. 1141).
Section 4.2.4
SN testing of structural components. The type of specimens shown in Fig. 4.26 may be taken as a part of a structural member. In many cases, the stress distribution of members is so complicated that the fatigue strength cannot be reliably assessed from single specimen data. Typical cases are tubular joints and built-up beams (Fig. 4.27). Tests of these types of models are in principle similar to small-scale specimen testing, but requires extensive test equipment, and are in general more closely monitored with regard to crack initiation and growth.
Fig. 4.27 Structural components which have been subject of large-scale fatigue testing, tubular joint (a) and welded beam (b). 4.2.4 Fatigue failure criteria
Fatigue life in an SN test is usually taken as life till complete fracture has occured, or till displacements become so large that the load cannot be maintained. In the last stage of a test, the crack size may therefore be larger than what can be tolerated in structures. Two main reasons for this situation are: a) Fatigue tests are normally constant amplitude tests with relatively small
loads. A crack can thus grow to a much larger length before becoming critical than in the case of realistic loading with occurrent peak loads. b) Fatigue tests are normally performed at room temperature and with scaled down plate thicknesses, leading to an unconservative fracture toughness. For most types of small scale specimens, the difference between the fatigue life at "end of test" and at a more realistic assessment of tolerable crack size is negligible, as shown in Fig. 4.10. In large scale structural testing, however, the situation is more complicated. Considering crack growth in a tubular joint, F'&. 4.15, there is a significant amount of fatigue life from a half
Section 4.2.5 through thickness to a through thickness crack, and the choice of fatigue life criterion may become important in the evaluation of fatigue data. A rational basis for assessing critical crack length is given in Chapter 9.
4.2.5 Fatigue limit In the past, much attention has been given to the fatigue limit and to experimental methods for determining the region of what has been termed nondamaging stresses. In offshore design, the concept of a fatigue limit has lost much of its significance, for three main reasons: i)
The stress range at the fatigue limit found in constant amplitude testing of welded specimens is very low, typically in the range 50-1 00 MPa depending on type of joint and test conditions. It would be very uneconomical to design offshore structures with design loads below the initial threshold level, since in practical design, there will always be some stress cycles above the threshold which will cause crack growth. Also, with growing crack lengths, the stress level corresponding to the crack growth threshold will be gradually lowered, thus allowing a greater part of the load spectrum to lie above the threshold level.
ii) The fatigue limit determined in small-scale testing is not representative of fatigue limits in large scale structures, since the limit is strongly linked to the size and occurrence of initial defects. In large-scale structures, the probability of exceeding a certain size of defect will be much greater than in a test series with small scale specimens. Moreover, localized corrosion may create pits and crevaces in the region of welds, causing a time-dependent growth of initial defects. iii) The fatigue limit, or crack growth threshold, is strongly dependent
on various factors like mean stress, load history, and environment. Environmental effects are in particular difficult to handle, due to a general lack of data. Assessment of the fatigue limit of real structures is therefore subject to large uncertainties. From the discussion above, it should be clear that the question of a fatigue limit or a fatigue threshold for offshore structures is very complicated. Because of the uncertainties involved, the fatigue limit is therefore set very low in design codes. A specific discussion on this topic is found in Secs. 11.1 and 11.2.
Section 4.2.6 4.2.6 Real structures versus test specimens In the previous sub-sections, frequent references have been made to differences between test specimens and real structures with regard to fatigue behaviour. Design criteria are mainly based on statistical analyses of SN data obtained with small scale specimens, and lack of similitude between tests and real structures in fatigue loading is an important point. Fabrication effects.
Most laboratory specimens are purpose-made, and are not production-line welds. The specimens are invariably produced in the most favourable conditions for welding, in a dry, clean, indoor environment, and with carefully controlled welding procedures. The liability of most experimentalists to discard "rare events" from their collection of data should also be mentioned. The test specimens should therefore be expected to display a much smaller scatter and a larger mean fatigue strength than production-line structural welds. Size effect - defect probability.
Fatigue is a weakest link process, the fatigue crack will start growing from the most severe notch or defect along the weld. Thus, the fatigue strength of specimens will tend to decrease as the weld length per specimen increases. The effect is shown in Fig. 4.28. In fatigue testing, the weld length is typically some centimeters, whereas in a structure, each welded joint will have dimensions of order meters. One should thus expect that structural joints will have a mean strength, in the lower part of the scatter band found in traditional testing. t
'
1
' & - - - - -
F u l l scale
Log N
Fig. 4.28 The effect of increasing the weld length tested per specimen.
Section 4.2.6 Structural redundancy. Considered as load-carrying members, test specimens either carry the full load or no load at all. Structural welded joints, however, will in most cases be part of a redundant structure. If a fatigue crack starts growing, the compliance of the joint will increase and the load will decrease. For part-throughthickness cracks, this effect is of little importance, because a main part of the fatigue life is spent in the growth of very short cracks with negligible influence on the compliance. For other failure modes, where a certain amount of cracking is allowed, the effect of redundancy may become significant.
Residual stresses. Residual stresses in structures may be separated into two types (Fig. 4.29):
Fig. 4.29 Residual stresses (schematic). (a) Long range stresses. (b) Short range stresses.
.'
1 . Short-range stresses exist only in and close to a weld, and are selfbalanced over the cross section of one member. The cause of these stresses is the thermal contraction of parts of the cross section, under restraint from the cooler portions. Stresses will generally be large, at or above yield magnitude, and with large through-thickness gradients. Due to the short range, the stresses will be associated with small end displacements. Hence, they may fairly easily be reduced by heat treatment, or by local yielding caused by peak loads.
Section 4.3.1
- 4.3.2
Long-range stresses are uniform throughout a structural member, and are self-balanced within the structure. Their origin is from the procedure of assembling a monolithic structure from pre-fabricated components, whereby welding shrinkage and the use of local heating, mechanical restraints, brute force, etc., in the process of fitting the pieces together, may cause significant locked-in stresses. Long-range stresses are generally small compared with the yield stress, with small gradients. However, the associated end displacements, and hence the stored strain energy, may be large. As a consequence, these stresses are not easily relaxed by local heat-treatment procedures, nor are they much affected by peak load conditions and local yielding. Very little is known about residual stresses in marine structures, their magnitude, through-thickness variation, and variations through service life. In one particular investigation on welds in a ship's deck, the residual stresses were found to be far in excess of stresses from applied loads. Long-range stresses were approximately 25 per cent of the short-range stresses (Ref. 1151). In small scale specimens typical of SN testing, short range residual stresses only will be present. In many types of specimens residual stresses will be unrealistically low, an effect which needs to be accounted for in the analysis of SN data, Sec. 4.7.3. The effect of residual stresses is particularly pronounced in the threshold region. In sea water with cathodic protection, residual stress effects are important also at higher load levels, see Sec. 7.3. 4.3
CYCLIC STRAIN AND MATERIAL RESPONSE
4.3.1 Introduction
The main purpose of this section is to present the basic principles of cyclic stress and strain response in engineering materials, and the derivation of fatigue strength criteria from this. Methods will be reviewed for the assessment of fatigue strength of structural components on the basis of material flow properties. The methods are well established for machined, notched components typical of automotive structures, aircraft structures, machine components, etc. They have also been applied in the analysis of the fatigue strength of welded structures but have not as yet found general acceptance except in low cycle fatigue. 4.3.2 Monotonic stress and strain
The stress-strain relation for a steel in monotonic loading (tensile test) is
Section 4.3.2
Fig. 4.30 Tensile test, typical specimen and stress-strain relation in monotonic loading. shown in Fig. 4.30. The data provided by such a test are well-known to all engineers, and constitute the most basic characterization of the strength of a material.
Sy - yield strength S, - ultimate strength
Strength parameters
A - elongation at fracture Z - reduction of area at fracture
Ductility parameters
In a tensile test, engineering definitions of stress and strain are applied. S = P/Ao
- engineering stress
(4.16)
e = AL/Lo
- engineering strain
(4.17)
True stress and strain may be derived by
o = S(l +e) e
= Qn(1t e )
For small strains, the difference between engineering values and true values is small and is neglected in most instances. In fatigue analysis, the state of stress and strain at fracture in monotonic loading is of some importance. Of
= Pfbf
- true fracture strength q
-
true fracture ductility
(4.20)
Section 4.3.3 4.3.3 Cyclic stress and strain
Fig. 4.31 The effect of strain hardening when unloading and reloading a plastically deformed material (schematic). When a material is stressed beyond the elasticity limit, the unloading curve will follow Hooke's law (Fig. 4.3 1). After yielding, there will be a permanent offset in strain and an increase in the yield strength due to strain hardening. After unloading, the next load cycle will therefore follow the previous unloading curve. The significant feature is the memory effect -the stress-strain curve in one load cycle depends on the previous stress-strain history. If the material is cycled further, a gradual change in the stress-strain relation will take place, generally along two possible courses - cyclic hardening or cyclic softening, Fig. 4.32. For most engineering materials, a fairly stable state is reached after some few hundred cycles, or at a number of cycles which is small compared to the fatigue life. This means that for a major part of the fatigue life, a proper description of the flow properties of
t 'I
Controlled functton, stress
0
Controlled function, strain
0
t
-Cycle dependent hardening; Cycle dependent hardening;
t
0 Cycle dependent softening;
Cycle dependent soften~ng;
Fig. 4.32 Material response under cyclic loading in stress control (left) and strain control (right).
Section 4.3.4 the material must be based on the cyclic stress strain relations, and not on the monotonic stress-strain curve shown in Fig. 4.30.
E
Fig. 4.33 Stabilized cyclic stress-strain hysteresis loop for a mild steel. A stable stress-strain hysteresis loop for a steel is shown in Fig. 4.33. All the stress and strain data needed for the fatigue characterization of a material are taken from the collection of stable hysteresis loops at different strain levels. The basic equation is that total strain equals plastic plus elastic strain:
For completely reversed testing (zero mean stress) the amplitude is equal to one half the range
Applying Hooke's law
the plastic strain amplitude is given by
4.3.4 Cyclic stress and strain resistance
The response of a material to cyclic stress and strain may be summarized as follows: i)
The flow properties of metals are in general different in cyclic loading than in monotonic loading. This in particular refers to yield stress and fracture stress.
ii) Metals respond in a different manner in stress cycling than in strain cycling.
Section 4.3.4 As a consequence it is necessary to distinguish between stress and strain fatigue resistance. Moreover, a relation between fatigue strength and material properties should be based on the cyclically stabilized properties of the material.
Stress resistance. A plot of the fatigue life vs. true stress amplitude for a metal gives in general a curve of the Basquin form (Ref. 1161)
N - cycles to failure 2N - load reversals to failure oi - fatigue strength coefficient b - fatigue strength exponent - the sign of b is negative
The fatigue strength coefficient is the stress intercept at one load reversal (2N = I), hence it is related to of,the true fracture strength in monotonic loading. For most materials it turns out that #
of 2 of
(4.27)
Plastic strain resistance. The plastic strain resistance is best described by the Manson-Coffin relationship (Ref. / 171, / 181)
E;
c
- fatigue ductiiity coefficient -
fatigue ductility exponent - the sign of c is negative
The fatigue ductility coefficient is the plastic strain intercept at one load reversal (2N = 1). The relationship between the e; and the monotonic true fracture ductility ~f is not as simple as noted for the case of oi and of. For a majority of the materials which have been investigated,
is a good approximation. But many steels fall far below this prediction, and a range of values has been found (Ref. / 19/),
Section 4.3.5
TotaE strain resistance. In most practical cases of fatigue design, the critical location will be a notch in which plastic strains are imposed by surrounding elastic material. Thus, the situation will be strain controlled with a total strain range composed of an elastic and a plastic part. Manson proposed that a metal's resistance to total strain cycling can be considered as a superposition of its elastic and plastic strain resistance (Ref. 1171). By combining Eqs. (4.25), (4.26), and (4.28)
The total strain life curve approaches the plastic strain life curve in the low cycle region, and the stress life curve in the high cycle region as shown in Fig. 4.34. Data for a high-strength steel are shown in Fig. 4.35 t o follow this trend (Ref. / 191). The significance of the cyclic strain properties in fatigue is illustrated in Fig. 4.36. In the high cycle region, strong materials will have a greater fatigue life. In the low cycle region, ductile materials will be superior. A tough material with an optimum combination of strength and ductility will give the best overall fatigue resistance. It appears that the crossover point in Fig. 4.34 is nearly the same for many materials and is found at a strain amplitude of 0.01 and a life of about 2000 reversals. Therefore, at this strain range, the fatigue life is quite insensitive to material properties. 4.3.5 Fatigue of notched members Most fatigue failures are initiated from notches, thus fatigue design need to take into account the effect of notches on fatigue strength. The basic idea of notch theory of fatigue is that fatigue life is life to crack initiation. Thus, if a local measure of the cyclic stress and strain at the notch can be obtained, the fatigue life of the notched member can be assessed by comparison with an unnotched specimen undergoing the same stress and strain, cf. Fig. 4.36. As a first, and often quite useful approximation, local stress at the notch is related to the nominal stress through the theoretical elastic stress concentration factor Kt
Related t o the fatigue strength of an unnotched specimen, for which data are generally available for most engineering materials, Eq. (4.3 2 ) states
Section 4.3.5
Log (2N')
1
I
Fig. 4.34 Representation of elastic, plastic, and total strain resistance fatigue loading. w
18ZNi Maraging ( 3 0 0 ) \
v Load control
Fig. 4.35 Test data and strain resistance curves for a high tensile steel (Ref. / 171).
Fig. 4.36
Fatigue of notched members. Fatigue life is assumed to be equal to the life of an unnotched specimen undergoing the same stress-strain loading as the most highly strained material.
Section 4.4.1 that the fatigue strength is reduced in inverse proportion to Kt. In most cases Kt can be assessed by relatively simple analytical or experimental means. For more detailed analyses, this method is inadequate, due to the fact that Kt is not directly related to the fatigue notch factor Kf. Experimentally, Kf is measured as Kf = fatigue strength of a smooth specimen
fatigue strength of a notched specimen
at the same fatigue life. Kf will in general vary with stress level and with notch acuity. At low stresses, where the material response at the notch is essentially elastic, Kf is approximately equal to Kt. There is still under elastic conditions a size effect in Kf, related t o the volume of material which undergoes large cyclic stresses. A practical formula for the size effect of Kf is the Peterson formula
where A is a material constant and r is the radius of curvature of the notch. As shown by Eq. (4.34), small notches have less effect in fatigue than predicted by Kt. At high stresses, or in specimens with sharp notches, the response at the notch will become plastic and non-linear. The elastic stress concentration factor Kt will then give a very inadequate description of the stresses and strains at the notch. In general, Kf will tend to decrease by increasing stress. As a consequence, a direct measurement of Kf for a given notch case will require testing at several stress and strain levels, and becomes expensive and time-consuming. 4.4
VARIABLE AMPLITUDE LOADING
Methods for calculating the stress response of a structure t o various forms of fatigue loading by waves are discussed in Sec. 2.6. The purpose of this section is to discuss the effect of irregular stress histories on the fatigue capacity of steel structural components.
4.4.1 Characterization of fatigue loading As stated frequently throughout this volume, fatigue is a cumulative effect of an irregular load history which for typical offshore structures spans a period of 20 years, or the order of 10%cycles assuming an average frequency
Section 4.4.1 of 116 6'. In order to be manageable in design procedures, this time history must be reduced to some convenient format, representing the characteristics of the loading.
Variable amplitude loading, spectrum loading, and irregular loading are frequently used synonyms for any loading which has not constant arnplitude. Various types of variable amplitude loading are defined below. Block loading is composed of blocks of constant amplitude cycles. Random loading or stochastic loading is a variable amplitude loading generated by a random process. With digital test systems, the load signal generation is often performed by an algorithm giving a fixed sequence of peaks and valleys. The term pseudorandom is often attached to this procedure. If a given sequence is repeated, it is termed random-ordered. In variable amplitude loading, certain events may be identified, cf. Fig. 4.37:
-Time
Fig. 4.37 Definition of terrns related to irregular load histories.
Reversal is the occurrence where the first derivative of the load-time history changes sign. Peak is the occurrence where the first derivative of the load-time history changes from positive to negative sign. Valley is the occurrence where the first derivative of the load-time history changes from negative to positive sign. Range is the algebraic difference between successive valley and peak loads (positive range) or between successive peak and valley loads (negative range). Note that range may have different definitions, depending on the counting method used. "Overall range" is defined by the algebraic difference between the largest peak and the smallest valley of a given load-time history.
Section 4.4.1 Mean crossings (or zero crossings) is the number of times that the load-time history crosses the mean load level during a given length of the history. Normally, only crossings with positive slopes are counted. Irregularity factor is a measure of the irregularity, or the bandwidth of the signal, defined as the ratio of mean crossings with positive slope to the number of peaks or valleys in a given load history. In fatigue analysis of welds, mean stresses are generally neglected, and mean-crossings are commonly referred to as zero-crossings. The irregularity factor I is linked t o the spectral bandwidth factor e (Eq. (2.9)) by
For narrow band loading, the irregularity factor will be close to unity (c % 0). Typical load histories for fixed offshore structures have an irregularity factor in the range 0.6 < I < 0.8. Root-mean-square (RMS) may be defined in two ways, either by a weighted average of the fluctuating stress itself
or by the stress ranges
will depend on the specific counting procedure In the latter case, applied for the definition of individual cycles (see below). Whereas RMS has a defined physical meaning related t o energy in many applications of signal analysis, it does not necessarily have so in fatigue analysis. As will be shown later, the power of two in Eq. (4.36) has no physical significance in fatigue. In cumulative damage calculations, it can be shown (cf. Sec. 4.5.2) that the effect of variable amplitude loading may be taken into account on an SN format by defining an equivalent stress range
where m is the slope of the crack growth curve (cf. Sec. 4.1.2 and Table 4.1). For welded joints the value of m is commonly taken as m = 3. The equivalent stress defined in Eq. (4.38) is often referred to as RMC or y'root-mean-cube"of stress. This stress entered into an SN diagram gives the number of cycles to failure for the corresponding irregular load history.
Section 4.4.2 Crest factor is a measure of the "peakedness" of the stress spectrum, defined as the ratio of maximum stress in a load history to SRMs.The crest factor may also be defined by the stress ranges, i.e. the maximum stress range divided by Sr,RMS The latter defmition is again subject to a choice of counting procedure. Clipping level is sometimes introduced in test procedures, due to limited
load capacity of the test equipment or for more technical reasons, e.g. to avoid buckling, excessive yielding, etc. A clipping level may be a fact in real structural loading as well, e.g. by safety-valve limitation of pressure in pressure vessels, automatic load limitations on cranes, one-sided (non-reversible) loading (both of the above), etc. Clipping of a load-time history is shown in Fig. 4.38. U n c l i p p e d random Loading;
---Clipping
----Clipping
level
level
Fig. 4.38 Clipping of a random load signal. 4.4.2
For cumulative damage analysis, the stress-time history is broken down into individual cycles which are summed up to a distribution of stress ranges. Various procedures commonly referred to as cycle counting methods have been devised. The problem of cycle counting is illustrated in Fig. 4.39. The load history may be broken down into individual cycles in several ways, leading to different assessments of fatigue damage. In many cases it is therefore important to apply a counting method which gives the physically most correct representation of the fatigue process. Several such methods will be discussed. - Cycle counts are normally represented by spectra: Occurrences spectrum is a representation of variable amplitude loading by the number of times a particular loading parameter (peak, range, level, etc.)
Section 4.4.2
1
Narrow bond
Ln
1
Broad band
Fig. 4.39 With narrow band loading, individual stress cycles are easily identified and counted, and most counting methods yield similar results. In broad band loading, large cycles are interrupted by small cycles with varying mean level, and the resulting cycle count may depend significantly on the counting procedure. occurs within each specified interval of the parameter. In statistical terms an occurrences spectrum is the frequency function or probability density function of the given parameter (Eq. (2.1)).
Exceedances spectrum is a representation of spectrum loading contents by the number of times specified values of a particular loading parameter (peak, range, level, etc.) are equalled or exceeded.
t
-
I
-
Occurrences of Level crossings Exceedances of peaks/valleys
Fig. 4.40 An irregular load-time history (left) converted into an occurrences spectrum of level crossings (right). The difference in counts between two adjacent stress levels is equal to the number of peaks (above S, ) or valleys (below S,) in that interval of stress. Thus an occurrence spectrum of level crossings is equivalent to an exceedances spectrum of peaks and valleys.
Section 4.4.2
Level crossing counting. The method is shown in Fig. 4.40. In order to reduce the counting events by a factor of two, positive going level-crossings are recorded at and above the mean load, and negative-going crossings below the mean load. The difference between the counts on two neighbouring levels on the positive side of the mean level is equal to the number of peaks in the corresponding interval of stress. Thus, an occurrences spectrum of stress levels is the same as an exceedances spectrum of peak levels. An exceedances spectrum of valleys is obtained in a similar manner on the negative side of the mean level. The main problem with the level-counting method is that no information is obtained about the irregularity of the load. The normal method of cycle count is to construct the largest possible cycle followed by the second largest, etc., until all level crossings are used as demonstrated in Fig. 4.4 1.
d
m
Time-
----
-
a ) L e v e l crossing coun t i n g
----
--Time-
-
( b ) L e v e l crossin counting w i t h 1 l e v e l leeadband ( l e v e l s counts d
-0-1
-----
4 1
0 1 2
( c ) Cycles derived from level c r o s s i n g count o f ( a )
Fig. 4.41 Level crossing counting of a broad-banded load history (a). The resulting distribution of ranges is shown in (c). In many cases, small stresses may be assumed to be non-damaging, and are therefore disregarded. In level crossing counting, this may be achieved by introducing a dead band, as shown in (b).
Section 4.4.2
B C
Time
I
O c c u r r e n c e s of
Cycle count
level crossings
Fig. 4.42 By level crossing counting, stress cycles with a mean level different from the overall mean level (a) will be accounted for in an unrealistic way (c). Reversal points are assumed to occur halfway between levels. By this method, narrow-band processes are represented in a realistic way. For broad band loading, stress ranges with mean values different from the mean level of the loading, are combined in an unrealistic way, cf. Fig. 4.42. For broad band load histories, the level count method therefore tends to be conservative.
Peak counting. Peak counting is illustrated in Fig. 4.43. Peaks are counted above, and valleys
I Peak
I~ounts]
( a ) Peak counting uRan n \ ? es Cycle counts
3
15
( b ) Cycles derived from peak c o u n t o f ( a )
Fig. 4.43 Peak count of a broad banded load history (a). The resulting cycles are shown in (b).
Section 4.4.2
( b ) Mean crossing peak counting
Fig. 4.44 Peak count of the same load history as shown in Fig. 4.55, but counting only extreme peaks and valleys between reference (mean) level crossings. are counted below the mean level. Results for peaks and valleys are usually reported separately. A variation of this method is to count all peaks and valleys without regard to the mean level. In some cases it may be justified to disregard small variations in stress ("ripples"). One practical way in which to do that is to count as peaks and valleys only the extreme values between successive mean level crossings, cf. Fig. 4.44. Similar to level counting, peak counts are combined by constructing the largest possible cycle, then the second largest, and so on. In this way, a conservative count is obtained. An alternative method is to combine pairs of peaks and valleys in a random way. Simple range counting. For this method, a range is defined as the stress difference between two reversals, Fig. 4.45. The method distinguishes between positive and negative
I
Ranges counted
Method 2 1-4
Fig. 4.45 Part of an irregular load history and two methods of counting ranges. With Method 1, each range between reversals is counted. With Method 2, small reversals are ignored. The difference in terms of cumulative damage may be significant.
Section 4.4.2 ranges. If the mean of each range is also counted, the method is called rangemean counting. If only positive ranges are counted, each range is counted as a cycle. If both positive and negative ranges are counted, each range is counted as one half-cycle. One problem with range counting is how to take care of small cycles within large cycles. The sequence shown in Fig. 4.45 may be counted as three individual and small half cycles, or as one large half cycle. The resulting damage summation will depend significantly on the choice of threshold level for counting small cycles.
Rainflow counting. Rainflow counting is often used as a common name of a large class of counting methods: range-pair counting, the Hayes method, the original rainflow method, range-pair-range counting, ordered overall range counting, racetrack counting, and hysteresis loop counting. The various methods are summarized in Ref. /20/. If the load history begins and ends with its maximum peak, or with its minimum valley, all these methods give identical counts. In other cases, the counts are similar, but not generally identical. Only one method of this class will be reviewed here, rainflow counting (Ref. 1211). This counting procedure is designed to count reversals in accordance with the material's stress-strain response, cf. Sec. 4.3. The principle may be illustrated by the strain history shown in Fig. 4.46 and the corresponding stress-strain path. The individual cycle 2-3-2' does not effect the remainder
Fig. 4.46 Part of a strain history (a) and the stress-strain response (b) of a material being subjected to this history. Note that the small cycle 2-3-2' forms a closed hysteresis loop within the large range 1-4, the latter being undisturbed by the interruption.
Section 4.4.2 of the stress-strain history. Each time the hysteresis loop is closed, a cycle count is made. The method is illustrated for a more complicated strain history in Fig. 4.47.
Cycles
2-3-2' 8-9-8' 5-6-5'
Half
1-2-4
cycles
4-5-7
7-8-1 0
Fig. 4.47 A more complicated strain history (a) and the corresponding stressstrain response (b). The rainflow counting method counts small cycles within large cycles similar to the way closed hysteresis loops are formed. The cycle count is thus reflecting the way in which the material is responding. Rainflow counting has obtained its name from an analogy of rain falling down a pagoda roof, Fig. 4.48. The strain history in Fig. 4.48 is the same as in Fig. 4.47. The rules of rainflow counting are as follows, 1. Rain will flow down the roof initiating at the inside of each peak or valley. When it reaches the edge it will drip down. 2. The rain is considered to stop, and a cycle is completed, when it meets another flow from above.
3. Starting from a peak, the flow also stops when it comes opposite a more positive peak than that from which it started. Starting from a valley, the flow stops when it comes opposite a more negative valley than that from which it started.
Section 4.4.2 Strain
Counting
t Time
Fig. 4.48 The same load history as in Fig. 4.47 (a) illustrating the pagoda roof rainflow analogy.
By inspection, it may be verified that this counting procedure reproduces the cyclic stress-strain loops of the material undergoing the same loading history. For wide-band loading, rainflow or similar counting procedures is therefore recommended. For narrow-band loading all the counting procedures reviewed above will yield similar results. Unless the load history is rearranged to start with its most positive peak or its most negative valley, a rainflow count will give a number of unpaired half cycles which are difficult to handle in cumulative damage analysis. Moreover, rain flow counting loses its physical significance when applied to cracked specimens where crack closure may occur under compressive loading. Symmary of cycle counting. The problems of cycle counting and choice of method arise only if the design is to be based on an actual load-time history. Such histories can be recorded as loads or stresses from an actual structure, simulated load histories from model experiments, or computer simulated time histories. Moreover, if the structural response is narrow-banded, all counting methods converge. Even for moderately wide band load histories, the different counting procedures give only minor differences when applied in fatigue analysis. Only for very wide band load histories with irregularity factor less than about 0.5 does the counting procedure become important.
Section 4.4.3
/23/), although experimental verification is scarce. A detailed discussion of various aspects of cycle counting is found in Ref. /22/. 4.4.3:
w=*
The most common way of representing irregular load histories for fatigue analysis is by an exceedances diagram of stress ranges, Fig. 4.40. This diagram is often called the stress spectrum. Note that for a given load history, the stress spectrum may depend on the counting method applied. Typical stress spectra are given in Fig. 4.49.
l o g ( E x c e e d a n c e s of
s t r e s s ranges)
Fig. 4.49 Typical forms of exceedances spectra of stress ranges, cf. text for discussion. a) Constant amplitude loading. . b) Maximum stress (range) is limited, stresses below this level are random (cranes, pressure vessels, etc.). c) Minimum load is above a certain level. d) Gaussian stationary (statistical properties do not vary with time) loading. e, f)Typical long term spectra for environmentally loaded offshore structures as discussed in Secs. 2.6 and 10.5. In many cases, the load spectrum can be approximated by a two-parameter Weibull distribution, which can be written on the following form: S, = S,,,
[l -(- 1% n
log no
)]K
Section 4.5.1 where: Sr,0 no n K
-
stress range which is exceeded once out of no stress cycles total number of stress cycles - number of stress cycles equal to or exceeding S, - shape parameter
This spectrum is shown for various shape parameters in Fig. 4.50. Eq. (4.39) is a convenient formula for cumulative damage calculations, in particular for simplified analyses at the early design stage as explained in Secs. 10.2.2 and 1 1.4.
I
4.5
2
3
4
5
6
7
8
log n
Fig. 4.50 Exceedances of stress ranges represented by the Weibull distribution with different shape parameters. (Eq. (4.39))
CUMULATIVE DAMAGE
4.5.1 The Miner summation
Fatigue design of welded structures is based on constant amplitude SN data. A marine structure, however, will experience a load history of a stochastic nature. The development of fatigue damage under stochastic or random loading is in general termed cumulative damage. Numerous theories for calculating cumulative damage from SN data may be found in the literature. However, the Miner summation has proved to be no worse than any other method, and much simpler. Hence, virtually all fatigue design of steel structures (bridges, cranes, offshore structures, etc.) is based on this procedure. It will be shown below that the Miner summation conforms with a fracture mechanics approach. The basic assumption in the Miner summation method is that the "damage" on the structure per load cycle is constant at a given stress range and equal t o
Section 4.5.1 where N is the constant amplitude endurance at the given stress range. In a constant amplitude test, this leads to the following failure criterion In a stress history of several stress ranges SrYi,each with a number of cycles ni, the damage sum follows from
with the failure criterion still given by Eq. (4.4 1). The procedure is shown in Fig. 4.5 1.
Jell
log N
Fig. 4.51 The Miner summation procedure for one particular stress block with stress range exceedances diagram (a) and SN-curve (b).
asumrnatian and the tractwe mechanics monstrated by assuming a block stress history as shown in Fig. 4.52. In a block of stress range Sr,i there are ni cycles. The fatigue life at stress range Sr,i is Ni. Assuming the Paris-Erdogan crack growth law (Eq. (4.4))
the number of cycles in each block may be expressed as (Sec. 3.2.2, Eqs. (3.38-3.42))
Section 4.5.2
Fig. 4.52 Block loading program in a fracture mechanics derivation of the Miner sum.
The constant amplitude fatigue life at a stress range Sr,iis given by Ni =
laf
1 da C (S, ,i)m a(] [(na)Om5 * F ] ~
and
Assuming a total of k blocks, the damage sum is
If this load history causes failure, the right hand of Eq. (4.46) will equal unity which it also should according to the Miner rule.
4.5.2 Equivalent stress range The Miner sum may be expressed in terms of an equivalent stress range S, , q. Inserting for the SN-curve N (s,,~)* = a (= const .)
(4.47)
Section 4.5.3 the Miner sum at fracture is
The total number of cycles to fracture is
Constructing from Eq. (4.48)
Eq. (4.50) now has the form of Eq. (4.47) for the SN-curve with an equivalent stress range given by
and the fatigue life given by the total number of cycles N. Thus, the Miner sum at fracture may be represented by an equivalent stress SN-curve, which for a weld detail with a given constant amplitude SN-curve will depend on the shape of the load spectrum. The Weibull distribution function has been shown to fit many stress spectra for marine structures. For this particular distribution, a closed form expression for Eq. (4.5 1) may be calculated, giving a simple method for computing Miner sums (Ref. /24/), cf. Sec. 10.2.2. With this procedure, no account is taken of any fatigue limit, leading to conservative estimates of fatigue life.
e of cycle-by-cycle plastic strains at a notch or at a fatigue crack tip. The state of stress and strain in the damage area is a result of the preceding stress-strain history. Hence, the damage in one cycle is not a function of that stress cycle only, but also of the preceding cycles, leading to interaction or stress memory effects.
*
wt
*&I
$$m
into account.
For that reason, the Miner summation may in many applications be biased, quite often in an unpredictable manner (Ref. /25/), leading to large uncertainties in the fatigue strength calculations. Stress interaction effects are closely linked to the characteristics of the load history. Thus, certain types of load histories are found to introduce a bias
Section 4.6.1 in the Miner sum, which may be accounted for by the so-called relative Miner sum. This quantity may be established by testing, and used as a reference which is valid as long as certain conditions of similitude are complied with. The load history of offshore structures is characterized by a randomly varying stress around a constant mean level, with a cumulative stress spectrum as shown in Fig. 4.50. For this type of loading, the interaction effects tend to give Miner sums less than unity. A mean value of 0.5 has been assessed from a large collection of data (Ref. 1261). This value has therefore been suggested as a relative Miner sum to be applied in design. However, all current design codes seem t o be based on a Miner sum of unity as a failure criterion, which means an overestimation with a factor 2 on cumulative fatigue life. The Miner sum is an assessment of cumulative damage. The uncertainty associated with the relative Miner sum seems to be no larger than the inherent uncertainty in SN data. In fact, test series have shown a reduced scatter in the Miner sums as compared to the basic constant amplitude data (Ref. 1271). Calculated against a design SN-curve, the Miner sum procedure based on the relative sum should thus give the same probability of failure as the SN-curve. In design codes, the required Miner sum is often set much lower than unity. The reasons are not effects of cumulative damage, but the need for an additional factor of safety. For example, the Miner sum for submerged parts of the structure may be set to 0.1, whereas identical weld details above the water may be set much higher (Ref. /28/). The rationale for this is accessibility for inspection and repair. For similar reasons, redundant and non-redundant parts of the structure may be designed to different Miner sums. In this way the Miner sum is not only used as a measure of cumulative damage, but also as a general safety factor in order t o optimize structural reliability.
4.6
FATIGUE OF WELDED JOINTS
4.6.1 Crack initiation versus crack growth There has been - and still seems to be - a certain amount of controversy over whether fatigue of welded joints is predominantly a crack initiation or a crack growth phenomenon. The current consensus, at least among European researches, is that the crack growth stage is dominating the fatigue life of welded joints. Only with certain post-weld improvement methods may an appreciable fatigue initiation life be introduced (Ref. 1291). This chapter is written in support of those views. The application of cyclic strain concepts to fatigue of welded joints is described in Ref. 1301.
Section 4.6.1 Poor weld prof l le
Undercut
I
~ a c kof f u t l o n
Root d e f e c t
Hydrogen cracking I
Lamellar tearing
Lack of penetration
Solidlf ication cracking
Fig. 4.53 Various types of weld defects which significantly affect fatigue life.
'IM mason why a crack initiation stam is urrimpt.jlaptantin welded j h t s , b that weld defects are always found, In this context, not only the normal engineering size defects are to be considered (Fig. 4.53). Even a nominally perfect weld contains defects along the weld toe or at interpass locations. In all arc welding processes, slag intrusions are found at the fusion line (Fig. 4.54).For manual metal arc methods, defect sizes are typically 0.1 mm deep. For tungsten inert gas or metal inert gas methods, the defect size has been shown to be significantly smaller, but defects of similar type are still found. Besides, undercuts and microcracks are common, depending on welding process and material quality (Ref. /3 11). These defects are to be taken as intrinsic features of any production type weld, and act as nucleating sites for Stag intrusions
Fig. 4.54 Even in sound welds, microscopic defects are present, acting as crack nucleation sites. The fatigue notch factor of a weld is therefore much greater than what can be predicted from the external geometry.
Section 5.2.1
Lamellar tearing (Fig. 5.3). Lamellar type cracks may appear when the plate material is subjected to stresses in the thickness direction during welding. The lamellar pattern is caused by separation of weak planes of rolled inclusions. Solidification cracks (Fig. 5.4).
Fig. 5.4 Solidification crack in butt weld. Solidification cracks may appear in the centre-plane of the weld. They are often caused by a high sulphur content in the weld (generally supplied by melted base material). High carbon content also increases the tendency towards solidification cracking, while basic electrodes remove sulphur from the pool and are beneficial.
Hydrogen induced cracking. Cracks which develop due to the presence of hydrogen. They occur when the welding results in a hardened HAZ structure and the stresses in the joint reach a certain level. Low carbon equivalent, high heat-input, preheat and low-hydrogen electrodes are common counteracting measures. Undercuts (Fig. 5.5). Undercuts are irregular grooves in the parent metal at the toe of a weld, or in previously deposited weld metal. The toe groove may be continuous and it may be wide and open or narrow and shut. The groove increases significantly the local stress, and in addition small slag inclusions at or below the bottom of the groove may add t o its severity. Undercuts are likely initiation points for fatigue cracks. The occurrence of undercuts may be minimized
st(eklc4hy-h
Section 4.6.3
I s M+yde fatigue, the m @ e stm@h and the ductility of the s dedding the f a w e strength. This is material are important p d ~ t e r in in contrast to the high cycke w ,where tensile pmyjerties have no significant influence o n drcngth weld geomeiry and initial defects behg the most imports'
am
-
The high-cycle range of fatigue is the range which is applicable t o most offshore design problems. The reason is that this is the range of the most damaging fatigue stresses for a majority of environmentally loaded structures. me finite Ilfe m@on is the region where fatigue data may be fitted to a log-linear curve 4.26). This is consisteht 4 t h a fracture rnechanios analysis using the Pasis-Erdogan crack growth law. In constant amplitude testing, there will be a fatigue limit in the range of 2.1 o6-1 o7 cycles, depending mainly on the residual stress state. With small residual stresses, the fatigue limit will be in the lower range. Small residual stresses in the as-welded condition is generally obtained with small-scale specimens, particularly with welds transverse to the loading axis where the whole cross-section is heated and allowed to cool simultaneously. This happens t o be a typical specimen for SN testing, and has led t o the misconseption that a life of 2 - lo6 cycles is a fatigue limit for welded joints. With more realistic residual stresses, the constant amplitude fatigue limit is found in the range 0.8-1.0.10~ cycles (Ref. 1321). This can be read from the crack growth curves shown in Fig. 4.4. The shift in crack growth threshold from R r 0 (no residual stresses) to R > 0.5 (large residual stresses) comes to a factor of two or more on the stress intensity range, corresponding to a factor eight or more in fatigue life.
(a.
4.6.3 %&% &'#kc# of geometry
rnttry. Consider a stressed member as shown in Fig. 4.55 with a uniform axial stress or nominal stress. If a hole is made, the stress distribution will be distorted. The cross section at the hole will be decreased, leading to a larger average stress, Snet = net section stress. Furthermore, the hole is a stress concentrator, leading to a magnification of the net section stress by a factor Kt - the (elastic) stress concentration factor. In complicated geometries the net section stress may not be easily defined, and the stress concentration factor is calculated on the basis of the nominal stress. Stress concentrations are not only caused by cross sectional decrease.
Section 4.6.3
Fig. 4.55 Stresses in an unnotched plate (left) and a plate with a circular cut-out (right). Also by increasing cross sections, the stress is locally raised as shown in Fig. 4.56. Stress concentration factors may be calculated from theory of elasticity by various methods. Analytical methods tend t o become mathematically complicated, and are applicable to simple geometries only. Finite element methods are more versatile, and can easily cope with two-dimensional problems. For three-dimensional cases, the finite element method is still practical, but is very expensive in many cases. Welded joints will often lead to cross sectional changes. Typical cases are reinforcements of beam flanges, reinforcement and stiffening of plates, etc. Stress concentrations caused by structural shapes are often called structural stress concentrations. For many structural details, the structural stress concentration factor may be difficult to assess, not only because of a com-
Fig. 4.56 Stress distribution across the plate at a weld showing the nominal stress (B - B) and the stress distribution across the weld toe (A - A).
Section 4.6.3 plicated geometry, but also because of a complicated stress pattern. Typical examples are cross girders where axial, bending, and shear stresses may act simultaneously (Fig. 4.27). Tubular joints are another example (Fig. 4.14).
ww In addition to the structural stress concentration, the weld reinforcement also is a stress concentrator in most cases, Fig. 4.56. Even welds which are longitudinal to the loading direction act as stress concentrators, due to the rippled surface of a weld layer. Only by careful machining of the weld surface may this local stress concentration be eliminated. Using welds transverse to the loading direction as an example, weld shape may be defined by the following parameters, Fig. 4.57,
- weld toe angle - notch root radius at the weld toe
8 p
-
s
L
-
tl t2 -
throat thickness, overfill leg length, an alternative parameter to s thickness of load-carrying plate attachment thickness
Fig. 4.57 Parameters defining the nominal geometry of welds.
nite element analysis it may be shown that the the stmm conmri'tration factor at the weld toe iatr is some influence from leg length (or throat thickness) and attachment thickness, but relatively minor. Stress concentration factors of welds may be calculated by finite element methods. Parametric formulas are also available (Ref. 1331). It should be noted, however, that stress concentration factors calculated by these methods refer to idealized shapes of welds. Real welds exhibit an irregular geometry, and even more important, there will always be defects of the
Section 4.6.3 types described in Fig. 4.54. For this reason, the fatigue notch factor Kf of a weld (Eq. 4.33) is significantly greater than the theoretical (ideal) stress concentration factor Kt which can be calculated from elastic theory. The role of Kt is t o give trends with regard to fatigue strength of various welded geometries. The actual fatigue strength can only be found by fatigue testing. I ',
,
Local nominal stress. Fatigue design is based on the local nomi~zalstress approach. The term nominal means that the stress concentration created by the shape of the weldment is to be disregarded. For example, the stress in Section A - A (Fig. 4.56) is assumed to be the same as it would be in the absence of the weld, and the relevant stress for design purposes would be S. The effect of the stress concentration caused by the weldment is included in the SN-curve as an implicit fatigue notch factor. The effects of stress concentrations due t o the overall geometry must, however, be taken into account. Thus, in Fig. 4.55, the fatigue design stress will be the nominal stress magnified by the stress concentration factor caused by the hole, hence the term "local". It is to be noted that the local nominal stress approach has been adopted also in fatigue design of tubular joints. The stress concentration effect of the overall shape of the joint is taken into account, but the notch effect of the weldment is disregarded by an extrapolation procedure of the stresses close to the weld, cf. Sec. 8.3.2. The one exception to the local nominal stress approach is cases when design is based on the stress in load-carrying transverse fillet welded joints. Then the design stress is the nominal shear stress on the minimum weld throat area, unless this requirement is overruled by the design stress for the plate, cf. Fig. 4.58. Stresses to be considered when SN-curves are used for fatigue life calculations are also discussed in Sec. 10.2.4. Secondary effects of geometry. So far, idealized or nominal geometries have been considered. In welding fabrication, production tolerances may have an effect on stresses. For transverse load-carrying welds, misalignment has been proved to have a strong effect on fatigue strength (Ref. 1341). Misalignments may be characterized by parallel and angular misalignment, as shown in Fig. 4.59. A special problem with longitudinal seam welds of pressure vessels is the "roof-topping" caused by angular misalignment, Fig. 4.60.
Section 4.6.3
Fig. 4.58 In load-carrying transverse fillet welds, fatigue cracks may develop from the weld toe (design stress S) or through the fillet (design stress r1).
Fig. 4.59 Misalignment of unrestrained load-carrying welds, parallel (a) and angular misalignment (b) with respective formulas for stress concentration factors. In misaligned joints subjected to a nominal axial stress, secondary bending stresses will arise. In general the secondary stress will be proportional to the nominal stress. Applying the concept of local nominal stress, capl be faken into account by a s t m w ~concentration factor ( & % ) . ' ~ ~ ~ i c SCF a l formulas are given in Figs. 4.59 and 4.60. The formulas in Fig. 4.59 are valid for unrestrained joints, e.g. butt welds. For cruciform
Section 4.6.3
Fig. 4.60 Roof-topping of seam-welded tubulars with a formula for the stress concentration factor. joints, or butt welds in stiffened plates, lateral or rotational restraint may reduce the secondary bending quite significantly (Ref. 1351). It is to be noted that a parallel misalignment of 20% of the plate thickness reduces the fatigue strength of an unrestrained joint by about 40%, which for instance is in excess of the effect of sea water observed in welded joints. In other words, the misalignment effect is significant.
Size effect - plate thickness. Increasing the size of a given type of fatigue specimen while maintaining all the other parameters, will in general cause a decrease in fatigue strength. This size effect in fatigue may be given several interpretations. The so-called statistical effect stems from the fact that fatigue is a weakest link process, nucleating at the location where stresses, geometry, defects, and material properties combine to form optimum conditions for fatigue crack initiation and growth. Increasing the size of a specimen will statistically produce locations which are more vulnerable to fatigue failures. For welded joints, this size effect will essentially be a function of weld length. Very little is, however, known about the statistical effect in fatigue of welds. As indicated in Fig. 4.28, the effect will tend t o lower the fatigue strength of large size welds from the mean value to the lower bound region found in small scale testing. Independent of the statistical effect of size, there is also an effect of plate thickness in welded joints. It has been noted experimentally as a decrease in fatigue strength by increasing plate thickness. Possible reasons for the influence of thickness are weld technology and residual stresses, which tend to be more adverse for heavy section welds. However, it has been shown that plate thickness primarily influences the fatigue strength of welds through effects of geometry, which act independently of any other effects of plate thickness. 220
Section 4.6.3
A useful model for describing the thickness effect in weld toe fatigue failures is obtained by the following assumptions (Ref. 1361): a) Welded joints of the same type in various plate thicknesses are geometrically similar (typical for load-carrying welds). b) Initial conditions of fatigue crack growth is independent of plate thickness (ai = const .).
for and
Fig. 4.61 Geometric model for the effect of plate thickness in fatigue of welded joints. @q taltial d e b t in the thicker joint will experience a larger stma than a corresponding defect irr the thinner joint. From these assumptions, the effect of plate thickness may be understood from a simple geometric model as shown in Fig. 4.6 1. From assumption (a), the stress distributions across the load-carrying plates in the plane of crack growth are geometrically similar, leading to a steeper stress gradient in the thinner joint. Hence, from assumption (b) the initial crack in the thinner plate will experience a smaller stress than the initial crack of the same length in the thicker plate, causing a smaller initial crack growth rate in the former case. The difference in initial crack growth rate overmatches the difference in crack length to cause fracture, hence the thinner joint will have a longer fatigue life. In fracture mechanics terms, the stress gradient through the plate thickness enters into a calculation of the stress intensity factor, leading to numerical assessment of what has been described in qualitative terms above. The thickness effect is thus caused by the following parameters: i) The magnitude of the stress concentration at the weld toe (mainly determined by the local weld geometry).
Section 4.6.3 ii) The gradient of the stress in the plane of crack growth (mainly determined by the plate thickness).
iii) The number of cycles in crack growth through the region of a steep stress gradient, relative to the total number of cycles t o failure (mainly determined by the size of the initial crack and the crack ellipticity). Using this model, it has been shown that the effect of plate thickness can be assessed by the following correction formulas (Ref. 1371): N = No (-)tto 314 (4.52)
where No and SN,o refer to fatigue life and strength for a reference plate thickness to. The corrections expressed by Eqs. (4.52) and (4.53) have been included as mandatory clauses in current design codes (Ref. 1381). The reference plate thickness t o , assumed to be a mean plate thickness in the tests from which the design SN-curves have been derived, is 22 mm for plane joints and 3 2 mm for tubular joints. In Fig. 4.62 are shown a collection of SN data on the thickness effect of welded joints, and the correction curves for two arbitrary stress levels. 200
-,
Fig. 4.62 Data showing the effect of thickness on fatigue strength for various types of welds (Ref. 1361).
Section 4.6.4
- 4.6.5
In Sec. 4.2.6 residual stresses in welded structures were discussed. The main conclusion was that in large welded structures, tensile residual stresses must be accounted for, even in parts of the structure which have been subjected to stress relief. On this basis, the so-called stress range approach has been adopted in fatigue design of welded structures. In the design SN-curves, endurance is given in terms of stress range S,. The mean stress, or stress ratio, does not appear explicitly. However, the SN-curves are assessed on the basis of large tensile mean stresses being present, hence the effect of residual stresses are taken into account implicitly. The procedure applied in including the effect is described in Sec. 4.7.3.
Fatigue of welded joints is essentially a process of fatigue crack growth. Only in post weld treated welds (grinding, peening, etc.) may the crack initiation or nucleation period be of significance. Crack growth data for steels are remarkably insensitive to material properties. In Fig. 4.6 are shown crack growth data for various structural steels, for parent plate, heat affected zone (HAZ), and weld metal respectively. As shown, all the data fall within the same scatter band. Even with large variations in material properties as in Fig. 4.5, the crack growth curves fall within the same band. Crack growth rates are in particular insensitive to the yield strength of steels. This means that provided fatigue is a process of crack growth, fatigue strength should be independent of parent or weld metal yield strength. This has proved to hold true in SN testing. In Fig. 4.63 are shown fatigue endurance data for steels as a function of yield strength. For machined plate, the effect of yield strength is large, as predicted by the cyclic strain models of fatigue initiation, cf. Sec. 4.3. For as-rolled plate, the initiation period is decreased, and a larger part of the fatigue life is occupied by the crack growth stage. The effect of yield strength is comparatively smaller. For welded joints, the fatigue strength is nearly independent of the yield strength as predicted by crack growth data. It is to be noted that the data and the conclusions referred above are for as-welded joints tested in air. For post weld improved joints and for steel in sea water environments, the effect of material properties in general and of yield strength in particular may be quite pronounced. These topics are discussed in Chapters 6 and 7.
Section 4.7.1
Machined p l a t e As rolled plate
Butt welds
200
400
600
BOO
1000
S,
Fig. 4.63 Fatigue strength of machined steel plate, as-rolled steel plate, and steel butt welds, as functions of yield stress.
L 1
,
,,
I,,
,,
The invariance of fatigue strength to the yield strength has some severe implications on design. The rationale for using high strength steels is to be able to increase the allowable stresses. In design against an ultimate load, this may well be acceptable. A consequence of an increased stress level is, however, a reduced fatigue life. Therefore, the use of high strength steels may lead to fatigue problems. For structural components which are fatigue critical, there is no advantage in using high strength steel. Particular fatigue problems in a structure may be solved by lowering of the stress level, by improvement of the fatigue strength by post weld treatment (Chapter 6), or by inserting cast components in the critical areas. If lowering of the stress level is mandatory, this may be achieved by improved design of the weld details, or by increasing the plate thickness. In many cases the latter is the only method viable.
4.7
SN DATA FOR WELDED JOINTS
4.7.1 Introduction In this section, a short review will be given of the data and the analyses and interpretations underlying present codes for fatigue design of welded steel structures. The discussion will be based on the fatigue clauses of the British code for design and construction of bridges (BS 5400), as it has evolved from the re-analysis work (Ref. /39/). The codes as such and their use in fatigue design are discussed in Chapter 1 1. The reason for the choice of BS 5400, apart from the work being well documented, is the fact that BS 5400 is the leading fatigue design code in
Section 4.7.2 Great Britain, and has formed the basis for several fatigue design codes for offshore structures. Other design codes may differ in certain respects. However, as revisions are being made, different codes should be expected to converge towards the same design criteria, as they indeed should - test data and methods of analyses being generally the same. 4.7.2 Classification of SN data
The core of any fatigue design code of welded joints is i) An allocation of the different joint designs into joint or strength "Classes" according to their comparative fatigue strength. ii) A set of design SN-curves, defining the fatigue capacity for each class of joints. Welded joints are classified with regard to fatigue strength on the basis of three charactbriStics, a) The geometry of the weld detail b) The direction of the fluctuating stress relative to the detail c) The method of manufacture and inspection of the detail The terms relating to this classification should be self-explanatory. However, some details will be discussed below. Weld geometry. Weld geometry may be described on a nominal level, a local level, and a "microscopic" level. Considering for example butt joint of two plates, this may be accomplished in several ways, cf. Fig. 4.64. On a nominal level, all these joints are butt joints. In terms of fatigue strength, the various joint designs may vary considerably, depending on the local geometry. On a "microscopic" level, the same local geometry may again be given various geometries, cf. Fig. 4.57, leading to a considerable variability in fatigue strength.
L
Fig. 4.64 Various forms of butt joining of plates and the different flows of stress.
Section 4.7.2
In the fatigue classification of welded joints, only the local weld geometry is specified. The "microscopic" geometry is assumed to follow from the weld method and is not defined explicitly. Loading direction. The design rules are in general based on test data obtained with uniaxially ti stressed specimens with welds either traniverse or longitudinal to the loading direction. Hence the terms "longitudinal" and "transverse" welds. The loading to consider in fatigue design is the fluctuating component of stress. In plated structures, nominal stresses are in general bi-axial. A basic problem is then t o define which component of stress to use, and the direction of this stress relative to the weld. As shown by Fischer (Ref. 1401) in his experiments on welded beams with attached stiffeners, fatigue cracks tend to grow in a direction normal to the largest principal stress. Principal stress may thus be taken as the "driving force" in fatigue, and not e.g. the von Mises equivalent stress. For design, the differences are in many cases negligible, but in some cases a detailed analysis may be required. The maximum principal stress range may not always be normal or parallel to the weld direction, but at some other angle. With the common type of classification of welds (Chapter 11, Appendix A) it may be difficult to decide which class is applicable. It has been proposed that if the maximum principal stress direction deviates more than 25' from the direction of the weld, the classification is "transverse" (Ref. 1411). A particular problem arises if the direction of the principal stress changes during each load cycle. If the fluctuations are periodic, design should be based on the direction of the peak value of the principal stress (Ref. /41/). If, however, the stress components are not correlated in phase, as is often the case for offshore structures (superposition of local and global loads, multidirectional waves), no recipe seems t o exist. In general, design rules describe the maximum principal stress range as the appropriate stress component. This is in accord with the reference (uniaxial) stress in fatigue testing, and corresponds to Mode I crack growth. The von Mises equivalent stress may be used, according t o some rules (Ref. 1411). The directionality of stress with regard to the weld is obviously subject to engineering judgement.
Manufacturing factors. The main effect of manufacturing methods is due to geometry. Different weld processes may lead to different "microgeometry" for nominally identical
Section 4.7.3 welds, cf. Fig. 4.57, and a subsequent effect on fatigue strength. The initial defects from which fatigue cracks are nucleated may also be a factor of production methods. A typical geometrical effect is the irregularity in weld profile caused by interruptions in a weld pass, often called stoplstart positions. In manual welding these interruptions are unavoidable whereas automatic welding may be performed without them. The stoplstart positions tend to lower the fatigue strength, particularly in longitudinal loading, and this is reflected in the classification of welded joints with regard to welding methods.
4.7.3 Assessment of design SN-curves Selection of SN data. Design SN-curves are based on experimental data. In the development of BS 5400, data from various sources were scrutinized for their applicability and reliability. Applicability criteria were a minimum of correspondance to structural welding in terms of material quality, welding procedure, plate thickness e t ~ As . a general policy, data obtained earlier than 1950 were discarded, as they were believed to be unrepresentative of current welding technology. The test data were obtained mainly in the high cycle region of fatigue endurance, i.e. at fatigue lives in excess of lo4 cycles. The analysis was restricted to data emanating from specimens tested under uniaxial tensile loading or from tests on beams in bending, where the stress conditions in the flange are similar to those in an axially loaded specimen. Statistical analysis. The SN data were analysed on the basis of a linear SN-curve on log-log scale, using standard methods of statistics. A mean line was fitted by regression analysis, and confidence intervals for individual test results were calculated. The confidence interval is a measure of the scatter of the individual results. The regression line is defined by two parameters, which may be taken to represent the slope and the abscissa intercept of the line respectively. Both these parameters are identified with an uncertainty, leading to a total uncertainty which increases at an increasing distance from the centre of gravity of the experimental data. The resulting confidence limits are hyperbolae, cf. Fig. 4.65. The shape of the confidence limits is reflecting the fact that SN data tend to be concentrated in an interval of fatigue life which is relatively small as compared to the scatter. The increased width of the confidence interval is therefore not reflecting the physical behaviour of welded joints in fatigue, but is rather a result of the particular statistical method employed.
Section 4.7.3
log N
log N
log N
Fig. 4.65 A collection of SN data with regression line showing uncertainty in slope (a), uncertainty in abscissa intercept (b), and total uncertainty (c) (schematic).
In fact SN-curves at low lives tend to become more horizontal, leaving the upper confidence level in this region over-optimistic, In the long life region there will be a fatigue limit, which leaves the lower confidence limit over-pessimistic. For these reasons, the confidence limits were approximated with straight lines, parallel t o the regression line and tangent to the hyperbolae as shown in Fig. 4.65 (b). The confidence interval defines the probability that similar SN test results will be within the given limits. E-g., a 95% confidence interval defines the limits within which there is a 95% probability that further test results will be falling, provided the results belong to the same statistical population. The lower limit thus defines a 97.5% probability of survival. The lower 95% confidence limit is often taken as a design curve in fatigue. This line corresponds to a lowering of the mean line approximately two standard deviations of individual test results. In this way the mean line and the standard deviation of fatigue life for a given class of welds may be used to define design curves representing different levels of safety, as shown in Fig. 4.66 and Table 4.2. Based on physical reasoning, three different adjustments to the regression analysis were found necessary as outlined below.
Consistency of data. In some data collections it was found that the individual test series were systematically different from the trend shown by the joint regression analysis. The cause for this was believed to be differences in weld procedures, specimen geometry, etc., in combination with differences in mean fatigue life for the different series. This would give a bias in the regression line which was adjusted for by analysing the data using a fixed slope taken to be the mean slope for the individual test series.
Section 4.7.3
Fig. 4.66 Regression line giving the mean fatigue life (a), mean minus one standard deviation (b), and minus two standard deviations (c) (schematic). Table 4.2 The relation between standard deviations, confidence levels, and probability of survival.
Number of standard deviations below mean line
1
2
3
Confidence level (per cent)
63.2
94.5
99.0
Probability of survival (per cent)
84.1
97.7
99.5
Residual stresses. In welded structures, residual stresses are found to be large. Even in structures with post weld heat treated welds, the residual stresses are significant in relation to fatigue stresses due to assembly welding and various other effects. For this reason, design criteria must take into account that the mean stresses are large and tensile. The specimens used in ordinary SN testing are in many cases too small to contain residual stresses representative of full scale structures. This is particularly true for welds which are transverse to the loading axis, in which the whole cross section is heated simultaneously in the welding process, with little restraint on the subsequent thermal contraction. For longitudinal welds, residual stresses are in general much larger, due to greater constraint. Local residual stresses will in general be relaxed by cyclic loading if the total stress - applied plus residual - exceeds yield. Residual stresses are therefore insigni-
Section 4.7.3 Mean S-N curve determined
07
9
I
I
1 o5
I I
2A06
Log N
Fig. 4.67 Correction procedure for stress-relieved specimens in order to include the effect of large residual stresses.
ficant in the low life range of SN-curves. Based on experimental evidence a correction procedure was designed in order t o correct SN-curves for lack of residual stresses. The procedure, leading to a rotation of the SN-curve, is shown in Fig. 4.67. An important consequence of the effect of residual stresses is that the mean applied stress is an insignificant parameter - effective stresses acting in the welded joint regions are assumed t o fluctuate from yield and downwards, cf. Fig. 4.68. This has led to the stress range philosophy of fatigue design, which has been adopted in all codes relevant to offshore structures.
-----
-
Local stress history a t weld
Nominal stress history
Fig. 4.68 Nominal stress history and local stress history at a weld with large residual stresses (schematic).
Section 4.7.3 It has been argued that in variable amplitude loading, local yielding during peak loads will lead to a shake-down of residual stresses, leaving the stress range philosophy over-conservative. For short-range stresses this may hold true, as has been demonstated in fatigue testing (Ref. 1231). The effect of peak stresses on long-range residual stresses, however, has not been investigated. It may be assumed that the effect will be small, due to the long range and the associated large end displacements of these stresses. On this basis, the stress range philosophy is applied in current design codes regardless of applied mean stress. The slope of SN-curves. With the two corrections discussed above, the statistical analysis gave regression lines for the different classes of joints of the form
N - s ~ : =a
N*(AG-)~ =
z
(4.54)
with the slope parameter m in the range between 2.74 and 2.79. The actual slope of the SN-curve is -l/m. a is constant for each joint class. From fracture mechanics theory of fatigue it is known that if the crack initiation phase is negligible, the slope parameter m of the SN-curve is identical to the exponent of the crack growth power law. This parameter depends mainly on the material property, hence all SN-curves for a given material should be parallel. Most experimental data for crack growth in structural steels give an exponent m = 3 . For this reason, and because the scatter in the slope of the corrected regression lines after all was rather small, a common slope parameter m = 3 was assumed for all SN-curves pertaining to welded joints. For plain plate, machined welds, etc., in which the initiation period is significant, shallower slopes as given by the SN data were adopted. In Fig. 4.69 an actual set of SN data is shown, with the correction to the regression line indicated. Design SN-curves. Based on corrected SN-curves, various types of welded joints for which SN data have been compiled, have been allocated to classes with regard to fatigue strength. For plane joints, the classes are termed ByC, D, E, F, ~ 2G,: and W, and a joint regression line and standard deviation have been calculated for each class. Details of the various types of welds are given in Chapter 11, Appendix A. The design SN-curves are assessed on the basis of a consideration of the probability of failure. Thus, in BS 5400, the mean minus two standard deviations is applied for safe life design, whereas for fail safe design the mean
Section 4.7.3
2
105
3
4
2
5
3
4
5
106
Endurance, cycles
Fig. 4.69 SN data for non-load carrying transverse butt welds, showing regression line corrected for slope (Ref. 1391). minus one standard deviation is assumed to be sufficiently conservative. The corresponding probabilities of failure are approximately 2.5% (safe life) and 15% (fail safe). Mean minus three standard deviations have also been proposed as design curve, for very critical components, corresponding to a 0.5% probability of failure. It should be noted that the confidence limits and survival rates mentioned, refer t o laboratory SN tests, and should not be taken as a measure of the reliability of structural components without a much closer consideration. The reason for this is that there is a certain lack of similitude between the laboratory tests and real life behaviour of full scale components.
Chapter 4. References The safe life design SN-curves generally applied for bridges and offshore structures and based on the mean minus two standard deviations are shown in Fig. 11.4. As can be seen a higher value of m has been adopted for structures in air when N > lo7 cycles. Numerical data for a and m are given in Tables 11.1 and 11.2.
REFERENCES
Most of Chapter 4 is of general nature, and specific references are kept to a minimum. Suggestions for further reading on topics related to basic fatigue properties of materials are given as references 1-6 below. 1. Dieter, G.E. :
Mechanical Metallurgy, McGraw-Hill, 1977. 2. Hertzberg, R.W. : Deformation and Fracture Mechanics of Engineering Materials, John Wiey & Sons, 1976. 3. Sandor, B.I.:
Cyclic Stress and Strain, The University of Wisconsin Press, 1972.
4. Fatigue under Complex Loading: Analyses and Experiments, Wetzel, R.M., ed., Society of Automotive Engineers, 1977. 5 . Frost, N.E., Marsh, K.J., Pook, L.P.:
Metal Fatigue, Clarendon Press, 1974.
6. Gurney, T.R.: Fatigue of Welded Structures, Cambridge University Press, 1979. 7. Ohta, A., and Sasaki, E.: Influence of Stress Ratio on the Threshold Level for Fatigue Crack Propagation in High Strength Steels, Engn. Fract. Mech., Vol. 9, 1977, pp. 307-315. 8. Rolfe, S.T. and Barsom, J.M.: Fracture and Fatigue Control in Structures, Prentice-Hall, 1977. 9. Maddox, S.J.: "Assessing the Significance of Flaws in Welds Subject to Fatigue", Welding Journal, 53, No. 9, Sept. 1974.
10. CP 118, Proposed fatigue design rules for welded aluminium structures, British Standards Institution.
Chapter 4. References 11. Moan, T. et al.: "The Alexander L. Kielland Accident", report of the investigation commission, NOU 1981 :11, Universitetsforlaget, 1981 (In Norwegian). 12. Frost, N.E. and Greenan, A.F. : Environ. Eng. 25, 11 (1967). 13. Bell, W.J.and Benharn,P.P.: "The effect of mean stress on fatigue strength of plain and notched stainless steel sheet in the range from 10 to lo7 cycles", STP 338, pp. 25-46, 1963, American Society for Testing and Materials. 14. Gurney, T.R.: Some recent work relating to the influence of residual stresses on fatigue strength, Weld. Inst. Autumn Conf. 1977, pp. 151-164. 15. Leide, N.: "The significance of residual stresses - some experimental results and practical experience in a shipyard", Residual Stresses in Welded Construction and their Effects, The Welding Inst., 1977. 16. Basquin, O.H.: Yroc., ASTM 10, Part 11, 1910, p. 625. 17. Manson, S.S. and Hirschberg, M.H. : Fatigue : An Interdisciplinary Approach, Syracuse University Press, Syracuse, N.Y., 1964, p. 133. 18. Coffin, L.F., and Tavernelli, J.F. : "The Cyclic Straining and Fatigue of Metals", Trans. of the Metallurgical Society of AIME, Vol. 215, Oct. 1959, p. 794. 19. Landgraf, R.W.: "Cyclic Deformation and Fatigue Behaviour of Hardened Steels", Report No. 320, Department of Theoretical and Applied Mechanics, Univ. of Illinois, Urbana, 11I., Nov. 1968.
20. Symposium on Statistical Aspects of Fatigue Testing, Warwick University, 1975.
Chapter 4. References 36. Berge, S.: "Effect of plate thickness in fatigue design of welded structures", Offshore Technology Conference, OTC 4829, 1984. 37. Gurney, T.R.: The influence of thickness on the fatigue strength of welded joints, Behaviour of Offshore Structures, London (1979). 38. Offshore Installations: Guidance on design and construction, Department of Energy, United Kingdom, 1984. 39. Gurney, T.R., and Maddox, S.J. :
Chapter 4. References 24. Nolte, K.G. and Hansford, J.E. : "Closed-form expressions for determining the fatigue damage of structures due to ocean waves," Offshore Technology Conference, OTC 2606,1976. 25. Brose, W.R., Dowling, N.E., and Morrow, J.D.: "Effect of Periodic Large Strain Cycles on the Fatigue Behaviour of Steels", Paper 74022 1, SAE Automotive Engineering Congress, Detroit, Mi., Feb. 1974. 26. Schiitz, W. : "Procedures for the prediction of fatigue life of tubular joints", Rapporteur's report PS5, ECSC Conference on Steel in Marine Structures, Institut de Recherches de la Siderurgie Fran~aise,Paris, 1981.
27. Schilling, C.G., Klippstein, K.H., Barsom, J.B., Blake, G.T. : "Fatigue of welded steel bridge members under variable-amplitude loadings", NCHRP - Project 12-12, Transportation Research Board, National Research Council, Washington D.C., 1975. 28. Rules for the Design, Construction and Inspection of Offshore Structures, Det norske Veritas, 1977. 29. Haagensen, P.J.: "Improvement of the Fatigue Strength of Welded Joints", Rapporteur's Report PS6, ECSC Conference on Steel in Marine Structures, Institut de Recherches de la SidCrurgie Frangaise, 1981. 30. Mattos, R.J. and Lawrence, F.U. : "Estimation of the Fatigue Crack Inititation Life in Welds Using Low Cycle Fatigue Concepts", Society of Automotive Engineers, SP-424,1977. 31. Fatigue Performance of Welded High Strength Steels, The Welding Institute Report Series, 1974. 32. Gurney, T.R.: "Cumulative Damage Calculations Taking Account of Low Stresses in the Spectrum", The Welding Institute Report 211976/E. 33. Nishida,M.: "Stress Concentrations", Morikita Publidung, 1973. 34. Wylde, J.G. :
"The effect of axial misalignment on the fatigue strength of transverse butt welded joints", The Welding Institute Research Report 9911979. 3 5. Berge, S. and Myhre, H.: "Fatigue strength of misaligned cruciform and butt joints", Norwegian Maritime Research, No. 1,1977.
Chapter 4. References 36. Berge, S . : "Effect of plate thickness in fatigue design of welded structures", Offshore Technology Conference, OTC 4829, 1984. 37. Gurney, T.R.: The influence of thickness on the fatigue strength of welded joints, Behaviour of Offshore Structures, London (1979). 38. Offshore Installations: Guidance on design and construction, Department of Energy, United Kingdom, 1984. 39. Gurney, T.R., and Maddox, S.J.: "A Re-Analysis of Fatigue Data for Welded Joints in Steel", Welding Institute Report No. E/44/72, 1972. 40. Fisher, J .W., Albrecht, P.A., Yen, B.T., Klingerman, D.J., McNarnee, B.M. : "Fatigue strength of steel beams with transverse stiffeners and attachments", NCHRP Rep. 147, Highway Research Board, National Research Council, Washington DC, 1974. 41. Regulations for the structural design of fixed structures on the Norwegian Continental Shelf, Norwegian Petroleum Directorate, 1977. 42. Austen, I.M.: "Factors affecting corrosion fatigue crack growth in steels," update paper, European Offshore Steels Research Seminar, Cambridge, 1978. 43. Scott, P.M., et al. : "The effect of sea water corrosion in fatigue crack propagation in structural steel", ibid . 44. Lohne, P. : "A fracture mechanics approach to fatigue analysis of welded joints in offshore structures", Det norske Veritas Report 79-0060, 1979.
45. Lindley ,T .C ., and Richards, C.E. : "Near-threshold fatigue crack growth in materials used in the electricity supply industry", Proc. Second Int. Conf. on Fatigue and Fatigue Thresholds, Engineering Materials Advisory Services Ltd., England, 1982.
CHAPTER 5
SIGNIFICANCE OF DEFECTS Stig Wastberg and Agnar Karlsen A.S VERITEC, Oslo
ABSTRACT
The first two sections describe common defects and other undesirable features that reduce the fatigue life of welded structures. Section 5.4 explains how weld quality may be described in statistical terms. Section 5.5 describes nondestructive inspection for detecting and sizing defects, and discusses the reliability of these methods. The final section gives a general view of the fitness-for-purpose approach to deciding whether disclosed defects should be repaired or not, and discusses the relative severity of defects of various size and shape. 5.1 INTRODUCTION
Defects in structures and components may act as initiation sites for fatigue cracks. Because a fatigue crack grows slowly initially, and then accelerates as the crack length and the stress intensity range increase, the initial size and shape of the defect have a much larger influence on the total fatigue life than the final crack size at which failure occurs. If a defect is large and/or the material is brittle, the defect itself may be capable of initiating unstable fracture without preceeding fatigue crack growth. 5.2 CLASSIFICATION OF DEFECTS ACCORDING TO ORIGIN
As far as assessing the significance of a defect, it is necessary to know the shape, size and location (with respect to the stresses) of the defect. However, it can also be desirable to know the possible reasons for the occurence of a defect. If one knows why defects occur, one knows where they are likely
Section 5.2.1 to occur and also how to prevent their occurrence. Also it is important to know the likely sites of defects because it makes them easier to disclose, and because sites likely t o contain defects should not be designed to carry high stresses. For example, a quick glance at the subjects in the rest of this chapter indicates that defects are likely to occur in welds. From the point of view of fatigue design it is therefore important to choose the correct welding consumables and welding procedures and to inspect welds for defects. If possible, welds should be kept away from stress concentrators. Defects may be divided into two types; those introduced during fabrication, and those arising after a period in service. 5.2.1 Fabrication defects
Lack of fusion (Fig.5.1).
0'
Fig. 5.1 Lack of fusion defect in MMA-weld (x7.5). A two-dimensional defect located on the line between weld metal and base material or between individual weld passes. This type of defect may occur when using gas shielded metal arc welding (MIG, TIG), and is generally caused by too low heat input or by oxidation of weld metal in the arc. Incomplete penetration. Incomplete filling of the weld root, generally caused by inappropriate welding parameters such as low heat input or by faulty groove preparation. Slag inclusions (Fig.5.2). Welds may contain porosities and slag inclusions of nearly spherical form. They produce only minor notch effects and have usually little or no influence
Section 5.2.1
6 Fig. 5.2 Slag inclusion in MMA-weld (x4).
on the fatigue behaviour. However, if located at the surface, they may significantly reduce the fatigue strength. Elongated slag inclusions may be of a twodimensional form and are considered more dangerous than the spherical types.
Fig. 5.3 Lamellar tearing in MMA-weld (x2).
Section 5.2.1
Lamellar tearing (Fig. 5.3). Lamellar type cracks may appear when the plate material is subjected to stresses in the thickness direction during welding. The lamellar pattern is caused by separation of weak planes of rolled inclusions. Solidification cracks (Fig. 5.4).
Fig. 5.4 Solidification crack in butt weld. Solidification cracks may appear in the centre-plane of the weld. They are often caused by a high sulphur content in the weld (generally supplied by melted base material). High carbon content also increases the tendency towards solidification cracking, while basic electrodes remove sulphur from the pool and are beneficial.
Hydrogen induced cracking. Cracks which develop due to the presence of hydrogen. They occur when the welding results in a hardened HAZ structure and the stresses in the joint reach a certain level. Low carbon equivalent, high heat-input, preheat and low-hydrogen electrodes are common counteracting measures. Undercuts (Fig. 5.5). Undercuts are irregular grooves in the parent metal at the toe of a weld, or in previously deposited weld metal. The toe groove may be continuous and it may be wide and open or narrow and shut. The groove increases significantly the local stress, and in addition small slag inclusions at or below the bottom of the groove may add t o its severity. Undercuts are likely initiation points for fatigue cracks. The occurrence of undercuts may be minimized
Section 5.2.2
Fig. 5.5 Undercuts in MMA-weld (x2.5). by keeping a correct position of the electrode during welding, and by a suitable choice of welding procedure and electrodes. Casting defects. The defects mentioned so far were welding defects. Also castings may exhibit defects which can affect the fatigue performance. During solidification, moderate stresses can create cracks due to segregations, non-metallic films, etc. During the cooling period shrinkage stresses may cause cracks, for example in fillets. Castings may also contain small internal cracks induced by hydrogen. Pores and inclusions located at the surface may have a significant influence on the fatigue strength especially if located at sites with high stresses. Such defects can be caused by segregation of non-metallic inclusions, by moisture or by high gas content in the melt.
5.2.2 In-service defects If a component or structure is examined after a period in service, the following defects may appear: Corrosion pits (Fig.5.6). Corrosion pits tend to spread either irregularly over a surface or concentrate to areas adjacent to welds. They may be rounded at the bottom, but there may also be sharp root-like extensions. These corrosion pits may act as initiation sites for fatigue cracks and therefore reduce the fatigue life. However, in the case of welds there are usually other, more severe, crack initiators present, so that the fatigue life of weldments is not significantly affected by corrosion pits.
Section 5.3
Fig. 5.6 Corrosion pit in weld metal. A fatigue crack has developed at the bottom (x4.5). Stress corrosion cracks. If a stressed surface is exposed to certain corrosive environments, stress corrosion cracking may occur. The stress corrosion cracks can lead to unstable fracture or they may act as initiators for fatigue cracks. Note that residual stresses, due to e.g. a weld, are often enough to induce stress corrosion cracking in the presence of certain corrosives. Fatigue cracks. Common in-service defects, and the subject of this handbook. Once discovered, they should be treated like any other sharp defect.
5.3 OTHER FAULTS IN FUSION WELDS
Welded joints often deviate from the geometry intended by the designer. Inaccuracy in matching leads to a misalignment of the joining plates. The misalignment may be axial and/or angular (Fig. 5.7). Both irregularities introduce an additional bending stress in the joint and thus influence the fatigue strength (Fig. 5.8). Misalignment may therefore be a factor to determine the initiation point of a fatigue crack. Thus in a straight plate, the crack may initiate from an internal defect, whereas the increase in surface bending stresses due t o misalignment may shift the initiation point to the weld toe. At the weld toe there is also a considerable stress concentration produced by the weld profile. A heavy weld reinforcement will lead to a high stress concentration at the toe and consequently lower the fatigue strength (Fig. 5.9). Undercuts further increase the stress concentration at the toe.
Section 5.3
Fig. 5.7 Axial (a) and angular (b) misalignment.
Fig. 5.8 The relation between misalignment and fatigue strength (Ref. / 11).
2E
Z\ 300 -cn
Plain plate (machined),, -
-
a,
N C
@ . \ ,
0
L
-c, 100
5
.L
s
YOOL\ \ * \
Plain plate ( w l th m i 1 l s c a l e )
ul 0
Reinforcement angle,@ (deg.)
Fig. 5.9 The relation between reinforcement angle and fatigue strength (Ref. /I/).
Section 5 -4 5.4 STATISTICAL DESCRIPTION O F WELD QUALITY Welded connections will inevitably contain some defects even if great care is taken to avoid them. The quality of a manual metal arc weld depends to a great extent upon the welder and his skill. However, even skilled welders who have passed qualification tests, will produce defects. The size and location of welding defects will show a considerable scatter which may be expressed in statistical terms. Also the fracture toughness of welds shows great scatter, which reflects the heterogenity of the weld metal. This scatter may be expressed statistically, as in the case of welding defects. A convenient way to present the statistical variation of a variable is by probability density functions, such as the normal or Gaussian distribution. All probability density functions have the following characteristic properties (Fig. 5.10): The total area under the curves is equal t o unity and the area under the curve between lines X = a and X = b represents the probability that X lies between a and b, and is denoted P ( a < X < b ) . Some examples of measured distributions of weld defects are discussed below.
X
X=a
X=b
X
Fig. 5.10 Illustrating the characteristic properties of a probability density distribution f(x). The first example is based on approximately 180 misalignment measurements of full penetration cruciform welded joints in semi-submersible drilling rigs (Ref. 121). The histogram given in Fig. 5.1 1 shows the results and is fairly well approximated by the one-sided normal distribution. The second example shows the distribution of the depth of undercuts obtained from 827 randomly selected point measurements on production welds at various shipyards (Ref. 131). The depth values were reproduced on replicas of liquid silicone rubber allowed to harden on the toe region of the welds. Of 827 measurements, 502 revealed no undercuts, and the histogram in Fig. 5.12 was obtained from the remaining 325 locations. The histogram was represented by the exponential probability density function:
Section 5.4
Fig. 5.1 1 Misalignment sample and fitted density function, f(e/t). n = number of measurements (approximately 180) (Ref. 131)
0.5 1.0 D e p t h of undercuts a (mm)
Fig. 5.12 Relative frequency of measured depths of undercuts and the applied density function (Ref. 131). Probability density functions for internal defects are difficult to obtain. Some examples based on ultrasonic testing reports exist, but the uncertainty of the testing method must be considered when the reports are evaluated. Distributions based on direct observations hardly exist. However, it is reasonable to expect that there will be a large number of small defects and a decreasing number of larger ones. Such distributions may be half-normal, log-
Section 5.4
5 Height of
Fig. 5.13
10
internal defects, (mm)
Calculated relative frequency of the depth of internal defects (histogram) and the applied density function, f(a) (Ref. 131).
normal, exponential, etc. Fig. 5.1 3 shows a probability distribution based on results from ultrasonic testing (Ref. 131). About 3200 m of production butt welds were tested. The test locations were randomly selected from a total weld length of 40000 rn and were assumed to give a fairly good picture of the workmanship. About 6400 lengths of 0.5 m each were inspected, and in 450 test lengths 327 defects were detected. Some of the defects extended over two test lengths, and some test lengths also contained more than one defect. The given numbers refer to defects which gave ultrasonic echoes above a certain reference level. Numerous small defects, giving echoes below the reference level, may have been present but were not detected or reported. It is also possible that some larger defects for one reason or another did not give an echo above the reference level and consequently were not disclosed. Taking account of the uncertainties in the ultrasonic detection method, the half normal probability density function given as the dotted line in Fig. 5.13 was established for the height of the internal weld defects. The examined welds were made between plates with thicknesses from 10 t o 25 mm. In Fig. 5.13 no attempt was made to divide the defects into various groups (e.g. crack-like and non-planar). A collection of ultrasonic test data is presented in Fig. 5.14 (Ref. 141). The data were divided into crack-like and non-planar defects. It is noted that the two types have different probability
Section 5.5.1
0
1
2
3
-----
Planar d e f e c t
------
Non-planar
4
5
6
7
8
defect
9 1 0 1 1 1 2
D e f e c t height ( m m )
Fig. 5.14 Weld defect height distributions (Ref. 141).
density functions. The data were obtained from inspection work on an offshore structure and consist of results from 12 vertical and 6 horizontal node joints with a total weld length of the order of 1000 m. All defects reported were embedded and the average defect rate was 0.7/m. After repair and final NDT the defect rate was reduced to 0.2/m. 5.5
NON-DESTRUCTIVE INSPECTION
5.5.1 Non-destructive inspection methods Liquid penetrant. This technique is used to reveal the presence of surface flaws, but can provide little information on the depth of the flaws. The surface must first be thoroughly cleaned. Then a brightly coloured or fluorescent dye is applied. After allowing the dye to penetrate possible cracks, the surface is wiped and a fine white absorbent powder is applied. The powder draws remaining dye out of the defects, enabling them to be located.
Magnetic particles. This is another technique suited for revealing surface flaws, and it will also indicate flaws just below the surface. Only ferro-magnetic materials can be inspected. Magnetic particle inspection does not require a clean surface, which gives it a practical advantage over liquid penetrant techniques as surface flaws often contain grease.
Section 5.5.1 A magnetic field is induced in the body to be examined, either by passing a large electric current through it or by attaching magnets. Iron filings in a light oil or water suspension is applied to the surface. The iron filings will gather around the defects and make them visible. Eddy currents. Eddy current techniques are most commonly used for automatic quality control of sheet, tube and wire. They primarily detect surface flaws, and are most simply applied t o non-ferrous metals. The method is based on the fact that eddy currents will be induced in a specimen subjected to an alternating magnetic field produced by a coil. The eddy currents produce a magnetic field which tends t o reduce the current in the coil. The degree of reduction depends on the magnitude of the induced currents which in turn depends on the electric resistance in their path. This resistance is a function of the conductivity of the material and the length and cross section of the current path. A defect which changes the current path will thus affect the induced magnetic field and consequently the current in the coil. The current is the measured quantity during testing. For various reasons the method is difficult to apply t o welds. Radiography. Radiography is a method of detecting internal defects. Radiation (x or y) is passed through the region to be inspected, and some of it is absorbed. Rays traversing a defect is less absorbed than those passing through homogeneous material. The intensity variations due to defects are generally recorded on photographic film. Thus, the image on the film is a "shadow picture" of the defects (Fig. 5.15). To obtain a uniform assessment of welds, the InternaX-ray
r:,
source
Defect
Dark oreb on photographic f i l m
Fig. 5.15 The principle of radiography for the detection of defects.
Section 5.5.2 tional Institute of Welding (IIW) has published a collection of reference radiographs of welds. The quality range is divided into five degrees and characterized either by a colour or by a number where 5 is the best degree and 1 is the poorest. Ultrasonics. Ultrasonic inspection is the most flexible and convenient way of detecting and sizing internal defects. The main disadvantage as compared with radiography is that a permanent record of the inspection is not easily obtained. Ultrasonic signals are generated by piezo-electric crystals contained in probes that can be moved over the surface in the region to be inspected. The waves are reflected by the surfaces of the examined body, and also by any defects that might come in their way. These echoes are usually detected by the same probe that generates the signal. By measuring the time delay between the emission signal and the reception of each reflection, the source of reflection can be located, and the position of defects identified. The signals are usually registered on a cathode-ray tube (Fig. 5.16).
Cathode-ray
@
tube
Reflected signal
\
Fig. 5.16 Ultrasonic testing of welds, principle. 5.5.2 Nondestructive inspection reliability A non-destructive testing method is often characterized by its ability to detect small defects with a specified confidence level. When the defects are later to be assessed by for instance fracture mechanics methods, it is necessary to determine both the type of defect and its dimensions, of which the height in the direction of the plate thickness is the most interesting. The reliability of ultrasonic inspection in determining the height of weld defects was examined in a Nordic research project, where 70 m of butt
Section 5.5.2 welds were inspected by several operators (Ref. 151). After inspection the welds were broken up and the real size of the defects was measured. It appeared that the ultrasonic echo amplitude was the only parameter which could be correlated with defect height and which was recorded during conventional ultrasonic examination. In Fig. 5.17 the average ultrasonic echo amplitude is plotted versus defect height. The uncertainty in predicting the defect height is seen t o be rather great.
1
10
D e f e c t height, (mm)
Fig. 5.1 7 Average ultrasonic amplitude for twelve ultrasonic operators versus defect height for lack of root penetration and lack of fusion defects. The broken curves indicate the 95% confidence limits for the regression line (Ref. 151). The individual operators evaluated the defects differently. Each one of the 12 operators investigated the same 70 m length of butt welds, and each one compared the ultrasonic echo amplitudes of the different defects with an "acceptance level echo" equal for all operators. Fig. 5.1 8 shows the probability of acceptance for the different defect heights, measured as the ratio between the number of accepted defects and the total number of defects of a particular size. It would be expected that defects of heights between 8-12 mm would show low acceptance by all operators. That is, however, not so, 6 operators are seen to accept 40% or more of rather large defects. In a radiograph there is no obvious parameter to correlate with defect height. In the Nordic reseach project there seemed to be a certain correlation between IIW degrees and defect height for lack of root penetration (Fig. 5.19).
Section 5.5.2
0
4 6 8 Defect height, mm
2
12
10
Fig. 5.18 Acceptance curves obtained by twelve ultrasonic operators. "Probability of acceptance" was obtained as follows: Assume that the inspected weldment contained eight defects of height approx. 5 mm. One of the operators detected six defects. Five of them gave an echo which exceeded 50% of the reference curve and were consequently "not accepted" by the operator. Therefore the operator "accepted" three out of eight defects with height equal to 5 mm, i.e. the probability of acceptance was 318 = 0.38.
IIW degree
0Lack' ( 5 ) Blue
00
( 4 ) -00
Green ( 3 ) - p Brown (
Red
2)--
(1)I
0
o
080 a
h
0
#
000000000
1
2
o
0
1
00
000000
1
4
1
6
1
~
8
~
10
1
1
~
12
D e f e c t height (mm)
Fig. 5.19 IIW degree versus defect height for lack of root penetration (Ref. 151). The rather poor capability of the conventional non-destructive testing methods in estimating correctly the defect sizes, should be born in mind when a defect is being assessed.
1
Section 5.6.1
5.6
ASSESSMENT OF DEFECTS
5.6.1 Fitness-for-purpose approach
When a defect is found, a decision must be made as to whether it should be repaired or not. The decision may be based on an arbitrary standard of good workmanship, but consideration should also be given to the loads that the structure is likely to encounter, the environment in which it will be used and the consequences of a failure. An approach that evaluates these factors is often called a fitness-for-purpose approach and should be preferred to the arbitrary standards because:
-
-
Repairs can be very expensive, particularly if the structure must be taken out of service or if the installation of a structure is being delayed. The fatigue life of a "repair" may actually be lower than that of the original execution. This is so because repairs are often made by grinding out the defect and subsequent rewelding. The repair weld itself may contain defects, the toughness may be low, and the welding may introduce additional residual stresses. Stress relief heat treatment is generally inconvenient and expensive to apply.
The fitness-for-purpose approach to defect assessment is summarized briefly below in a five step procedure. More detailed descriptions of the various aspects are given in the design codes, e.g. PD6493: 1980 (Ref. 161):
-
The defect is characterized with respect to size and location. This involves measuring the size of the defect or defects by NDI, and then making appropriate simplifying assumptions. As stress intensity factors are readily available for straight, elliptical and semi-elliptical cracks, the defects are often idealized to one of these geometries.
- The local stress spectrum is determined.
-
A fatigue crack propagation calculation is performed. The possibility of non-propagation should be considered.
- The critical size to which the defect can grow before fracture occurs, is determined (Chapter 9).
- If the calculations show that the critical size is reached within the next inspection period, (which frequently may be the total expected service life), a repair will be necessary.
Section 5.6.1 The following example demonstrates the procedure: A surface flaw was detected at the toe of the butt weld of a pipe with outside diameter D = 965 mm and wall thickness WT = 25 mm. Allowing for the uncertainty of the NDI method, the maximum depth of the flaw was estimated to 3.0 mm and the maximum length to 25 mm. Based on these data the flaw was idealized by a semi-elliptic crack with half axes a = 3 mm and c = 12.5 mm, with its plane vertical to the pipe axis. The maximum applied axial stress oaPp was estimated to 250 MPa and the effective dynamic stress range Ao to 40 MPa. A rough estimation of the stress intensity factor at the bottom of the crack was obtained (Section 3.1.3):
6
In a weld the stress ratio is high, and 4 MPa was assumed to be above the threshold value for non-propagating cracks. The crack growth was therefore calculated using a cycle by cycle integration of Paris' equation in the direction of the two semi-axes (Chapter 3):
AK, and AK, are the stress intensity factors in the thickness direction, respectively along the surface, and dependent on a/2c and the ratio between a and the plate thickness b. mm The results are shown in Table 5.1 for C = 2 10- l 3 and m=3. (MPam)m Table 5.1. N a c
Section 5.6.2 The fracture toughness in terms of critical CTOD value 6, at operating temperature was estimated to minimum 0.5 mm. The pipe had not been heat treated after welding, and residual stresses of magnitude equal to the yield strength Re = 420 MPa would prevail in and close t o the weld. Based on these assumptions the allowable through-thickness crack size , , a was calculated, using the CTOD design curve (Chapter 9):
It is seen in Table 1 that an unstable fracture may be expected after approximately 1.2 lo7 load cycles. At that stage the crack has developed almost through the plate thickness, and for such crack depths the imavalue is equivalent to the half length of the crack. Consequently it was decided t o carry out a repair within approximately lo7 load cycles which in this case corresponded to two years. 5.6.2 Defect severity
5.6.2.1 Sharp defects The service loads must be considered in a fitness-for-purpose analysis. However, it can be useful to compare the severity of defects under equal loading conditions as this can lead to a better feeling for what might represent a dangerous defect. It should be pointed out that the sharper a defect, the more severe it is. Thus, a planar fatigue crack of 10 mm radius is more severe than a spherical defect of radius 10 mm, assuming that the maximum tensile stress acts perpendicular to the crack plane and is the same in both cases. In predicting design lives, defects are usually assumed to be as sharp as a fatigue crack. Apparently this is a lconservative approach, but is justified since rounded defects often have sharp edges. The elastic stress field near the tip of a sharp crack subjected to Mode I deformation is described in Chapter 3 by Eqs. (3.1 a - 3.1 0. These equations show that the distribution of the elastic stresses at the crack tip are invariant in. all components, and that the magnitude can be described by the stress intensity factor KI.
Section 5.6.2 The severity of planar defects can be compared by comparing the stress intensity factors for the different defects under equal loading conditions. A few examples are given below (Fig. 5.20).
Embedded d e f e c t
Surface defect
Fig. 5.20 Usual defect size convention. 1. For embedded elliptical cracks, the stress intensity factor is given by:
where @ = 1 + 4.595
-)
(2ac
It is seen that equal severities exist for constant stress when the ratio a/@ is kept constant. Thus the following embedded cracks have equal severities :
2. If c is greater than 5 a, the severity of the crack is nearly independent of c. For example, a slag line or lack of penetration defect which is 2 mm high and 10 mm long would not be significantly more severe if its length were increased to 100 mm or more.
3. For the same a and c values, surface defects are about 12%more severe than embedded defects. In some cases, large defects need not be repaired or considered in a detailed fracture mechanics analysis because more severe defects may limit the life of the structure. Consider the cruciform joint loaded in tension in Fig. 5.21, Ref. / 7 / . There will always be small surface defects of depth about 0.1-0.5 mm at the weld toes. Due to the stress concentrating effect of the
Section 5.6.2
I
Weid t o e d e f e c t depth assumed to be 0.1 mm
p -
Fig. 5.21 Diagram showing whether fatigue cracks will develop from the toe or root defects (Ref. 171).
weld geometry, these small cracks experience high local cyclic stresses and may therefore grow by fatigue at lower applied cyclic loads than needed to extend substantially larger root defects. In that case the root defect need not be repaired. In Fig. 5.2 1 it is not expected that fatigue failure will occur from root defects of size less than 0.5 5 P if a/P is around 0.7. 5.6.2.2 Rounded defects
The elastic stress field in the vicinity of narrow rounded notches subjected to tensile stresses normal to the notch plane may be described by adding a term to the set of equations for sharp cracks (Fig. 5.22).
('~y)notch
= ('xy )crack
-
KI (27rr)'l2
.
--
2r
38 sin 2
Section 5.6.2
Fig. 5.22 Coordinate system for notch tip stress field. KI is the stress intensity factor for a sharp crack of length equal to that of the notch and subjected to the same loading. The second term represents the influence of the blunt notch with radius p. From these equations it is seen that the maximum stress at the bottom of the notch is:
This equation indicates that the severity of blunt notches and other rounded defects may be compared by the ratio K I / f i . It is expected that the parameter K I f l will lose its significance when the plasticity at the notch is extensive. However, if the plastic zone is small, the sourrounding elastic stress field will govern the strains of the localized plastic zone. And it is as a characterizing parameter for non-propagating cracks that K I / f i can be used. The following threshold values for the K I / f i ratio have been found experimentally from testing of ferritic-pearlitic, martensitic and austenitic steels (Ref 181). ferritic-pearlitic steels martensitic steels austenitic steels n : strain hardening exponent. For a 5 mm deep surface notch in a ferritic-pearlitic steel of yield stress Re = 360 MPa subjected to a stress range Aa = 50 MPa, no initiation of fatigue cracks should thus be expected if:
Chapter 5. References
These relationships have been obtained from testing of specimens with machined blunt notches and should not be applied t o real defects such as slag inclusions which may have sharp edges. Also their range of validity is limited. For tests with ferritic-pearlitic HY-130 steel (Re 900 MPa) it was found that the fatigue crack initiation behaviour was independent of the notch tip radius p for p < 0.2 mm and p > 6.4 mm.
-
REFERENCES 1. Gurney, T.R. : Fatigue of welded structures. Cambridge University Press. Second Ed. 1979. 2. Berge,S. andMyhre,H.: Fatigue strength of misaligned cruciform and butt joints. Norwegian Maritime Research, April 1977. 3. Bokalrud, T. and Karlsen, A. : Control of fatigue failure in ship hulls by ultrasonic inspection. Norwegian Maritime Res. No. 1. Vol. 10. 1982.
4. Wong, W.K.and Rogerson, J.H.: Weld defect distributions in offshore structures and their influence on structural reliability. OTC, Houston, 3-6 May 1982. 5. Fsrli,O.: Reliability of ultrasonic and radiographic testing. Conference on Fitness for Purpose Validation of Welded Constructions. The Welding Institute. London, 17-19 Nov. 1981. 6. British Standards Institution: "Guidance on some methods for the derivation of acceptance levels for defects in fusion welded joints." PD 6493: 1980. 7. Bokalrud, T. : Finite element analysis of butt weld and cruciform joints to determine the significance of internal crack-like defects. Norwegian Maritime Research. No. 31 1978. 8. Rolfe, S.T. and Barsom, J.M.: Fracture and fatigue control in structures. Application of fracture mechanics. PrenticeHall,Englewood Cliffs, New Jersey, USA, 1977.
CHAPTER 6
IMPROVING THE FATIGUE STRENGTH OF WELDED JOINTS Per J . Haagensen SINTEF, Trondheim
q-
ABSTRACT In this chapter several methods for improving the fatigue strength of welded joints are reviewed. An evaluation of existing test results shows that improved weldments made from high strength steels have consistently higher fatigue strengths than mild steel connections having been treated with the same methods. In a comparison of improvement methods it is shown that each method has its strength and weakness when considering service loading, cost, case of application and quality control. Thus the most effective method depends on the type of structure and type of welded joint.
6.1
INTRODUCTION
6.1 .1 General Any weld in a structure usually represents a weakness both with regard to brittle fracture and fatigue strength. The low fatigue strength of welded joints is a limiting factor for the design of more efficient structures, in particular since the fatigue strength normally does not increase with static strength.
1.
dsrtdl , fbr example by subtitu&th one having s higher iil#igue strength.
2. k p h g the fatigue -q$h
~ t h d .
of the jobt
a lower class jaint g an improvement
Section 6.1.2 Improvement methods are usually employed as remedial measures t o extend the fatigue life of welds that have failed prematurely and have been repaired, or to extend the life of welds that through service load monitoring have been shown to be more severely loaded than assumed during the design phase. A strong incentive for applying improvement methods to new structures is the potential for increasing the fatigue strength in some relation to the static strength, i.e. to make an improved welded joint behave like a mildly notched component as shown in Fig. 6.1.
m Cn C
0
'tooVI VI
I 0
G saR=O Steel to
I
BS 4360
Grade SOB
Cycles
Fig. 6.1 Relationship between endurance limit and ultimate tensile strength for some components (Ref. / 11). The use of higher allowable stresses for welded joints in higher strength steels entails other benefits as well: The thickness effect in fatigue is reduced, bringing about a further reduction in weight as compared with a lower strength steel joint with the same load bearing capacity. A reduced section size in general also improves the brittle fracture properties of the joint. The lower welding, handling and erection costs may partially offset the higher fabrication expenses incurred by the improvement methods. In this survey the emphasis is on the degree of improvement in fatigue strength that is possible to obtain using the various improvement techniques. However, from a practical point of view other consideration such as costs and reliability of the treatment (quality assurance) may be important. Various aspects of quality control and costs are discussed briefly at the end of the chapter. 6.1.2 The potential for improving fatigue strength
In order to exploit the full potential of fatigue life improvement methods
Section 6.1.2
ln
? 3;
400
600
800
ULtlmate tensile strength o f steel, MPa
Fig. 6.2 Typical fatigue strengths at R = -1 of unnotched, mildly notched and welded components, dependent on the tensile strengths of the steels. it is useful to look at the reasons for the poor fatigue performance of welded joints. The low fatigue strength of welded joints as compared with other notched components is illustrated in Fig. 6.2. Welded joints differ from other notched components in several ways even if the elastic stress concentration factors Kt are similar. It is important to identify the main factors that tend to reduce fatigue life in order to choose efficacious methods for improving the fatigue performance mmnm beCw^mbatBed and wnwelded, notched cornpanents are :
1. Mo&h s e e curd defem l!/k % a ; ~ ~ ~ f Mnotoh c n l of the weld toe region which is the m&t fatigue critical are* is generally less uniform than notches in a machined component, see Fig 6.3. Moreover, welded joints contain an assortement of defects, most of which are so sharp that they start growing as fatigue cracks when the structure is subjected to dynamic loads, 'thus reducing or bhinating the crack a&atksnstage of the fatigue life;.
~Od;laflY
2. MetafIurgical chaages
in the base material. The material in the heat
effected zone (HAZ), in which the fatigue crack is likely to initiate and propagate, undergoes metallurgical changes that may affect the local fatigue properties. Thus the softened material in the HAZ of a higher grade steel whose high strength has been obtained by thermomechanical treatment, may limit the fatigue strength that is possible to obtain by improvement techniques.
3. RddtasC #tI"esesare set up in and near the weld due to the contraction of the weld metal as it cools to ambient temperature. These local
Section 6.1.3
CRACK-LIKE
clm f, aE :cT CONCENTRATION
\
/
/HYDROGEN '
CRACK
FUSION L I N E
,
-
LACK OF FUSION
LACK OF PENETRATION
Fig. 6.3 Factors affecting fatigue life of welded joints: a) 1 - cracklike defect; 2 - undercut; 3 - hydrogen crack; 4 - lack of fusion; 5 - lack of penetration, b) residual transverse stress field across the weld. residual stresses due to welding which may attain yield stress magnitude, affect the fatigue properties in a similar manner as externally imposed mean loads, i.e. a tensile residual stress reduces fatigue life while a compressive stress increases life. The distribution of transverse residual stresses in a welded plate of simple shape is shown in Fig.6.3 b). Residual stresses do not arise only from the thermal strains associated with the welding process and subsequent cooling. Global or long range residual stresses are introduced in a structure whenever members are forced together due to misfit, uneven thermal expansion or when restraint is being used. Long range stresses act over large areas and are therefore not relaxed by peak loads at stress concentration or by local treatment. They are generally of smaller magnitude than welding stresses.
4 . Environmental effects. A corrosive environment may have a strong adverse effect on fatigue life as discussed in Chapter 7. The fatigue life of common welded joints are typically reduced by a factor of two to four under free corrosion in seawater. However, the prevention of corrosion by either cathodic protection or protection coatings, which may restore the air fatigue properties of a welded joint, are not regarded as improvement methods per se because corrosion protection is part of normal practice for the construction and operation of offshore structures. 6.1.3 Improvement methods
In the preceding discussion the three factors that most strongly affect the
Section 6.1.3 We of welded joint were identified as: 1. Slesg concentration due to joint and weld geometry; 2. Defects, shape and di-stsibution; 3. Residual
d&s.
According t o the main principle on which the improvement is based,
for i n c d g the fatigue strength of weiMed structures can be grouped in two basic categories: 1. Weld geometry modification and defect removal methods. 2. Residual stress methods. The various workshop techniques within the two groups are shown in Fig. 6.4.
1A-
)
GRINDING
MACHINING METHODS
5L.y
w DRESSING
REMELTING
DRESSING
I
SPECIAL WELDING TECHNIQUES
(AWS) SPECIAL ELECTRODES
-
PEENING METHODS
-
-
MECHANICAL METHODS
I
- OVERLOADING METHOOS -
SHOT PEENING HAMMER OR WIRE BUNDLE PEENING INITIAL OVERLOADING
LOCAL COMPRESSION
THERMAL - STRESS RELIEF
+
THERMAL METHODS
HEATING
GUNNERTS METHOD
Fig. 6.4 Classification of some weld improvement methods.
1
;n9
Section 6.2.1 A brief discription of each method and the degree of improvement which has been achieved in laboratory tests are given in the following sections.
6.2
WELD GEOMETRY MODIFICATION AND DEFECT REMOVAL METHODS
6.2.1 Grinding techniques
By full profile burr grinding the entire weld face is machined and given a favourable shape to reduce the stress concentration and t o remove harmful defects at the toe, see Fig. 6.5. For all types of grinding it is of vital importance that material is removed to a depth of 0.5 to 1-0mm t o remove defects such as intrusions and undercuts, Fig. 6.3 b). Toe burr grinding usually results in a somewhat lower increase in fatigue strength compared with full profile burr grinding. For example in Ref. /3/, full burr grinding gave 100% increase in fatigue strength, while toe grinding gave 60%. The cost for toe grinding is, however, substantially lower. Disc grinder R o t a r y burr grinder
1L
Full profile grinding
0.5-1.0
\ ~ o e g r i nding mm
Fig. 6.5 a) Two grinding methods: 1 - rotary burr grinding; 2 - disc grinding. b) 3 - full profile grinding; 4 - toe grinding. Disc grinding is the least time-consuming grinding process, but the fatigue strength of disc ground joints is usually found to be somewhat lower than for joints subjected to toe burr grinding because of the score marks that are transverse to the applied stress. However, test results do not show a clear trend as exemplified in Fig. 6.6, where toe burr grinding gives higher fatigue strength than disc grinding for a high strength steel, while the situation is the reverse for a lower strength steel. The effect of free corrosion in sea water was investigated by Booth, Ref. 151, and deBack et al, Ref. 161. In Ref. /6/ the fatigue lives of as-welded and ground joints were reduced by similar amounts by corrosion. In Ref. / 5 / however, only the lives of improved (ground) joints were reduced significantly,
Section 6.2.1 500'
'\
\\
\
\
Heavy d l r c ground
400Toe burr ground 0 IJ,
5
300-
L
ul
240-C
Ln
200K.y 1 8 0 - B S 4360 160140-
(+
43A
( 2 4 5 MPa yleLd
strength)
--
SuporeLso 7 0 ( 6 8 5 MPa yield strength)
120-
100 1o 4
I
I
I
I
r
1 1 1 1
1
1
o5
1
1
1
1
1
1
1
1
1
I
1
1
1
1
1
1
lo6
1
1o7
Endurance, c y c l e s
Fig. 6.6 Fatigue strength improvements due to burr toe grinding and disc grinding, data from Ref. 131.
air r e s u l t s
-
Number o f c y c l e s t o f a i l u r e , Nf
Fig. 6.7
he effect of free corrosion in sea water on the fatigue strength of as-welded and ground specimens (Ref. 151).
Section 6.2.2 see Fig. 6.7. This was attributed to the formation of corrosion pits. The pits would act as stress raisers and thus shorten the fatigue life considerably, whereas the more sharply notched as-welded specimens would be less affected by corrosion. The variation of improvement with base material strength for ground specimens is shown in Fig. 6.8. The data show that high fatigue strengths are obtained consistently for the higher strength steels. For medium and high strength steels the increase is always greater than two classes in the design curve system of BS-5400.
Symbol
Ref.
O O A V
3
@
B
Typeof weldmen t
7
Cruclform Fillet welded' do l n t s B u t t welds
600
800 1 0 0 0
Polish
BS 5400
- ---- -----
---cycles
50
1 - 0 200
400
600
Ultimate tensile
800 1 0 0 0 , R,(NPa)
strength
200
400
Ultimate tensile s t r e n g t h , R,(MPa)
Fig. 6.8 Variation of improvement in fatigue strength due to grinding, dependent on base material strength. Data from Refs. 131, /4/, and 171. 6.2.2 Weld toe remelting methods
Remelting the weld toe region using either a tungsten inert gas (TIG) or a plasma torch generally gives large improvements in fatigue strength for two reasons: Remelting gives a smooth transition between the plate and the weld metal, and secondly, non-metallic contarninents such as slag intrusions are melted and removed. While both methods are somewhat time consuming, they share one advantage in that they are suitable for mechanization.
TIG dressing. TIG dressing is performed with standard equipment for thin plate TIG welding. The material in the toe region is melted to a shallow depth without the addition of filler material, Fig. 6.9a). Slag particles are brought to the surface and the remelted zone is essentially defectfree. Optimum conditions have
Section 6.2.2
Fig. 6.9
$&g: a) single run; b) double run. 1- tungsten electrode; 2 nozzle; 3 - shielding gas; 4 - HAZ; 5 - remelted metal; 6 - remelted metal from second TIG run; 7 - HAZ from second run, Ref. / 121.
been proposed by Kado (Ref. 191) and Millington (Ref. /lo/). The heat input should exceed 1.0 kJ/mm (Ref. 171) to obtain a good profile. A high heat input should also be maintained to obtain a low hardness in the heat-affected zone (HAZ) of C-Mn steels. Argon is the most commonly used shielding gas, but results by Fisher (Ref. / 1 11) indicate that helium would be a better choice as higher heat input (about 14%) and greater depth of penetration (about 40%) were obtained with helium. Fisher (Ref. 1111) found the deep penetration of the helium-shielded TIG arc particularly useful for the repair of welded joints containing small fatigue cracks. Using a penetration depth of about 6 mm, he found that 3 mm deep fatigue cracks could be removed successfully. Reduced hardness in the HAZ can also be achieved by a double-run TIG dressing technique, Fig. 6.9 b). The heat from the second TIG pass made on the weld metal tempers the HAZ from the first and brings the hardness level down to an acceptable level of about 300HV10 for C-Mn steels, (Ref. 1121). The weld and plate should be clean in order to avoid pores and irregularities in the remelted metal; this can be achieved preferably by sandblasting or light grinding. A particular problem with the TIG and plasma remelting techniques is that of stopping and restarting the remelting run which tends to give very irregular bead profiles. Stopping and reinitiating the arc on the weld surface is one solution to this problem, see Fig. 6.10.
Section 6.2.2
Fig. 6.10 Restarting technique for TIG remelting run after accidental stop (Ref. /lo/).
Typical results from tests on TIG-dressed specimens (Ref. / 121) are shown in Fig. 6.1 1. Large improvements were also obtained in other test programmes (Refs. 161, /7/, 113-1 81). The summary of air results in Fig. 6.12 indicates that the improvements due to TIG dressing increase with increasing static strength of the base material. Bateriak FG 47 CT Loading; const. amplitude Environment; lab. air Frequenc 5 Hz Load r a k ; R=0.1
.
TIG dressed
welded
8=
0-0-
Number o f c y c l e s
Fig. 6.1 1 Effect of TIG dressing on the fatigue strength of a medium strength steel (Ref. / 171). Fig. 6.13 shows results from tests in sea water (Ref 1171) indicating a strong influence of free corrosion on the fatigue lives of TIG-dressed specimens; however, significant improvements were still evident. Similar results were found in Japanese (Ref. 1151, / 16) and Dutch (Ref. 161) tests, but not in the British (Ref. 151) which showed no improvement in sea water.
Section 6.2.2
50
1 O ' zbo 460 200 400 600 800 I 0 0 0
d o d o lob0 Ultimate tensile strength , Rm(MPa)
Ultimate tensile s t r e n g t h , Rm(MPa)
Fig. 6.12 Variation in fatigue strength improvement due to TIG dressing dependent on base material strength.
Material; OX602 Loading; constant ampli tude Environment; sea water Frequency; 1Hz Load ratio; 0.1
50
1 lo4
I
2
1
1
1
3 4 5
1
1 1 1 1
lo5
I
2
1
1
1
3 4 5
1 1 1 1 1
to6
t
2
I
1
1
3 4 5
1
1 1 1 1
10'
Number o f cycles t o failure, N
Fig. 6.13 Influence of sea water corrosion on the fatigue strength of aswelded and TIG-dressed specimens (Ref. 1171).
similar to TiG dressing, the main cNfYerena? being higher put, and a wider weld pool. In Ref. 1201 a minimum heat input of 2.1 kJ/mm is recommended. The wider weld pool tends to make plasma dressing less sensitive to electrode position relative to the weld toe,
Section 6.2.3 and the resulting improvement in fatigue life is generally larger than for TIG dressing (Ref. 171). Test results from several investigations (Ref. 161, 171, and 119-2 1/) are summarized in Fig. 6.14. The data in Fig. 6.14 indicate that the improvements in the fatigue strength of plasma dressed specimens increase with static strength, i.e. the same trend as for TIG dressed specimens (Fig. 6.1 2). 0 Ref. 6 R e f . 21 A Ref. 20
+0
a
200 400 600 800 1 0 0 0 U l t i m a t e t e n s i l e s t r e n g t h . R.(MPa)
v
" " "
X
Ref. 19
O
200 400 600 800 1 0 0 0 U l t i m a t e t e n s i l e s t r e n g t h , R,(MPa)
Fig. 6.14 Variation in fatigue strength improvements due to plasma dressing dependent on base material strength. In one investigation (Ref. 1211) weld metal was added to the toe during plasma dressing, this gave an increase similar to those obtained by conventional plasma dressing.
6.2.3 Improved welding techniques Instead of employing costly post weld improvement methods, the philosophy of the American Welding Society (AWS) has been to attempt to control the shape of multipass welds to obtain, firstly, a favourable overall geometry and secondly, a smooth transition at the weld toe (Ref. /22/). In Japan similar ideas have led to the development of special electrodes for use in the capping pass in high strength steel joints. The first approach has met with only limited success as described below.
A WS improved profile welds. In the AWS Structural Welding Code (Ref. /22/) a reduction in the largescale stress concentration factor due to weld shape as well as a lowering of the local stress at the toe is sought by specifying an overall concave weld
Section 6.2.3 profile and a smooth transition at the toe, see Fig. 6.1 5. In the latest modification to API RP2 (Ref. /23/), the use of non-profiled welds is discouraged through use of a lower SN-curve. Dime test to be applied to weld toes (A) and weld face irre ularltles (interpass notcfes) Coin or disc yith radius R
1 mm wire shall
Fig. 6.15 The American Welding Society (AWS) improved profile weld and "dime test" (Ref. 1221). Tests on specimens with various weld geometries showed no particular trends for nominal weld angles of 70' and 45'; this may stem from the fact that the local geometry at the toe (weld contact angle and radius of curvature) was not closely controlled (Ref. 161). Tests on tubular joints (Ref. 1241) fabricated to AWS improved profile specifications were also inconclusive as no difference in fatigue life could be found between specimens which had passed the dime test and those which failed, see Fig.6.16. Gurney (Ref. 1251) has shown that welds with improved profiles obtained by grinding the weld metal alone to a concave shape without grinding the toe region gave no significant increase in fatigue life. This may explain the results inFig. 6.16. Thus the AWS improved profile can only be expected to give consistent improvements in fatigue life if the toe region is carefutly ground as indicated in Fig. 6.5 b).
electrodes. Systematic investigations of the effect on fatigue strength of special MMA electrodes designed to give a smooth transition profile at the toe have been carried out only in Japan (Refs. 171, /8/ and 126-281). These electrodes were developed specifically for use in the final weld pass at the toe of joints made from high strength steels in the 500 to 800 MPa yield strength range to avoid
Section 6.2.3
0 Pass
e l ? .
Endurance,
cycles
Fig. 6.16 Results from fatigue tests on tubular joints with improved weld profiles according t o AWS (Ref. 1241).
costly weld improvement treatments. Good wetting and flow characteristics are obtained by the use of a suitable flux composition. The improvement in fatigue strength as a function of base material strength is shown in Fig. 6.17.
.. .
V R e f . 15 A ., 0 Ref. 2 8 n
0 .,
- 3 - 4
200 400 600 800 1000 Ultimate t e n s i l e s t r e n g t h , Rm(MP.)
..
n
n
O 200 400 600 800 1000 Ultimate t e n s i l e s t r e n g t h , Rm(t'lPa)
Fig. 6.17 Variation of improvements in fatigue strength with base material strength as a result of using special electrodes.
Section 6.3.1 - 6.3.2 6.3
RESIDUAL STRESS METHODS
6.3.1 General
Due to the presence of high tensile stresses in as-welded joints, applied stresses become wholly tensile in the weld area, even if the applied stress cycles are partly compressive. Thus as-welded components are insensitive to the stress ratio of the applied stresses. Stress relief can therefore be used to improve fatigue strength, but the degree of improvement is strongly dependent on the mean stress of the applied load cycles. Significant improvements due to stress relief are possible only if the applied stress cycles are at least partly compressive. Since long range reaction stresses will always be present in a large welded structure, stress relief itself cannot be regarded as a life improvement method. For this reason stress relief is not at present incorporated in any design codes that apply to offshore structures. To obtain significant improvements in fatigue strength, it is necessary not only to remove tensile stresses but also to introduce compressive stresses of sufficient magnitude in fatigue critical areas, to make even completely tensile applied stress cycles partly compressive. An important limitation to this principle is that the peak service loads, particularly those in compression, should be so low that yielding does not occur, as this would relax the residual stresses. Several methods have been developed to introduce compressive residual stresses (Fig. 6.4), the more important are described below. 6.3.2 Hammer peening Peening is a surface cold working process which produces a layer of heavily deformed material containing high compressive residual stresses. Hammer peening is performed with a pneumatic hammer fitted with a solid tool with a rounded tip of 6-14 mm radius, the air operating pressure is typically in the 5-10 bar range. Alternatively the tool consists of a wire bundle, each wire of approximately 2 mm diameter and the tip rounded. It has been found (Ref. /3/) that four passes along the weld toe with a solid hammer tool producing an indentation approximately 0.6 mm deep, represent an optimum treatment for mild steel. This type of hammer peening gives much higher fatigue strengths than either shot peening or wire bundle (multiple point) peening, the probable reason being the large amount of cold working and the beneficial effect of reducing the stress concentration by the severe deformation of the toe region. Most of the work on hammer peening has been carried out at The Welding Institute (Refs. 131, /4/, /29/), but some tests have been performed
Section 6.3.2
A s welded Hammer peened
PLate f a i l u r e away Plate failure from No failure
60
0
1
o4
1
I
I
1 1 1 1
I
I
1 o6
1 o5
1
1
1
1
1
1
~
1 0'
Cycles
Fig. 6.18 Improvement in fatigue strength due t o hammer peening (Ref. 1291).
in the US on cover-plated beams (Ref. 1111) and in Belgium on cruciform joints (Ref. 1301). Typical UK tests results on fillet welds are shown in Fig. 6.18. The effect of base material strength on the increase in fatigue strength is shown in Fig. 6.19.
'
0
200 400 600 800 1 0 0 0 Ultimate tensile s t r e n g t h , R,(MPa)
0
0 200 400 600 800 1000 Ultimate t e n s i l e s t r e n g t h , R,(mPa)
Fig. 6.19 Variation of fatigue strength improvement with base material strength due to hammer peening.
Section 6.3.3 6.3.3 Shot peening
As an improvement method for welded joints shot peening has attracted a lot of attention in recent years, possibly because it can be applied to large areas at relative low costs. It gives large increases in fatigue strengths and, because practical experience in its use has been gained over a long time in other industries, there is a fairly well developed system for defining optimum conditions and for quality control of the process. The shot -peening process is similar to sand blasting. However, instead of sand, small diameter cast iron balls or small pieces of high tensile steel wire are fed into a high velocity air stream. Specification of all shot peening variables is cumbersome and therefore impractical. Two parameters, the Almen intensity and the coverage are used instead. The intensity of the peening (the degree of surface plastic defonnation) is determined by Almen strips, which are small steel strips attached to the component. The strip develops a curvature due to the surface deformation on the exposed side. The curvature (the height of the arc) in a strip of a given material and thickness then defines the Almen intensity. The coverage is related to the amount of area covered by the dimples produced by the shot. Complete or 100% coverage is obtained when visual examination at 10X magnification reveals that the dimples just overlap. The commonly used specification of "200%coverage" then implies that the object is peened for twice the time required for 100% coverage.
0 200
400
600
1 800 1000
Ultimate tensile strength, Rm(MPa)
O
' zoo 460
6i0 860 l o b 0
Ultimate tensile strength , R,(MPa)
Fig. 6.20 Variation of fatigue strength improvement due to shot peening dependent on base material strength.
Section 6.4 - 6.5 The size of shot is also important. In order to reach the bottom of all notches the shot should be small, but the peening intensity decreases with decreasing shot size. Typical shot size is in the range of 0.2 to 1.0 mm, typical velocities are 4 0 to 60 m/s. Test results from three separate investigations (Refs. / 181, 1301, 13 1/) are summarized in Fig. 6.20, which shows that shot peening produces large improvements in fatigue strength, particularly for high strength steel joints. 6.4 COMBINATION OF IMPROVEMENT METHODS
Compounding two or more improvement techniques can give very large improvements in fatigue strength. This can be used in situations where costs are of minor importance, for instance when extra fatigue strength is needed to avoid extensive redesign when a damaged structure is to be repaired. Combinations of methods from each of the two main improvement groups are likely to give best results. Thus Gurney (Ref. 1341) found that combining full profile grinding with hammer peening gave a fatigue strength for fillet welded specimens in mild steel equivalent to that of the base material. Similarly, Bignonnet et a1 (Ref. 1321) observed a large improvement when combining a controlled profile weld technique with shot peening (Fig. 6.2 1). It may be possible to offset partially the higher costs of combined methods by incorporating one of the techniques as part of the normal fabricating procedure. Shot peening for instance, could possibly be used instead of sand blasting to clean parts before applying surface protection systems. 6.5 TEST ON LARGE SCALE COMPONENTS
The only European tests on improved welds on large scale structures are those previously mentioned on tubular joints (Ref. 1241) with welds conforming to the AWS improved profile. Although these tests were inconclusive with respect to life increase, tests made by Fisher (Ref. 11 11) on coverplated beams with hammer peened and TIG-dressed welds gave improvements of at least one design category in the A A S H T O % ~specifications. ~~~~ Grinding gave smaller improvements. However, the full potential of the improvement techniques was not realised because of premature failures originating at the weld root. German tests (Ref. 1141) on beams similar to Fisher's (350 mm web depth, 24 mm flange thickness) also gave very modest increases in fatigue strength because of premature failures originating at hydrogen-induced cracks in the web-to-flange welds. Swedish tests (Ref. 1341) on beams that were almost identical to Fisher's also resulted in small but significant increases *) American
276
Association of State Highway and Transportation Officials
Section 6.5
2;:. Scat ter band for speci&n In the as-welded condl tion A
Welds f u l l y ground Welds f u l l y round,then hamrnw poene8
Endurance,
cycles
Improved profile
E 460 30 mn Air, R=0.1 10-20 Hz inlt.
50
o
As welded Shot peened ! l l l l
1 o5
I
I
,
failure
1 1 1 1 1
I
1 o6
I
l l l l l r l
10 '
Number o f c y c l e s
Fig. 6.21 Fatigue strength improvements obtained by compounding; a) grinding and hammer peening (Ref. 1341); b) improved prome and shot peening (Ref. 1321).
Section 6.6 in fatigue strength. The small increase was, as in Fisher's test, attributed to failures starting at the roots of the cover plate fillet welds. 6.6 COMPARISON OF IMPROVEMENT METHODS
Typical results from various improvement methods are shown for a mild steel, Fig. 6.22, and a high strength steel (HT60), Fig. 6.23. In all cases large increases in fatigue strength were obtained , particularly at low stress ranges. The shallow slopes of the SN-curves indicate that the improvements arise mainly from the addition of a crack initiation stage.
Endurance, cycles
Fig. 6.22 Effect of some improvement techniques applied to mild steel transverse fillet welded joints (Refs. / 2 / , /19/). A statistical analysis has been carried out on a large number of test results to compare the improvements obtained by various methods (Ref. /36/). The main results are shown in Fig. 6.24. Although two weld classes (butt and fillet welds) are mixed and the scatter therefore is large, the trends are similar to those observed in the test series surveyed here with 49, 83, and 57% average increase in fatigue strength for machined, remelted, and peened specimens, respectively. The strengths and weaknesses of some of the more important improvement methods are listed in Table 6.1.
Section 6.6
Plasma dressed
\.
-c
TIG dressed ----------
\.-Ground
---As welded
HT 60 steel
50 1 o4
R, I
I
2
1
1
4
1
1
= 589 MPa 1
6
1
1
I
lo5
Number of
I
1
2
1
I
1 1 1 1 1
4 6
lo6
1
2
1
1
4
1
1 1 1 1
6107
cycles t o failure, N
Fig. 6.23 Effect of some improvement methods applied t o high strength steels (Ref. 1351); data from Ref. 1211. Table 6.1 Evaluation of improvement methods. GROUP. METHOD w
8 E
Relatively simple and easy to perform. Give large improvement.
Applicable mainly to planar joints that can be expected to fail from the toe. All grinding techniques give a poor working environment regarding noise and dust. Access to weld may be a limiting factor. Marginal increase can be expected for large size welds tubular joints due to stress concentration effect of groove.
Full profie b u n grinding
Relatively simple to perform, inexpensive. Simple insection criterium (depth min. 0.5 rnrn below plate surface or undercut). Very slow. Expensive due to h a labor costs and high tool wear rate. Very fast compared with burr grinding. Can cover large areas
H
@
0
n8 ;gding C3
DISADVANTAGE
GRINDING METHODS General
Zi
C
ADVANTAGE
Large improvements to be expected for all types of welds. Score marks give lower improvements than burr grinding. Improper use may introduce serious defects.
Section 6.6
Table 6.1 (Continued) -
-
ADVANTAGE
GROUP METHODS
REMELTING Large improvements are possible. Suitable for METHODS mechanization. General
DISADVANTAGE Operator needs special training.
TIG dressing
Small physical effort required. Inexpensive.
Careful cleaning of weld and plate necessary. High hardness may result in C-Mn steels due to low heat input.
Plasma dressing
Easy to perform due to large weld pool.
Lower hardness than TIG dressing.
Somewhat larger improvement than TIG dressing
Heavy, cumbersome equipment. Accessibility may limit use.
The improvement is introduced in the welding process itself
Defects at weld toe not removed.
Well defined inspection criterion (the "dime test")
Very large scatter in test results due to variations in microgeometry at weld toe. Consistent improvements only possible if method is combined with others, e.g. toe grinding, hammer peening or shot peening.
WELD PROFILING METHODS General AWS improved I profile
Suitable for large welds and tubular joints
Easy to perform. Suitable for smalljoints. Inexpensive
Special electrodes General
1
Large improvements possible.
Improvement smaller than e.g. grinding or TIG dressing.
Not suitable for low cycle fatigue applications.
~eneficialeffects may disappear under variable amplitude loading involving peak compressive loads. Hammer peening
Limited to toe treatment only. Very large improvements possible for poor quality welds. Simple inspection criterion Excessive peening may cause (depth of groove > 0.6 mm) cracking.
Shot peening
Well developed procedures for small parts. Covers large areas. Simple methods for quality control. Improves resistance to stress corrosion cracking.
Practicable application to large scale structures not demonstrated. Best suited for mild notches. Very thin surface layer deformed; corrosion may quickly remove beneficial effects.
Type of joint
Type of joint
Fatl ue improvement by a piasma
Fatigue improvement by shot-or hammer-peening
AG
arc dressing
1
2
0.8
Ratio 6i/%,50z
2
1
4
R a t i o 6; /6A,S0x
Type of joint Probability onaly s i s of characteristic fatigue strength UA
Fatigue improvement by machining
0.01 1
2 R a t i o 6; /d,,50x
30
50
Characteristic
100
150
f a t i g u e strength
(MPa)
Section 6.7 6.7 COST OF IMPROVEMENT METHODS
Most techniques for improving the fatigue strength are time consuming and considerable costs are therefore involved. Obviously costs and increase in fatigue strength are equally important factors when evaluating improvement methods, particularly when the treatment is to be included in the fabrication process of a new structure. Little information about the costs of improvement methods is available; some data are listed in Table 6.2. Table 6.2 Comparison of costs of improvement methods. RELATIVE COSTS METHOD
Ref. 1371 Ref. 1301 Ref. /3/ TIG dressing Hammer peening Toe burr grinding Full profile burr grinding Heavy disc grinding
1 113
37
1 3
1
3
3-4
15
12
2
.
Ref. /38/ Butt w. T-joint 1
1
0.7-1 -1
0.4-1.7
Large uncertainties are associated with the figures in Table 6.2. It is not clear, for instance, if the costs of checking that the treatment has been correctly performed are included. However,Table 6.2 indicates that the costs of TIG dressing, hammer peening and disc grinding are of similar magnitude, while full profile burr grinding is extremely expensive. In a Swedish study on the economics of disc grinding and TIG dressing (Ref. 1381) it was found that the type of joint had a strong bearing on the costs. Thus disc grinding which was found to be generally faster and cheaper than TIC dressing when applied to butt welds, was the more expensive method when access to the weld was limited.
Section 6.8.1 - 6.8.2
6.8
APPLYING IMPROVEMENT METHODS TO OFFSHORE STRUCTURES
6.8.1 General
Almost all current knowledge about improvement techniques has been gained from tests on small planar joints. The question of the relevance of these data to large scale structures then has to be addressed. The fatigue properties of large components of complex shape differ from those of small scale planar specimen in the following ways: 1. Higher levels of residual stresses exist in larger components. Long range reaction stresses are not relaxed at stress connections by occasional large peak loads. 2. Plate thicknesses are larger. 3. Stress distributions are more complex; the peak stress may not occur at the weld toe, but somewhere on the weld reinforcement.
The higher levels of residual stresses in larger components may to some extent be simulated in tests on small specimens by applying high stress ratios or correcting the results for the influence of mean stress. However, the size effect in thick plate improved joints and the implications of stress distributions differing from those found in simple planar joints should be considered in more detail. 6.8.2 Effects of size and stress distribution in improved joints.
The effect of plate thickness on fatigue strength of welded joints is mainly due to two factors: a) Severity of the stress concentration and b) Stress gradient in the thickness direction at the notch root. Other influencing factors are the size and distribution of defects and the static strength of the base material. Due to the reduction of the stress concentration factors of joints that have been improved by modification of the weld profile, it can be shown both by considering crack initiation at notches and by fracture mechanics calculations of crack growth that size effects are much less dominant in geometry improved joints than in untreated ones. In contrast to small joints where the peak stress occurs at the weld toe, the area of highly stressed material in a large scale joint encompasses several weld runs and fatigue cracks may initiate anywhere in this area, see Fig. 6.25 a) - b). For welds in tubular joints this effect is even more pronounced, especially for joints with large ratios of brace to chord diameters as illustrated in Fig. 6.26.
Section 6.8.2
v
( aI
(b)
Fig. 6.25 Stress distribution in a) small joint with peak stress in toe region affecting material in one weld pass only; b) large scale weld with peak stresses including several weld passes.
Chord wall Peak stress i n veld fillet
Stress a t weld toe
Fig. 6.26 Typical stress distribution across weld in a tubular joint.
The stress distributions in Figs. 6.25 and 6.26 have important implications for the choice of improvement methods for large scale joints. Firstly, removing material by grinding the toe region of a weld in a tubular joint means that the leg length is reduced and the stress distribution is altered as shown in Fig. 6.27. The resulting peak stress may well be higher at the toe of the ground weld and the improvement in fatigue life marginal. Thus a weld which is to be improved by toe grinding must have a sufficient large leg length to avoid moving the new toe into a higher stress field. Stress prior to grinding
, \
\yk,
from original
material removed by grinding
Fig. 6.27 Stress distribution in the weld of a tubular joint prior to and after toe grinding.
Section 6.8.3 The second aspect of highly stressed welds is that an effective improvement involves treating the entire weld, not only the toe region. Thus improvement methods that cover large areas such as shot peening or disc grinding are likely to be preferred. Alternatively, if choosing a method which is normally used for local (toe) treatment, e.g. burr grinding or TIG remelting, the treatment should be extended to cover all interpass notches.
6 3 . 3 Inspection criteria Although the many test programmes surveyed here have verified that it is possible to obtain large increases in fatigue strength by various improvement techniques, it is still necessary to establish procedures and inspection criteria to ensure consistent results. The depth of grinding, Fig. 6.2, at the weld toe is a simple inspection criterion. However, cracks at the bottom of deep undercuts could possibly remain after grinding, and such cracks would be difficult to detect because of the heavily deformed surface, particularly after heavy disc grinding. To ensure consistent improvements following a remelting treatment, it would probably be necessary to establish remelting procedure qualification tests for welders, similar to the procedure tests used for welding, to ensure sufficient heat input and low hardness in the HAZ. Visual inspection would probably be sufficient to detect pores and defects that tend to result from improperly deslagged welds or contaminated electrodes. For hammer peening the indentation depth is a simple and reliable inspection criterion. Shot peening, however, presents a more difficult problem because recent work (Ref. 1301) has shown that there is a poor correlation between Almen strip intensity and the resulting fatigue strength following shot peening. To ensure adequate coverage the erosion of an ultraviolet sensitive coating may have to be used (Ref. 1301).
6.9 CONCLUSIONS On the basis of a large number of results from many test programmes, the following conclusions are drawn: 1. All techniques gave improvements in air corresponding to a shift of at least two design classes in the BS 5400-SN-curves. 2. In free corrosion most improvement techniques gave small but significant increases of fatigue strength. 3. The full potential of the weld toe improvement techniques can be realised only if premature failure from other sites, e.g. the weld root, can be avoided. 4. The amount in increase in fatigue strength due to post weld improvement is larger for higher strength steels than for mild steel. 285
Chapter 6. References REFERENCES 1. Maddox, S.J. : "Avoiding fatigue failure by good design and construction practice." Welding Institute, Seminar, Bradford, April 1980.
2. Gurney, T.R.: "Fatigue of welded structures." 2nd ed., Cambridge University Press, 1979. 3. Knight, J.W.: "Improving the fatigue strength of fillet welded joints by grinding and peening." Welding Research Int'l, 8 ( 6 ) , 1978.
4. Booth, G.S.: "Constant amplitude fatigue tests performed on welded steel joints in air." Select Seminar "European Offshore Steels Research", Abington, 27-29 November 1978, Paper 4. 5. Booth, G.S.: "Constant amplitude fatigue tests performed on welded steel joints in sea water." Select Seminar "European Offshore Steels Research", Abington, 27-29 November 1978, Paper 9. 6. deBack, J. et al.: "Fatigue and corrosion fatigue behaviour of offshore steel structures." 72 10-KB/6/602 (5.7.1 f/76) Final report, April 1981. 7. Hanzawa, M. et al.: "Improvement of fatigue strength in welded high tensile strength steels by toe treatment." IIW Doc. XIII-829-77. 8. Ikeda, K. et al.: "Improvement of fatigue strength of fdlet welded joint for 80 kg/mm2 high strength steel." IIW Doc. XIII-835-77. 9. Kado, S. et al.: "Influence of the conditions in TIG dressing on fatigue strength in welded high tensile strength steels." IIW Doc. XIII-77 1-75. 10. Millington, D.: "TIG dressing for the improvement of fatigue properties in welded high strength steels." Weld. Inst. Rep. C215/22/71, July 1971. 11. Fisher, J.W. et al.:
"Improving fatigue strength and repairing fatigue damage." Fritz Engineering Lab. Report No. 385.3, Lehigh University, Dec. 1974. 12. Haagensen, P.J.: "Effect of TIG dressing on fatigue performance and hardness of steel weldments." ASTM Symposium "Fatigue Testing of Weldments", Toronto, May 1977. ASTM STF 648,1978.
286
Chapter 6 . References 13. Minner, H.H. and Seeger, T.: "Investigation on the fatigue strength of welded and TIG dressed high strength steels." IIW DOC.XIII-9 12-79. 14. Minner, H.H. and Seeger, T.: "Fatigue strength of welded beams of high strength steels. Interim report." IIW DOC.XIII-95 1-80. 15. Todoroki, R. et al.: "Effect of toe profile improvement on corrosion fatigue properties of welded joints." IIW Doc. 875-78. 16. Todoroki, R. et al. : "Problems on improvement of corrosion fatigue strength of steel in sea water." 8th Congress "Metalic Corrosion", Mainz, 6-1 1 September 1981. 17. Haagensen, P.J.: "Fatigue strength of TIC dressed welded steel joints." ECSC Conference "Steels in Marine Structures", Paris, 5-8 October 1981. 18. Simon, P. and Bragard, A,: "Am6lioration des proprietks de fatigue des joints soud6s." Commission du Communaut6s Europ6en.e~. Con. no. 6210-45//202, Report Final. 19. Booth, G.S. and Baxter, C.F.G. :
"Fatigue tests on plasma dressed fillet welded joints." Welding Institute Report 8711979. 20. Kado, S. et al.: "Fatigue strength improvement of welded joints by plasma arc dressing." IIW DOC.XIII-774-75. 2 1. Shimada, W. et al. : "Improvement of fatigue strength in fillet welded joint by C02 soft plasma arc dressing on weld toe." IIW Doc. XIII-830-77. 22. AWS D1.l: "Structural welding code." American Welding Society, 1980. 23. API RP2 : "Recommended practice for planning, designing, and constructing faed offshore platforms." American Petroleum Institute, January 1980.
24. Tornkins, B. : "Fatigue design rules for steel welded joints in offshore structures." OTC Paper 4403,1982.
25. Gurney, T.R.: "The basis for the revised fatigue design rules in the Department of Energy Offshore Guidance notes. Paper 55 Second Int. Conf. on Offshore Welded Structures, The Welding Institute, London 16-1 8 Nov. 1982.
Chapter 6. References 26. Kanazawa, S. et al. : "Improvement of fatigue strength in welded high tensile strength steels." IIW DOC.XIII-735-74.
27. Kado, S. et al.: "The improvement of fatigue strength in welded high tensile strength steels by additional weld run with coated electrodes." IIW Doc. XIII-772-75. 28. Kobayashi, K. et al. : "Improvement in the fatigue strength of fillet welded joint by use of the new welding electrode." IIW Doc. XIII-828-77. 29. Booth, G.S. : "The effect of mean stress on the fatigue lives of ground or peened fillet welded steel joints." Welding Institute Report 34/1977/E. 30. Maddox, S.J.: "Improving the fatigue lives of fillet welds by shot peening." IABSE Colloquium, Lausanne, 1982. 31. Miisgen, B.: "Verbesserung der Schwingfestigkeit von Schweissverbindungen hochfester wasservergiiteter Feinkornbaustahle durch therrnische und mechanische Nachbehandlung der Nahte", Stahl und Eisen 103, 1983, p. 225. 32. Bignonnet, A. et al.: "Improvement of the fatigue life for offshore welded connections." IIW Conference "Welding of Tubular Structures", Boston. 33. Bergquist, L. and Sperle, J-0. : "Influence of TIG dressing on the fatigue strength of coverplated beams." IIW DOC.XII1.-826-77. 34. Gurney, T.R. : "Effect of peening and grinding on the fatigue strength of fillet welded joints." British Welding Journal, Dec. 1968.
35. Haagensen, P.J. : "Improving the fatigue performance of welded joints." Paper 36, Second Int. Conf. of Welded Structures, The Welding Institute, London 16-18 Nov. 1982. 36. Olivier, R. and Ritter, W.: "Improvements of fatigue strength of welded joints by different treatments - statistical analysis of literature date.'' Int. Conf. on Steel in Marine Structures, Paris 5-8 Oct. 1981.
Chapter 6 . References 37. Watkinson, F. et al.: "The fatigue strength of welded joints in hlgh strength steels and methods for its improvement." Welding Institute Report C215/16/70, 1970. 38. Lindskog, G. "TIG dressing. A technical and economical assessment of a method to increase the fatigue properties of welded joints." IVF-RESULTAT 7864 1, Sveriges Mekanforbund 1978 (in Swedish).
CHAPTER 7
EFFECTS OF MARINE ENVIRONMENT AND CATHODIC PROTECTION ON FATIGUE OF STRUCTURAL STEELS Einar Bardal SINTEF,Trondheim
ABSTRACT This chapter deals with various effects of marine environment and cathodic protection on fatigue of structural steels. The mechanisms of different effects are reviewed. Environmental effects and influence of cathodic protection on SN-curves and crack growth data are quantitatively treated in separate sections. The significance of weld type and quality, materials properties, load variables, environmental factors and corrosion protection measures are reviewed. Based on crack growth data the effects of corrosion and cathodic protection on fatigue life have been shown by calculation examples for typical crack-load conditions. The main trends of the results are discussed and compared with British design guidelines. 7.1
QUALITATIVE PRESENTATION OF EFFECTS, MECHANISMS AND IMPORTANT FACTORS
The effects of marine environment and cathodic protection (CP) on SN- and crack growth diagrams are schematically shown in Fig. 7.1 a and b. The SNcurves show that free corrosion in marine environment reduces markedly the fatigue life of plain specimens, whereas the reduction is less for welded joints. The fatigue limit is eliminated or at least drastically reduced by corrosion. A normal degree of cathodic protection usually restores the air fatigue life. In the high cycle region, fatigue life and fatigue limit may even be increased by CP. At high load levels, however, cathodic protection may reduce fatigue life. This is particularly the case for high degrees of CP (overprotection) and for high strength steels. 29 1
Section 7.1
k
Sea water+CP P l a ~ n specimen
Sea water+CP
<:.\:\,\A
Specimen w ~ t hw e l d or n o t c h ir
x ? ~ P l a ~ ns p e c ~ m e n
S e a watey?%free corrosion
log
(number
d
aKth
of
cycles
/
With or
failure
weld notch
Nf )
Fig. 7.1 Effects of sea water corrosion and cathodic protection on a) SN-curves and b) crack growth rate curves.
Log nK
log ( s t r e s s i n t e n s ~ t y r a n g e
<,: '
A
K)
For corrosion fatigue and fatigue of welded joints it has been shown that the crack growth period represents the major part of fatigue life (Section 7.2). Much attention is therefore given to crack growth data. Compared with the growth in air, free corrosion in sea water accelerates the crack growth rate to a higher or lower degree (Fig. 7.1 b). Cathodic protection reduces crack growth at lower AK-levels and increases it at higher levels. Both corrosion and cathodic protection influence fatigue by different effects and mechanisms (Refs. / 1, 2, 3 /) . Some of the effects are counteracting, and the total effect on fatigue data depends on the prevailing conditions. The main mechanisms acting on structural steels in sea water, and the typical conditions favouring each mechanism are briefly reviewed below.
Section 7.1 a)
Corrosion pits and grooves act as stress raisers and thus contribute t o crack initiation at an earlier stage and at a lower nominal stress than initiation in air (Fig. 7.1 a). For ordinary welded joints this mechanism is probably less important because weld defects may be more effective stress raisers than corrosion defects. In the case of improved welds, however, corrosion defects o n the surface are more significant. For low carbon steels in chloride solutions, the significance of pitting corrosion as the initial stage of corrosion fatigue has been questioned (Refs. 11, 21). Pits are often found near fatigue cracks but they might have been formed after the cracks had started.
b) Corrosion fatigue is governed by a synergistic mechanism : Local plastic flow and the creation of new, active surfaces at the initiation site or at the crack front accelerate anodic dissolution, and vice versa, local anodic dissolution promotes plastic flow. This mechanism is responsible for easier and accelerated initiation as compared with fatigue in air, with marked effect on the SN-curves for plain specimens (Fig. 7.1 a). It also favours the conditions for crack growth. The reduced threshold value AKth in corrosive environment (Fig. 7.1 b) may be explained by this mechanism.
c)
Particularly during stressfree periods, corrosion may blunt the crack front and retard crack growth for some time after the stressfree period, and thus counteract mechanism b. Under variable load amplitudes the resulting effect of mechanisms b and c are difficult to assess.
d) Sea water corrosion at or near the crack front may make the crack environment acid. This allows hydrogen development to take place inside the crack, and the development is further stimulated by the enhanced anodic dissolution mentioned under item b. At medium to high load levels the crack growth may therefore increase by hydrogen embrittlement (Fig. 7.1 b). e)
Full cathodic protection eliminates the mechanisms a, b and c. In deep cracks, however, the effects under items b and c and the cathodic polarization to prevent them, may not be 100% effective (Ref. 141). Also compare mechanism h.
f)
At medium to high load levels hydrogen embrittlement due to cathodic protection may increase crack growth (Fig. 7.1 b).
g)
Under cathodic protection, calcareous deposits may be produced on the
Section 7.2.1 crack surfaces and lead to crack closure. Subsequently lower crack growth rates and a higher threshold value AKth will result (Fig. 7.1 b). h)
Mass and charge transport within the crack affect both corrosion and cathodic protection at the crack front. Supply of reactants t o and removal of products from the crack tip region are restricted, and there will be a potential drop between the crack front and the free surface.
Several factors are important for the environmental effects on corrosion. When test data are applied for practical purposes such as design, evaluation of damage tolerances etc., it is essential that these factors and their effects are known. Load frequency, type of environment, e.g. that 3% NaClsolution does not simulate sea water properly, stress level and electrochemical potential are among the most important factors. The effect of environment also depends on temperature, stress ratio, material strength and weld quality. High pressure and low rates of water flow may have some significance. Quantitative effects of the majority of these factors are shown in the following sections. For some factors, the available information is incomplete.
7.2
EFFECTS OF CORROSION AND CATHODIC PROTECTION ON EXPERIMENTALLY DETERMINED SN DATA
7.2.1 Plain specimens and different types and qualities of welded joints. In dry fatigue of structural parts and specimens with plain surfaces, the initiation period may be the dominant part of fatigue life. In a corrosive environment, however, the initiation period is greatly reduced. E.g. in a low carbon steel in 3% NaCl solution, 0.1 mm deep cracks may be produced during the first 10% of fatigue life (Ref 121). Welds of ordinary quality with sharp notches may reduce the initiation period to about the same extent as does corrosion. There is also an additive effect of geometrical stress concentration and corrosion which is reflected in the fatigue life (Ref. /I/). This is illustrated in Fig. 7.2, which shows SN-curves for cruciform joints in air and synthetic sea water, as welded and as ground (Ref. 151). Ground and other improved welds have smaller weld defects, hence the fatigue initiation period is longer. When such welds are exposed to sea water, the reduction of fatigue life due to corrosion is greater than in the as welded condition. In other words, the improvement of welds is less effective in sea water than in air (Ref. 161).
Section 7.2.1
air
results
-
Number o f c y c l e s t o f a i l u r e ,
Nf
Fig. 7.2 SN-curves for transverse welded joints of BS4360-50D steel in as welded and ground condition, tested in air and sea water at t = 5-8OC. Stress ratio R = 0 and frequency f = 0.167 Hz (Ref. 151). The effect of corrosion is also strong on full penetration butt welds. This is shown in Fig. 7.3, where synthetic sea water gives a life reduction factor varying from 3 to 6, with the highest reduction at the lowest stress
I
o4
1 Number
o5 1 o6 I o7 of cycles t o failure Nf
Fig. 7.3 Effects of corrosion on SN-curves for butt welded joints in steel BS4360-50D, exposed in synthetic sea water, compared to air data. t = 10-12"C, f = 1 Hz (Ref. 171).
Section 7.2.2
1 o5
1 o4 Number
Fig. 7.4
of
1 o6 cycles
to failure
1 o7 Nf
As Fig. 7.3, but with saline atmosphere instead of synthetic sea water (Ref. 171).
(Ref. 171). A saline atmosphere has a smaller effect (Fig. 7.4). Cathodic protection at -780 and -1 100 mV vs SCE (approx. -800 and -1 120 mV vs Ag/AgCl/sea water) gives fatigue lives similar to those in air (Ref. 171). For other types o f welded joiuzts which have generally larger defects, the corrosive effect is smaller, mostly with a life reduction factor from 2 to 3 (Refs. 18, 91). Examples are shown for different ioints and stress ratios in . results are from Figs. 7.5 and 7.7 for 20°C and in Fig. 7.6 for 5 " ~ These small scale tests, but a similar reduction factor has been found for tubular joints (Ref. /lo/).
7.2.2 Significance of environmental factors and corrosion protection measures Most corrosion fatigue tests referred to in the present chapter have been conducted in synthetic sea water and some in naturul sea water. When the results from the different laboratories are compared, it seems as if synthetic sea water is a satisfactory substitute for natural sea water. This was also confirmed by a few tests run at Norges tekniske hsgskole and designed so that a direct comparison was possible. 3% NaCl solution on the other hand can not replace natural sea water in all cases. The life reduction factors given in Section 7.2.1 refer to free corrosion under continuous immersion in sea water (Figs. 7.3, 7.5 and 7.7). Fig. 7.6 also shows the effects of intermittent immersion which seems to give about the same fatigue life reduction as does continuous immersion. Other tests indicate, however, that the intermittent immersion results are closer to air results (Ref. 181) and similar to those observed in saline atmosphere
Section 7.2.2
Cruciform non-load c a r r y i n g f u l l penetration weld , B - t y p e s a s welded
)
Air Sea water-----T-form, non-load c a r r y i n g f u l l p e n e t r a t i o n we.Ld, A-type,as welded
Air
-
Base series
Sea water
Cruciform load full penetration weld, C-type, as welded 0 Air
)carrying
50
1
...........
I
1
1
I
1 1 1 1 1 1
I
I
I
1 1 1 1 1 1 1
16
-.---
A I I 1 1 1 1 1
1 o6
1
I
I
I
I I I I I ~
o7
I o0
Number o f c y c l e s t o failure, N f
Fig. 7.5 Fatigue results for different joints in air and sea water. t = 20°C, R = 0.1 ,f = 0.2 Hz in sea water tests. Steel Euronorm 1 13-72, Grade FeE 355 KT (Refs. /8,9/).
- 400 0
a
200
-
0
S e a water a Sea water 0 Sea water
C .-
E
2
50
I
1 o4
I
1
( f r e e corrosion) i n t e r m i t t e n t immersion) cathodic protection)
Mean Line f o r air data
I
1 1 1 1 1 1
I
1
1
1 o5 Number
of
1
1
1 1 1 1
I
1 o6 cycles
t o failure,
I
Nf
1
1
1
1 1 1 1
1 o7
Fig. 7.6 SN-data for welded joints of B4360-50D steel in air and sea water under free corrosion, intermittent immersion and cathodic protection. t = 5" C, R = -1, f = 0.167 Hz (Refs. /5,8/).
Section 7.2.2
F u l l p e n e t r a t on w e l d , as w e l d e d 1 sea w a t e r air sea w a t e r
Air Sea w a t e r
Number o f c y c l e s t o f a i l u r e ,
Nf
Fig. 7.7 Fatigue behaviour of T-shaped specimens in air and sea water at stress ratios R = 0.1 and -1. t = 20°C, f = 0.2 Hz in sea water tests. Steel Euronorm 113-72, Grade FeE 355 KT. As welded (Ref. 191). (Fig. 7.4). Under sea water drip at t = 20°C and f = 0.125-1 Hz, an average
life reduction factor of about 2 compared with air was found for the as welded condition, but with a larger scatter than usually observed under free corrosion (Ref. / 1 11). Temperature is an important variable to consider. Som British SN tests of welded joints at 5OC have shown very little effect from sea water compared with air, while similar Dutch tests at 20°C have resulted in the typical reduction factor 2-3 mentioned earlier (Ref. 181). Hydrostatic pressure in the range of 70-140 bar gives a significant but not very large reduction of corrosion fatigue strength, as compared with usual values under atmospheric pressure (Ref. / 11). Variation of oxygen content and pH over wide ranges affects corrosion fatigue. However, the real variations of these properties are small in marine environments and their effects are not significant (Ref. / I/). Water velocity may be of some importance when the specimen is under cathodic protection. (Section 7.3 -3) As seen in Fig. 7.6, cathodic protection restores the air fatigue life, and may even give longer lives than in air at the lower stress levels. This is a result obtained in several investigations, but less benificial effects of cathodic protection have also been observed. E.g. in one case, cathodic protection of a tubular joint gave the same life as free corrosion, but with slower initiation
Section 7.2.3 and faster crack growth (Ref. /lo/). (Compare Section 7.4) Paint coatings will prevent corrosion fatigue as long as they remain intact and are not scratched or cracked.
7.2.3 Significance of loading variables and materials proper ties. In the as welded condition the applied stress ratio R has only a small effect both in air and under free cprrosion (Fig. 7.7) (Ref. /9/), or no significant effect at all (Ref. / 1/). If the joint is stress relieved, however, there is a significant effect of R on the SN-curve as shown in Fig. 7.8 (Ref. 191). It will also be seen that the effect of R is greater in a corrosive environment, in other words the effect of corrosion is greater at R = 0.1 than at R = -1.
-
F u l l p e n e t r a t i o n w e l d , PWHT
0.1. a i r 0 . 1 sea water
0.
water
-1
air
-1
sea water
Air
Number o f c y c l e s t o f a i l u r e , N f
Fig. 7.8 As Fig. 7.7, but with stress relieved specimens (Ref. /9/).
The frequency effect on corrosion fatigue depends on the conditions. The contribution of corrosion to corrosion fatigue is greatest in the initiation period, and lowering the loading frequency, markedly reduces initiation life. During crack growth, the frequency effect is more pronounced at medium and high stress intensity ranges than at low ones (Section 7.3.2). Corrosion fatigue SN data should be determined with a frequency of the right order of magnitude to ensure their validity in design. High cycle corrosion fatigue strength does not increase with increasing tensile strength of the material. High strength steels are usually the most sensitive to hydrogen embrittlement, and this may reduce fatigue life, particularly at low potentials. The quantitative effects of hydrogen embrittlement are insufficiently investigated.
Section 7.3.1 The effect of sea water under variable amplitude loading is also insufficiently studied. However, a similar fatigue life reduction factor as reported for constant amplitude seems to exist. An average factor of 2.2 was found with a narrow band spectrum and with Raleigh and Gaussian peak distributions (Ref. 181). Ref. 1121 reported a factor of less than 2 under realistic stress sequences. In this work it was interesting to observe that the loading frequency did not significantly influence fatigue life in the range between 0.2 and 10 Hz, and that appropriate cathodic protection completely eliminated the damaging effect of sea water (small specimens, f = 1-10 Hz, R = -1). 7.3
EFFECTS OF CORROSION AND CATHODIC PROTECTION ON
CRACK GROWTH 7.3.1 Different effects at different levels of crack growth
3 4 6 10
20
40 60 90
Stress ~ntensity r a n g e n K (MPaCrn)
Fig. 7.9 Mean crack growth curves showing tests in air, under free corrosion in sea water and with cathodic protection at two potentials. R = 0.5. (Refs. 113, 14, 151)
3 4 6 10
20
406090
Stress intensity r a n g e A K (MPaTrn)
Fig. 7.10 Crack growth data. Free corrosion in sea water. R = 0.5 (Ref. 1141)
Section 7.3.2 Mean crack growth curves at R = 0,5,based on results from Ref. /13/ with high crack growth rates and from Refs. /14,15/ with low growth rates, are shown in Fig. 7.9. The effects of sea water and cathodic protection at different growth rate levels were also discussed in Section 7.1. Fig. 7.10 shows growth rates under free corrosion, supplying background data for Fig. 7.9.
7.3.2 Significance of loading variables and materials properties The effects of environment and cathodic protection at different AK-levels are shown in Fig. 7.9. It can be seen in Fig. 7.1 1 (Ref. / 131) that the growth rate under free corrosion increases with increasing stress ratio R up to R = 0.7. A similar dependence is found for growth under cathodic protection. In air, however, the same authors found little or no effect of R in the actual high crack growth region. In other words, the crack growth accelerating effects of corrosion and cathodic protection in this region, as compared with air, are stronger at a higher than at a lower R. For free corrosion this is in agreement with the SN-curves in Figs. 7.7 and 7.8. A similar trend was found at lower AK-levels at SINTEF (Ref. / 151).
1 i
1
A r
2
Free c a r r
CP
d
.
3 mY
. 4
.v
I - Garwood
2
- Br
3
-
Bardal
4
-
Booth
siol
Scatterband (Lfndley and R ~ c h a r d s )
0.2 0.4 0.6 0.8 1.0 AK
(MPaCrn)
Fig. 7.1 1 Effect of stress ratio R on crack growth under free corrosion in sea water (Refs. / 13, 81).
Stress rat
10,
R
Fig. 7.12 Effect of stress ratio R on the threshold stress intensity range AKth (Ref. / 161, revised).
Section 7.3.3 At lower growth rates, there is a clear effect of R both in air, under free corrosion and with cathodic protection, as is indicated by the effect on the threshold value AKth in Fig. 7.1 2 (Ref. / 161). In Ref. 1171, the R-influence under free corrosion has been taken into account by replacing AK in the crack growth equation by AK + 4R. Thus, the crack growth curve moves to the left by an amount of 4R when R is increased above zero. These results were obtained in 3.5% NaCl solution, but tests in synthetic sea water show a similar dependence (Refs. 113, 15, 191). For growth rates below mmjcycle, loading frequencies between 1 and 0.1 67 Hz are giving the same growth rates, under free corrosion as well as under cathodic protection (Refs. 14,201). However, at higher growth rates, corresponding to AK = 10 - 40 M P a f i , a decrease of frequency produces a marked increase of the growth rate. The effect is largest for specimens under cathodic protection where a reduction of frequency by one decade may cause a 4-8 times increase of da/dN (Refs. 121, 22, 231). This shows that many of the earlier corrosion fatigue growth data which were conducted at increased frequencies are in fact invalid. Only for low growth rates can some acceleration be accepted (up to 1 Hz). Corrosion fatigue crack growth under variable amplitude loading is not sufficiently studied. Several investigations (Refs. 11, 24, 251) indicate that corrosion has approximately the same effect on crack growth under spectrum loading as under constant amplitude loading (Fig. 7.1 3). One difference may be that the corrosive effect is clear also at rather high frequencies (e.g. 6.5 Hz) for variable amplitude loading (Ref. 1241) (cf. the last comment on SN-results in Section 7.2.3). Crack growth rates of welded specimens are similar to those of the base metal (Ref. 1271). Within the class of low and medium strength structural steels (R, < 700 MPa) there seems to be no significant effect of strength and microstructure on the crack growth behaviour (Ref. / I / ) However, this is sparsely investigated, and one might expect that cathodic protection at low potentials would increase the growth rate in high strength steels. 7.3-3 Significance of environmental factors A raise in temperature from a range of -1 - +5"C to a range of 20 - 24°C has been found to increase the crack growth rate by a factor of 2 (Refs. / 1, 131). In Ref. /27/ a factor of 5 was found for AK = 10 - 50 M P a f i , and the same temperature raise. At lowerAK values, however, the effect is smaller (Ref. /I/). In Ref. /28/ a temperature raise from 30 ti1 8S°C produced a threefold increase of the growth rate.
Section 7.3.3
66
i7 -8
0
0' Const.rnean/Stat.rms
6'"
--
S e a water t e s t s ; Gauss Const.rnin./Stat.rrns Const.rnin./Stat.rrns Linear Const.mean/Stat.rrns -L i n e a r Const.mean/Var.rrns
L
0 I
1 Stress
I
3
1
1 1 1 1 1
10
i n t e n s ~ t yf a c t o r
1
1 1 1 1 1 1
30
90
aKrms(~PalTm)
Fig. 7.13 Comparison of different crack growth curves for variable amplitude loading of BS4360-SOD steel in air and sea water. Constant mean or constant minimum load, and stationary o r variable root-meansquare values. Gaussian spectrum with an irregularity factor of 1 and a crest factor of 4.5. Omission level 15% of maximum load. Log linear spectrum composed of four Gaussian spectra. f = 1 Hz, t = 12OC (Ref. 1251) Water flow may prevent the unfavourable effect of strong cathodic polarization as compared with free corrosion (Ref. /I/). This is illustrated in Fig. 7.9 for AK = 10 - 40 MPaTm. As far as Ref. 1291 can be understood, the applied water velocity has been lower than 0.1 m/s. A similar trend has been found at SINTEF (Ref. /1 St), for water velocities of 0.2-0.4 m/s. According to Ref. 1131, a reduction of the oxygen concentration in sea water from 7 mg/l (air saturated) t o 1 mg/l causes a reduction of the free corrosion crack growth rate by a factor of 4. There is no similar effect when the specimen is under cathodic protection. In some hydrocarbons and possibly in sea bed sediments, a considerable concentration of H , S may be present. It is shown in Fig. 7.9 that a strong degree of cathodic polarization produces a large increase in crack growth rate == 30 MPaKm). H2Sin the water produces a at AK % 15 MPa fi (K,, similar but much stronger effect under free corrosion as well as under catho-
Section 7.4 dic protection (Ref. 1301). In sea water saturated with H2S, the crack growth is accelerated by a factor varying from 9 to 570 compared with growth in air at AK = 30 M P a f i for R = 0 . 0 5 , and at AK = 12.5 M P a r m for R = 0.7. The effect of H, S decreases with decreasing concentration (Ref. /31/). However, no information has been found on the effect of low H qS concentrations.
7.4
PREDICTION OF EFFECTS OF CORROSION AND CATHODIC PROTECTION ON FATIGUE LIFE BY MEANS OF CRACK GROWTH DATA
It has been shown (Ref. 1141) that the effects of cathodic protection compared with free corrosion can be completely different for conditions resulting in fatigue lives of 40 -300 years, as compared to conditions producing lives of 1 -- 10 years. Such differences can not be disclosed by SN tests, where the whole life is spent in the test. However, long time effects of environmental conditions can be shown by fatigue life calculations based on fracture mechanics and crack growth data, assuming that reliable data are available at low stress intensity ranges near to the threshold value AKth. That procedure is based on the knowledge that the major part of the fatigue life of joints in plates and tubulars is spent on crack growth under conditions that can be described by linear elastic fracture mechanics. Some results of fatigue life calculations are shown in the following pages (Refs. 114, 151). Appropriate data for tests conducted with variable amplitude loading are scarce. Therefore a linear load distribution is assumed, and the crack growth is calculated based on the constant amplitude growth rate curves in Fig. 7.9. It should be observed that by using this approach, possible sequence effects escape attention. A stress ratio of R = 0.5 is assumed, simulating high residual stresses. The calculation is based on a numerical integration of Klesnil-Lukas equation:
where the values of A, m and AKth are taken from Fig. 7.9. The following environmental conditions are considered: Air, free corrosion, and cathodic protection with two different polarization levels, viz. -800 to -850 mV and -1 I00 rnV (Ag;Agcl/sea water). The latter potential is considered the most unfavourable possible when sacrificial anodes are being used. The load spectrum constitutes a linear plot of AolAcr,, versus logN
Section 7.4 and is divided into 73 blocks at 30 different load levels. The block succession used in the integration process is drawn randomly and independently for each return period of 1.6 15.604 cycles. Incremental crack growth Aa for each individual block is calculated, and AK is updated for the new crack length ai+l = ai Aa. Crack growth lives have been calculated for three different defect-load conditions: A. A small initial defect, a ,constant nominal stress spectrum as the crack propagates, and load levels giving life times of 20 - 200 years corresponding to 1o8- 1o9 cycles. Such conditions apply to fixed platform elements, where large defects have been disclosed by inspection and repaired. The calculation has been carried out for an edge crack propagating from a plane surface, and from a semi-circular stress raiser as shown in Fig. 7.14. Initial and final crack lengths are respectively ai = 1 mm and af = 10 mm, notch radius r = 2 mm.
+
Fig. 7.1 4 Model geometries applied in the calculations (Ref. / 141). ai = initial crack length, af = final crack length. B.
A somewhat larger initial defect, assumed to have escaped detection by the inspection after fabrication, a constant nominal stress spectrum, and load levels leading to fracture after a period of 1 - 10 years. Geometrical conditions as shown in Fig. 7.14 with ai = 10 mm, af = 100 mm and r = 50 mm. Unstable fracture may occur for a
K,(l- R) = 80(1 - 0.5)= 40 M P a f i .
C. Geometrical conditions as in case B. Redistribution of stresses during crack growth so that AK is constant during crack growth. Constant nr( is being approached when cracks propagate in tubular joints, Refs. 133, 341 and Chapter 8 in this book.
Section 7.4
Results. Figs. 7.15 to 7.17 show the calculation results when the crack grows from a plane surface. Similar results are obtained in the case of growth from the semi-circular stress raiser. For case A with long life conditions (Fig. 7.1 S ) , corrosion decreases the life by a factor of three while a normal and high degree of cathodic protection increase life by the same factor. Both comparisons refer to air life. For case B with short life conditions (Fig. 7.16), the relative effect of free corrosion is the same as in case A, that is a life reduction factor of three. However, a moderate degree of cathodic protection does not increase the life above that of free corrosion, and overprotection reduces it to two third of the free corrosion life. In case C with a stress redistribution during crack propagation, the relative effect of free corrosion and normal cathodic protection is the same as in case B, in that they both reduce life by a factor of three with respect to air. However, overprotection is even more serious in this case since it lowers the life by a further factor of two compared with free corrosion. In case C the effect of overprotection is extreme: High stress ratio R, stress intensities nearly as high as possible for variable amplitude loading, and a very low protection potential.
-
Q
Q
N=16.4~10~.*..:.~
'~=1.86x10~
-
'. ~ = 5 . 6 5 x 1 0 ~
~=16.7x10~..' 4'
2
-
3/
1
-
50 1
1
2
1
100 1
4
1
150 1
6
1
1
8
200 1
1
10
1
'
Years a t 10 cpm)
250
1
12
1
300
1
14
1
1
1
16x10~
N (cycles)
Fig. 7.1 5 a-N curves for a crack of initial length 1 mm under long life conditions. Crack from a plane surface in air (1), under free corrosion in sea water ( 2 ) , and with cathodic protection at -850 mV (3) and -1 100 mV (4) (Ag/AgCl/sea water). Ao,,, = 28.4 MPa.
Section 7.4 50
-
1
End o f c u r v e s ; F r a c t u r e at AK,,
=40MPa Tm
. - - - - ~. = 0 . 0 7 3 ~ 1 0 ~
5 30-
......
m
ir
i
c
N=o.(~s~(oB ~ = 0 . 1 2 3 x l 0 ~ ..- ~ = 0 . 3 2 9 x 1 0 ~
( Y e a r s at I O c p m )
2
0
I
1
0
4 I
8
6 I
I 1
10
I
I
I
0.2
I'
I
0 . 6 ~ o1 8
0.4
Fig. 7.1 6 a-N curves for a crack of initial length 10 mm under short life conditions. crack from a plane surface in air (I), under free corrosion in sea water (2), and with cathodic protection at -850 mV (3) and at -1 100 mV (4). Ao,, = 23.2 MPa.
/ //
Z mV OO
250
/ 20 I
I
40 I
I
60 I
I
80 I
( Y e a r s at 10 c p m ) 120 140 160
100
I I
I
I I
I
I
I
1
Fig. 7.1 7 a-N curves for a crack of initial length 10 mm, grown from a plane surface. Constant AK-spectrum with AK,, % 37.5 MPacm. These results tally with SN test results concerning the effect of free corrosion. As for cathodic protection they clearly show some features which have also been revealed in a few SN tests: Normal cathodic protection is no better than free corrosion at short lives (Ref. / lo/), but better than air at long lives (Fig. 7.6). The calculation results may also explain the often contra-
Section 7.5
-
7.6
dictory conclusions on effects of cathodic protection drawn from SN tests. The applied geometrical model is simplified. The calculation of the relative effects of corrosion and cathodic protection is, however, thought to be relevant for other geometries as well (Ref. 1141). The possible sequence effects not considered may be an uncertainty. The main trends in the calculation result are, however, in agreement with SN tests with variable amplitude loading (Ref. 1351). As mentioned earlier, the effects of corrosion and cathodic protection under variable amplitude loading are little different from those under constant loading.
7.5 DESIGN GUIDE-LINES, BRITISH PROPOSAL In "Offshore Installations: Guidance on Design and Construction" (Ref. /36/), corrosion is accounted for in the SN-curves for unprotected welded joints by a life reduction factor of 2 on air data. A slope of -3 is adopted for all lives. The air curves are recommended for cathodically protected joints, as well as for joints protected by paint coatings, provided that the coating remains impervious to sea water. The recommendations are limited to steels with Re < 400 MPa (Ref. 1371). The justification of the recommendations has been questioned (Ref. /38/), but they are continuously under revision, and will be adjusted when more reliable experimental results are available.
7.6 CONCLUDING REMARKS The results reported in Sections 7.2 and 7.4 indicate that free corrosion in sea water is fairly well taken care of in the British guide-lines. What is most correct, a life reduction factor of 2 or 3 , is open for discussion. The design basis for cathodically protected structures is less clear. One trend should be noted (Ref. 1351):Cathodic protection gives fatigue data as good as or better than air at long lives, while at short lives, moderate CP and free corrosion may give about the same fatigue life. The change from one behaviour to the other occurs at a lower N-region for small scale specimens than for large scale joints. On the background of the results of the calculations in Section 7.4 and Refs. 110, 391, it seems reasonable to use the same design curves for cathodic protection as for free corrosion at least up to N = lo7 cycles, provided that overprotection is avoided. If there exists any risk for insufficient cathodic protection at some sites, the free corrosion design curves should be applied.
Chapter 7. References REFERENCES 1. Jaske, C.E., Payer, J.H.and Balint, V.S.: Corrosion fatigue of metals in marine environments, Springer Verlag and Batelle Press, 1981. 2. Laird, C. and Duquette, D.J.:
"Mechanisms of Fatigue Crack Nucleationy',in Corrosion Fatigue Chemistry, Mechanics and Microstructure, NACE-2, pp. 88-1 17 (1972). 3. Duquette, D.M.: "Environmental Effect 1 : General Fatigue Resistance and Crack Nucleation in Metals and Alloys", Fatigue and Microstructure, American Society for Metals, Metals Park, Ohio (1979), pp. 335-363. 4. Bardal, E., Ssndenfor, J.M. and Gartland, P.O. : "Slow Corrosion Fatigue Crack Growth in a Structural Steel in Artificial Sea Water at Different Potentials, Crack Depths and Loading Frequencies", Proceedings of European Offshore Steels Research Seminar,Welding Institute, Cambridge, UK, Nov. 1978, pp. VIIP16-1 - VI/P16-12.
5. Booth, G.S.: "Constant amplitude fatigue tests on welded steel joints performed in sea water", Ibid, pp. IV/P9-1 - IVIP9-14. 6. Haagensen, P.J.: "PS6 - Improvement of the fatigue strength of welded joints': International conference on steel in marine structures, Paris 1981, Institut de Recherches de la SidErurgie Franqaise, Special and plenary sessions pp. 309-364. 7. Solli, 0 . : "Corrosion fatigue of weldments of C-Mn steel and the effect of cathodic protection, stress relieving treatment and saline atmosphere", Ibid., paper 2.2.
8. Walker, E.F.: "PS4 - Effect of marine environment': Ibid., Special and plenary sessions,pp. 195-252. 9. Van Leeuwen, J.L., de Back, J. and Vaessen, G.H.G. : "Constant amplitude fatigue tests on welded steel joints performed in air and sea water", Ibid., paper 2.1.
10. Dijkstra, O.D. and de Back, J.: "Fatigue strength of tubular X- and T-joints (Dutch tests)", Ibid, paper 8.4. 11. Berge, S.: "Constant Amplitude Fatigue Strength of Welds in Sea Water Drip", Proceedings of European Offshore Steels Research Seminar,Welding Institute, Cambridge, UK,Nov. 1978, pp. IVIP12- 1 - IVIP12-5.
Chapter 7. References 12. Schiitz, W.: "PS5 - Procedures for the prediction of fatigue life of tubular joints", International conference on steel in marine structures, Paris 1981, Institut de Recherches de la Sid6rurgie Fran~aise,Special and plenary sessions, pp. 253-308. 13. Morgan, H.G., Thorpe, T.W., Rance, A., Sylvester, D.R.V. and Scott, P.M.: "An investigation of the corrosion fatigue crack growth behaviour of structural steels in sea water", Ibid., paper 5.1. 14. Bardal, E., Haagensen, P.J., Grovlen, M. and Szther, F. : "Effects of cathodic protection on corrosion fatigue crack growth in a platform steel in sea water", Proceedings of Fatigue 84, University of Birmingham, Ed. C.J. Beevers, EMAS 1984, pp. 1541-1552.
15. Grsvlen, M., Bardal, E. and Eggen, T.G.: "Fatigue crack growth in structural steels in air and in sea water with and without cathodic protection", SINTEF Report, Trondheirn 1985. 16. Booth, G.S., Wylde, J.G. and Iwasaki, T.: "Corrosion fatigue crack propagation and threshold determinations in structural steel': Proceedings of Fatigue 84, University of Birmingham, Ed. C.J. Beevers, EMAS, 1984, pp. 1471-1484. 17. Vosikovsky, 0.:
"Effects of Stress Ratio on Fatigue Crack Growth Rates in X70 Pipeline Steel in Air and Saltwater", J. Testing and Eva., 8(2), 68-73 (March, 1980). 18. Havn, T.: "Korrosjonsutmatting av st31 i sjsvann", Dr-ing. thesis, Institutt for rnaterialer og bearbeiding, NTH, Trondheim, 1983 (In Norwegian). 19. Scholte, H.G. and Wildschut, H.: "Fatigue crack propagation tests on welded specimens in air and sea water", Conference on steel in marine structures, Paris 1981, Institut de Recherches de la Sid6rurgie Franqaise, paper 5.2. 20. Vosikovsky, 0 . :
"Effects of mechanical and environmental variables on fatigue crack growth rates in steel. A summary of work done at Canmet", Canadian Metallurgical Quarterly, 19 (1980), pp. 87-107. 21. Austen, I.M.: "Factors affecting corrosion fatigue crack growth in steels", Proceedings of European Offshore Steels Research Seminar, Welding Institute, Cambridge, UK, Nov. 1978, pp. 364-386.
22. Vosikovsky, 0 .: "Fatigue-Crack Growth in an X-65 Line-Pipe Steel at Low Cyclic Frequencies in Aqueous Environments", Trans. ASME, J. Eng. Mater. and Technol., Series H, 97(4), 298-304 (October, 1975).
Chapter 7. References 23. Scott, P.M. and Silvester, D.R.V.: "The Influence of Seawater on Fatigue Crack Propagation Rates in Structural Steel", Department of Energy, UK Offshore Steels Research Project, Interim Technical Report UKOSRP 3/03, (December 19,1975).
24. Haagensen, P.J.: "Fatigue Crack Growth of Steel in Air and Sea Water under Constant Amplitude and Random Loading", Paper presented at The Fourth International Conference on Fracture, University of Waterloo, Ontario, Canada, June 1977. 25. Brjasaeter, 0. and DrAgen, A.: "Fatigue crack growth in sea water under random loading", Proceedings of Fatigue 84, University of Birmingham, Ed. C.J. Beevers, EMAS 1984, pp. 1553-1564. 26. Jaske, C .E., Broek, D., Slater ,J .E., Utah, D .A. and Martin, C.J. : "Corrosion Fatigue of Cathodically Protected Welded Carbon Steel in Cold Seawater", Final Report to American Petroleum Institute, Committee on Offshore Safety and Antipollution Research, Dallas, Texas (February 1 1, 1977). 27. Socie, D.F. and Antolovich, S.D. : "Subcritical Crack Growth Characteristics in Welded ASTM A537 Steel", Welding J., 53(6), pp. 267-s-271 -s (June, 1974).
28. Telseren, A. and Doruk, M.: "Temperature Dependence of Water-Enhanced Fatigue Crack Growth in Mild Steel", Engineering Fracture Mechanics, 6(2), pp. 283-286 (September, 1974). 29. Sullivan, A.M. and Crooker, T.W.: "Fatigue Crack Growth in A516-60 Steel - Effects of Specimen Thickness, Saline Environment, and Electrochemical Potential", Proceedings of International Conference on Fracture Mechanics and Technology, Hong Kong, March 21-25, 1977, Vol. 1, pp. 687-698. 30. Austen, I .M. and Walker, E.F. : "Corrosion fatigue crack propagation in steels under simulated offshore conditions", Proceedings of Fatigue 84, University of Birmingham, Ed. C.J. Beevers, EMAS 1984, pp. 1457-1470. 31. Edwards, J.D.A.: A study of the sulphide stress corrosion cracking behaviour of high strength low alloy steels, Dr.ing. thesis, Institutt for materialer og bearbeiding, NTH, Trondheim, Norway, 1984. 32. Maddox, S.J.: "A fracture mechanics analysis of fatigue cracks in fillet welded joints", Int. J. Frac11(1975), No. 2, p. 221. ture, 33. Gibstein, M.B. : "Fatigue strength of welded tubular joints tested at Det Norske Veritas Laboratories",
Chapter 7. References International conference on steel in marine structures, Paris 1981. Institut de Recherche~de la Sid6rurgie Fran~aise,paper 8.5. 34. Wilson, T.J. and Dover, W.D. : "Corrosion fatigue of tubular welded joints", Proceedings of Fatigue 84, University of Birmingham, Ed. C.J. Beevers, EMAS 1984, pp. 1495-1 504. 35. Bignonnet, A.: Resistance i la fatigue corrosion des aciers utilisgs dans les structures soudies marines, Report RE1003 Institut de Recherches de la Sidirurgie Franqaise (IRSID) June 1983. 36. Offshore Installations: Guidance on design and construction, Dept. of Energy, London, 3. Ed. (1984).
37. Background to new fatigue design guidance for steel welded joints in offshore structures, Dept. of Energy, London 1984. 38. Dower, W.D. and Dharmavasan, S.: "Fatigue of offshore structures - a review", Proceedings of Fatigue 84, University of Birmingham, Ed. C.J. Beevers, EMAS 1984, pp. 1417-1434.
39. Holrnes, R. and Booth, G.S.: "Fatigue and corrosion fatigue of welded joints under narrow band random loading", International conference on steel in marine structures, Paris 1981, Institut de Recherche~de la SidCrurgie Fran~aise,paper 7.2.
CHAPTER 8
FATIGUE OF TUBULAR JOINTS M.B.Gibstein and Einar T. Moe A .S VERITEC, Oslo
'y-ABSTRACT Special aspects of fatigue life evaluation of tubular joints are treated in this chapter. Procedures far the determination of stress concentration factors and hot spot stresses are described. SN-curves for welded tubular joints are presented, and a design procedure for the fatigue life verification of tubular joints is outlined. In-service experience with welded tubular joints is discussed. Furthermore some considerations have been given on the design of heavy duty joints. NOMENCLATURE
Ab D d
E e
g p L 11, l2 Mb
P R r N
- cross section area of brace - chord outside diameter -
-
-
-
SCFb SCF
brace outside diameter Youngs' modulus eccentricity gap gap-parameter for gap between individual braces length between supports of chord length of weld, overlap joints bending moment axial load chord radius brace radius number of cycles to failure stress concentration factor brace SCF
Section 8.1
SCF, SNCF SNCFNT t W X a -
chord SCF strain concentration factor strain concentration factor perpendicular to weld front chord wall thickness brace wall thickness cross section modulus leg length of fillet weld
L/D
P
-
Y
- R/T - hot spot strain (maximum numerical value of
eHS
ON
-
v 0
-
e HSN EN
7
-
-
d/D
the principal strain) hot spot strain perpendicular to weld front nominal strain in the brace nominal stress in the brace Poisson's ratio brace angle with the chord thickness parameter t/T
8.1 INTRODUCTION Offshore steel platforms are usually constructed as truss frameworks in which tubular members constitute the structural elements (Fig. 8.1). Tubes are well suited as structural members for offshore steel platforms. Waves and currents generate comparatively small forces on tubular members because of their low drag coefficient. Due to their uniform and symmetrical cross section, tubular members exhibit minimal stress concentrations, outstanding buckling strength, and no sensitivity to lateral load direction. The latter is especially important in the offshore environment, where wind and wave forces can come from any direction. However, interconnections and joints, which in the case of offshore platforms usually are welded, represent structural discontinuities which give rise to very high stress concentrations in the intersection area (Fig. 8.2). Lowered fatigue strength due to high stress concentrations at the weld toes of the connecting welds is a major problem in welded tubular joints. Proper design of tubular joints against fatigue failures must therefore be based upon detailed knowledge of the magnitudes of the stress concentration factors (SCF) and the corresponding values of the peak stresses at the weld toes of the connections, and on empirical data obtained from fatigue tests on tubular joints.
Section 8.2
Fig. 8.1 Offshore platform constructed with tubular joints. In principle terms, the design procedure to verify that tubular joints have adequate fatigue strength, is one in which the sum of fatigue damage arising from the expected magnitude and number of dynamic peak stresses are compared with the fatigue lives of similar joints in laboratory tests. See Section 8.3 and Chapters 4, 10 and 1 1 for more information. Tubular joints must also be designed to sustain the ultimate static design loads (i.e. 100-year storm conditions). Furthermore, the joints must have adequate weldability and toughness to prevent brittle fractures. _4FIT;n
G ~ I - c L c * ~.
8.2 TYPES OF TUBULAR JOINTS Tubular joints appear in a great variety of shapes and design types. Since such joints are not regulated by standards, their configurations and dimensions can be freely chosen to suit structural needs. Tubular joints consist ordinarily of joints between main and secondary
Section 8.2
NUMBERS DENOTE S C F VALUES G / G N ,
.... . .. .
INDICATES
GN =
P
~ ~ d f
PHOTOELASTIC ANALYSIS
INDICATES FINITE ELEMENT ANALYSIS
Fig. 8.2 Stress analysis of a cross joint under axial brace load. member tubes. The former, which are larger in diameter, are denoted as chords, and the latter, which consist of smaller sized tubes, are denoted as braces (Fig. 8.3). Tubular nodes may be classified and grouped in accordance with their geometrical configuration, the action and transfer of loads, and the design types. The design types fall into the following categories:
-
simple welded joints - overlapping joints - complex joints - cast steel nodes
1
heavy duty joints
Simple welded joints may appear as uniplane or multiplane designs formed by welding of tubular members without overlap of the brace tubes and without stiffeners or reinforcements. Fig. 8.3 shows some typical simple uniplane joint types. An overlapping joint is defined both by its geometry and its force transfer. Such joints are designed with braces, which are partially joined together at their connection with the chord. At least part of the loads are transferred between the braces through their common weld. This results
Section 8.2
A X- j o i n t
--
.+,
.-
t
Fig. 8.3 Simple (ordinary) welded joints. in reduced shear force and smaller ovalization of the chord, and consequently smaller stress concentrations and improved fatigue life.
-
-
Complex joints include : joints with internal stifferners joints with external stiffeners grout reinforced tubular joints less readily categorized joints of complex geometry and load transfer mode
Complex joints are often "heavy duty" type nodes which possess substantial improvements in fatigue and static strength performance, see Section 8.4.
,.'I)(
Section 8.3.1
A
.
Cast steel joints are nodes which have been fabricated by casting. The connection weld bracelchord is thereby eliminated and replaced by fillet transitions. Cast steel nodes (CSN) can be designed to exceptional efficiences in terms of fatigue strength performance, see Section 8.4.3.
8.3
SIMPLE WELDED TUBULAR JOINTS
8.3.1 Definitions and symbols The nodes in the main structure of offshore steel jackets are often multiplane joints. Uniplane joints are found in the bracings between main legs in horizontal planes and in secondary structural elements. In the present state of the art the joints are normally classified and evaluated in tenns of the simpler uniplane joints such as T-, Y-, K-joints etc., disregarding the effect of braces which are not lying in the considered planes (Fig. 8.3). It should be emphasized that the classification should not be based only on the geometry of the nodes, but also on the load transfer mode. Thus for example, a joint of X-configuration may only be evaluated as an X-joint if the vertical axial loads in the braces are equal and of opposite signs. Similarly, a joint of K-configuration may only be evaluated as a K-joint if the components of the axial forces in the braces perpendicular to the chord are in equilibrium. For further illustration, a joint of X-configuration, in which an axial brace load is applied to only one of the braces must be evaluated as a T-joint, despite its geometry (Fig. 8.1 9).
Fig. 8.4 Tubular joint symbols. Fig. 8.4 shows the geometrical parameters which define simple welded joints. They are : - chord outside diameter D - brace outside diameter d (cont. next page)
Section 8.3.1
-
chord wall thickness brace wall thickness - brace inclination angle - gap between braces - chord total length - eccentricity
T t 8 g
L e
The non-dimensional geometrical parameters are:
-
diameter ratio
P = d/D
- cord stiffness
r = R/T
= C
1c - < ~ i r
,
The y ratio gives an indication of the chord radial stiffness, and it plays a dominant role in the SCF formulas and the ultimate strength of tubular joints.
-
wall thickness ratio
T
-
gap parameter
P'
= t/T
g/D
The degree of overlapping braces is indicated by negative values of the gap parameter. Other definitions are often found in the literature, such as g/d or g sinold.
-
chord length parameter a = L/D
For the fatigue analysis of tubular joints it is convenient to separate the loads in multiples of three basic load cases, viz. axial load, in-plane bending load and out-of-plane bending load (Fig. 8.5). Each load case has its particular distribution of stresses along the intersection line and thereby its particular influence on the fatigue life. The combined effect of the load cases is discussed in Section 8.3.7.
kwrrl load
l* plane bend i n
AL
I PB
one OPB
Fig. 8.5 w c twbulau joint load cases.
A =
k * . ..-
d .
Section 8.3.2 i
1
>
8.3.2 Definition of the hot spot stress, and stress and strain concentration factors Global stress/SCF - distribution along the intersection line of an axially loaded Y-joint
Hot Spot L o c a t i o n
Strain
Local strain distrilJ ~ t l O n
.-t h ~
n n r m a l tn
..s.A.*".*
'
W P M tne
A
~ t r a ~ n
4
at the hot
Fig. 8.6 Example of global and local distribution of stresses/strains in axially loaded Y-j oints. The stress distributions at the intersection of tubular joints are very complex. Fig. 8.6 shows the strains along the brace and chords of a Y-joint as well as the stresses along the intersection line of the same joint. The locations, or
Section 8.3.2
points at which the highest stresses occur, are called hot In welded joints two diffemnt hot spots are found, one at the weld toe on the brace side, the other on the chord side. The maximum stress value may be on the chord side or brace side dependent on the design and geometry of the joint. The stress concentration factor (SCF) is defined as the ratio of the hot in the brace: spot stress om, to the nominal stress
Unless otherwise specified, the stresses considered in analysis of tubular hour4 joints are the principal stresses. In the process of design evaluation, the hot spot stresses on the chord and brace side of the weld must be considered individually. SCF, and SCFb denote the SCF on the chord and brace side respectively. They are both multiples of the same nominal brace stress. The mod influential factor deciding the fatigue strength of tubular joints, are the values of the SCF and the companding magnitudes of the hot spot stresses. Reliable and accurate knowledge of the SCF and hot spot stresses are therefore an absolute necessity in order to ensure adequate fatigue strength. The sensitivity of the fatigue strength to the values of the SCF is illustrated by the fact that an underestimation of 18% of the value of the SCF may cause a 100% overestimation of the fatigue life prediction. In order to be a useful tool in design, the definition of the hot spot stress and the SCF must be compatible with the presently available SNcurves. Some confusion exists in the literature regarding the definition of the hot spot stress which also affects the definition and values of the SCF. The fatigue life depends on the true peak stresses where the fatigue cracks are expected to develop. In welded tubular joints, these locations are the weld toes at the hot spots. Thus, theoretically, the hot spot stress should be based upon the values of the maximum true stresses at the weld toe. However, in welded joints the maximum true stresses are influenced by weld shape irregularities such as unavoidable notches, and discontinuities. These are highly localized and difficult to quantify and are therefore not suitable for systematic stress analysis. Instead, the hot spot stress is defmed as the stress at the weld toe localitions due to all geometrical influences except for the !ocal weld notch effects at the weld toe;' experimental determination of the hot spot stress value requires therefore the extrapolation of the stress distribution curve to the weld toe from a point which is located just outside the limit of the influence of the notch on the stress distribution. For this purpose, strain gages are placed in strips close to the weld, and the stress curve is extrapolated based upon
I
Section 8.3.2 the measurements gages placed atthe end of the notch influence--zone. - -- - - -- -- -from -This requires a knowledge of the limit of influence of the notch on the stress distribution close to the weld toe. At present the manner and distance of stress extrapolation to the weld toe are handled somewhat differently by different research institutions resulting in slight differences in the values of experimentally determined hot spot stresses. Extensive research indicates that the hot spot stress definition should be based upon extrapolation from a point located 0.25 T from the weld toe on the chord side, and 0.25 t on the brace side. Furthermore, this distance should not be less than 4 mm (Fig. 8.7).
b.) ,: ,
1
-
':
y
1
.
f
Strain
,
>,,
t
,
, ,-7 1 1 ' I
(
i
a-
; ,
r
'7
,
,
,
# C
x
I
d
,
e.
-;
Chord
Fig. 8.7 Determination of the hot spot strain value eHs at the weld toe by linear extrapolation from the end of the notch affected zone. The hot spot stress measured in this manner provides SCF values which are in very good agreement with the values, obtained from finite element (FE) calculations. Furthermore, and most important, it provides consistent fatigue life results independent of the type and complexity of the tubular joint design tested, see Ref. 1181 and Fig. 8.8. The conditions at the weld toe, although not quantified by SCF definition, have a significant influence on the fatigue life. They can be graded as follows (Ref. / 181) :
Section 8.3.2
T-JOINTS T - JOINTS, SEA WATER D=508
0=300
T=l6mm
T=lOmm
2000-
-
1000-
500
AW S - X
197 5 % SURVIVAL
\
200 100 , 10
10
. . -- ----
A lo6
1 o7
lo8 CYCLES
Fig. 8.8 VERITAS fatigue test results based on VERITAS's SCF - and hot spot definition. Note consistency and small scatter.
- Nafch fie,
i.e. continuous stress distribution extending into the weld toe (Fig. 8.9). Such conditions are found in ground welds, or quite often on the brace side of the weld where smooth weld toe transitions are more readily obtained in fabrication. - Notch effect, weld toe discontinuity. The welds should be provided with regular and smooth transitions. However, discontinuities at the toe are to be expected. Fig. 8.10 shows the strain distribution resulting from different notch effects. The majority of the welded tubular joints tested at VERITAS showed an average notch No of about 1.2. (For definition of notch No see Fig. 8.10.) - Micro cracks. Micro cracks at the weld toe may be too small to be detected by ordinary NDT-methods. Their presence is discernible from their typical influence on the adjacent stress pat tern (Fig. 8.1 1). Micro cracks or severe notches reduce the fatigue crack initiation period of the fatigue life of the joint. Grinding of the weld toe may be a preventive action. G,a x ( -f-,>,o Hot spot location (l@U is the location of the very ma-urn stress at the weld toe of the brace or chord members of the joint. In one and the same joint the location is different for different loads. The locations may also vary, to a lesser extent, depending on the geometrical parameters of the joint. - Hot spot stress OH denotes the maximum value of the stress at the weld toe at the hot spot obtained in the case of notch free weld conditions.
-
y
;
t j(1,
lrJ~\c -:'Y/'
Section 8.3.2 5s
4
e
fi
??
:,
n .*d
-ri
CHORD
"-
1
t
i -
,
CHORD
AXIAL LOAD = 7 TON
AXIAL LOAD = 7.5 TON
500-
500NOTCH NO = 1.00 EHS
450 =440
\
400 -
400 -
300 -
300
\
\
LIMIT O F NOTCH ZONE
\\ [
.
200-
2
.
4
. -
6
;
;/*f,?
{2(dT+-,
8
-
10
2
,
12
0
0 - I 2 4
mm FROM WELD TOE
mm
BRACE AXIAL LOAD = 10 TON E
*
NO.
440
I
.
3
6
8
= 1.02
-
.
10
12
FROM WELD TOE
BRACE OOP LOAD, M = 0.88 TON M SCF
I SCF = 8
1
NOTCH
I I
6
L
0 1.6 3.6 5.6 7.6 9.6 mm FROM WELD TOE
0 1.6 3.6 5.6 7.6 9.6 mm FROM WELD
TOE
Fig. 8.9 Notch free stress and strain distribution at the weld toe of tubular Tjoints with D=508mrn, d=244.5 mm, T = 16mm, t = 10 and 12mm.
The strain concentration factor SNCF is defined as the ratio of the hot spot strain eHs divided by the nominal brace strain eN . That is:
SNCF = eH s
,
(8.2)
1
The corresponding concentration factor for the hot spot strain perpeGdicular to the weld front, SNCFN,is defined as:
Section 8.3.2 CHORD AXlAL10AD=15T(*1
300
,
,I
7
4
,
, 6
, 8
, 10
CHORD AXIAL LOAD = ISTON Y- JOINT
-
300J
12
, 2
mrn FROM WELD TOE
I
,
,,
,
,
b
8 1 0 1 2
rnm FROM WELD TOE
rnrn FROM W E L D TOE
Fig. 8.10 Effect of notch on the strain distribution at the weld toe of tubular joints. D = 508 mm, T = 16 mm, d=244.5 mm, t = 10 mm, a=4S0. Most design calculations are based on the SCF values although the fatigue tests and SN-curves are based on the SNCFN values. Even where SN-curves are given in terms of stress range, the latter are based on uniaxial strain, i.e. o = E H S E. Assuming that the hot spot strain, which is perpendicular to the weld front direction, coincides with the direction of the principal stress at the hot spot, the following conversion formula between SCF and SNCF can be used:
SCF = SNCF
1+
e2 /eHSN
1 -v2 where: e2 = hot spot strain normal to eHsN v = Poisson's ratio
In a similar manner, the conversion between the biaxial hot spot stres.: and the uniaxial stress E E H s ~used in SN-curves reads :
In the majority of hot spot locations in ordinary tubular joints, the ratio between e2 and eHSis found to be about 0.24-0.28 from which follows:
SCF r 1.2 SNCF Therefore, when entering SN-curves with calculated hot spot stresses, the designer should be aware that the results may include a conservative factor of about 1.2 in terms of stress value, corresponding to a factor of about 2.0 in the fatigue life. 325
Section 8.3.3 STRIP GAUGE ( 1 )
STRIP GAUGE ( 2 )
400 -
I
I
30,-
I
,
I
NOTCH ZONE
I
,
!
2
L
.
6
0
,
1
,
0
1
,
2
-
DISTANCE FROM TOE mm
I
E
v= 'HS
Fig.8.11b)
I I
O
MICRO 2 6 '0 CRACK DISTANCE FROM TOE mm
1
I
I Axial load 2.5 ton
440
t = 12mm T = 16 ))
400-
I
llmm
DZSOII
1
I
L---J
NOTCH ZONF 300-
I
I
I
1
Fig. 8.1 1 a) and 8.11 b) S U P E R IMPOSED FIG. 8.1 1~
20 0
2
4
6
8
1
0
1
2
DISTANCE F R O M TOE mm
Fig. 8.1 1 Determination of the notch zone by superposition of strain readings taken 11 mm apart. Note that VERITAS definition provides the same value independent of notch. 8 -3.3 Methods for stress analysis of tubular joints
The most common techniques for stress analysis of tubular joints are: 8.3.3.1 Finite element analysis Stress analysis with the finite element method (FEM) is by far the most
Section 8.3.3.1 common approach to determine the stress distribution and hot spot stress in tubular joints. r
\
\ Brace w a l l
mi dd l e sur face
ml dd l e sur face
Node a t middle surface Intersection
Fig. 8.12 Model representation based on thin-shell elements. Note that the weld cannot be accounted for with this element type.
The shell elements have traditionally been ones with mid-plane nodes only (Fig. 8.12). This allowed no possibility of modelling the geometry in the weld region which in this case is idealized to the intersection line. Fig. 8.13 shows a typical thin-shell element mesh for a T-joint.
BRACE
PLUG 7
CHORD
7
Fig. 8.13 Typical thin-shell finite element mesh for T-joints.
Section 8.3.3.1 Gibstein, Ref. /15/, compared steel model tests and thin-shell FEM calculations and found that the experimental chord SCF's were well approximated by the values in the integration points immediately adjacent to the mid-plane intersection line. On the brace side he found that the FEM stresses at the corresponding points exceeded experimental values by 20%. FEM analyses of tubular joints have previously been very expensive, mainly due to the man hours involved in generating the finite element mesh. Since the beginning of 1980, finite element analysis of tubular joints has undergone a spectacular and rapid development. It is currently the most efficient, reliable and economical tool for detailed stress analysis of tubular joints. The main reasons are:
- The increased efficiency of equation solvers, requiring less CPU-time. - The very large reduction of the cost of computers.
-
The introduction of programs featuring automatic (and semiautomatic) meshing of tubular joints, thus eliminating very time consuming manual work.
-
The possibility of weld modelling and the inclusion of 3-D solid elements at the intersection.
Stress analysis by FEM remains the work of specialists which must be fully aquainted with the analysis programs as well as with the special problems related to modelling and interpretation of results. When properly carried out, FEM-results are accurate, reliable and compatible with the experimental results and corresponding SN4ata. There are at present ( 1984) two program packages which are of principal interest:
PMBSHELL PMBSHELL is a FEM program designed for effective stress analysis of tubular joints. PMBSHELL was developed by PMB SYSTEMS ENGINEERING INC., and features automatic mesh generation of simple joints with or without overlaps. Complex joints, such as stiffened joints and multiplane joints, can be effectively modelled semiautomatically. Fig. 8.14 shows the element configuration used in PMBSHELL. Chord and brace are modelled with 16 node shell elements, each having two nodal planes. The weld is modelled with either eight or twelve node solid elements according to AWS specifications, Ref. /2/. The program has efficient post processors, which facilitate the ease and efficiency of representation of analysis results, such as:
Section 8.3.3.1
Fig. 8.14 Element configuration used in PMBSHELL. Ref. 1341
-
-
nodal displacements surface stresses (principal and von Mises) strain at the integration points principal stresses extrapolated into the weld toe summary of stresses along the intersection lines, and indication of maximum and minimum stresses and their location.
PMBSHELL is a linear elastic finite element program and operates in batch mode only. In addition to the testing undertaken during development, MPBSHELL has been independently calibrated at VERITAS. It has been found that by extrapolating stresses to the weld toe, reliable SCF values are obtained without further adjustment.
WJAP TUJAP is an interactive semiautomatic mesh generator developed by SINTEF and VERITAS, and is the latest and most efficient dedicated program for tubular joint analysis. Being interactive, TUJAP represents a further enhancement over PMBSHELL. The semiautomatic approach is more efficient than the automatic mesh generation featured in PMBSHELL, and furthermore extends to all types of joints. TUJAP also models grouted joints and includes also fracture mechanics applications. The finite element scheme, utilized in TUJAP, is shown in Fig. 8.15. It consists of eight node mid-plane shell elements for the tubular members, twenty node solid elements in the weld, and transition elements adjacent
Section 8-3.3.2 Number of Group
Illustration
Name and description
S H E L L
SCQS, Subparametric curved quadrilateral thick shell
nodes pr.node d.0.f.
8
6
18 15 12
316 316 316
20
3
TRSI, Transition element between T R A N S I
I HEXIIPRI elements may be coupled with the SCQSISCTS elements. Three versions of the transition element are needed: TRSI TRS2 TRS3
T I 0 N
TRS3 S 0 L I D
IHEX, Isopararnetric hexahedron
Fig. 8.15 Element configurations used in TUJAP. Ref. 1351 to the weld. The modelling of the chordlbrace intersection is highly efficient, and allows different weld shapes, and even transition fillets. TUJAP utilizes SESAM 80 interface files and is compatible with this system. The system has also non-linear analysis capabilities. 8.3.3.2 Strain gage measurements on scaled steel models A full stress analysis of a tubular joint is usually carried out in two steps:
1. Instrumentation in order to determine the stress distribution along the line of intersection on the chord and brace side, and thereby find the hot spot locations. 2. Detailed instrumentation of the hot spots in order to determine SCF and SNCF at the weld toe. An example of the instrumentation of a tubular joint with strain gages is shown in Figs. 8.16 and 8.17.
Section 8.3.3.3 - 8.3.4.1 Because the strain at the weld toe may vary significantly over just a few millimeters and because it is difficult to measure the strain at the weld toe due to the physical size of the gage, an extrapolation procedure is required. The hot spot stress or strain has to be determined by extrapolation from measurements taken some distance away from the weld toe. The stress gradient close to the weld toe may be very steep. Therefore the value of the extrapolated hot spot stress may be very sensitive to the position of the strain gages, which should be located just outside the notch affected zone as indicated in Figs. 8.9, 8.10 and 8.1 1. It follows that due attention should be paid to the extrapolation methods as well as t o the stress calculations when reviewing tubular joint fgtigue test results or comparing results from different investigators. Testing of steel models is a highly specialized undertaking which also requires complex and costly test rigs and instrumentations.
8.3.3.3 ikbrntory methods Pkroto ehtleityi Three-dimensional photo elasticity is a highly efficient experimental approach for analysis of complex joints, or for analysis of very local stress peaks of geometrical details. Photo elasticity is also most efficient in systematic studies related to optimalization of weld profiles, grind repairs or specialized items of the design (Ref. 1201). It is a highly specialized discipline. A c ~ l i cmodels: The method utilizes models of acrylic plastics fitted with strain gages. It is recommendable for stress analysis where rough approximations are adequate.
concentrationfactors 8.3.4.1 *m @f IiPfiemntpmmetde f o m l a d 8.3.4
In Appendix A four tables with parametric formulas for stress concentration factors developed at different institutions are presented.
Table No. A1 (Kuang's formulas) Refi / I 4 / . The formulas in Ref. / 14/ are based on thin-shell FEM-analysis of the different joint
Section 8.3.4.2
6 < 0.5. The Kuang formulas also tend to be overconservative for the SCF in the braces independent of 6. Therefore in the recommended design formulas in Table A4 the SCF on the brace side is reduced according to Marshall, Ref. 171.
Table No. A2 (Smedley and Wordsworth's formulas) Refs. 126, 271. The formulas in Ref. /26/ are based on measurements with strain-gages on scaled-down acrylic models and are listed in Table No. A2. The models were fabricated as straight pipes without including the weld. The authors propose a correction factor to account for the influence of the weld leg length as follows:
where: SCF = stress concentration factor at the weld toe X = weld leg length It is recommended to use X = T in the calculation, i.e. K = 0.794. That weld leg length and that correction factor are also used for X-joints in the recommended design formulas listed in Table A4.
Table No. A 3 (Gibstein 's formulas) Re5 11.51. The formulas in Ref. /15/ are based on thin-shell FEM-analysis of T-joints and are listed in Table No. A3. The indicated hot spot stress is taken at the integration point nearest to the intersection of the brace- and chord-wall midplanes. 8.3.4.2 Comments on the parametric formulas As can be seen above, the basis and the evaluation procedures have differed between the various sets of parametric formulas, and the computed SCF's may differ. Hence care should be taken when selecting parametric equations for a specific design purpose. An important limitation of the formulas is that they have been developed for uniplane nodes only. An actual joint will often have braces adjoining in two or more planes. The incorporation of a second-plane brace may alter considerably the state of stress in a joint. An example is given in Fig. 8.18, Ref. 1261. Here, a simple T-joint with a loadfree brace perpendicular to the loaded vertical brace has been analysed. The full lines show the straindistribution along the circumference of the chord. Broken lines show corresponding strain-distribution for a simple T-joint, i.e. with the horizontal brace removed. By loading axially brace B, the strain concentration may be greatly increased beyond that shown in this figure.
Section 8.3.4.2
.-
STRAIN DISTRIBUTION WITH BRACE B REMOVED
Fig. 8.18 Strain distribution in joint with axial load on brace A. Broken lines indicate strain distribution with brace B removed. Ref. 1261
Formulas for stress concentration factors are referred to the geometry of the joint, and a prescribed load condition. For the X-joint in Fig. 8.19 a the joint is acting as assumed in the parametric formulas. The joint in Fig. 8.19 b, although it appears to be an X-joint , behaves more like a T-joint and should be evaluated by the parametric formulas for T-joints when values of PZ are small. In Fig. 8.19 c a K-joint with balanced forces in the braces is shown. This is the configuration used for derivation of parametric formulas. Fig. 8.19 d shows the same geometry but with another load configuration, leading to quite different stress concentration factors depending on the relative magnitudes of the forces. Therefore, when parametric formulas are used for fatigue design, it must be verified that they represent the physical behaviour of the joint under consideration. Furthermore, the formulas should not be used outside the validity range they have been developed for. In cases in which the load conditions, or limit of validity, significantly depart from those representable
Section 8.3.4.3
'p2 -PI =2P+P2
PI sine, =-P s l n 0 2 - 2 P K - j o i n t f o r r m a f l v a l u e s of P X-joint for s m a l l v a l u e s of P T - j o i n t for s m a l l v a l u e s of P 2 Y - j o i n t for s m a l l v a l u e s of P2
Fig. 8.19
The effect of load configurations on the joint type evaluation.
by the parametric equations, an ad. hoc. analysis of the joint in question must be carried out. 8.3.4.3 Genenrl considemtiom concerning stress concentrations in tubular joints. Cross sectional ovalization. The designer should be aware of certain basic principles related to the SCF values of tubular joints. The SCF values are basically related to the degree of ovalization of the chord section under the action of the brace loads. In X-joints the vertical forces acting at each side of the cross section, produce a greater ovalization than the single load in a T-joint. Therefore SCFx is greater than SCFT. In a Y-joint only the vertical component of the force contributes to the ovalization, consequently SCFT is greater than SCFy . In the case of a Kjoint, the load transfer occurs through the braces, and the chord is only slightly affected. This is even more accentuated in overlap Ktjoints, in which direct force transfer takes place through the braces.
Section 8.3.4.4 Thus, when the geometrical parameters are equal : SCFx
> SCF, > SCF, > SCF,
SCF's for different joint types with the same geometrical parameters are shown in Table 8.1. SCFx follows from the corrected Wordsworth/Smedley formulas, SCFT and SCFY from Gibstein's formulas, whereas SCFK is obtained from FEM analysis. The values for the overlap K-joint are calculated by a parametric formula developed at VERITAS. Table 8.1 SCF values with braces under axial loads. Joint type
X-joint
SCF, SCFb
2 1.9 14.8
T-joint 13.6 9.6
Y-joint 10.6 7.5
K-joint Overlap K-joint 5.9 4.8 4.3 4 .O
p = 0 . 6 , y = 1 5 . 8 8 , ~ = 0 . 8 3 1 , 0= 6 0 ° , e = 0 8.3.4.4
of geometrical pruvrrneters
y,
P and
r on the SCF in
tubular joints Within each group of joints, the influence of the geometrical parameters may be evaluated from the parametric equations for SCF. However, to give the designer some general guidance on the influences of the geometry, the following observations can be made:
The influence of
4 The SCF increases with increasing 7 , see for example
Fig. 8.20. These results were derived for a T-joint with an axial load in the
Fig. 8.20 The influence of y on the principal stress distribution at the chord side of a T-joint. Ref. / 151
Section 8.3.4.5 brace, Ref. 1151. According to Kuang, Gibstein and Marshall, Refs. /7,14,15/, the SCF is a power function of y, while Smedley has assumed a linear relationship.
Fig. 8.21 Influence of P on the SCF at the chord side of a T-joint for axial load in the brace. Ref. 1151
The influence of 0. The influence on the SCF is parabolic (Fig. 8.21), Ref. / I S / . This figure shows the SCF at the chord side and has been derived for T-joints with axial loads in the brace. Similar shapes are obtained at the brace side and for the other loading conditions. Maximum SCF is measured for p in the region around 0.5, and SCF approaches a minimum as 0 approaches 1.O. These observations are generally valid for all tubular joint types. The influence of T . The SCF increases with increasing T (Fig. 8.22). In this figure the SCF is a power function of r. The Kuang formulas show corresponding relations, while Smedley has assumed a linear relationship. The infltlence of boundary conditions. During FEM-analysis or experiments it is difficult to simulate the actual behaviour of the joint in an offshore structure with the true boundary conditions. For example, the real life boundary for the chord in a T-joint is neither fixed nor free to move. In FEM-analysis it is advisable to use pin supports because this is somewhat more conservative than using fixed supports. 8.3.4.5 Design SCF,the relative magnitudes of SCFc versus SCFb Both SCF, and SCFb must be considered in fatigue evaluation. Which of the SCF is most critical and relevant for the fatigue strength will depend on their relative magnitudes.
Section 8.3.5
CfiORD
Y
:20
I
AXIAL
LOAD
IN
BRACE
i
Fig. 8.22 The influence of T on the SCF in a T-joint.
Gibstein has shown that the value of the SCFb may become equal to, or even larger than the SCF, when the thickness ratio T is about 0.4-0.5 or smaller. Furthermore, SCFb may become larger than SCFc when SCFc is less than 3 .O-3.5. mm pwthah attention must be given to the SCFb when:
8.3.5
Fa#guc testing, expimental results and establishment of SN-curves'
Based on experimental results, SN-curves for design against fatigue failure of tubular joints are presented in different rules and regulations, Refs. / 1,4 and 51 and Chapter 11 in this book. The curves are relationships between the hot spot stress range Ao and the allowable number of stress cycles at a stress range Ao: where: log Z = intercept of the curve of the logN axis -l/m = the slope of the curve
Section 8.3.5 The basic values of log Z and m for the different curves are given in Table 8.2 for structures in air and in sea water with cathodic protection. Table 8.2.
Curve MIX VERITAS X DEn T
log
a
15.06 14.57 12.16
m 4.38 4.10 3.00
Remarks cut off level at N = 2 x 10' cutofflevelatN=2x10' f0rN>10~:10~Z=15.62,m=5,00
The AWS X-, API X-, VERITAS X- and DEn T-curves are shown in Fig. 8.23. The AWS- and API-curves are lower envelopes of fatigue test results, while the VERITAS- and DEn-curves are determined through statistical analysis of fatigue test results, and represent a 97.6% probability of survival. DEn, NPD and VERITAS intend to incorporate a size effect in their next revision of the fatigue design rules. This size effect, or wall thickness effect, can be justified theoretically as explained in Chapters 4 and 10, and has also been observed in some fatigue tests on plate specimens.
lo5
lo6
lo7
cycles
lo8
Fig. 8.23 SN design curves for tubular joints according to AWS, API, VERITAS and DEn. Refs. 12, 1 , 4 , 5 /
10'
Section 8.3.5 The number of cycles to failure is given versus the hot spot stress range, although generally in experimental results, the strain range is reported. The stress range has been obtained on the basis of uniaxial stress, i.e. by rnultiplying the strain range with the Young's modulus, i.e.
The true stress at the intersection, or the stress obtained by calculations, is a biaxial stress (Section 8.3.2), defined as:
It was shown in Section 8.3.2 that the biaxial stress is about 1.2 times the uniaxial stress at the hot spots of ordinary tubular joints. Thus, when
ENDURANCE (CYCLES)
Fig. 8.24 Experimental results expressed i terms of the number of cycles
to through-wall cracking, N2 . Ref. / 121
Section 8.3.5 entering SN-curves with calculated hot spot stress ranges, the results contain an inherent underestimation of the fatigue life of about factor 2. The fatigue crack growth in tubular joints shows a rather different behaviour from that of less complex welded connections. In the latter, a fatigue crack grows rather slowly in the beginning, but accelerates rapidly towards the end of the fatigue life. In tubular joints, the growth rate is nearly constant throughout the fatigue life, even when the crack depth represents a considerable fraction of the chord wall thickness. This means that even if a large crack is found in a tubular joint, a significant part of the fatigue life may still remain. Thus the presence of a sizable crack may not be immediately critical provided no significant load shedding to adjacent members has taken place and that the remaining static capacity is still sufficient to sustain the forces occurring during the design storm. In brittle materials, however, even shallow cracks may be critical.
10
10
10'
ENDURANCE ( CYCLES)
Fig. 8.25 Experimental results expressed in terms of number of cycles to end of test, Ng . Ref. / 12/
Section 8.3.5 Figs. 8.24 and 8.25 are taken from Ref. 1121 and deal with simple non-overlapping unstiffened joints. Fig. 8.24 shows the number of cycles g. 8.25 the number of cycles to end of test. which may be partially explained as follows:
-
A consistent method to measure the hot spot stress has not always been used by the experimental workers. Furthermore, inappropriate definition and approach to the measurements may lead to serious misrepresentation of the results, and to "fabrication" of undue influences. Thus, if the manner of measuring the hot spot stresses is inappropriately related to the joint dimensions, the results will "introduce" an undue fatigue size effect. Indeed, for this same reason, serious doubts have been expressed concerning the validity of the "size effect" which some of the fatigue test results seem to indicate. Side B
1
Side A
Side B
I
Side A
T= chord thickness N= 282 220 Side 6 1 Side A
T= chord thickness N= 400 000 Side B I Side A
T= chord thickness N= 488 000
T= chord thickness N= 1 005 450
Fig. 8.26 Development of a fatigue crack in an axially loaded K-joint. The depth of the crack is drawn in a scale ca. 2.6 times larger than the scale of the outer section line. Ref. 1231
Section 8.3.5
-
The influence of the notch, i.e. the stress peaks due to local discontinuities at the weld toe are not included in the hot spot stress. This local stress concentration will vary from specimen to specimen due to differences in welding process, weld shape etc., as explained in Section 8.3.2.
-
Different workers have used different failure criteria, such as throughthickness crack, crack branching into the chord wall, length of crack, specimen becoming too flexible, etc. Side A
I
Side B
T= chord t 4 ickness N= 506 070 Side A
I
1
Side B
T= c h o r d t h i c k n e s s N= 696 420
SideA
I
SldeB
T= chord tAlckness N= 616 110
SideA
I
SldeB
I
Tzchord t h i c k n e s s
N= 796 220
Fig. 8.27 Development of a fatigue crack in an axially loaded Y-joint. The depth of the crack is drawn in a scale ca. 2 -3 times larger than the scale of the outer section line. Ref. /3 1 /
Section 8.3.6 In spite of the presence of a sizable crack, the global joint stiffness remains unchanged until rather late in the fatigue life. Therefore, in a jacket structure, significant changes in the global load transfer due to early fatigue cracks are not to be expected. Fig. 8.26 shows a typical example of the fatigue crack development in a K-joint. Fig. 8.27 shows the fatigue crack development in an Y-joint, Ref. /3 11, and Fig. 8.28 shows the surface crack development in an axially loaded T-joint, Ref. 1171. The linear, non-accelerating character of crack development in tubular joints is very beneficial from a point of view of safety. It facilitates early detection and repair of cracks.
I
500.000
I
1 .000.000 1.500.000 Number o f c y c l e s
Fig. 8.28 Surface crack development in percentage of the intersection circumference in an axiallly loaded constant amplitude fatigue tested T-joint, Ref. / 171. 8.3.6
n and fabrication
With respect to joint design and fabrication the following recommendations are given to improve fatigue properties:
- Design for joint-configurations with low SCF.
-
The angle between brace and chord axes should not be less than 30" in order to enable good access for welding.
-
Due regard should be paid to local stress raising if external or the internal stiffeners are used in the design.
Section 8.3.7
-
Measures should be taken t o avoid the intersection of welding seams. Any girth- or longitudinal weld should be positioned away from incoming braces by at least twice the chord wall thickness. Otherwise post weld heat treatment and grinding of weld seams should be performed.
-
Attention should be paid to the preparation of weld grooves and the contour of the finished weld (Ref. 141). The finish of the weld toe may be improved by grinding, as explained in Chapter 6 .
-
Generally, welding of secondary members, such as brackets, fittings etc., should be avoided closer to the bracelchord connection than twice the chord- or brace-wall thickness.
- If the stress concentration is too high, it may be considered to reinforce the chord, and hence reduce local chord ovalization. 8.3.7 Procedure for fatigue evaluation of tubular joints For the prediction of fatigue life of tubular joints, a procedure based on the hot spot stress, SN-design curves and the linear cumulative damage summation is most appropriate. The hot spot stress range and stress distribution along the chordlbrace intersection should preferably be determined through FEM-calculations or tests. However, 'estimates of SCF can also be derived from parametric formulas, Section 8.3.4, but due regard should be paid to validity restrictions and the uncertainties of the results. It is recommended that the fatigue life is checked at 8 points along the bracelchord intersection (Fig. 8.29). In each point and for each load-case considered, the stresses due to the elementary load-cases, i.e. axial load, inplane bending and out-of-plane bending should be superimposed. A common practice is to use a linear superposition: ox -PISCFy 02 ox - P2 SCFy o3 = a3SCFx ox o4 = a4SCFx ox + P4SCFy o, = a, SCF, ox P5 SCFy o6 = a6SCFx ' Ox + P6SCFy o, = a7SCFx ox
0,
= a1SCFx = a2SCFx
+
omy omy + 7 2 SCFz om, -I-7 3 SCFz ' Omz omy + 7 4 SCF, om, omy omy -y,SCFz ' om, -
77 SCFZ
O
~
Z
Section 8.3.7
A x i a l load Moment Loading
a,,
SCF,
I n plane
qy,
SCF,
Fig. 8.29 Superposition of stresses in fatigue analysis of tubular joints. ox, any and a,
are maximum nominal stresses due to axial load and bending loads respecti-l ss shown in Fig. 8.2**& 106 yi m y be underst& as variabla reflecting that the hot spot stresses may occur at different places along the periphery dependent on the loading situa ig. 8.30).
AXIAL
b LOAD
b OUT
- OF - P L A N E
BENDING
b
IN
- PLANE
-
3.27
BENDING
Fig. 8.30 Distribution of principal stress in chord in a T-joint for the three basic load cases. a = 5.3,P = 0.65,y = 30,T = 0.71.
Section 8.3.8 As the SCF is only given as a maximum value without specifying the location, it is recommended that all the ai,Pi and Ti factors be set equal t o 1.0 when using the equations for design purpose. In that case maximum stresses will occur at point Nos. 2, 4, 6 and 8 , and therefore a Miner analysis should be performed with respect to these points. The calculation procedure for the Miner-analysis is described in Chapters 10 and 1 1, and the corresponding SN data for tubular joints (T-curve) are shown in Tables 1 1.1, 1 1.2 and 8.2. For unprotected joints in corrosive environment, Table 1 1.1 may be used when the resulting number of cycles is reduced with a divisor of 2. No cut off level is allowed. The thickness effect should be accounted for as described in Chapter 1 1.
8.3.8 In-service experience. Repair. In 198 1 a systematic investigation was carried out in order to prepare a review of repairs to offshore installations located on the North Western European continental shelf, Ref. 1321. The investigation included the early 1960 platforms located in 20-30 m depths as well as the typical North Sea platforms at depths of 100-1 50 m, yielding a valuable compilation of damage types and the most probable reasons for their occurrence. The investigation showed that 35% of all major repairs to offshore installations were performed t o correct metal fatigue damage. However, the reanalysis and subsequent fatigue evaluation of all the cases reported have indicated that the actual joints were underdimensioned. Fatigue damage could have been avoided if the joints had been properly designed. The reasons for the occurrence of the fatigue problems appear to be:
- Fatigue analysis of secondary structural elements, such as conductor frames, caisson manifolds, riser clamps etc., had been inadequate. 70% of all fatigue cracks occurred at such elements.
- In cases where the main structure had cracked, the main reasons appear to be increased environmental forces due to marine growth, i.e. the maintenance of the structure had been insufficient, or the value of SCF had been underestimated at the design stage. There is presently (1 984) no evidence based on cases of fatigue damage on offshore structures located on the North Western continental shelf which indicate inadequacy of present fatigue design data and procedures. However, the need for repair of tubular joints is already very substantial due to damage caused by collisions, dropped objects etc., and it is expected that this need will increase as platforms get older.
Section 8.3.9 - 8.4 Substantial research is currently being undertaken by VERITAS on proper repair procedures and data over the remaining fatigue life of repaired tubular joints. Additional research projects sponsored by the industry will begin at VERITAS in the near future:
-
Grind repairs of welded structures Grind repairs of tubular joints Improved design of grouted clamps Weld repairs of tubular joints
1984 1984-1985 1984-1 985 1985-1986
The fracture mechanics approach to predict fatigue crack propagation in tubular joints is receiving increasing interest, but is still at an early stage of development. The theory and methodology is at hand, but the tools available are not yet sufficiently powerful to deal with such complex structures as tubular joints in a systematic manner. There is a general need for more efficient FEM computer-programs to determine stress intensity factors and in particularZTor pre-processors for automatic mesh-generation that can deal with cracks of variable geometries in the model. This will reduce the high costs of element-generation by hand. A problem with the fracture mechanics approach is the paucity of relevant experimental data for the calibration of the calculation procedures. Unfortunately, in many experimental series, numerous parameters regarding the fatigue crack growth have been recorded, but there are few reported results detailing the step by step development of fatigue cracks. Nevertheless, it is anticipated, that fracture mechanics will give a significant contribution to the science of predicting fatigue crack growth in tubular joints in the future. 8.4 HEAVY DUTY JOINTS
4
With the development of offshore exploration into progressively deeper waters and arctic conditions, structures will become correspondingly larger and more demanding. In order to avoid extreme wall thicknesses with the associated heavy costs and severe problems related to fabrication and welding, designers will make increasing use of heavy duty nodes. They represent somewhat more complex node designs, but provide significant improvements in t e m s of fatigue and static strength performance. Heavy duty joints include overlapping joints, complex joints and cast steel nodes. Each type will be discussed in turn.
Section 8.4.1 8.4.1 Overlapping joints
Fig. 8.31 Photograph showing details of the intersection in an overlap K-joint tested in VERITAS' laboratories. The continuous brace is to the right. Overlapping joints are such in which part of the brace forces are directly transferred between the overlapping braces through their common weld (Fig. 8.3 1). They can be designed as uniplane - or multiplane joints. K-joints with equal brace diameters are the most common types. The geometric parameters defining an overlapping K-joint are given in Fig. 8.32 and Fig. 8.4. The joint consists of a through-brace and an overlapping brace. The gap g between the braces is negative. In the literature the nondimensional gap parameter is defined variously as: sin 8 P = g/D, gld or
*
The dimensions l1 and l2 are often used to define the weld length as shown in Fig. 8.3 2.
Section 8.4.1
1 Through brace
Over l a p p i n g brace
I
We l d concea l e d by the o v e r l a p
N e g a t i v e gap "g"
Definition of parameters applicable to overlap joints: 1, : Circumference of the portion of the considered brace which contacts the chord. 1, : The projected length of the overlapping weld (one side) measured perpendicular to the chord. 8 , : Angle between chord and through-brace. O 2 : Angle between chord and overlapping brace. g : Overlap (see sketch above). Other parameters are as for simple welded joints, see Section 8.3.1 and Fig. 8.4. Fig. 8.32 Definition of geometrical parameters for overlappingjoints.
Overlapping K-joints represent an improved design in terms of obtainable fatigue and static strength compared to ordinary K-joints, as discussed in Section 8.3.4.3. When the braces are under axial loads, SCF reductions up to 50% may be achieved. Overlapping IS-joints are being increasingly used in jack-up rigs, in which favourable strengthlweigth-ratio is an important aspect, as well as in jacket structures.
Section 8.4.1 Parametric formulas for the SCF in overlapping joints are presently not available in the literature (1984). To obtain the most benefits of the design, it is recommended that numerical stress analysis by FEM is carried out. Computer programs in which the weld is included and modelled by 3-D solid elements should be preferred. Where FEM results are not available, it has been common practice to substitute the gap parameter p = g/D in the ordinary K-joint formulas (see Kuang's formulas in Table A l ) by the value p = 0.0 1 which will give a conservative estimate of the SCF in overlapping K-joints. Systematic research into the fatigue behaviour of overlapping Kjoints were carried out at VERITAS in the years 1982-1 984. Stress analysis was carried out with the object of deriving parametric formulas for SCF. Fatigue tests were conducted in order to verify the validity of the hot spot definition and the applicability of the SN-curves to overlapping joints. Particular attention was given to the study of crack propagation rates and mode of failure of such joints. The following general comments and recommendations are based on the investigation :
- Overlapping K-joints represent a heavy duty joint type and can be designed to provide improved fatigue strength properties compared to ordinary joints.
-
Overlapping joints do not seem to represent a superior alternative to ordinary K-joints when the /3 ratio is greater than 0.85.
-
A gap parameter, p = g sine Id, greater than 0.8 should be avoided. The stress level of the "concealed" part of the joint, i.e. the througbrace chord intersection which is covered by the overlapping brace, is generally quite moderate and does not seem to represent an hazard to the safety of the connection.
- Overlapping K-joints tend to have the maximum SCF at the brace. And, the joints tested failed due to cracks developing on the brace side.
-
The mode of failure was typical for brace failures in as much as the joint failed shortly after the cracks had passed the through-thickness stage.
-
The application of overlapping joints can provide considerable benefits, provided that the design is undertaken with the necessary expertise.
Section 8.4.2.1
8.4.2 Complex joints 8.4.2.1 General Complex joints are joints in which the chord has been reinforced by various systems of welded plates or by grouting. Figs. 8.33, 8.34,8.35 and 8.36 show a number of methods of stiffening by welded reinforcement. They include: - internal ring stiffeners - external ring stiffeners - internal longitudinal stiffening ribs - internal diaphragms - through gussets - external gussets - external wing plates Generally, welded reinforcement influences the joint behaviour iri two ways:
-
The reinforcement increases the joint stiffness, reduces ovalization and reduces the general stress level.
-
The reinforcement, if not properly designed, can produce high local stiffness. This can attract force, and give rise to high local stresses.
The efficiency of welded reinforcements is quite dependent on the node type and the node's design as well as the load type. Thus, as was the case with overlapping joints, the efficiency of the reinforcement depends on the node's initial stiffness against ovalization. Reinforcements are most effective in flexible joints such as X-, T-, and Y-joints with high y-ratios and small P-ratios. Reinforcements are less effective in stiff joints. For instance, the incorporation of stiffeners and reinforcements in an overlapping K-joint of p = 1 has shown to be counter productive except in the case of out~f-planebending loads.
Fig. 8.33 Tubular joints with internal ring stiffeners. 353
Section 8.4.2.1
Fig. 8.34 Tubular joints with external ring stiffener.
Fig. 8.35 Tubular joint with through gusset plate.
r
d l agona 1
Fig. 8.36 Tubular joint stiffened by wing plates.
Section 8.4.2.2 Internal ring stiffeners are the most frequent forms of welded stiffeners. Longitudinal stiffeners are often used in conjunction with internal ring stiffeners in large complex joints as, for instance, in semi-submersible rigs. External ring stiffeners may be used in cases where access for internal welding is difficult, or in situations when post fabrication upgrading is carried out. Through gusset plates are occassionally used at lifting points. External gussets and wing plates have been used to strengthen tubular joints when static strength upgrading was deemed necessary. Gusset plates are not recommended when fatigue strength is important, because high stress concentrations may be generated at the gusset plate welds. Further research on this point is needed. r)
8.4.2.2 Ring stiffenedjoints The following general recommendations concerning the positioning of ring stiffeners are based on literature review and studies at VERITAS in 19831984. AXIAL LOADS: One stiffener : Place stiffener at the saddle position. Two stiffeners : Locate the stiffeners at a distance of 0.7 d/sine symmetrically about the brace axis intersection with the chord. Three stiffeners : Place one stiffener at the saddle position and the other two at, or near, the ends of the intersection line bracelchord. Analysis shows that a single ring stiffener can be quite effective in reducing SCF. Two stiffeners provide only a modest additional improvement, and three stiffeners provide very little further improvement. MOMENT LOADS : One stiffener : One stiffener is quite efficient for out-of-plane bending loads. However, one stiffener is not recommended in the case of in-plane bending loads. Two stiffeners : Locate the stiffeners as for axial loads. Three stiffeners : Locate the stiffeners as for axial loads. Parametric formulas for ring stiffened joints are not available. Finite element analysis or tests are required in order to determine the SCF and stress distributions. A number of "equivalent thickness" - and "smear out"
Section 8.4.2.3 approaches have been proposed for approximate evaluations of the SCF in ring stiffened joints, see Ref. 1331. However, these approaches lack numerical, or experimental substantiation. When designing ring stiffened joints, careful attention should also be given to ensure adequate strength of the weld between the chord and the stiffener. When adequatly designed stiffened joints are tested to failure under fatigue loads, they ordinarily fail by cracks developing at the hot spots at the chordlbrace intersection. The tests indicate that the hot spot stress approach and SN-curves for ordinary joints are applicable to ring stiffened joints.
8.4.2.3 Grout reinforced tubular joints A double skin Bout reinforced tubular joint and the parameters defining the joint are shown in Fig. 8.37. Double skin grout reinforced (DSGR) joints represent an efficient alternative design to joints with welded stiffeners. In both designs, the reinforcement stiffens the chord against ovalization. However, contrary to the case of local stiffeners, in DSGR joints the reinforcement is continuous and provides smooth and low peaked stress distribution.
Fig. 8.37 Double skin grout reinforced tubular joints. In new platform designs, DSGR joints can be used to very great advantage whenever a combination of superior ultimate strength and fatigue strength is required, and where added weight is not a serious detriment. Many existing structures have tubular piles driven through and grouted into the legs of the structure, thus creating a large number of DSGR joints along the legs as shown in Fig. 8.38, where the circled locations represent DSGR joints.
Section 8.4.2.3
Fig. 8.38 Locations circled represent double skin grout reinforced tubular joints in a jacket stmcture due to grouted piles throughout the leg.
Section 8.4.2.3
DSGR joints provide a number of important practical advantages which greatly enhance their use in offshore applications:
-
Grouting is a straight forward operation, which can be carried out expediently on location.
- Grouting can be carried out on short notice and does not require long fabrication time.
-
The costs involved in fabrication of grout reinforced tubular joints are considerably lower than the corresponding costs for joints reinforced by welded stiffeners.
Substantial research and development work into DSGR joints has been going on in VERITAS since 1978 with the object of gaining detailed knowledge of DSGR-joint's ultimate strength and fatigue strength behaviour, Ref. /21/. A large number of stress analyses and fatigue tests were carried out on X-, T-, Y-, K- and overlapping K-joints. Furthermore, the FEM approach has been applied with considerable success for the numerical analysis of the tested joints. DSGR tubular joints have also been investigated in the U.K. The results of VERITAS research are at present (1984) unavailable for publication. However, the following general comments can be made:
-
The grout reinforcement provides remarkable increases in the static strength of the connections, which may amount t o four fold or higher, even under tensile axial brace loads. Under compressive axial loads the DSGR-chords are virtually undestructible.
-
Remarkable SCF reductions (versus ungrouted joints) are obtainable. SCF reductions to the order of 1/3 are readily obtainable. Even larger reductions can be obtained.
- The stress concentration factor of grouted joints is load dependent. The dependency is non-linear.
-
The SCF reductions (versus ungrouted state) under compressive loads are larger than those under tensile loads.
SCF and general behaviour of DSGR joints are stable under fatigue load conditions.
- The
-
Grouted joints can be evaluated for fatigue strength using SN-curves applicable t o ungrouted joints.
Section 8.4.3
-
DSGR joints can be numerically stress analyzed. This requires the use of non-linear FEM calculations. Otherwise the SCF must be determined by laboratory tests.
-
The use of "equivalent thickness" approach to analyze DSGR joints is unsafe and should be avoided.
8.4.3 Cast steel nodes (CSN) The advantages of cast steel nodes over ordinary welded tubular joints are substantial. Cast steel nodes can be designed and fabricated to virtually arbitrary configurations and can be optimized to provide very low SCF values. Furthermore, the designs are provided with regular and smooth fillets at the bracelchord transition, a fact which further reduces the SCF and improves fatigue strength. Most important, cast steel nodes do away with welds at the locations of high SCF's, which is a major problem with ordinary tubular joints. Cast steel nodes are suitable for multi-unit - or mass production, and this is one of the reasons why they have already made their debut in jack-up rigs. Even in the case of single-unit production, CSN may be a viable and cost effective solution for joints of complex geometries and large wall thicknesses. In order to make full use of CSN, the designers should develop structures with high repeatability of nodal configurations. High quality cast steel nodes can at present be delivered by British Steel Corporation in the U.K. and Hoesch Huttenwerke in Germany. Kobe Steel in Japan has commenced development of CSN and is expected to receive certificate of approval of its concept shortly. VERITAS has carried out numerous stress analyses, photoelastic investigations and fatigue tests on prototype cast steel nodes, see Refs. / 19, 20, 221. The results of fatigue tests on 5 cast steel overlapping K-joint prototypes manufactured by Hoesch Huttenwerke can be summarized as follows:
-
The SCF in the CSN was about half the value in the comparable welded overlapping K-joint .
-
The fatigue life of the CSN was about 100 times greater than the fatigue life of comparable welded joints.
-
Local weld repairs did not seem to influence the fatigue life of the CSN.
-
Severe defects in one CSN of rejectquality influenced the fatigue life only by factor 2 compared with that of bestquality nodes.
Chapter 8. References
-
During the fatigue tests, the crack growth was found to be stable, slow and non-accelerating during the major part of the life.
Due to the variations of shapes and dimensions, no parametric equations for SCF are available. The SCF values must be determined by FEM analysis or model tests. The SN-curves for welded tubular joints are not applicable to CSN designs. SN-curves for the particular base material must be utilized. The design of CSN requires specialized expertise, and should be undertaken by, or in close cooperation with the respective foundry. REFERENCES 1. American Petroleum Institute : "Recommended Practice for Planning, Designing and Constructing Fixed Offshore Platforms". API RP2A, Thirteenth Edition 1982 Plus Supplement 1, March 1983. 2. American Welding Society : "Structural Welding Code". AWS D l , 1-82, 1982. 3 . Norwegian Petroleum Directorate :
"Regulation for the Structural Design of Fixed Structures on the Norwegian Continental Shelf ', 1977. 4. Det norske Veritas: "Rules for the Design, Construction and Inspection of Fixed Offshore Structures". DnV, 1977.
5 . Department of Energy: "Offshore Installation Guidance on Design and Construction, New Fatigue Design Guidance for Steel Welded Joints". Issue May 1982. 6. Marshall, P.W.: "General Consideration for Tubular Joint Design". Proceedings of Welding Institute Conference. Welding in Offshore Construction, Newcastle, February 1974. 7. Marshall, P.W.: "A Review of Stress Concentration Factors in Tubular Connections". Report CE-32, Shell Houston, April 1978. 8. Bouwkamp, J.G.:
"Concept of Tubular Joints Design". Proceedings ASCE, Vol. 90 no. st. 2 1964. 9. Bouwkamp, J.G.: "Tubular Joints under Alternating Loads". Proceedings, Third Conf. on Dimensioning, Hungarian Academy of Sciences, Budapest 1968.
Chapter 8. References 10. Wardenier, J.: "Hollow Section Joints". Delft University Press, 1982. 11. Graff, W.J.: "Introduction to Offshore Structures". Gulf Publishing Co., Houston 1981. 12. Department of Energy: "Background to New Design Guidance for Steel Welded Joints in Offshore Structures': March 1982. 13. Department of Energy : "Guidance on Design and Construction. New Fatigue Design Guidance for Steel Welded Joints in Offshore Structures". Revision Drafting Panel. August 1983, Issue N. 14. Kuang, J.G., Potvin, A.B. and Leick R.D.: "Stress Concentrations in Tubular Joints". Paper OTC 2205, Texas 1975. 15. Gibstein, M.B.: ''Parametric Stress Analysis of T-joints". Paper 26, European Offshore Steel Research Seminar, Cambridge, November 1978. 16. Gibstein, M.B.: "Fatigue Strength of Welded Tubular Joints". Conference Steel in Marine Structures, Paris, October 1981. 17. Gibstein, M.B.: "Fatigue Failures of T-joints". European Offshore Steel Research Seminar, Cambridge, November 1978. 18. Gibstein, M.B.: "Stress Concentration in Tubular Joints, its Definitions, Determination and Application". Conference Steel in Marine Structures, Paris, 1981. 19. Gibstein, M.B. and Harsem, 0.: "Consideration concerning Strength Evaluation of Prefabricated Cast Steel Nodes". yeritas Report No. 77-247,1977. 20. Gibstein, M.B.:
"Photoelastic Stress Analysis of Cast Stee1 K-node Designed by Hoesch. Veritas Report 81-0023,1981. 21. Gibstein, M.B.: "Double Skin Grout Reinforced Tubular Joints". Proposal for Joint Industry Project. Veritas 1983. 22. Moe, E.T .,Gibstein, M.B. and Kristiansen, P. : "Stress Analysis and Fatigue Testing of Cast Steel K-Nodes". Veritas Report No. 82-1096,1982.
23. Moe, E.T. and Gibstein, M.B.: "Stress Analysis and Fatigue Failure of K-joint". Veritas Report No. 80-1 127, 1980.
Chapter 8. References 24. Bberg, T.: "Stress Analysis of Overlapping Tubular K-joints". Veritas Report 83-0249, 1983. 25. Laursen, H.K. and Bberg, T.: "Stress Analysis of Tubular K-Joints with Diameter Ratio 82-0407.
P = 1. Veritas Report No.
26. Wordsworth, A.C., Smedley, G.P.: "Stress Concentrations at Unstiffened Tubular Joints". Paper 3 1, European Offshore Steel Research Seminar, Cambridge, Nov. 1978.
27. Wordsworth, A.C.: "Stress Concentration Factors at K - and KT Tubular Joints". Proceedings Fatigue in Offshore Structural Steels, London Fabruary 1981. 28. Gantke, F.: "Design Concept of Cast Steel Nodes". Conference Steel in Marine Structures, Paris,
1981. 29. Edwards, C.D. and Fessler, H. : "Design and Stress Analysis of a Cast 90°-45' K-joint". Conference Steel in Marine Structures, Paris, October 1981. 30. Rodabaugh, E.C. : "Review of Data Relevant to the Design of Tubular Joints for Use in Fixed Offshore Platforms". Welding Research Council Bulletin 256, New York. 3 1. Moe, E.T. and Gibstein, M.B.: "Fatigue Failure of Y-Joint". Veritas Report No. 80-0796
32. Repairs to North Sea Offshore Structures - A Review UEG Report UR21. 33. Complex Joints and Loading Fatigue Study.
Lloyds Register of Shipping. Report No. OSG/T3/83001. 34. PMBSHELL. Tubular Joint Analysis Program. Phase 11: Program Verification. PMB Systems Engineering Inc. 3 5. Tubular Joint Analysis Program (TUJAP). Program Description. Cornputas, October 1983.
APPENDIX A
Parametric formulas for stress concentration factors
Table A4
RECOMMENDED STRESS AXIAL LOAD
+:4-&
-1
~ g c y [1.5
,
- 3.88(0 - 0.47)~1.
.
sh1.694 8
-
z
X
1.35
~-1
1.51
-
7 r W2.42 2.28 p2.2) ~ i n f l ~ ( ~ ' - ~ ~ . ~ f l ) O
C kU U
m
.yo.67. p-o.s9, ,1.1, po.067, sh1.52 e
,30°
.
1-83 y0.54. p . 1 2 . 71.07,
13.8
K-3
.
0-0.36. 70.68. (P,+P2)0.13. sin2'98, 45"
4-89 y0.12. 0-0-4. ,0.68.
+~~)0.16 sin2-27 . B
The following reduction may be performed for all brace side SCF's with exception o f X-, Y- and T-joints:
0.5T
+
a
SCFbrace
) but not less than 0.7
should not be taken less than 2.5.
< 0 < 90"
Table A4
CONCENTRATION FORMULAS
[0.95 - 0.65@- 0.41)~]
7°.29-
sin0.218
0.794+ 0.63 SCFc 2-83. P-0.35.
p.76 - 1.92(p- 0.72)']
0.794
To.3s, sino.s
e
+ 0.63
,0°<8<900
SCFC
See T & Y
See K-1
See T & Y
See K-1
SeeT&Y
RANGE OF VALIDITY T & Y-TYPE
X-TYPE
K-TYPE
r0-47*sin2.038
<
APPLICATION
KUANG'S STRESS CONCENTRATION FORMULAS /
Chord
Brace SCF = 4.076
-
I
/
-
I
1
. yo-55. e - 1 . 3 5 ~ 3 . ,.
2 . sinl.94 8
Chord
Brace
.
SCF = 1.301 y0.23. 0-0.38. +).38. si,0.21 8 Chord
. S C F = 0.462 . r l . 0 1 4 .
SCF = 1.024 +.014. 0 0.787. 70.889. ,i,1.557 8
Brace
p-0.619. ,0.889,
sinl.557 8
SCF = 1-52. y0-852. 00 .801. 70.543. ,i,2.033 8
1
/
Chord
VALIDITY RANGE see e n d of table
APPLICATION
KUANG'S STRESS CONCENTRATION FORMULAS Chord SCF= 1 8 3 . y o - 5 4 . P 0.12. ,-1.068,
I
Brace normal to chord and inclined SCF = 4-80. y0-123. P-0.396. ,0.672, @1+p2)0.1S9. sin2.267 8 2
SCF = 6.056
1
I
Chord
.To.'. 0-0.36. p . 6 8 . (Pi + P 2 ) ~ . 1 2 6 . sin^.^ 8
VALIDITY RANGE I1
oO
G
+
e c
900
I1 +
o0 g e
G 450
I
Table A2
Table A2
Table A3
CHAPTER 9
UNSTABLE FRACTURE Stephen ~latcher*and Jon ~ereim** * ~ e r i t a sResearch, Oslo, * * ~ e tnorske Veritas, Oslo
ABSTRACT Various failure modes that may represent the end of the fatigue lifetime are mentioned. Most of the chapter concentrates on the failure mode of unstable fracture. Simple methods for calculating the critical combinations of load and crack length are described and illustrated by examples. The material property that is required in these calculations is fracture toughness, the definition of which is very closely linked to the testing procedures. For this reason the testing procedures are briefly described, and examples of test result calculations are included. Because fracture toughness can be very sensitive to small changes in conditions (e.g. temperature), some of the factors that influence fracture toughness are discussed in the final section of this chapter.
9.1 FAILURE MODES Fatigue failure occurs when a fatigue crack grows to a length that leads to failure of the structure. There are at least four possible failure modes for a structure or component:
O V n s t a b l e fracture: Unstable fracture occurs when a critical combination of tensile load and crack length is attained, and is the failure mode given most consideration in this chapter. a* Plastic collapse: This is also considered briefly, in Section 9.5.3. Buckling: Fatigue crack growth can significantly reduce the buckling load of a structure. Some guidelines for the inclusion of the effect of cracks on the buckling load are given in PD 6493 (Ref. / 11). Leakage: This will occur if a fatigue crack grows through the thickness &t of a container or pipe.
Section 9.2
9.2 MODES OF UNSTABLE FRACTURE When a cracked structure is loaded, there are three possible modes of fracture for metals:
1 . Brittle fracture (Fig. 9.2): The body behaves in a linear-elastic fashion right up to the point of fracture. In other words, the macroscopic behaviour of the body is brittle. In such cases, the microscopic mode of fracture is usually also brittle and is known as cleavage fracture.
A
i s the displacement b e t w e e n two points ( e . g . A , B ) on either s ~ d eo f the c r a c k
Fig. 9.1 Definitions of P and A to be used in Figs. 9.2-9.4.
Fig. 9.2 Brittle fracture - macroscopic fracture behaviour, and fractograph showing a cleavage fracture (see Fig. 9.1 for definitions of P and A).
Section 9.2
/
Fracture
Elastic-plastic behav i our
------
t
Fig. 9.3
Linear-elast i c behav i our
Elastic-plastic behaviour with cleavage instability - macroscopic behaviour, and fractograph showing a cleavage fracture (see Fig. 9.1 for definitions of P and A).
P o i n t where f i b r o u s crack s t a r t s t o extend
Fig. 9.4 Failure by fibrous crack growth and plastic collapse - macroscopic behaviour, and fractograph showing a ductile fracture (see Fig. 9.1 for definitions of P and A). 2. Elastic-plastic behaviour with cleavage instability (Fig. 9.3): The structure shows some degree of macroscopic plasticity before fracture. However, the final fracture, which may be preceded by a small amount of ductile crack growth, is by cleavage, i.e. it is microscopically brittle.
Section 9.3.1 Failure by ductile crack growth and plastic collapse (Fig. 9.4): In this case the fracture is ductile in both a macroscopic and microscopic sense. As the load increases and the net section ligament deforms plastically, the fibrous crack extends in a stable fashion, until a point is reached when the rate of reduction of load bearing capacity due to crack growth is equal to the rate of work hardening. At this point the load reaches a maximum value. If the load is not dropped, the system will become unstable at this point, and the structure will fail by a combination of unstable fracture and plastic collapse.
9.3
TOUGHNESS PARAMETERS
9.3.1 Charpy toughness Notched bar impact testing is often used to determine the susceptibility of steels to brittle fracture. By using a notched test piece and impact loading, brittle fracture is encouraged in the steel, and therefore the test is able to give reasonable indications of how brittle the steel would be in service. The notched bar impact test that has found most general acceptance is the Charpy V-notch test. To obtain the maximum amount of information, a full transition curve should be established, Fig. 9.5 (Ref. /2/).The region of interest is the transition regime. Here the fracture mode changes from a low energy absorbing mode that involves cleavage fracture and little plastic deformation, to a high
-80
-60 -40 -20 0 20 40 Test temperature ( " c )
Fig. 9.5 Example of a Charpy V-notch transition curve for the weld metal of an E70 16 type electrode (Ref. 121).
Section 9.3.2 energy absorbing mode that involves ductile fracture and considerably more plastic deformation. One way of characterising a steel by the Charpy V-notch test is to determine the temperature at which this transition in properties takes place. The Charpy V-notch test is also applied as a simple quality control test by merely specifying a minimum allowable energy absorption at a particular temperature. It is used in a similar way as a welding procedure acceptance test. For this purpose, the required Charpy toughness should depend on the strength of the weldrnent, and the test temperature should be related to the design temperature. It should be emphasized that the only way that Charpy test results may be used in design is through empirical methods based on prior experience. It is not advisable to extrapolate these empirical methods to new situations. For quantitative engineering design against fracture, it is preferable to use an approach based on fracture mechanics. 9.3.2 Fracture mechanics parameters to characterise unstable fracture
As explained in Chapter 3, bor&~d M y is a function of the s
acting on the body, the size of tho md geometry of the crack and the bod#. If the structure behaves in
r-elastic fashion prior to fracture, the fracture will initiate from a preexisting crack or sharp defect when the stress intensity factor reaches a critical value. If the body shows a significant amount of plasticity, the stress intensity factor approach becomes invalid and an elastic-plastic fracture mechanics parameter must be used to describe the crack tip stresses and strains. The parameters most widely used are the J-integral and the crack tip opening displacement (CTOD), also referred to as the crack opening displacement (COD). Although there now exist engineering methods for the application of the J-integral (Refs. 13-51), they have not yet reached the same level of recognition by standardising institutions as K and CTOD based methods. For this reason the J-integral will not be discussed further in this chapter. Physically, the CTOD is the displacement of the crack surfaces, as measured at the position of the original crack tip (Fig. 9.6). Like the stress intensity factor, the mOl3 38 ahw a function of the on the body, ahkk size, aMil She @metry of the crack and structure:' The CTOD describes the crack tip stresses and strains both before and after significant amounts of yielding (if the yielded area is surrounded by material that has experienced only elastic deformation), and therefore fracture occurs at a
Section 9.4 F o r z e r o load, t h e r e i s no c r a c k opening
On a p p l i c a t i o n o f the c r a c k opens
load,
Fig. 9.6 Definition of the crack tip opening displacement ( 6 ) . It is defined to be the displacement of the crack surfaces at the position of the original crack tip.
critical value of CTOD. Unlike the stress intensity factor which is usually related t o stresses acting on the body, the CTOD is conventionally related to strains. Rigorous relationships between the CTOD, strains and crack size are unfortunately not readily available for most geometries, but by making suitable approximations, the CTOD has proved to be valuable in establishing defect acceptance criteria (see Section 9.5). The principle behind the use of fracture mechanics is the same for both the K and the CTOD approach. Namely, the critical values of K or CTOD are determined using small scale tests. Then, by using these critical values and a knowledge of the defect sizes and shapes present, critical loads may be calculated for the structure of interest. Alternatively, knowing the loads to which the structure will be subjected, maximum allowable defect sizes can be calculated. These procedures will be discussed in more detail in Sections 9.4 and 9.5.
9.4 FRACTURE TOUGHNESS (KI, AND CTOD) TESTING
The procedures for fracture mechanics testing are relatively sophisticated and therefore only a brief summary can be given here. For full details, the relevant testing standards should be consulted. For KI, testing, it is probably best to consult either the ASTM standard E 399 (Ref. 161) or the British Standard BS 5447 (Ref. 171). The two standards differ in detail but are essentially the same. For CTOD testing the British Standard BS 5762 (Ref. /8/) is usually used. The theoretical background for fracture toughness testing and fracture mechanics design are dealt with in Chapter 3 in this book.
Section 9.4.1
9.4.1 KI,testing According to the standards, two test piece types may be used; the compact tension test piece or the bend test piece. The bend test piece uses somewhat more material, but is cheaper to machine. If welds are being tested, then the compact tension geometry usually gives no saving in the length of weld per test piece, making the bend test piece the usual choice. In Figs. 9.7 and 9.8 these test pieces and the modes of loading are illustrated, and the symbols describing the test piece dimensions are defined.
Width = W Thickness B 0.5W Half loading s an = L E f f e c t i v e cracR length Load = P
= 2W = a
0.45~-0.55~
Fig. 9.7 Standard bend test piece for fracture toughness testing.
Net w i d t h = W Total width C = 1.25W B r e a d t h = B = 0.5W H a l f h e i g h t = H = 0.6W E f f e c t i v e crack length = a = 0.45W-0.55W Load = P
Fig. 9.8 Standard compact tension test piece for fracture toughness testing.
Section 9.4.1 Before testing, a sharp fatigue crack is grown from the notch to a depth of approximately 0.5W.To ensure consistent KI, values, the standards specify maximum fatigue loads. Then the test piece is loaded monotonically at a rate that is slow enough to avoid dynamic effects. The displacement across the notch mouth is measured by means of a clip gauge (Fig. 9.9) and plotted against load on an X-Y recorder. This is done for two reasons; to verify that the test piece behaves in a linear elastic fashion prior to fracture (as in Fig. 9.2), and to help determine the load at which fracture initiates.
gauge
Output
x-ax i s
plotter
Fig. 9.9 Schematic diagram of the knife edge and clip gauge arrangement used to measure the notch-mouth opening displacement in a fracture toughness test.
After testing, the crack length, a, is measured on the fracture surface and a provisional KIc value, KQ, is calculated:
where PQ is the load at fracture initiation, and Y is a function of a/W given in the testing standards. The dimensions of the test piece that ensure plane strain conditions, and a valid KIc , test are given by :
I?[
2
a and I3 2 2.5
If all the requirements of a KIc testing standard have been met, the KQ value may then be called a ISI, value.
Section 9.4.1
A valid KIc value is a material property that may depend on the orientation of the test piece. However, if the ISI, value is invalid, it may be dependent on parameters such as the test piece thickness or the fatigue pre-cracking loads. Invalid KIc values may be useful, but they should be employed with great caution and a knowledge of the errors likely to arise. If a KI, test has proved to be invalid, it is usually preferable to calculate a CTOD value for the material, rather than merely quote an invalid KIc value. The KIc and CTOD test procedures are almost identical, so it is no problem to reanalyse an invalid KIc test in terms of CTOD, providing the displacement axis of the test record is calibrated.
EXAMPLE 1: Calculation of KIc . The KI, value of a high strength low alloy steel of yield strength 1580 MPa is required. A standard bend test piece of width 50 mm is machined, fatigue pre-cracked and tested. The load rose to a maximum value of 3 1.6 kN, where there was a rapid load drop indicating that fracture initiation had taken place. The crack length was measured and found to be 25.7 1 mm. a = W = B = Pa= Re =
25.71 mm 50.00mm 25 .OO mm 31.6 kN
1580 MPa
Solution. a/W = 0.5 14, therefore using the table in E 399 or BS 5447, Y = 11.1 1.
We must now ascertain whether or not the test is valid. We will assume that all the necessary checks on the maximum fatigue load, quality of the fatigue pre-crack, and the linearity of the test record have been made.
As both the crack length and test piece thickness are greater than 4 mm, the test piece is large enough to make the test valid, and the KQ value may be quoted as a Krc value.
Section 9.4.2
9.4.2 CTOD testing For lower yield strength materials, the test piece size requirements for a valid KIc test become restrictive due to testing machine capacity and the availability of material in sufficiently thick sections. The CTOD test was developed to provide a more convenient test that is of greater practical significance for lower strength, tougher materials. It is relevant to those situations described under points (2) and (3) in Section 9.2. According to BS 5762, three point bend test pieces are to be used for CTOD testing. The dimensions are not rigidly specified but the geometry illustrated in Fig. 9.7, with the test piece thickness equal to the plate thickness, is preferred. The CTOD testing procedure is basically as for KIc testing, the main difference being that the notch-mouth opening displacement axis of the test record must be calibrated. If the fracture initiated from the fatigue pre-crack tip as a cleavage fracture, the critical CTOD value should be denoted by 6,. If the fracture initiated from the fatigue pre-crack by stable ductile crack growth, and cleavage fracture subsequently initiated from the ductile crack, the critical CTOD value should be denoted by 6,. In both these cases the load versus notch-mouth opening displacement plot will look like that in Fig. 9.10. The two cases may be distinguished by examination of the fracture surfaces. If the final fracture occurs solely by fibrous crack growth, the critical CTOD should be denoted by 6,. In this case, the load versus notch-mouth opening displacement plot will be similar to that shown in Fig. 9.1 1. The CTOD at the initiation of ductile crack extension, denoted by ai, is more difficult to measure and apply, and will not be considered further here. Load
/
P
Notch-mout h opening displacement
Fig. 9.10 Schematic test record for a CTOD test that gives a 6, or 6, value.
Section 9.4.2 Load
1
P
,
,/Measurement p o i n t ( f i r s t attainment o f maximum l o a d )
ine constructed p a r a l l e l t o Loading
,
Notch-mouth
opening
line
displacement
Fig. 9.1 1 Schematic test record for a CTOD test that gives a ,6
value.
If a 6, value is to be calculated, the load, P, and the plastic notchmouth opening displacement, Vp, are measured as shown in Fig. 9.10, and the crack length, a, is measured from the notch mouth to the tip of the precrack. If a 6, value is to be calculated, P and Vp are measured as shown in Fig. 9.1 0, but the crack length is measured to the tip of the ductile crack. If a 6, value is to be calculated, then P and Vp are measured at the first attainment of maximum load as shown in Fig. 9.1 1, and the crack length is measured to the tip of the pre-crack. K is calculated using
and the CTOD (6,, 6 , or ) , 6
by
where v is Poisson's ratio, Re is the yield strength, E is Young's modulus, and B and W are defined in Fig. 9.7, and z in Fig. 9.9. The first term of Equation (9.4) represents the CTOD due to the elastic deformation of the test piece, and the second term the CTOD due to the plastic deformation. EXAMPLE 2 : Calculation of CTOD . A full-thickness test piece of the preferred geometry was taken from a 20 mm thick plate of a structural steel with a yield strength of 450 MPa. After fatigue pre-cracking and testing according to BS 5762, the fracture surface was
Section 9.5 - 9.5.1 examined. There was a small amount of fibrous crack growth before the cleavage fracture, and the distance from the notch mouth to the tip of the fibrous crack was 22.5 1 mm. The load at which the cleavage instability occurred was 18.2 kN, and the plastic notch-mouth opening displacement was 0.81 5 mm. The knife edge height was 3 mm. What was the critical CTOD value of this steel? a W B z P
= 22.51 mm = 40 mm (W = 2B)
= 20 mm = 3mm = 18.2 kN
Vp= 0.815 mm R e = 450 MPa Assume : E = 200 GPa v = 0.3
SoEution. a/W = 0.563, which according to the table in BS 5762 gives Y = 13.14.
As there was some fibrous crack growth prior t o the cleavage fracture, the critical CTOD value should be quoted as a 6, value.
9.5
APPLICATION OF FRACTURE MECHANICS TO UNSTABLE FRACTURE
There are now several more or less standardised methods for assessing the risk
of unstable fracture (Refs. / 1, 3-5 and 9-1 61). In this section a brief description of the principles behind some of these methods will be given, together with examples to illustrate how the principles may be applied in simple practical situations.
9.5.1 The stress intensity factor approach This approach, which is the basis of many fracture mechanics design and
Section 1 1.5.3
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..
..I
.. .. .. .. .. .. .. ..
.. .. .. .. .. .. .. ..
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.. .. .. .. .. .. .. .. . . .. .. . . . . . .. .. .. .. .. .. .. .. .. .. ............................................................ . . . . . . . . .. .. .. .. .. .. .. .. . . . . . . . . ...................................................................................... . . . . . . . . . . . . . . . . ...........................................................................................
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-
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--a-.-.-
r..--.r
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-
L
#
A
.%
a-
..... .. .. .. .. .. .. .. ........................ .. .. --... .. .. .. .. .....--..-. .._ ................... .. .. .. .. ............. .. .. .. .. ... ... ... ... ... ... ... . . .----. . . ............ . . . . .-.............................. .. .. .. .. .. .. .. .. ... ... ... ... ... ... ... ... . . . . . . . ec ................................... . ................ ..... ............-....-.. ..... ............. .... ... . . . . . . . . .. ...,. .. .. ............... .. .. .. .. .. .. .. .. .. .. .. .. ........... ............................................... . . .,. ................. . . . . . . . . . . . . .................................. . . . . . . . . . . . . . . .
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t
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2
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- 4 . .
1
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a
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Fig. 11.18 Tubular joints in air. Surface cracks at the weld toe. m = 3.1. Ref. /8/.
1
1
1
Section 9.5.1 9% Ni steel. Fracture mechanics testing was carried out on the steel at the design temperature of -155°C. At the lower bound of a large scatter band, valid KI, values of 75 MPa fi were obtained. If the design stress, od, of the tank is 150 MPa, at what length could a through-thickness fatigue crack become critical?
Solution. We will assume here that the case may be treated as a through-thickness crack in an infinite plate subjected t o uniform tensile stresses (F= I):
where a is the half-length of the crack. Unstable fracture occurs when a reaches its critical value, ac,it. This may be calculated from the critical form of the above equation:
i.e. the total length of the critical crack is 160 mm. This value is unacceptably small; after the discovery of a crack, there should be enough time for the tanker to get to a harbour before the crack grows to a critical size. It may be concluded that another steel should be selected for the LNG tank. Note that assuming F = 1 actually gives an slightly unconservative analysis (see Fig. 20 1 of Ref. / 191). EXAMPLE 4: Calculation of the critical defect size in a large rotor forging.
A fatigue crack initiates from an irregularity on the surface of a large rotor forging. The maximum stress, rrd, in the region of the crack is 800 MPa, and the KI, of the forging steel is 1 15 MPa fi. The crack grows as a semi-circle. At what crack depth will the rotor fail? Solution. We will use the notation in Fig. 9.1 3 (Ref. /19/). The rotor forging is large, therefore c/b is approximately zero. Also the crack is semi-circular, so c/a = 1. From Fig. 9.13 it can be seen that in this case &/KO = 0.65. From the equation in Fig. 9.13 it can be seen that
Section 9.5.1
9.13 F factors (ISI/% = F) to give the stress intensity factor at point A on a semi-elliptical crack subjected to a uniaxial tensile stress (figure taken from Ref. 1191).
Section 9.5.2 which is actually Equation 9.5 with different notation. The critical form may be written: KIc = (KI/Ko) Od
KI,
cc=l (KI/Ko) .[
'4- ] ' = + . 0.65 [ ~ ~800 ] ~ . 1 0 3 = 1 6 ~ ~ Od
9.5.2 The CTOD design curve
In this semi-empirical approach which is used in PD 6493 (Ref. /I/), the critical CTOD value (here called 6, even if it is actually a 6, or ,6 value) is related to the strain e in the region of the crack, and the maximum allow-
able defect size, am. The design curve incorporates a degree of conservatism so is not a critical crack size, but represents a crack size that may be safely tolerated. Also note that refers to the half-length of a throughthickness defect in an infinite plate loaded in tension. If the actual configurakvalue must be converted tion differs significantly from this situation, the to a defect size for the actual situation such that the defects in both cases have equal severities. This process will be illustrated by example at the end of this section. The critical CTOD values to be used in the CTOD design curve should be obtained using full-thickness test pieces of the preferred geometry, as described in Section 9.4.2. It is common practice to run three parallel CTOD tests and use the lowest measured critical CTOD value. Due to the design curve's empirical basis, in some cases the analysis may be extremely conservative, with safety factors as high as 20; in other - will be very close to the critical crack size. The main advantage of cases a, the CTOD design curve is that it is relatively simple to use, and if the result indicates that the weld or structure is satisfactory, a more complicated analysis is unnecessary. The CTOD design curve actually takes the form of a plot of 4 against the applied strain normalised by the yield strain, e/ey, where 4 is the dimensionless CTOD and defined by
a
=
2) c
-
2 * r 0 e y*amdX
The design curve is defined by = (~/e,)* for 4 = (€ley) - 0.25
for e/ey
< 0.5 > 0.5
The CTOD design curve is illustrated in Fig. 9.1 4.
Section 9.5.2
Fig. 9.14 The CTOD design curve, 8 = Sc/2
T
-
ey am.
EXAMPLE 5 : Calculation of maximum allowable crack size in an LNG tank. Another candidate material, also a 9%Ni steel, with Re = 800 MPa, was tested for possible use in the LNG tank described in Example 3 in Section 9.5.1. None of the fracture toughness tests gave a valid KIc value, the lower bound of the critical CTOD values being 0.28 mm. Estimate the maximum allowable fatigue crack size. Solution. As the design stress does not exceed the elastic limit:
The dimensionless CTOD : Q , = --ti c
2*n*ey*a,
e/ey
-
0.28 l o 3 -200 1o3 - 0.01 11 assuming 2*n.800*-+ amax E = 200 GPa
< 0.5, therefore use the relationship
The maximum allowable crack size is therefore 640 mm.
Section 9.5.2
EXAMPLE 6: Calculation of the maximum allowable defect size in a butt weld. Ultrasonic inspection revealed a crack located in the weld metal of a stress relieved butt weld in a 150 mm thick plate. It was a surface crack with an aspect ratio c/a of approximately one (Fig. 9.1 3). The yield stress of the weld metal is 470 MPa and its minimum critical CTOD was determined to be 0.36 mm. To what depth may the crack be allowed to grow before the structure is replaced? Assume that the weldment is loaded in uniaxial tension perpendicular t o the crack plane, and that the stress in the weldment does not exceed 0.75 of the yield stress of the weld metal.
Solution. e/ey = 0.75
e/ey > 0.5, therefore use the relationship
a = ( e / e y ) - 0 . 2 5 ~ 0.0244 amax - = 0.049 m = 49 mm a,
= 0.75 -0.25
This now needs to be converted to the crack depth of a semi-circular surface crack of equal severity. The assumption is usually made that cracks of equal severity have the same stress intensity factors for uniform tensile loading, regardless of whether or not the actual loading causes significant plasticity. For the through-thickness crack of half-length Z in an infinite plate subjected to uniaxial tension, F is equal to one, i.e.
K= o e J Z But for any other crack geometry subjected to uniaxial stresses, F is not generally equal to one, and must therefore be included in the formula that relates K to the crack depth c:
Now if the cracks of half-length same stress,
and depth c are of equal severity for the
Section 9.5.3 In this example the aspect ratio of the crack will remain reasonably constant as it grows. According to Fig. 9.13, F is approximately 0.7 for a/c = 1, and c/b values of about 0.75. Therefore, the maximum allowable crack depth c is 100 mm. 9.5.3 The R6 failure assessment diagram
The COD design curve allows cracks to be assessed with respect to unstable fracture, but does not make any allowance for the fact that the presence of a crack will also reduce the plastic collapse load of the structure by reducing the net cross-sectional area. For long cracks in rather tough materials, plastic collapse will be the predominant failure mode, and this fact should be allowed for in design and defect assessment. While the check for plastic collapse should be performed as a separate step in addition to a K based or CTOD design curve analysis, the R6 failure assessment diagram (also known as the CEGB or CERL failure assessment diagram) combines the criteria for brittle fracture and plastic collapse into a single procedure (Ref. / I I/). Two parameters are considered in the R6 procedure; K, and S, :
K, = stress intensity factor
fracture toughness applied load (stress o or pressure P) S , =collapse load (stress ol or pressure PI )
Some examples of plastic collapse solutions for simple pressure vessel geometries are given below. The pressure vessels are of internal radius R1 and external radius R2,and contain a long surface crack of depth a. The flow stress, of, is usually taken to be the mean of the yield stress Re and the ultimate tensile strength R, . Internal axial crack:
External axial crack:
Internal circumferential crack:
Section 9.5.3
External circumferential crack:
See Ref / 1 I / for other plastic collapse solutions. Like the CTOD design curve, the R6 failure assessment diagram has a semi-empirical basis. It is based on a 'strip yielding model' that, strictly speaking, is only applicable to thin sections of materials that do not work-harden. However it has been demonstrated that the R6 diagram provides an approximate lower bound solution for practical situations. It takes the form of the failure locus that is illustrated in Fig. 9.1 5 and expressed mathematically by
u
0 . 2 0.4
0.6
0.8
1.0
1.2
sr Fig. 9.15 The R6 failure assessment diagram. K, is the ratio of K to KIc and S, is the ratio of load t o limit load (Ref. 1111).
To use the failure assessment diagram, values of K, and S, must be calculated for the structure under consideration. If the point (S,, K,) lies with-
in the failure locus the structure will be safe, but if it lies outside the failure locus the structure will be unsafe. A useful concept that may be derived from the R6 procedure is the load factor, L:
Section 9.5.3
where OA and OB are defined in Fig. 9.1 5 for a given K, and S, . The load factor is the safety factor on the applied load, and enables the relative safety of various situations to be quantified. If L is less than one, the situation is unsafe. If L is greater than one, the situation is safe and the higher the value of L the greater the degree of conservatism.
EXAMPLE 7: Calculation of the critical defect size in a pressure vessel. A cylindrical pressure vessel of internal radius 5.00 m and external radius 5.25 m contains a long axial external surface crack, which is growing by fatigue. The steel from which the pressure vessel is constructed has a yield strength of 340 MPa, a UTS of 460 MPa, and a KI, of 100 MPa*. If the maximum pressure inside the vessel is 5 MPa, what is the crack length at which failure of the vessel will occur? Solution. We will calculate S, and K, for the crack depths: a = 0.08, 0.09, 0.10, 0.11 and 0.12 m.
Use Equation 9.12 to calculate Pl ,where Of
1
= - (Re 2
+ R,)
= 400 MPa
The S, values for the various crack lengths are shown in Table 9.1.
Table 9.1.
Section 9.5.3
Fig. 9.16 Stress intensity factors for an external radial edge crack subjected to a uniform internal pressure (Ref. / 191).
Section 9.5.4
To calculate K for the various crack lengths, use Fig. 9.16 (Ref. 1191). From this figure it can be seen that K (called K1 in the figure) is given by
Substituting for P, R1 , and R2,gives
R1/R2= 0.95, therefore the factor KI/KO, as a function of a/(Rz - R1), must be read off this curve in Fig. 9.16. The K, values for the various crack lengths are shown in Table 9.2. Table 9.2.
Each crack length thus corresponds to a point (S,, K,) on the R6 failure assessment diagram. These points are plotted in Fig. 9.17, where it can be seen that the failure boundary is reached when the crack reaches a depth of approximately 0.105 m. Also it may be seen that the pressure vessel is predicted to fail at a load considerably lower than its plastic collapse load, and at a K value slightly lower than its KI,. 9.5.4 Stress concentrations and residual stresses If the crack under consideration is close to a stress concentrator (e.g. a hole, notch or weld toe), this must be allowed for in the calculation of the stress intensity factors for use in a K based procedure. For some cases, the appropriate F factor for the actual stress concentrating geometry may be available. Otherwise, stress intensity factors may be estimated from a knowledge of the stress concentration factor, SCF. Take the example of a short crack
Section 9.5.4
'3r
Fig. 9.17 The R6 failure assessment diagram with points representing a growing crack at constant load. growing from a circular hole in an infinite plate (Fig. 9.18). Here, the stress concentration factor is 3; i.e. the stresses at the edge of the hole are raised by a factor of three. Thus the situation in Fig. 9.18 may be approximated by that in Fig. 9.19 for which the F factor is readily available (F = 1 .12 for an edge crack in a semi-infinite plate with remote tensile loading). However, as the distance from the edge of the stress concentrator increases, the stresses fall off rather rapidly, so this approach can be very conservative for longer d
d
Fig. 9.18 Small crack at a large hole in an infinite plate with a uniaxial tensile stress, o.
Section 9.5.4
Fig. 9.19 Equivalent situation to that in Fig. 9.18 - small edge crack in a semiinfinite plate with a uniaxial tensile stress of 30. cracks. If the crack is long compared with the size of the stress concentrator, the effect of the stress concentrator may be ignored completely; e.g. if a crack at the toe of a fillet weld is greater than 0.15 of the thickness of the plate it is growing into, the stress concentrating effect of the weld geometry may be ignored (PD 6493, Ref. /I/). For cracks of intermediate length a knowledge of the F factors for the geometry in question are necessary for an accurate analysis. When using the CTOD design curve for cracks in the presence of a stress concentrator, the nominal applied strain is usually assumed to be raised by a factor equal to the SCF, providing this does not increase the strain to a value greater than 2ey (PD 6493, Ref. / 1I),in which case a full elastic-plastic stress analysis should preferably be performed. It is also important to consider residual stresses in design against brittle fracture. For welds that have not been stress relieved, it is common practice to assume that the residual stresses are of yield strength magnitude. The residual stresses must be added to the applied stresses to give the stress that is to be used in the calculation of the stress intensity factors. Adding the residual stresses to the applied stresses will probably give stresses that are high enough to cause extensive crack tip plasticity, invalidating a K based design approach. Therefore 'plastic zone correction factors' may be used to allow for the plastic deformation, as described in the R6 procedure (Ref. /11/) for example. When using the CTOD design curve, it is recommended that the estimated residual stresses, o, be converted to strains using Young's modulus, and added to the applied strain eapp, to give the E to be used in the procedure.
Section 9.6
-
9.6.1
EXAMPLE 8: Calculation of maximum allowable size for a crack in the weld metal of an as-welded fillet weld. A surface fatigue crack has been found growing from the toe of an as-welded fillet weld into the base plate material. The yield strength of the base plate material is 360 MPa and its critical CTOD value at the design temperature is 0.46 mm. Given that the nominal strain to which the plate is subjected is 0.6 of the yield strain and that the SCF at the toe is 2.5, calculate the depth to which the crack may be allowed to grow.
Solution. E
= (eapp SCF)
+ ((rres/E)= 0.6
cy 2.5
+ ey = 2.5
ey
> 0.5, therefore use the relationship
E / E ~
-a,
= 0.018 m = 18 mm
This defect size must then be converted to a surface crack defect size of the appropriate geometry using the procedure given in Example 6, Section 9.5.2.
9.6
FACTORS AFFECTING FRACTURE TOUGHNESS
There are many ways in which the fracture toughness, and hence fatigue life, may be influenced; some of these will be briefly discussed here. 9.6.1 Thickness
If toughness is defined as the K value, Kc, at which the initiation of fracture occurs, then the toughness can vary with test piece thickness (Fig. 9.20). However, for test pieces greater than a certain thickness, the Kc value is constant and called the plain strain fracture toughness, KIc. Similar effects are also found if critical CTOD values are plotted against plate thickness (Fig. 9.21, Ref. 1201). This variation of CTOD with thickness partly explains why the thickness of the preferred CTOD test piece is equal to the plate thickness.
Section 9.6.2
Fig. 9.20 Showing the variation of Kc with test piece thickness. Test
ternperature,oC o -40 0
50
-25
100
0 , t h i c k n e s s (mm)
Fig. 9.21 Variation of critical CTOD values with test piece thickness. Data for a ship hull steel (~ef.'/20/).
9.6.2 Temperature The comments here apply primarily to bcc metals, an important class of materials that includes most engineering steels apart from austenitic stainless steels. Austenitic stainless steels, aluminium alloys and other fcc metals show a less marked temperature dependence. The fracture toughness (Kc or critical CTOD) varies with temperature in a similar fashion to the Charpy energy (Fig. 9.22, Ref. 121). That is, there is a high temperature regime of relatively high toughness values, a low temperature regime of low toughness, and a transition regime in which there is a
Section 9.6.3
-1 5 0 Test
-50 temperature (
50 O C )
Fig. 9.22 Variation with test temperature of critical CTOD values of the weld metal of an E7016 type weld metal (Ref. 121). rapid change of toughness for little variation in temperature. Also as with Charpy testing, the high toughness regime corresponds to the ductile mode of fracture, the lower toughness regime corresponds to the cleavage mode of fracture, and the transition regime to mixed fracture modes. However, note that the Charpy V-notch transition temperatures cannot be readily correlated with fracture toughness transition temperatures. It is also important to note that, unless valid KI, values are obtained for the whole temperature range, the transition temperature is very dependent on the test piece size or plate thickness. Therefore, it is important to measure a material's toughness with a full thickness test piece (unless it is a valid KI, that is being measured), and to perform the test at the design temperature. If there is a lot of scatter in the toughness values, it is possible that the material is being tested in its transition regime, in which case one should be particularly careful to establish a true lower bound toughness for use in design or defect assessment. 9.6.3 Strain rate
In the KIc and CTOD testing standards, it is specified that the loading rate should be within certain limits. This is because for impact loading conditions, the toughness may vary considerably with strain rate (Fig. 9.23, Ref. /2 11). For bcc materials, increasing the strain rate encourages the cleavage mode of fracture, and thus has a similar effect to that of lowering the temperature. Therefore, if the structure of interest is subjected to high strain rates, one should be wary of applying conventionally obtained toughness values.
Section 9.6.4
Fig. 9.23 Variation of maximum load CTOD values (6) with the CTOD rate (5). Data for a ship hull steel (Ref. /2 I/). The toughness values should be obtained at the strain rate corresponding to the practical situation. A testing standard that covers high strain rate fracture mechanics testing, is currently being prepared (Ref. 1221).
9.6.4 Metallurgy It is difficult to cover briefly such a wide topic as the effect of metallurgical variables on toughness. However, two broad generalisations may be made. One is that most microstructural features that contribute to strength tend to reduce the toughness. This often leads to an inverse correlation between strength and toughness (Fig. 9.24, Ref. /23/). An exception to this rule is that refining the grain size improves both strength and toughness. Note that higher strength materials are also expected to carry greater stresses. Thus the introduction of high strength materials can lead to smaller critical defect sizes and unstable fracture problems, due both to a reduced fracture toughness and to greater design stresses. The second generalisation is that increasing the non-metallic inclusion content usually lowers the upper shelf toughness. Because the volume fraction of inclusions increases with the content of sulphur and oxygen in the steel, varying the sulphur content of a steel can affect the fracture toughness (Fig. 9.25, Ref. 1241). In plate material, the inclusions are usually elongated in the rolling and transverse directions, and this can lead to marked anisotropy in the upper shelf toughness properties, as shown in Table 9.3 for a case hardening steel (En 32 B, which is approximately equivalent to B.S. 970 080 M 15). The notation used to describe the test piece orientations is standard and given in Fig. 9.26 (Ref. / 2 5 / ) .
Section 9.6.4
0
I
I
I
I
500
1000
1500
2000
R,(MPal Fig. 9.24 Figure illustrating the inverse relationship bet ween strength and fracture toughness that is usually found for particular alloy systems (Ref. 1231). 100
Sulphur content 0
1.4
0.008%
1 . 6 1.8 2.0 Rm(GPa)
Fig. 9.25 Effect of sulphur content on the room temperature upper level fracture toughness of a quenched and tempered alloy steel (Ref.1241).
Fig. 9.26 Standard fracture toughness test piece orientations.
Chapter 9. References Table 9.3. Orientation
Initiation CTOD value (mm)
LT
TL
0.13 0.10 0.09 0.06 0.04
SL
0.04
LS TS ST
.
Thus, particularly if the fracture mode is fibrous, test pieces should ideally be taken from the material such that the crack and crack tip lie in the plane and direction of practical interest. Also it should be noted that impurity elements can cause temper embrittlement. This is relevant for certain classes of alloy steels (particularly Ni-Cr steels). Trace amounts of impurity elements such as P, Sb, As and Sn can sometimes, at certain temperatures, segregate to and thereby weaken the grain boundaries of these steels, thus substantially reducing the fracture toughness.
REFERENCES 1. British Standards Institution: Guidance on some methods for the derivation of acceptance levels for defects in fusion welded joints, PD 6493 :1980. 2. Slatcher, S., Saether, S. and Lereim, J.: Post Weld Heat Treatment of Welded Constructions - C Mn Manual Metal Arc WeldMetal Toughness, Veritas Report No. 82-07 18,16.08.82.
3. Turner, C.E.: "Further Developments of a J-Based Design Curve and Its Relationship to Other Procedures", Elastic-Plastic Fracture: Second Symposium, Volume I1 - Fracture Resistance Curves and Engineering Applications, ASTM STP 803, C.F. Shih and J.P. Gudas, Eds.,American Society for Testing and Materials, 1983, pp. 11-80-11- 102. 4. Shih, C .F., German, M.D. and Kumar, V. : International Journal of Pressure Vessels and Piping, Vol. 9, 1981, pp. 159-196.
Chapter 9. References 5. Kumar, V., German, M.D. and Shih, C.F. : "An Engineering Approach for Elastic-Plastic Fracture Analysis", EPRI Topical Report NP-1931, Electric Power Research Institute, Palo Alto, California, USA, July 1981. 6. American Society for Testing and Materials:
Standard Method of Test for Plane-Strain Fracture Toughness of Metallic Materials, E 399.
7. British Standards Institution: Method of test for Plane strain fracture toughness (KI,) of metallic materials, BS 5447:1977.
8. British Standards Institution: Methods for Crack opening displacement (COD) testing, BS 5762:1979. 9. American Society of Mechanical Engineers : Boiler and Pressure Vessel Code, Section I11 - Rules for Construction of Nuclear Power Plant Components. 10. American Society of Mechanical Engineers: Boiler and Pressure Vessel Code, Section XI - Rules for In-Service Inspection of Nuclear Power Plant Components. 11. Harrison, R.P., Loosemore, K., Milne, I. and Dowling, A.R.: Assessment of the integrity of structures containing defects, CEGB Report RIHIR6Rev 2, April 1980. 12. Japan Welding Engineering Society Standard : Method of assessment for defects in fusion-welded joints with respect to brittle fracture, WES 2805- 1980. 13. Denys, R.M.: The wide plate test and its application to acceptable defects, Paper 12, Int. Conf. on "Fracture Toughness Testing", The Welding Institute, 9-10 June 1982, London. 14. Denys, R.M. and Miisgen, B. : Gross section yielding crack tolerance of STE 36 and STE 70 steels, Paper 13, Int. Conf. on "Fracture Toughness Testing", The Welding Institute, 9-10 June 1982, London. 15. Soete, W.: The wide plate test and the gross strain criterion, Paper 24, Int. Conf. on "Fracture Toughness Testing", The Welding Institute, 9-10 June 1982, London. 16. Kiefner, J.F., Maxey, W.A., Eibner, R.J. and Duffy , A.R. :
"Failure Stress Levels of Flaws in Pressurized Cylinders", Progress in Flaw Growth and Fracture Toughness Testing, ASTM STP 536, American Society for Testing and Materials, 1973, pp. 46 1-48 1.
Chapter 9. References 17. Shih, G.C.: Handbook of Stress-Intensity Factors, Institute of Fracture and Solid Mechanics, Lehigh University, Bethlehem, Pennsylvania, 1973. 18. Tada, H., Paris, P. and Irwin, G.: The Stress Analysis of Cracks Handbook, Del Research Corporation, Hellertown, Pennsynvania, 1973. 19. Rooke, D.P.and Cartwright, D.J. : Compendium of Stress Intensity Factors, Her Majesty's Stationery Office, London, 1976.
20. Lereim, J.: Elastic-plastic fracture analysis of heavy walled structural elements, Paper 13, The Second International Conference on Offshore Welded Structures, The Welding Institute, London, 16-1 8 November 1982. 21. Larsson, T-B., Lereim, J. and Saether, S.: Influence of strain rate on J- and COD-fracture toughness of steel plates of DnV qualities NVA, NVD and NVE 36, Veritas Report No. 83-0194,25.02.83. 22. The UK Briefing Group on Dynamic Testing, IIW Commission X, Paper 35. Proposed standard test methods for measuring K I ~and CTOD at high load rates, Fracture Toughness Testing - Methods, Interpretation and Application, Welding Institute, London, 9-10 June 1982.
23. Broek, D.: Elementary Engineering Fracture Mechanics, 3rd Edition, Martinus Nijhoff Publishers, The Hague, Holland, 1983. 24. Birkle, A.J., Wei, R.P.and Pellissier, G.E.: Transactions of the American Society for Metals, Volume 59, pp. 981-990, 1966.
25. Willoughby, A.A., Pratt, P.L.and Baker, T.J.: Advances in Fracture Research, Ed. Francois, Proceedings of 5th International Conference on Fracture, Cannes, France, 29th March3rd April, volume 1, 179-186, 1981.
CHAPTER 10
FATIGUE LIFE CALCULATIONS Inge htsberg* and A. ~lmar-N-** (Example 9) *A.S VERITEC, Oslo, ** Norges tekniske hegskole, Trondheim
$ - ABSTRACT The importance of fatigue life estimation at the design stage is pointed out in order to arrive at feasible and cost-effective solutions considering the total lifetime of the structure. of fatigue lives by use of SN-data and Miner-Palmgren approach have been discuss&, Constant and variable arnplitude loading have been considered. Closed form equations for fatigue life predictions have been derived. Stresses to be used for calculation of fatigue lives are defined. Prediction of fatigue lives based on crack growth analysis has been discussed. Examples of fatigue life predictions and crack growth analysis are given. Some of the main uncertainties associated with fatigue life prediction are discussed. Three formats for fatigue design are presented. Some practical guidelines and considerations on the application of the allowable stress format are given. At the end the effect of yield strength and relieving of residual stresses on fatigue is discussed.
10.1
RTANCE OF FATIGUE LIFE ESTIMATION AT THE DESIGN STAGE
After a design of an offshore structure has been finished, there are rather small possibilities for increasing the fatigue life. Some improvements may be made during the fabrication, see Chapter 6. So far, however, grinding of the transition weldlbase material has been the only practical and reliable method for increasing fatigue life. It is generally accepted that a factor of approximately 2 on fatigue life may be achieved by grinding, assuming good workmanship. Such grinding should preferably be carried out by a rotary burr. The process is time-consuming and will only be cost-effective in few designs.
Section 10.2.1 During the design period it should be kept in mind that the need for inservice inspection is rather depending on the calculated fatigue lives for the different joints. The extent of in-service inspection with respect to fatigue cracks is normally based on the calculated damage ratio during design, Ref. / 1/. It should be mentioned that the reliability of in-service inspection may be rather uncertain and depends on several factors. Thus, the considered areas must be cleaned in order to ensure a reliable inspection, and the associated costs are rather large. Also, inspection for fatigue cracks below water level is generally very expensive. The effort of required in-service inspection should therefore be considered at an initial design stage, in order to achieve a costeffective design solution. To obtain a good design, the total costs should be considered, i.e. costs of the fabricated structure including control and inspection during design and fabrication, and inspection costs during service. The expected costs associated with a structural collapse may also be included. Such cost optimization may be carried out with requirements to structural reliability as a boundary condition. The optimum cost may be found for stricter requirements to structural reliability than those specified as a minimum in the design codes. This may for example be relevant for new types of structures in deep waters, Ref. 121. In order to arrive at a cost optimal design, it is therefore necessary that fatigue life estimates are carried out for the different design solutions. Such estimates are also important at an early design stage for verification of the code requirements. A change of design parameters is most easily carried out at the beginning of the project. At this stage simplified assumptions of the long term stress range distribution may be used (two-parameter Weibulldistribution). For the final design, however, the stress range distribution must be determined with sufficient accuracy, see Chapter 2.
10.2
PREDICTION OF FATIGUE LIFE BY USE OF SN DATA AND THE MINER-PALMGREN APPROACH
10.2.1 General The fatigue life is normally calculated by the Miner-Palmgren formula:
where : k = number of stress blocks ni = number of stress cycles in stress block i with constant stress range Aoi Ni = number of cycles t o failure at constant stress range Aoi
Section 10.2.1 The Miner-Palmgren equation assumes fracture for a damage ratio D = 1. The calculated fatigue life is i=k
where: Lo is the time for the total number of stress cycles no = Z ni. i= 1
For constant amplitude loading the number of cycles to failure for a given stress range AD, is determined by going into the SN-curve as shown in Fig. 10.1. Different SN-curves are reproduced in Chapter 1 1. It may also be calculated from the analytical expression for the SN-curve:
LO^ N = log a - m logAa
(10.3)
where: m = the inverse negative slope of the SN-curve log Z = the intercept of the logN axis Values of m and ii are given in Chapter 1 1 for different types of welded joints.
N
6 log N
Fig. 10.1 SN-curve, schematic.
ress range distribution F&. 10.2. The damage onstant stress es within each block is calculated, and the summation is carried out according to the Miner-Palmgren rule. Following this procedure the cut off level in the SN-curve is accounted for in the calculations.
Section
Log n
Fig. 10.2 Stress distribution divided into stress blocks. EXAMPLE 1
Fig. 10.3 Section through tube wall.
What is the fatigue life of a tube welded from one side and subjected to the long term stress range distribution in Fig. 10.2? The tube weld is shown in Fig. 10.3. The tube thickness t = 40 mm. The tube is part of a structure in seawater. It is assumed that the cathodic protection is working. According to the joint classifications in Chapter 1 1, the welded connection falls in class F2. Including the thickness effect, the corresponding SN-curve reads: log N = log a -
a 4
log$$)
-m
= 1 1 . 6 3 - p3*0 a log(--)40
4 .o
l o g N = 11.44 - 3 . 0
22 logAo
logno
- 3 .O
logAo
According to the damage calculation in Table 10.1, the total damage
Section 10.2.2 ratio is 0.32. The number of cycles to failure is then:
Table 10.1 Calculation of fatigue damage.
Block
ni
1 2 3 4 5 6 7 8 9 10 11
4 6 30 70 300 700 3000 7000 30000 70000 300000
Aoi ---+ Ni 455 400 345 300 250 210 170 130 90 55 30
2924 4303 6707 10200 17627 29740 56060 125363 377809 1655434 10200847
no =411110
10.2.2
ni/Ni 0.0014 0.0014 0.0045 0.0069 0.0 170 0.023 5 0.0535 0.0558 0.0794 0.0423 0.0294 D = 0.3151
fonm fatigue life equations
It is assumed that a structural detail is subjected to no stress cycles in total. It is further assumed that these stress cycles are randomly distributed with a probability density function f(Ao). This means that the number of cycles with stress range within Aa and (Aa + d o ) is no f(Au) dAa. The damage ratio Eq. (10.1) is then:
where N(Ao) is the number of cycles producing failure at a constant stress range Ao. Combination of Eqs. (10.4) and (10.5) yields:
where Mm is the moment of order m of the probability distribution of the stress range. Moments for different types of probability distributions of the stress range may be found in the litterature, see eg. Ref. 131.
Section 10.2.2 For offshore structures the probability density function of stress range may be represented by a two-parameter Weibull-distribution:
where h and q are Weibull parameters. Combining Eqs. (10.6) and (10.7) yields for the damage ratio:
Introducing
we get
The gamma function is defined as:
Substituting Eq. (10.1 1) into Eq. (10.10) yields:
The gamma function is tabulated in mathematical handbooks, e.g. Ref. Some values are listed in Table 10.2.
141.
It is convenient to eliminate the Weibull parameter q by introducing the maximum stress range Aao during no number of cycles. The probability that the stress range Ao is exceeded is:
The interpretation of Q(Ao) is shown in Fig. 10.4. The total area below the f(Ao) curve is equal t o 1-0. Combining Eqs. (1 0.7) and (1 0.13) and integrating, yield for the exceedance function:
Section 1 0.2.2
Fig. 10.4 Density function of Weibull distribution of stress ranges with h = 1.0
The probability that the maximum stress range Aa, is reached or exceeded for a total of no stress cycles is:
Combining Eqs. (10.14) and (10.15) yields:
and finally when Aoo in Eq. (1 0.1 6) is substituted into Eq. (10.14):
An example of $#e exceedance function Q(Ao) is shown in Fig. 10.5. It has been derived for the Weibull probability function shown in Fig. 10.4 with h = 1.O. Since Q(Aa) represents the probability that Aa is exceeded, we have for the number of cycles n that exceeds Ao:
"
Q(Ao) = no = exp
-[(& lh inn,] A00
Section 10.2.2
Fig. 10.5 Probability of exceedance of the stress range Au for the Weibull distribution in Fig. 10.4.
and
Ao = AD,[ 1 - logn ] l I h
1% no n = number of stress cycles that exceeds Ao Ao, = maximum stress range for a total of no cycles no = total number of stress cycles The long term distributions of stress ranges corresponding to waves in a 20 year period with no = lo8 cycles according to Eq. (10.19), is shown in Fig. 10.6 for different values of the Weibull parameter h.
I:
hz0.5 Q7 a9 1.0 1.1 1.3 15
0
,
,--,
1
2
3
4
5
6
7
8 log n
Fig. 10.6 Long term distribution of stress ranges.
Section 10.2.3 Sometimes Eq. (10.1 9) is written with
K
= l/h, see e.g. Chapter 2 and
Ref. 151. When no and Aa, are introduced instead of q, Eq. (10.16), we get for the damage ratio (Eq. (1 0.12)):
This expression implies :
-
-
the Miner-Palmgren rule an SN-curve with no cut-off level the two-parameter Weibull distribution for the probability density function of stress ranges Aq, is the maximum stress range for a total of no cycles h is the Weibull parameter describing the shape of the long term stress range distribution. For guidance on selection of values for h, see Section 10.6.2.
10.2.3 4hhlation of equivalent stress range
If the loading is variable, an equivalent constant stress range may be calculated. We divide the long term stress distribution into a stress histogram consisting of a number k of constant stress range blocks, each block characterized by its number of cycles ni and stress range Aui, Fig. 10.7.
"0
Number o f cycles
Fig. 10.7 Long term stress range distribution divided into a stress histogram. Using the Miner-Palmgren rule Eq. (10.1) and assuming a straight SN-curve without cut-off level Eq. (1 0.4), the damage ratio for the long term
Section 10.2.3 stress range distribution in Fig. 10.7 is given by:
We now want to calculate an equivalent stress range, (Aoeq .) (Fig. 10.8),
"
0
Number o f c y c l e s
Fig. 10.8
Equivalent stress range distribution giving the same fatigue damage as the long term stress distribution in Fig. 10.7.
which by definition is constant through the total number of cycles and gives the same damage ratio as that of Eq. (10.2 1). The damage ratio for this stress distribution is:
Requiring that the two stress distributions in Eqs. (10.2 1) and (10.22) result in the same fatigue damage, we obtain for the equivalent stress range:
If the stress distribution can be described by Eq. (10.1 7), the equivalent stress range may be derived by setting equal the damage ratios of Eqs. (10.20) and (10.22). It leads to:
where: (next page)
Section 10.2.4
'I
= gamma function
AD,= maximum stress range of no stress cycles no = total number of stress cycles h = Weibull parameter m = negative inverse slope of the SN-curve Some values of the gamma function are listed in Table 10.2.
EXAMPLE 2
term stress
Calculate the equivalent stress range and damage ratio for t distribution in Fig. 10.2. Use Eqs. (10.22) and (10.23). Solution. From Table 10.1: 11
no.= z n i = 411110
=
l\i
=
i=1 11
B
i= 1
AO:''*
n i = 8.68
10"
-
C: ; - A(T 1
From Eq. (10.23)
m 'QG-~~-.CL'C-.S { r r ~ 1
L
-LC,i c ; L~i
.
,68 10' 011/3.0 = 59.5 MPa (8_411110 From Eq. (10.22)
This is equivalent to the result in Example 1. 10.2.
&abe considered
Ma !
The procedure for the fatigue analysis of welded structures is based on the assumption that only the cyclic stress range is considered, i.e. the mean stress is neglected. In situations where the potential fatigue crack is located at the weld toe, the relevant stress is the maximum principal stress range adjacent to the potential crack location. The joint classifications and corresponding SNcurves take into account the local stress concentrations created by the joints themselves and by the weld profde. The design stress can therefore be regarded as the stress, adjacent to the weld under consideratio&. If the joint is situated in a region of stress concentration resulting from the gross shape of the structure, this must be taken into account in calculating the local 415
0
.4
Section 10.2.4 Table 10.2 Table of the complete gamma function. n
r(n+ 1)
log n n + 1)
5.10 5.20 5.30 5.40 5.50
142.451 169.406 201.813 240.833 287.885
2.153668 2.228929 2.304949 2.381717 2.459219
5.60 5.70 5.80 5.90 6.00
344.701 413.407 496.606 597.494 719.999
2.537443 2.616378 2.696012 2.776333 2.857332
6.10 6.20 6.30 6.40 6.50
868.956 1050.317 1271.423 1541.336 1871.254
2.938998 3.021320 3.104290 3.187897 3.272132
6.60 6.70 6.80 6.90 7 .OO
2275.032 2769.830 3376.921 4122.709 5039.999
3.356987 3.442453 3.528520 3.615182 3.702430
7.10 7.20 7.30 7.40 7.50
6169.593 7562.288 9281.392 11405.88 14034.40
3.790256 3.878653 3.967613 4.057 129 4.147 194
7.60 7.70 7.80 8.00
17290.24 21327.69 26339.98 32569.40 40319.99
4.237801 4.328943 4.420615 4.512809 4.605520
8.10 8.20 8.30 8.40 8.50
49973.70 62010.76 77035.55 95809.45 119292.4
4.698741 4.792467 4.886691 4.981408 5.076613
8.60 8.70 8.80 8.90 9.00
148696.1 185550.9 231791,8 289867.7 362879.9
5.172299 5.268463 5.365098 5.462199 5.559763
9.10 9.20 9.30 9.40 9.50
454760.7 570499.0 716430.6 900608.9 1133278.
5.657782 5.756254 5.855174 5.954536 6.054336
9.60 9.70 9.80 9.90 10.00
1427482. 1799844. 2271560. 2869690. 3628799.
6.154570 6.255234 6.356324 6.457835 6.559763
7.90
-
Section 10.2.4
Fig. 10.9 Local stress when the weld is situated in a region x of stress concen-
tration resulting from the gross shape of the structure. stress. For example, for the weld shown in Fig. 10.9 a) the local stress would be the tensile stress, AD, on the cross-section, whereas for the weld shown in Fig. 10.9 b) it would be SCFglobal Ao, where SCFglobal is the stress concentration factor for the hole. Another example of stress concentration due to the gross shape of the structure is that produced by misalignment during fabrication. We have in general: &IOC~
SCFglobal ' &*om inal
Values of SCFglObal is given in Chapter 11.
/
/
It is emphasized that the AulOol shall be used in connection with Skurves D,E,F,F2 and G (Section 10.1.5). @$g$&wrjoints, i.e. brace to chord connections, the local stress to iBt the i d d b d hot spor srrem sdjmt to the weld toe. be used lisr It is defined as the stress value produced by the extrapolation to the weld toe of the maximum principal stress distribution immediately outside the
Section 10.2.4 region --effected by the geometry of the weld. This is further discussed in Chapter 8. For potential cracks in the throat of load-carrying fillet welds, the relevant stress is the maximum shear stress range in the weld metal. I It is important to make sure that the Aolocal calculated for design -; I purpose corresponds to the Aolocal measured on the test specimens when : the SN-data were established. If Aol,,,l is determined by finite element analysis, due consideration must be given to type of element, element mesh and procedure for extrapolation of stresses in order to evade that the part of the stress increase caused by the joint itself, is included in Aolo al. Correspondance between experimental SN-data and hot spot stresses derived by finite element analysis of tubular joints is discussed in Chapter 8. c
1 1 ?I@
EXAMPLE 3
Fig. 10.10 Welded connections in Example 3. Two plates A and B are connected by a double-sided butt weld. Another plate C is welded to plate A by fillet welds as shown in Fig. 10.10. The plate is subjected to cyclic loading with a constant stress range of Ao = 80 MPa and a total number of cycles no = lo6. It is assumed that the fabrication meets the required tolerances in Ref. / 6 / . Here, the maximum misalignment of the butt weld is set to 3 rnm.
Section 10.2.4 a) Where are fatigue cracks most likely to be expected? b) Which SN-curves should be applied? Consult Chapter 11 Appendix A for joint classification. c) What is the fatigue damage for the welded connections? Solution. a) Fatigue cracks most likely develop at the transition between the weld and the base material due to possible fabrication imperfections and geometric stress concentrations. Fatigue cracks may therefore start at the butt weld toe between plate A and B, Cracks may also start at the fillet weld toe in plate A and most likely at the ends of plate C. b) Chapter 11 Appendix A advices that SN-curve C be used for butt welds and curve F for fillet welds. But as the fillet welds are going out to the edge of the plate, G is the correct choice. (See detail 4.2 in Appendix A.) c) Due t o the misalignment of the butt joint, a bending moment will arise in the plates, Fig. 10.1 1. The corresponding bending stress range at the butt weld is:
For a unit width of the plate:
i
I
i i
This yields:
The maximum stress range cstS the Butt weld:
hl
According to Chapter 1 1 Appendix A for curve C, m = 3.5, log = 13.63. This gives for the damage ratio, Eq. (10.22) :
Section 10.2.4
S t a t i c system; ad 1
c) 38
A x i a l +bending stress range
ad[l+
)
ad
Fig. 10.11 Misalignment and stress distribution in the plates in Example 3.
Section 10.2.5 The local stress range at the fillet weld, Fig. 10.1 1 c), d), e), is: According to Chapter 11 Appendix A for curve G, m = 3.0, log a = 11.39, and we get for the damage ratio:
D is larger than 3.0 and the design is not acceptable.
10.2.5 SN-curves and joint c h ~ ~ c a t i o n s For practical fatigue design, welded joints are divided into several classes, each with a corresponding design SN-curve. All simple tubular joints are assumed to be Class T, whereas other joints, including tube to plate, may fall into one of the eight classes specified in Chapter 11, Appendix A, i.e. ByC, D, E, F, F2, G or W depending upon: ( pa' v'~-'' i) the geometrical arrangement of the detail ii) tke direction of the fluctuating stress relative to the detail C lmf) iii) the method of fabrication and inspection of the detail ( kq A r ) > . I
In any welded joint, there are several locations at which fatigue cracks may develop, e.g. at the weld toe in each of the two parts joined, at the weld ends, and in the weld itself. Each location should be classified separately. The basic SN-curves are based on statistical analyses of appropriate experimental data. The design curves are linear relationships between log Ao and log N, and are defined as the mean minus two standard deviations of log N. Thus the SN-curves can be written logN= l o g a - 2 or
logs-m -log(Ao)
(10.26)
-
log N = log ii m log (Ao)
where: N = log a = log s = m = log a=
predicted number of cycles to failure for stress range Aa the cut of the log N axis by the mean SN-curve standard deviation of log N the negative inverse slope of the SN-curve log a - 210g s
In Chapter 11 values of log Z and m are given for details in air and details subjected to sea water with and without cathodic protection.
Section 10.3.1 10.3
PREDICTION OF CRACK PROPAGATION BY USE OF daldn-AK CURVES
10.3.1 General Different formulas for crack growth calculations based on fracture mechanics are discussed in Chapters 3 and 4. The formula proposed by Paris is most frequently used :
: where: a
= crack depth n = number of cycles
<
I[--I
m = material constants
(
i
AK= range of stress intensity factor in mode I fracture = K,,, - Kmin K = a * f l - F o = nominal stress in the member normal t o the crack F = correction factor depending on the geometry of the member and the crack
The crack length is found by integration of Equation (10.28). Provided that the threshold stress range intensity factor AKth can be sufficiently documented, a modified formula can be used for the crack growth:
AKth is the stress range intensity factor below which no growth takes place. Eq. (10.29) results in lower da/dn values than Eq. (10.28). Normally, it is assumed that compressive stresses do not contribute to crack propagation. However, for welded connections containing residual stresses, the whole stress range should be applied, Ref. 171. Only stress components normal t o the propagation plane are considered. The stress t o be used in crack growth calculations is always the local stress of the plate as calculated without the crack being present. In the case of tubular joint the hot spot stress as defined in Section 10.2.4 is required. If fatigue analysis based on crack propagation is used for design purpose, the C-value determined as the mean plus 2 standard deviations should be used in order to comply with the safety of the corresponding SN-curve.
Section 10.3.2 10.3.2 Constant amplitude loading
For constant amplitude loading with stress range do and constant F, Equation (10.28) integrates to:
where ai is the initial crack depth and af is the crack depth at unstable fracture or yield of the remaining section (Chapters 3 and 4). An example of crack growth in a simple butt joint without reinforcement is given below. EXAMPLE 4 Crack
7
Fig. 10.12 Crack growth in a simple butt weld. What is the number of stress cycles that the butt weld connection in Fig. 10.12 can endure before it fractures? The member is subjected to a constant stress range Ao = 20 MPa. The material properties are: fracture toughness KIC = 70 MPam = 3.1 c = 3.3 lo-l3
(
K
b-u-dd
mm ( M Pm ~m)3.1
SoEution. For the geometry in Fig. 10.12 when a < 0.7 W, Ref. 181:
With a/W = 0.7:
The maximum stress intensity factor for a = 0.7 W:
K = aJiFZaF=
20 o-TJ
6.0= 40MPa\/iii
Section 10.3.2 As K < KIC for a = 0.7W, fatigue crack growth according to Eq. (10.28) may take place up to this depth. Setting the crack depth at failure t o af = 0.7W = 35 mm will therefore give a safe value for the fatigue life. The initial crack depth will depend on several factors as for example welding procedure and workmanship. Even with good workmanship undercuts of a depth of 0.2 mm may result. In the bottom of undercuts microcracks may be present. As no other information about initial crack depth has been given, ai = 0.5 mm is assumed. Eq. (10.30) was derived assuming constant F. For real structures, e.g. that in Fig. 10.1 2, F is not constant and Nf is calculated by dividing the crack growth into intervals, where F is assumed constant within each interval. The number of cycles for crack growth from aj to aj+ 1 is then:
In Table 10.3, the crack growth from 0.5 mm to 35 mm has been divided into four intervals, and AN calculated for each interval. Table 10.3 Crack growth calculation.
The integration intervals should be shortest where the contribution to the number of cycles is largest, i.e. at the beginning of the crack growth. The crack growth is plotted against the number of cycles in Fig. 10.13.
Section 10.3.3 - 10.3.4
Number o f cycles
Fig. 10.13 Crack depth as function of number of fatigue cycles in the joint in Fig. 10.12. 10.3.3 Variable amplitude loading
Provided that threshold stress intensity factors are not included in the fatigue analyses, Equation (10.23) or (10.24) may be used to calculate the equivalent stress range, which is then inserted into Eq. (10.29) for Nf instead of Ao. 10.3.4 Geometry functions and crack growth integrals
The crack growth is found by integration of Eq. (10.28). Introducing a nondimensional crack depth a = a/W, where W is the plate thickness, we get the following expression: pf da
where: Nf = number of stress cycles for increasing the defect from ai to af Ao = stress range To determine the number of stress cycles causing a certain amount of crack growth, the integral:
is evaluated for the specific geometry and boundary conditions. The geometry correction factor, F, may be a relatively complicated function of the crack size and obtained by numerical analyses, e.g. finite element calculations. Other methods are discussed in Chapter 3. The boundary conditions used
Section 10.3.4 in such analyses generally have an essential influence on the values of F. Due consideration should therefore be given to the boundary conditions. The depth of the initial crack, ai, to be used in the calculation should be considered in each case, taking into account experienced imperfection or defect sizes for various weldments and geometries, and access and reliability of the inspection method. For surface cracks starting from transitions of weldlbase material, a crack depth of 0.5 rnrn may be assumed if no other documented information is available. Since most of the stress cycles to failure are associated with the first part of the crack growth, an exact definition of failure is not essential, and may be assumed to be the crack growth through the plate thickness. For high stresses or material with low ductility, the relevant crack depth at unstable fracture, af,should be used in Eq. (10.3 1). In Chapter 11 the integral I in Eq. (10.32) has been calculated for a buttweld, a cruciform joint and a simple tubular joint in air and in sea water. The results are shown graphically in Figs. 1 1.1 1-1 1.19 as a function of ai for a final crack size equal t o the plate thickness, i.e. for ai = 1. The number of stress cycles required for the defect to grow from a, t o a, is then:
For crack growth through the thickness, the number of cycles to failure is :
EXAMPLE 5
Calculate the number of cycles to failure for the joint in Example 4 using Eq. (1 0.34) and Fig. 1 1.12.
Section 10.4.1
AD = constant = 20 MPa W = 50mm
Solution.
Fig. 11.12 gives I(O.O1) = 2.2. Then from Eq. (10.34):
10.4
SENSITIVITY AND UNCERTAINTY ANALYSIS OF FATIGUE LIFE
10.4.1 General There are many different uncertainties associated with fatigue life predictions of offshore structures, Refs. 15, 9, 121. They may be associated with the following parameters :
-
Load calculation including wave heights wave periods distribution of waves wave theories hydrodynamic coefficients marine growth
-
Stress calculation including structural analysis calculation of stress concentration factors
-
SNdata including natural scatter corrosion protection selection of SN-curve definition of failure thickness effect
-
Fabrication tolerances
-
Cumulative damage hypothesis
Section 10.4.2 In order to get some feeling about the influence of each of these parameters on the fatigue life, an expression for the fatigue life as derived from Eqs. ( 10.2) and ( 10.20) is considered :
where: Lo = noo = no = m = -a = h =
fatigue life in years as required during design maximum stress range of a total of no cycles total number of stress cycles in Lo years negative inverse slope of the SN-curve the cut of the N-axis by the design SN-curve Weibull parameter describing the shape of the long term stress range distribution
10.4.2 Load calculation
The uncertainties with respect to the load calculation are rather dependent on the length of the period used for collection of environmental data, marine growth, the wave theory used, type of structure, calculation procedure etc. Even with good information about environmental data, it is rather difficult to give reliable estimates of uncertainties associated with the fatigue loading calculation. In general the uncertainties are estimated to be of the same magnitude as those associated with the SN-data. In order to give more exact values, more detailed investigations of the actual structure, environmental data and type of analyses are required. Assume that the error in wave periods and wave directions results in an error of the estimated no of An,. Then from Eq. (10.35) the relative error in fatigue life is: no -AL- L no + An,
* [
ln(no + Ano) m/h I In no
Suppose that m = 3.0 and h = 1.0. no is the total number of stress cycles during a design life of 20 years, and equal to 1.05 lo8 for a wave period of 6 s. Equation (10.36) proves that an error of the total number of stress cycles no of 10%results in an error of the fatigue life of 8%. Error in the wave period may have a rather large influence on the calculated force due to the inertia part of the Morison equation (see Chapter 2).
Section 10.4.3 From Eq. (10.38) it is seen that the fatigue life is inversely proportional to the maximum stress range Aoo in third power. Thus a moderate error of the stress range may have a significant impact on the fatigue life. From wave theories and the Morison equation it follows that the force and hence the stress in the structure is proportional to the wave height for inertia dominated structures. Correspondingly the stress is proportional to the wave height in square for drag dominated structures, like jackets in moderate water depths. As the wave heights become smaller, however, in the region where the waves give the largest contribution to fatigue damage, the force becomes inertia dominated also for these structures. Thus errors in wave period, wave height, wave theories and hydrodynamic coefficients lead to corresponding errors in the stresses. This may also be the case for marine growth as the member diameters are increased. Marine growth may also effect the value of the hydrodynamic coefficients depending on type of species. It is evident from Eq. (10.35) that the fatigue life is very sensitive to the Weibull parameter h. This parameter depends on:
-
-
-
distribution of waves water depth type of structure including structural behaviour position of the joint in the structure
-J
1
For further consideration, see Section 10.6.2. The fatigue life for a class F2 detail as a function of h is shown in Fig. 10.14. The curve is based on Eq. (10.35) and the following data:
Lo = no = -a -m = Aao =
20 years lo8 cycles 1011.63 3.0 250 MPa
10.4.3 Stress calculation Uncertainties associated with structural analysis and calculation of stress concentration factors are rather dependent on the refinement of the analyses. Usually frame analyses of e.g. jacket structures are carried out using elements going from center to center of tubular joints. The accuracy of the structural analysis depends on whether eccentricities at tubular joints are accounted for or not. Calculated stresses will also
Section 10.4.3
I
I
1 .O
1.5
Weibull parameter h
Fig. 10.14 Fatigue life L as a function of the Weibull parameter h. differ from the simplified analysis if the local flexibility at the tubular joint is included in the analysis. The uncertainties associated with calculation of stress concentrations are also rather dependent on how they are derived. Calculation of stress concentration factors of tubular joints is frequently based on parametric equations, as discussed in Chapter 8. The different equations may produce a great scatter in the calculated SCF values, and the equations leading t o the safest design are recommended. Also the combination of stresses due t o axial loading and bending about the two axis is somewhat uncertain. However, the procedure given in Chapter 8 should give results on the safe side. If the combination of loads is known, the error may be reduced by direct finite element calculation of the stress concentration factors. Also the stress concentration factors are believed to be more accuratly determined by finite element analyses carried out today than by parametric equations which were established some years ago. The uncertainty of calculated stress concentration factors depends on the type of elements used, refinement of element mesh and the method
Section 10.4.4 applied for extrapolation of stresses back to the weld toe. For a normal analysis the results are considered to have an accuracy within + 20%. The effect of this error on the calculated fatigue life is given by Eq. (10.35). It should also be mentioned that the parametric equations for stress concentration factors of tubular joints have been derived for "theoretical" joints with members in one plane only. Several joints have members in different planes. This increases the uncertainty of the calculated hot spot stresses. Another uncertainty is the determination of the type of tubular joint. The behaviour of the joint is dependent not only on the geometry, but also on how the joint acts in the structure, i.e. how the forces are transferred through the joint as discussed in Chapter 8.
10.4.4 SN data There is a rather large uncertainty associated with the determination of SNcurves. The ratio between calculated fatigue lives based on the mean SNcurve and mean minus two standard deviations SN-curve is therefore considerable. Using Eq. (10.35) to calculate the fatigue lives based on the mean SNcurve and the design SN-curve, the following ratio is obtained:
For the F2-curve with a = 10' *.'
and ii = 10'
',a/Z = 2.9.
The probability of having fatigue lives above that of the design F2curve for a given stress range is 97.6%,considering only the uncertainties of the SN-data. Also it should be remembered that SN-curves are derived from laboratory experiments. In real structures the fabrication tolerances are likely to be larger. There are few experimental SNdata for N > lo7 cycles. The uncertainties associated with fatigue calculations with SN-curves are therefore very large when the curves are extrapolated beyond lo7 cycles. Three different extrapolations are recommended, and the choice of curve influences the calculated fatigue life as shown below, Ref. 1141. Consider the basic F2xurve for N polations for N > 10' ,~ i10.1 ~ 5. .
< 10'
and three different extra-
1. Prolongation of the F2-curve beyond lo7 cycles. No cut-off level. 2. Prolongation of the F2-curve up to 2 lo8 cycles, then cut off. This curve is recommended for cathodicly protected areas in sea water (Chapter 11).
Section 10.4.4
I
6
I
I
I
7
8
9
I
log N
Fig. 10.15 Extrapolation of SN-curves beyond N = l o 7 .
Table 10.4 Predicted fatigue lives. 1
SN-curve
Predicted fatigue lives relative No
1
N1/No = 1.OO
2
N2 /No = 1.06
3
N3/No = 1.40
3. Change of slope at lo7 cycles from -113 to -115. No cut-off level. The curve is recommended for areas in air (Chapter 1 1).
The predicted lifetimes in cycles relative to No are shown in Table 10.4 for a 20-year period with a total of No = no = 10' cycles. A long time distribution of stresses as described by Eq. (10.19) was assumed with a maximum stress range Aoo = 234 MPa. It is seen that the choice of extrapolation beyond N = 10' has no serious consequence for the design life for this type of long term stress distribution. The three types of extrapolations with their recommended use, hardly represent a true physical behaviour of the joint above lo7 cycles, but are justified in that they agree with experience and are simple to use. There is some uncertainty associated with classification of details and selection of SN-curves. The error introduced in the calculated fatigue life by wrong selection is indicated in Fig. 10.16. The thickness effect is also a parameter associated with uncertainty. It is rather dependent on the stress gradient over the thickness. This means that the thickness effect will depend on type of detail as well as on type of loading. For practical use, simplified expressions have been included in codes and standards, as explained in Chapter 11.
Section 10.4.5
G
F2
F
E
F a t i g u e curve
Fig. 10.16 Fatigue ratio N/NG versus classification of detail. The failure criterion used when SN-data are obtained, is another uncertainty which should be kept in mind. Especially for tubular joints the SN-data may be influenced by the chosen criterion. For the new design curve for tubular joints (Chapter 1I), the failure criterion is crack growth through the thickness. Other criteria such as crack growth along a larger part of the circumference of the weld have also been proposed. In a real structure, the load amplitude is variable, and one single load may be high enough to cause unstable fracture even before the crack has grown through the thickness of the considered chord or brace. The probability of that event depends on the long term stress distribution, the stress gradient in the joint and the fracture toughness of the material. For joints of normal thickness and fracture toughness this type of failure has so far not been considered in design. 10.4.5 Fabrication tolerances
For simple joints like butt welds, even a small misalignment implies increased stress. The increase is represented by a stress concentration factor:
As shown in Section 10.2.4, Example 3, e is the misalignment and t is the thickness of the plates jointed. With a normal allowable fabrication tolerance of e/t = 0.15, Ref. /6/, the stress increases by a factor of 1.45. As the fatigue life for a butt joint is inversely proportional to the stress range raised to a power of 3.5, the fatigue life is reduced by a factor of 3.7. It may be even larger if the fatigue
Section 10.4.6 - 10.4.7 life is derived from an SN-curve with a cut-off level, in that stresses falling beyond the cut-off level may be raised to values that give contribution to the fatigue damage, if a misalignment is introduced. It is therefore recommended that due attention is given to stress raisers produced by misalignment and secondary deformations due to local restraint. For butt welds in tubulars the misalignment effect is not as severe as in the example above. However, it's importance increases with increasing diameter-thickness ratio D/T. Misalignment of tubular joint connections is discussed in Ref. / 6 / . The effect must be evaluated and quantified during design. In section 10.2.4 the importance of correspondance between the SNdata and the stresses calculated during design was pointed out. This statement may now be enlarged by expressing that there should be correspondance between the SN-data and the stresses "felt" at the considered hot spot. It means that the weld shape of the fabricated structure should correspond to that of the SNdata. Thus use of a specific SN-curve automatically implies requirements to weld shape and workmanship. Determinations on weld shapes and profiles for tubular joints are specified in the API-code API RP 2A (Ref. /1 61) and in the Veritas-rules (Ref. 161). 10 -4.6 Cumulative damage hypothesis The hypothesis on cumulative damage adds to a number of uncertainties in fatigue life predictions. Experimental studies of variable amplitude loading indicate that fatigue failure occurs for damage ratios below 1.0, Ref. 1151. Values between 0.4 and 0.8 are reported and include all steels for which SN-data were available, tested in air and under corrosion, and for all stress levels investigated. If a damage ratio of 1.0 is used in design, it implies that the fatigue life is overestimated by a factor of 1.25-2.5. Due to natural scatter in SN-data testing, it is difficult to quantify the uncertainty associated with variable amplitude testing. The uncertainty incorporated in the fatigue design due to the damage hypothesis is, however, believed to be rather small as compared to the uncertainties in hot spot stress and SN-data. 10.4.7 Probability of failure
Several uncertainties have been discussed in the preceding chapters, and one should be careful in relying too much on the calculated fatigue lives. The parameters used in the calculation should preferably be chosen so that they lead to a conservative life. In particular one should be careful not to underestimate the stresses. 434
Section 10.4.7 The probability of failure can be determined based on a suitable reliability theory, when the variabilities of the parameters governing the fatigue life are known, Ref. 1231. The calculated probability values should be looked upon with a certain degree of scepticism, whereas the partial derivatives of the probability with respect to the different parameters are considered more reliable. A simple probabilistic analysis only including the variability of the SN-data is shown below.
EXAMPLE 6 Calculate the probability of failure as a function of the design damage ratio for a class F detail with a stress range Aa = 70 MPa. Only the variability due to the uncertainties in the SN-data should be considered. A normal distribution of the SN-data is assumed. Solution. Neglecting the thickness term, we have for the design SN-curve, Eq. (10.26):
Inserting for an F detail values for log a, log s, and m according to Chapter 11, Table 11.1 :
The probability of failure for a normal distribution of log N is, Fig. 10.17:
log N
Fig. 10.17 Graph of normal distribution illustrating reliability index 0, failure surface and probability of failure. 43 5
Section 10.4.7 In this connection, p is generally referred to as the reliability index. With f l = 2 and Pf = a(-2)= 0.023 we get:
By definition of the SN-curve, this value of N corresponds to a damage ratio of 1.
Suppose that the allowable damage ratio is redused to 0.3. According to Eq. (10.1):
This value of no results in a value of the reliability index 0:
and Pf = 0(-4.2) = 2 10-5 Repeating this procedure, Pf can be plotted as a function of the allowable damage ratio, Fig. 10.18. It is seen that reducing the damage ratio is an efficient means of reducing the probability of fatigue failure.
0.1
0.3
0.5
1 .O
ALlowable f a t i g u e damage r a t l o
Fig. 10.18 Probability of failure versus fatigue damage ratio for a type F.
Section 10.5.1 It is emphasized that probabilistic failure analyses can not take care of gross errors in design, fabrication and installation, since such errors can not be quantified. They may be due to limitation of knowledge and errors in the design analysis, incorrect use of material, incorrect fabrication etc. Sufficient inspection and control during the different phases of the project are important measures to reduce the occurrence of gross errors.
10.5
DESIGN FORMATS
10.5.1 General
Depending on the refinement of the fatigue analyses different design check formats may be used. The simplest format is the allowable stress format:
where Au is the local stress range referring to a given probability of occurrence during the design life. Often the maximum stress range occuring once during the design life or during a defined period of for example 100 years is chosen. Uallowable may be determined from SN-data, allowable cumulative damage ratio, and knowledge about the stress distribution. Most used today is the allowable cumulative damage format:
where: D = damage ratio k = number of stress blocks ni = number of stress cycles in stress block i Ni= number of cycles to failure at constant stress range Aoi within stress block i q = usage factor or allowable damage ratio as given in the design codes, see e.g. Refs. 16, 161. The third format is based on partial coefficients. For many years partial coefficients have been efficiently used in design with respect to static loading, Refs. 16, 17, 181. Also codes for fatigue based on partial coefficients have been presented, Ref. 1191. The design format can be written:
Section 10.5.2 where: Aoi = ni = noR= m = k = yf = y,
stress range in stress block i number of stress cycles in stress block i fatigue strength for ni = NR negative inverse slope of SN-curve number of stress blocks partial coefficient on loading = partial coefficient on SN-data
The value of the partial coefficients is a function of factors like:
-
environmental data type of structure type of detail - importance of detail - possibility for inspection and repair
The partial coefficients should be assessed by advanced probabilistic analysis, so that the uncertainty of the different design parameters is sufficiently accounted for. So far, however, sufficient work has not been put into determination of the coefficients, and in practical fatigue design only the two first formats are being used, and only these will be discussed in the next sections.
10.5.2 Allowable stresses It is assumed that the long term stress distribution for an offshore structure is represented by the two-parameter Weibull distribution described in Section 10.2.2, and the matching cumulative damage ratio :
where: Aoo = no = m = log;= h =
r
maximum stress range during no stress cycles total number of stress cycles negative inverse slope of the SN-curve the cut of the log N axis by the design SN-curve Weibull parameter describing the shape of the long term stress range distribution = gamma function
By allowing a cumulative damage D = q , we get for the maximum allowable stress range:
Section 10.5.2 (10.42) Some values of
v r q are given in Table 10.5. Table 10.5 Values of
drq.
Values of maximum allowable stress range are specified in the design codes, based on equations such as Eq. (10.42). It can be seen that a fixed value of Aoo results if fixed values are given to the parameters q , a, m, h, and no. Even if the stress range complies with the specified code values, it is recommended that it be checked with Equation (10.42) or another appropriate equation corresponding to the relevant stress distribution.
EXAMPLE 7 Calculate the maximum allowable stress range for a semi-submersible with a long term stress range distribution as described by Eq. (10.19) and the Weibull parameter h = 1.l. Total number of stress cycles no = lo8, allowable damage ratio q = 1-0, class F weld with plate thickness less than 22 mm. Solution. The max. allowable stress range happening once is obtained from Eq. (10.42):
Aoo = (
1.0. 1011.80 113.0. lo8
-1
(1n10811/l-l
-
160 MPa
If the allowable maximum stress range is wanted for another value of q, the result is scaled by a factor 111/3. For example for q = 0.3 the maximum
Section 10.5.3 allowable stress range becomes: Ao, = 160 0 . 3 ~ '=~ 107 MPa Eq. (10.42) is based on a linear SN-curve without cut-off level. Neglecting the cut-off as done here yields conservative values of the fatigue life.
10.5.3 Allowable cumulative damage ratio The design format most frequently used in design building codes is that of allowable cumulative damage ratio. In most codes it is stated that the damage ratio shall not exceed unity. Most codes also outline that the degree of redundancy shall be considered when the allowable damage ratio is determined. According t o AWS D1.l (1980), Ref. 1201, D should be limited to a fractional value e.g. one-third for critical members whose sole failure mode would be catastrophic. API RP 2A, Ref. 1161 prescribes that D should in general be below 0.5. For critical elements whose sole failure could be catastrophic, use of an additional margin of safety should be considered. In the new proposal of Department of Energy's Guidance Notes, Ref. /2 1/, it is said that D should be below 1 .O, and: "An additional factor on life should be considered for cases of inadequate structural redundancy. In defining this factor on life, account should be taken of the accessibility of the joint and the proposed degree of inspection as well as the consequences of failure. Because of the sensitivity of calculated life t o the accuracy of estimates of stress, particular care should be taken t o ensure that stresses are not underestimated ." In the Veritas Rules, Ref. / 6 / , the same basic philosophy is presupposed. In addition specific values of D are given, depending on importance of detail and access for inspection and repair. If a detail of major importance can not be inspected, D shall not exceed 0.1. In the proposed Norwegian Petroleum Directorate regulations the requirements t o D are even stronger as D is set equal to 0.1 for a non-redundant member, whatever the inspection possibilities. As shown in section 10.6, it may be difficult t o determine the Weibull parameter h without detailed and large computer analyses of the structure. It is assumed that the maximum stress range Ao, and the number of cycles no in Eq. (10.19) are known from a computer analysis simulating the maximum wave height. Then a similar analysis for another wave height is sufficient to determine the value of h. The wave heights should preferably correspond to those giving the main contribution to fatigue damage. This will depend on
Section 10.5.3
Fig. 10.19 Contribution to fatigue damage from the different stress blocks in a stress exceedance diagram. type of structural behaviour. It is seen that the maximum contribution to fatigue damage in Fig. 10.19 comes from waves with a frequency of 1O5 -1 O6 times in the design life. For a detailed design, however, it is not usual to work with any parametric equations for the long term stress range distribution. In a deterministic analysis one usually proceeds as follows: The wave distribution around the structure is divided into a number a) of sectors, for example 8 equal sectors. Within each sector a wave height exceedance diagram is established, b) Fig. 10.20 a). I
In a sector a wave height Hi with the corresponding number of waves c) ni is selected, Fig. 10.20 a). The wave period Ti belonging to Hi is determined, Fig. 10.20 b). Forces on the structure may now be calculated according to the Morid) son equation, Chapter 2. The wave is stepped through the structure in intervals - at least 6 intervals as shown in Fig. 10.20 c). For each joint in the structure selected for fatigue calculation, the e) stresses corresponding to the different positions of the wave referred to in c), are calculated, Fig. 10.20 d) .
Section 10.5.3
H
1
y
p
n,
e
s
s
i:
---------
Hi
: ---llog
T
Ti
nl
I c
1
log n o log n
I I
T
log ni
log no log n
I Fig. 10.20 Procedure for establishing the long term stress range distribution in deterministic fatigue design. After the stress at the considered joint has been determined for several f) wave positions, the stress range Aoi is identified, Fig. 10.20 d). The stress range Aai corresponding to ni cycles is now plotted in a diagram for long term stress range distribution, Fig. 10.20 e).
g)
The procedure c) - g) is repeated for a number of different wave heights. At least four heights should be used for determination of the long term stress range distribution. The number however, depends on the structural behaviour. h)
The procedure b) - h) is repeated for the other sectors, and the stress i) range distribution for all sectors is determined.
Section 10.5.4 - 10.6.1 The cumulative damage ratio Eq. (10.40) is now calculated for each stress range distribution, as shown in Section 10.2.1 , Example 1. The summation is normally carried out numerically, in that the stress distribution is divided into a number of blocks that may vary between 20 and 100, dependent on the integration procedure.
j)
Finally the damage ratios for each sector are added, and a total cumuk) lative damage ratio for the considered joint is obtained. 10.5.4 Comments on the design formats
In previous versions of the API Rules, Ref. / 161, the fatigue design was limited to a check that the maximum stress range was less than a certain value. Such values were specified in the codes, based on equations such as Eq. (10.42). he allowable stress format is justified in cases when the long term stress range distribution can be adequately expressed by closed form equations such as Eq. (10.42). Today it is mostly used for pre-engineering design check, whereas the allowable cumulative damage format is best suited for detailed and final design.
10.6 ALLOWABLE
STRESS FORMAT FOR DESIGN CHECK
PRE-ENGINEERING
10.6.1 Design chart
In Section 10.5.2 an example of calculation of the allowable extreme stress range was given foi- fatigue class F. By carrying out corresponding calculations for other SN-curves and for other values of the Weibull parameter h, the design chart for Aao in Fig. 10.2 1 is obtained. The thickness effect is disregarded in Fig. 10.21. For SN-curves B-W when t > 22 mm the allowable stress in Fig. 10.21 is corrected as follows: 22 114 effect included) - *'o(~i~. 10.21) ' (i)
thickness
where t is the actual thickness in mm. For the T-curve when t # 32 mm: Aoo(thicknesseffect included)
-
- " o ( ~ i ~ .10.2 1) '
32
1/4
The allowable stress range in Fig. 10.2 1 is obtained for a usage factor q = 1.O.. For other values of q :
Section 10.6.1
Fat i gue c l a s s
Fig. 10.21 Allowable extreme stress range as function of fatigue class for different values of the Weibull parameter h. The usage factor q = 1 and the total number of cycles no = lo8.
m is the negative inverse slope of the SN-curve for the considered fatigue class, see Chapter 1 1 . It is emphasized that the stresses in Fig. 10.21 are local stresses at the detail as defined in Section 10.2.4.
EXAMPLE 8 In order to arrive at the first dimensions of a joint in a semi-submersible, we want to calculate the maximum allowable stress range Ao, . We assume that
Section 10.6.2 the joint is designed with stiffeners and that it is a class F2 joint. Further assumptions: Weibull parameter h = 1.1 (usual for a semi-submersible) design life L = 20 years usage factor q = 1.0 plate thickness t = 40 mm
Solution. From Fig. 10.2 1 for class F2 the maximum allowable stress range : Aa, = 140 MPa
From Eq. (10.43):
thickness effect included) =
40
22 'I4= 120 MPa (m)
10.6.2 Considerations on the Weibull parameter h
The Weibull parameter h is an essential parameter when working with the allowable stress format, as was shown in the sensitivity study in Section 10.4.2, Fig. 10.14. Naturally, the designer will ask how to determine the Weibull parameter, but there is no straight forward answer. Two methods are proposed : Choose a suitable value based on experience from fatigue analysis of a) similar structures. Carry out numerical analyses as described in section 10.5.3. h is derived b) from Eq. (10.19) after calculation of the stress ranges for two different wave heights. The value of the Weibull parameter depends upon such factors as: 1. wave climate (long term distribution of wave heights) 2. water depths 3. type of structure (e.g. drag versus inertia dominated) 4. dynamic amplification 5. position of the joint in the structure
A first estimate of h for pre-engineering purpose can be obtained from Fig. 10.22, which is the result of an investigation by Marshall and Luyties, Ref. 1221. The figure shows h for the Gulf of Mexico and for a homogenous wave climate, that is a climate where the design storm wave is
Section 10.6.2 D e p e n d s on s h o a l i n g (shelf profile) Depends on nat. period Very
narrow
0.5 Broad Gulf
of Mexico
I
I
I
I
I
1
10
20
30
40
60
80
(A)
1.0 L
a
L
0
n
120
Water d e p t h ( m )
--
-l-J
E 0
I
1
-
0.5
--
Gulf of Mexico
-
Water depth L 3 0 m
a,
I
o
5
a
L
I
I
MSL
U)
-5
I
I
-20
-10
IB)
I
I
-30 - 4 0
Posttion in m below MSL
I
f
-60
structure,
4
3
ea,
-
Gulf of Mexico Water depth I
I
(C)
1
L 3Om I
N a t u r a l period ( s )
Fig. 10.22 Weibull shape parameter h, Ref. 1221.
I
Section 10.7.1 - 10.7.2 the extreme wave of frequently occurring weathers during for example a 100year period. A homogenous wave climate prevails in the North Sea. It is seen in Fig. 10.22 that h depends on the shelf profile when this is a relevant parameter. For structures in the North Sea the other parameters listed are more important. Contribution from draglinertia in the Morison equation seems to have the largest influence. As the natural period exceeds the 3-s. region, this also becomes an important factor. The influence of the depth below water level of the considered joint is also noted.
10.7
CONSIDERATIONS ON YIELD STRENGTH AND RELIEVING OF RESIDUAL STRESSES
10.7.1 Yield strength
For carbon steel structures in air and in sea water with cathodic protection, the fatigue strength is considered independent of the yield strength as long as Re < 400 MPa. If the fatigue design is governing the element thicknesses, material with less yield strength may therefore be considered. Such considerations may, however, be in conflict with other failure criteria like yielding, punching and buckling. 10.7.2 Post weld heat treatment
For laboratory specimens it is well known that post weld heat treatment reduces the tensile stresses and increases fatigue lives provided that some part of the stress range is compression. For real structures, however, one should be careful to give credit for stress relieving of joints due to the following reasons: The relief of residual stresses in complex thick welds is not complete. a) Experiments, particularly in the nuclear industry, indicate that relaxation of weld residual stresses is very slow and may not occur at all, even if the heat treatment is conducted in furnace. The complete component would have to be heat treated in a furnace b) with no later welding. Long range built in stresses will still exist in the structure, because no c) structure is perfectly aligned and no welds are made without distortions or shrinkages. d)
Often local stress relief is performed in-situ, where there are only
Section 10.8 limited possibilities for thermal movements to occur freely. This will install new residual stresses. Should a fatigue problem arise in service, there may be no possibility e) to make weld repairs which include stress relief treatment. Even if stress relieving has been carried out successfully so that residual stresses are relieved, stress concentration in the joints may imply that the stress range at a hot spot becomes fully tensile after some loading with plastic yielding. f)
For fatigue analysis of regions in the base material not significantly affected by residual stresses due to welding, the stress range may be reduced dependent on whether the mean cycling stress is tension or compression. This reduction may apply to e.g. cut-outs in the base material for classifications of type 1, Appendix A, Chapter 11. Before entering the SN-curve, the calculated stress range is multiplied by the reduction factor p as obtained from Fig. 10.23. Reduction u factor ,
6, = d 2
Compression
d,=O
cj
= -ad 2
6," Tenslon
Fig. 10.23 Stress range to be used in connection with SN-curves for unwelded structures. Ao = p Aocalc.. 10.8 EXAMPLE 9. REDESIGNING OF CROSS JOINT IN A LOADING BUOY. DISCUSSION ON THE CHOICE OF SN-CURVE AND POSSIBLE USE OF STRESS RELIEF HEAT TREATMENT.
After some years of use, cracks were discovered in the cross joint between the cone and the funnel in the loading buoy shown in Fig. 10.24 a). Replacement of the cracked section with the welded ring shown in Fig. 10.24 b) was considered. The plate thicknesses in the ring were increased as compared to the
Section 10.8
Fig. 10.24 a) Structure of loading buoy. b) Redesigned ring to replace the original buoyancy tank-funnel transition. c) Redesigned cross joint. original design, and the ring was to be welded into the buoyancy tank-funnel transition, possibly after a stress relief heat treatment. A section of the improved design cross joint is shown in Fig. 10.24 c). The highest stresses were found at location 3. The fatigue life of the redesigned cross joint is required. Long-term stress range distribution Based on the procedure described in Sec. 2.7.2, the long-term stress range distribution in the joint was calculated for an average one-year period. This distribution is shown in Table 10.6 and Fig. 10.25 for location 3, where the highest stresses were found. The stresses are local stresses at the weld surface perpendicular to the weld direction. Selection of SN-curve The fabrication regulations demand that the weld fillet at location 3 is ground with a radius of 30 mm, and that the joint is inspected by ultrasonics. Defects disclosed by the inspection are to be repaired. The stress range distribution in Table 10.6 refers to the local stresses at the surface. From a fatigue point of view, the joint can thus be compared with a transverse butt weld with no overfill of type 3.1 in the Joint
Section 10.8 Table 10.6 Long-term stress distribution in one year and resulting damage for the cross joint at location 3. SN-curve D has been assumed.
Mean stress range Ao (MPa)
Number of cycles
16.0 19.7 22.9 26.7 31.6 35.4 39 .O 42.8 47 .O 5 1.4 56.4 61.6 67.2 73.4 80.2 87.4 95.2 104 113 123 133 145 157 171 185 202 218 236 256 278 302
1.351 E 5 1.000 5 1.OOO 5 1.000 5 0.626 5 0.525 5 0.450 5 0.381 5 0.320 5 0.266 5 0.217 5 0.175 5 0.139 5 0.109 5 0.834 4 0.628 4 0.463 4 0.333 4 0.234 4 0.160 4 0.106 4 0.678 3 0.420 3 0.247 3 0.140 3 0.740 2 0.370 2 0.170 2 0.6 1 0.1 1 0 0
ni
Accumulated number of cycles n
Damage Di
Accumulated dam age
7.851 E 5 6.500 5 5.500 5 4.500 5 3.500 5 2.874 5 2.349 5 1.899 5 1.518 5 1.198 5 9.320 4 7.150 4 5.400 4 4.010 4 2.920 4 2.086 4 1.458 4 9.95 3 3 6.62 4.28 3 3 2.68 1.62 3 9.42 2 5.22 2 2.75 2 1.35 2 6.1 1 2.4 1 7 1 0
0 9.348 E -4 1.468 -3 2.327 -3 2.415 -3 2.853 -3 3.264 -3 3.652 -3 4.062 -3 4.416 -3 4.760 -3 5.001 -3 5.157 -3 5.270 -3 5.260 -3 5.126 -3 4.884 -3 4.580 -3 4.128 -3 3.640 -3 3.049 -3 2.527 -3 1.987 -3 1.510 -3 1.084 -3 7.457 -4 4.687 -4 2.732 -4 1.231 -4 2.627 -5 0
0 9.348 E -4 2.403 -3 4.730 -3 7.145 -3 9.993 -3 1.326 -2 1.691 -2 2.097 -2 2.539 -2 3.015 -2 3.515 -2 4.031 -2 4.558 -2 5.084 -2 5.597 -2 6.085 -2 6.543 -2 6.956 -2 7.320 -2 7.625 -2 7.877 -2 8.076 -2 8.227 -2 8.335 -2 8.410 -2 8.457 -2 8.484 -2 8.496 -2 8.499 -2 8.499 -2
D
Section 10.8 MPa 3 0 0 d
102
1 o3
1 o4
105
106
CYCLES
Fig. 10.25 Long-term stress range distribution at location 3 in the cross joint.
Classification in Chapter 11, Appendix A, corresponding to fatigue class C or D. The choice between C and D depends on the care with which the grinding of the joint profile and the inspection are conducted. The cross weld is approximately 24 m long and 70 mm wide, and would have to be ground with hand tools. Obviously, the perfect geometry shown in Fig. 10.24 c) can not be achieved this way. Deviations will arise, and any local deviation from the ideal geometry will increase the stresses. This points to curve D rather than curve C. Also curve C requires that the joint is proved free from defects. This can be difficult to achieve if the joint is produced by normal workshop procedures. So curve D seems to be the correct choice. Thickness effect The effect of plate thickness discussed in Secs. 4.6.3 and 11.2.4, can be disregarded if true local stresses are used in the calculation of accumulated damage. However, the argument given for the choice of the D curve above, involves that the true stresses may rise above those in Table 10.6, because of local deviations from the ideal weld geometry, or of stress concentrations around undetected weld defects. Therefore the SN-curve must be corrected for the thickness effect. Damage calculation As welded. We have for the SN curve D for joints in sea water and cathodic protection (Table 11.2) :
Section 10.8
and for the accumulated damage
The cut-off stress So = 20 MPa, which means that stress ranges below 20 MPa can be ignored. The result of the calculation is shown in Table 10.6, giving the accumulated damage in one year as
D = 0.085 Most codes specify an allowable damage ratio of 113 for critical members whose sole failure would be catastrophic. Thus the fatigue life becomes L=
1
0.085 3
- 3.92 years
Limiting the allowable damage ratio to 113 should not be regarded as introducing a safety factor of 3. The Miner-Palmgren rule disregards the sequence effect of the stress cycles, and experience shows that fatigue failure occurs for a Miner's sum between 0.4 and 1.O. Stress relieved. Obviously a design life of 4 years is too short. A recalculation based on the 9N-curve C will give a design life of 12 years, or 25 years if the thickness effect is disregarded. If curve C applies, true stresses have been assumed, and logically, the thickness effect factor should be set equal to 1. However, it is unrealistic to expect that the C curve will apply. Curve C might come closer to realisation if a method could be developed for machining the weld surface to the exact shape determined for the stress calculation. Stress relieving of the joint will reduce the mean stress and thereby increase the fatigue life. The various codes are, however, reluctant in giving credit for stress relieving of joints as explained in Sec. 10.7.2. If we assume that the complete welded ring shown in Fig. 10.24 b) is heat treated in one piece, and caution is exercised when it is welded into the buoyancy tank, so that long range stresses are kept within reasonable limits, then the stress range for calculation of the damage increments can be reduced by the factor y in Fig. 10.23. For zero mean stress, y = 0.8, which will decrease the damage by a factor of ( 0 . 8 ) ~= 0.5 12. A further decrease results because the first two damage increments in Table 10.6 are now below the cut-off stress level, and
Section 10.8 1
do not count in the damage summation. We therefore have for the damage and
-
1
Lstress relieved - 0.0423
.3
= 7.9 years
Consequently, stress relieving doubles the fatigue life of the joint.
Length of crack initiating fast fracture There are two different approaches for calculating design lives: The SNcurve approach and the crack growth rate approach. The latter computes the time needed for the crack to grow to a length which might initiate fast (uncontrolled) fracture. As welded. The CTOD approach yields for the allowable crack length, Sec. 9.5.2:
*=
6c ~
.
T
~
-
E -
E
EY ~
- 0.25 ~ &
~
~
CTOD
@
= nondimensional
6, ey
= CTOD at fracture, measured to 0.23 mm = yield strain of steel = 355/200 000 = 1.775 lo-' = strain around the crack, including welding strain
E
imaX = allowable half-lengt h of a through-thickness crack It is assumed that the crack has run out of the stress concentration area when fast fracture is initiated. The stress that drives the fast fracture is therefore close to the maximum nominal stress in the funnel wall, which has been calculated to 55 MPa.
This t hrough-t hickness crack half-lengt h is now converted to the depth c of a surface crack, assuming that the elastic stress intensities are equal for both cracks. Assuming further an apex ratio c/a = 0.2, and using the procedure explained in Sec. 9.5.2, gives
Section 10.8
F = shape correction factor for the surface crack. Stress relieved. We will make the conservative assumption that stress relief heat treatment reduces the weld stresses to 5 5 MPa, that is to the value of the max nominal stress in the funnel wall. That gives
and from Eq. (9.7)
Consulting Fig. 9.13, we find that F = 1.6 for a through-thickness crack with c/a = 0.2 and -
We may therefore conclude that if the joint is stress relieved, the fatigue crack may grow through the plate thickness without becoming critical. Crack growth rate calculation As welded. Our first step is to calculate the equivalent stress range at the surface of the joint at location 3, using Eqs. (10.21) and (10.22) and the accumulated damage in Table 10.6
The stress concentration factor at location 3 has been calculated t o 2.6. We assume that Aoeq falls off in the wall thickness direction so that it reaches 10 MPa at a depth of 20 mm below the surface, and stays at this value for the remaining 40 mm (please correct figures in Fig. 10.24 c) accordingly). This gives for the stress range distribution of equivalent stress in the thickness direction
Section 10.8 when c is the distance below the fillet surface (Fig. 10.24 c)). The stress distribution above will give a mean stress in the section equal to the nominal stress 4512.6 = 17 MPa. We proceed by computing the time needed for the crack to grow to i depth of 20 mm, using the procedure explained in Sec. 10.3. The number of cycles needed to propagate the crack from a depth ci to a depth ci+] is given by EQ.(10.33) ai+l 1 An = da S -c.wO.5-1. (A0eq,c)" ai ( F - E U ) ~ C
m
W
= crack growth rate factor = 3.3
10-
13
mm
-
(Table 11.4)
m)m
(MP~ = crack growth rate exponent = 3.1 (Table 1 1-4) = plate thickness = 50 mm
The value of the integral is determined by the graph shown in Fig. 11.12 (plane plate) and comes out as the difference Ii - Ii+ The results of the calculation are shown in Table 10.7. The crack propagates to a depth of 20 mm in the course of 1.393 10' cycles. Fast fracture takes place at 20 mm, so the design life of the joint is
Also in this case the life must be reduced by the utility factor 113, since we base the calculation of the equivalent stress on the Miner-Palmgren principle. The design life calculated by SN-curve D was 4 years, so the two methods give comparable results. The crack growth rate life depends on the assumption made for the stress gradient in the thickness direction, a parameter which is generally not part of the stress computation. Stress relieved. We have concluded that for a stress relieved joint, the crack may grow through the plate thickness without becoming critical. Furthermore, stress relief reduces the part of the stress range that produces fatigue by a factor of 0.8, thereby increasing the fatigue life by a divisor of 0.8'.'. The design life of the stress relieved joint is therefore (Table 10.7) - - 2.513- lo7 -- -- 2 1 years LstreSSrelieved 7.851.105.0.501.3
which should be compared with 7.9 years found by the SN-curve approach.
Chapter 10. References Table 10.7 Crack growth through the cross joint. Number of stress cycles. *
Crack depth ci (mm) 0.5
a -
ci
50
1 - Ci
2
+
Aoeq,&
M P ~
cyclesn
2.40 0.75
0.02
2
0.04
3
0.06
4
0.08
5
0.1
6
0.12
7
0.14
8
0.16
9
0.18
10
0.20
15
0.30
20
0.40
50
1.O
Ii
ci+
0.01
1.0
Accumulated Ii - Ii+ 1 of cycles number of An
1.5
43.7 42.4
1.50 I
0.9
2.605 E6
2.605 E6
0.59
1.875 6
4.480 6
0.25
9.090 5
5.389 6
0.15
6.178 5
6.007 6
0.10
4.808 5
6.488 6
0.06
3.335 5 * 6.821 6
0.05
3.269 5
7.148 6
0.05
3.839 5
7.532 6
0.04
3.677 5
7.900 6
0.03
3.030 5
8.230 6
0.1
2.086 6
1.032 7
0.04
3.613 6
1.393 7
0.04
1.120 7
2.513 7
0.91 2.5
40.6 0.66
3.5
39.0 0.5 1
4.5
37.1 0.4 1
5.5
35.4 0.3 5
6.5
33.6 0.30
7.5
31.9 0.25
8.5
30.1 0.21
9.5
28.4 0.18
12.5
23.1 0.082
17.5
14.4 0.040
35.0
10.0 0
i
REFERENCES
1. Mjelde, K.M., Lotsberg, I. and Lee, P.C.S.: Cost - Reliability - Consequence of Resource Allocation. Application t o an Offshore Structure. To be published in Ocean Engineering.
Chapter 10. References 2. Sletten, R., Mjelde, K.M., Fjeld, S. and Lotsberg, I.: Optimization of Criteria for Design Construction and In-service Inspection of Offshore Structures Based on Resource Allocation Techniques. European Petroleum Conference. London. 1982. 3. Gran, S.: Evaluation of High Cycle Fatigue in Welded Steel Connections. Det norske Veritas. Report No. 76-339. 4. Abrarnowitz, M. and Stegun, I.A.: Handbook of Mathematical Functions. Dover Publications. New York.
5. Wirsching, P.H.: Probability - Based Fatigue Design Criteria for Offshore Structures, API-PRAC Project 81-15, January 1983. 6. Veritas Rules for the Design, Construction and Inspection of Offshore Structures, 1977. 7. Publication Document 6493 : 1980. Guidance on Some Methods for the Derivation of Acceptance Levels for Defects in Fusion Welded Joints. British Standard Institution. 8. Hellan,K.: Introduction to Fracture Mechanics, McGraw Hill, New York, 1984. 9. Gran,S.: Fatigue and Crack Failure Prediction Methods in Marine Structures. Veritas Report No. 80-0688, May 1980. 10. Moan,T.:
Safety of Offshore Structures. Fourth International Conference on Applications of Statistics and Probability in Soil - and Structural Engineering. Firenze 1983, pp. 41-85. 11. Engesvik, K.M.and Moan, T. : Probabilistic Analysis of the Uncertainty in the Fatigue Capacity of Welded Joints, Engineering Fracture Mechanics, Vol. 18, No. 4, pp. 743-762,1983. 12. Lotsberg, I., Fines, S. and Foss, G. : Reliability of Calculated Fatigue Lives of Offshore Structures. To be presented at Fatigue 84. Birmingham. Sept. 1984. 13. Edvardsen, G. and Halvorsen, R.:
Calculation of Stress Concentration Factors in Chord and Brace after Different Formulas. Veritas Report No. 8 1-0367, April 1981. 14. Gran, S.: Comparison between different S-N Curves used in Design of Offshore Structures. Veritas Technical Note, Aug. 1981.
Chapter 10. References 15. Schiitz, W.: Procedures for the Prediction of Fatigue Life of Tubular Joints, Steels in Marine Structures. Int. Conf. Paris. Oct. 1981. 16. API RP 2A. Recommended Practice for Planning, Designing, and Constructing Fixed Offshore Platforms. Thirteenth Edition, January, 1982. 17. Regulations for the Structural Design of Fixed Offshore Structures on the Norwegian Continental Shelf, Norwegian Petroleum Directorate, 1977. 18. NS 3472 E. Design Rules for Steel Structures. Norges Standardiseringsforbund, May 1973. 19. Eurocode 3, Common Unified Code of Practice for Steel Structure, Draft, March 1983. 20. AWS Dl .1 -83. Structural Welding Code, American Welding Society, 1983. 21. Offshore Installations: Guidance on Design and Construction. New Fatigue Design Guidance for Steel Welded Joints in Offshore Structures, Department of Energy "Guidance Notes" Revision Drafting Panel. August 1983, Issue N.
22. Marshall, P.W. and Luyties, W.H. : Allowable Stress for Fatigue Design, Boss 82, Boston, Aug. 1982. 23. Thoft-Christensen, P. and Baker, M.J.:
Structural Reliability Theory and Its Applications. Springer-Verlag, 1982.
CHAPTER 11
FATIGUE IN BUILDING CODES BACKGROUND AND APPLICATIONS Inge Lotsberg and H&an Andersson VERITEC, Oslo
ABSTRACT This chapter produces a brief review of the various building codes for fatigue design. Simple joints and tubular joints have been examined. Recently developed design codes are presented with examples explaining fatigue design based on fatigue strength tests. Similarly, new fatigue design regulations based on crack growth tests and fracture mechanics are produced and discussed. Damages caused during installation or service are debated, and repair and reinforcement methods are described.
1 1.1 THE VARIOUS CODES ON FATIGUE REQUIREMENTS The aim of the various fatigue design codes is to ensure that the structures are designed so that adequate fatigue lives are obtained. Fatigue design may be carried out by methods based on fatigue strength tests (SN-curves) and/or methods based on crack growth rate tests (da/dn - AK curves). For design purposes, fatigue analysis based on fatigue strength tests is normally the most suitable methods, evaluating the actual design against a set of standard details as shown in Section 11.2. For assessment of in-service cracks with respect to maximum inspection intervals or time before repair, the crack propagation is evaluated by means of fracture mechanics and da/dn curves. The principles for establishment of design SN-curves were outlined in Chapters 4 and 10. Detailed background for fatigue design codes is given in Refs. 11, 21. Ref. / l / has been used as basis for several codes relating to simple joints 13, 4, 51. Also BS 5400, Ref. /6/, which is a code for fatigue design of bridges is founded on Ref. / I / .
Section 1 1.I At the present time several fatigue design codes and regulations are being revised. A revision of the Department of Energy's Guidance Notes has been going on for the last few years, Ref. / 7 / . For simple joints the fatigue design in these notes is still based on the work presented by Gurney, Refs. 11, 21. In Refs. 13, 4, 5 / the slope of the SN-curves is kept constant below N = 2 l o 8 , with a horizontal cut-off level at this number. In Ref. /7/ the slopes are constant and equal to the values in Ref. / 1/ and Table 1 1.1 up to 10' cycles, where they all change to -115. In Ref. /7/ also a thickness effect has been included. This will be further discussed in Section 1 1.2. The new proposal by the Department of Energy on new fatigue design guidance, has been the basis for the revision of the Veritas' rules for design of offshore structures, Ref. /8/ and NS 3472, Design rules for steel structures, Ref. /9/. In a coming revision of the regulations of the Norwegian Petroleum Directorate, reference will be made to NS 3472 regarding fatigue design. This means that the fatigue design codes in U.K. and Norway will be equal, except for cathodicly protected areas when N > l o 7 , Section 11.2. The SN-curve for design of tubular joints in the Department of Energy's Guidance Notes and the Veritas' Rules, Refs. 14, 51, is identical to that of the AWS of 1972, Ref. /lo/. In the Guidance Notes this curve is denoted Q, Ref. 141, and X in the Veritas' Rules. The AWS X-curve has later been modified. The X-curve of AWS of 1980, Ref. 11 11, is shown in Fig. 11.1 together with the modified AWS X-curve of 1983, Ref. 1121. Except for the c u t ~ f f level, the X-curve of API, Ref. 1131, is equal to that of the modified AWS X-curve. Two SN-curves recommended by API are shown in Fig. 11.2. For further use of the AWS and API curves the reader is referred t o Refs. 112, 131.
C y c l e s of load,
N
Fig. 11.1 SN-curves for tubular joints from AWS, Ref. 1121.
Section 11.1
0
t-
Permissible
cycles
of
load
N
Fig. 11.2 SN-curves from API, Ref. / 131. The API X-curve results in a fatigue life which is in the order of 30% less than that of the X-curve and Q-curve in Refs. / 10,5,4/. Certain requirements to the shape of the weld must be fulfilled when the API X-curve is employed. If this requirement is not satisfied, the API Xt-curve should be used. It reduces the calculated life by a factor of approximately 2.2 for typical offshore structures as compared to the API X-curve. The reason for API to modify the AWS X-curve for large values of N is the uncertainty about the behaviour of cathodicly protected joints in sea water. Experiments indicate that below N = lo7 cycles, fatigue lives of cathodicly protected joints are of the same magnitude as of joints in air. No test has been carried out for N > lo7. Due to uncertainties about the efficiency of the cathodic protection, such as shielding effects etc., and of threshold effects during crack propagation, it has been decided by API that a more conservative SN-curve should be used for design of joints in sea water than for joints in air when N > 10" cycles. The same uncertainties are also considered in the revision of the Norwegian fatigue design codes, Refs. /8,9/. In the last years, rather large test programs on tubular joints have been conducted. The test results have been taken into account by the Department of Energy in the establishment of a new design curve for tubular joints, namely the T-curve, Ref. 171. The T-curve will also be used in Norway, Refs. 18, 91. The slope of the T-curve is -1 13, while that of the older X-curve and Q-curve was -1 14.1, Refs. / 10, 5, 41. The curves are intersecting at approxi-
Section 11.2.1 - 11.2.2 mately N = 4 lo5 , which implies that the calculated fatigue lives for typical offshore structures will not be much different for these two SN-curves, provided the thicknesses of the considered joints are about 32 mm. As the thickness increases, the T-curve with the included thickness effect will result in shorter calculated fatigue lives than those of the X-curve. Fatigue life considerations based on da/dn - AK curves and fracture mechanics are included in the Veritas rules for design of offshore structures, Refs. /5,8/.Application of the rules is discussed in Section 1 1.4.
1 1.2
FATIGUE DESIGN STRENGTH TESTS
REGULATIONS
BASED ON FATIGUE
11.2.1 General
In the following the New Fatigue Design Guidance for Steel Welded Joints in Offshore Structures by the Department of Energy and NS 3472: Design rules for steel structures, will be reviewed, Refs. /7,9/. The SN-curves are obtained by experiments. The fatigue life calculation is founded on the assumption of linear cumulative damage (Miner-Palmgren rule). Application of this assumption implies that the long term distribution of stress range is replaced by a stress histogram, consisting of a convenient number of constant amplitude stress range blocks. The fatigue criterion then reads for the damage D:
where: k = ni = Ni = noi = q
number of stress blocks number of stress cycles in stress block i number of cycles t o failure at a constant stress range Aoi stress range in block i = usage factor
The number of stress blocks, k, should be large enough to ensure reasonable numerical accuracy and generally not less than 20. This, however, depends on the integration method used. 1 1.2.2 Stresses to be considered
Fatigue analysis of welded joints is based on the assumption that only the cyclic principal stress range is considered, i.e. the mean stress is neglected. In situations where the potential fatigue crack is located in the parent material
Section 1 1.2.3 at the weld toe, the relevant stress is the maximum principal stress range adjacent to the potential crack location. For a tubular joint, the stress is the idealized hot spot stress range defined as the greatest value of the extrapolation to the weld toe of the maximum principal stress range distribution immediately outside the region effected by the geometry of the weld. For examples see Chapter 8 and Chapter 10. 11.2.3 SN-curves and joint classifications For practical fatigue design, welded joints are divided into several classes, each with a corresponding design SN-curve. All tubular joints are assumed to be Class T, whereas other joints, including tube to plate, may fall in one of the eight classes specified in Appendix A of this chapter, i.e. B, C, D, E, F, F2, G or W depending upon: i) the geometrical arrangement of the detail ii) the direction of the fluctuating stress relative to the detail iii) the method of fabrication and inspection of the detail Each construction detail at which fatigue cracks may develop, must be placed in its relevant joint class in accordance with the criteria given in Appendix A. Details which are not classified in Appendix A should be treated as Class G, or Class W for load-carrying weld metal, unless a higher classification can be justified. It should be noted that, in a welded joint, there are several locations at which fatigue cracks may develop, e.g. at the weld toe in each of the two parts joined, at the weld ends, and in the weld itself. Each location should be classified separately. The basic SN-curves are founded on statistical analyses of appropriate experimental data. They consist of linear relationships between log Au and log N. The design curve is defined as the mean minus two standard deviations of log N and thus corresponds to 97.6% probability of survival. The SN design curves are written: where: N = log a = log s = m = logZ=
predicted number of cycles to failure for stress range Au cut of the log N-axis by the mean SN-curve standard deviation of log N negative inverse slope of the SN-curve logs-2.10gs
Values of log a, log s, log 11.1.
and m applying to details in air are listed in Table
Section 1 1.2.3 Table 11 .1 Details of basic SN-curves - Air.
N > 107
N G 107 Class
log a
log s
log i
m
log;
m
B C
15.3697 14.0342 12.6007 12.5169 12.2370 12.0900 11.7525 11.5662 12.6606
0.1821 0.2041 0.2095 0.2509 0.2183 0.2279 0.1793 0.1846 0.2484
15.01 13.63 12.18 12.02 11.80 11.63 11.39 11.20 12.16
4.0 3.5 3.0 3.0 3.0 3.0 3.0 3.0 3.0
17.01 16.47 15.63 15.37 15.00 14.72 14.32 14.00 15.62
5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0
D E F F2 G
W T
A
For joints exposed to sea water and adequately cathodicly protected, a cut-off level So is introduced at 2 lo8 cycles, Table 1 1.2 and Fig. 1 1.3. It is assumed that stress range levels below this limit do not contribute to fatigue damage. It should be noted that the effectiveness of cathodic protection in relation to fatigue has not been proved for structural steels with yield strengths larger than 400 MPa.
Table 11.2 Details of basic SN-curves cathodic protection.
-
Sea water and
Section 1 1.2.4
Number
o f cycles
Fig. 11.3 SN-curve D dependent on environment.
SN design curves for non-tubular and tubular joints in air and sea water with cathodic protection are drawn in Figs. 1 1.4 and 11.5. For unprotected joints in sea water, the basic SN-curves are reduced by a factor of 2 on life for all joint classes, Fig. 11.3. However for steels with yield strengths larger than 400 MPa, a penalty factor of 2 may not be sufficient. The curves are continuous with a constant slope equal to that in Table 1 1.1 for N < 1O7 cycles. 11.2.4 Thickness effect
The basic SN-curves-relate to 3 2 rnm wall thickness for tubular joints and to 22 mm for other joints. Since the fatigue strength of welded joints decreases with increasing plate thickness, Eq. (1 1.2) must be corrected for thicknesses other than 32 mm and 22 mm (Chapter 4). Tubular joints: l o g N = l o g ; - m . l o g ( - ) - mt 4 32
.logAo
t = thickness in mm through which the potential crack will grow. Other joints:
logN= log;-rn
4
t log(-)-m 22
10gAo
Values of t below 22 mm are not permitted in Eq. ( 11.4).
Section 1 1.2.4
Section 11.2.4
Section 11.2.5
-
11.3 - 11.4
11.2.5 Fatigue failure criteria inherent the SN-curves It should be kept in mind that the failure criterion utilized in the SN-curves is somewhat uncertain. Normally it is the fatigue growth through the thickness of the considered member.
11.3 STRESS CONCENTRATION FACTORS For calculation of the relevant stress in the material near to a change of geometry, the nominal stress must be adjusted with a global stress concentration factor (SCF), as discussed in Chapters 8 and 10. Stress concentration factors for different types of circular and rounded rectangular holes are shown in Fig. 11.6. This figure has been derived from information in Ref. 161. Some other geometries are dealt with in Ref. 1141. Stress concentration factors of tubular joints are discussed in Chapter 8.
11.4 EXAMPLES OF FATIGUE STRENGTH TESTS
DESIGN
BASED
ON
FATIGUE
In this section some examples on how to use the design codes are given. It is also referred to the examples in Chapter 10. EXAMPLE 1 At an early design stage simplified analyses are used to determine approximate member dimensions. Assume an F2 detail, a life time of 20 years, a Weibull two-parameter stress distribution and a utility factor q = 1.0. What is the maximum allowable stress range? Solution. The equivalent stress range giving the same damage as the Weibull stress distribution is, Eq. (1 0.24):
m = 3 for an F2 detail and h = 1.1 for a semi-submersible. With a wave period of 6s, no 1O8 cycles. Values of the radical sign are tabulated in Chapter 10, Table 10.5.
Section 11.4
4.8 SCF
Fig. 11.6 Stress concentration factors for rounded rectangular holes. The areas of the cut-outs are small compared with the dimensions of the plate. Ref. /8/
Section 11.4
F2 curve: log N = log Z - m log Ao log lo8= 11.63 - 3 logAoeq Aoeq.= 16.22 Finally : no, = 16-22 = 141 MPa
0.1 15
If the thickness of the plate is larger than 22 mm, the max. stress range is reduced to :
EXAMPLE 2
F a t i g u e f a i l u r e in weld startin from the roo?
Fig. 11.7 Cross joint with lack of penetration. Consider the fatigue life of the cross joint in Fig. 11.7. The joint is subjected to lo6 stress cycles with a constant stress range Ao = 60 MPa. The effective throat length of the weld a = 10 mm. Is the design fatigue life of the joint accept able? Solution. According to Appendix A, Joint Classification Type 5.4, the joint belongs to class W.
Section 11.4 Symmetry of the joint and stress equilibrium in the transverse direction yield Fig. 11.7:
Stress equilibrium in the direction of Ao yields: and ..-..
A ~ = - L . L = 60 fl.2 a fi.2
30 10
-
63.6 MPa
From Eq. (1 1.6): log N = log i - m log (A)- m log Ao 4 22 and for curve W:
which gives : N = 4.9. lo5 and = 106/4.9 los = 2.0
i.e. the design is not acceptable. EXAMPLE 3 Suppose that the weld in Fig. 1 1.7 is made with full penetration. Is the design fatigue life now acceptable? Solution. With full penetration the weld is of type number 5.1, Class F. Eq. (1 1.3) yields: logN = 11.80 -3.0 log(-)30 - 3.0 log 60.0 = 6.36 4 22
which gives:
Whether the design is acceptable or not will depend on the usage factor q required in the fatigue design code. It varies with the importance of the member and the possibilities for inspection and repair.
Section 1 1.4 Possible misalignment due to fabrication tolerances was not considered above. The general rule, however, is that the effect of fabrication tolerances on the fatigue life should be included in the calculation. See Chapter 10, Example 1.
EXAMPLE 4 A steel structure in a water depth of 147 m in the North Sea shall be checked for fatigue at a conceptual stage. The structure is assumed t o be fixed t o a foundation at mudline level. The design life is 40 years. The preliminary geometry of the structure based on static strength calculation is shown in Fig. 11.8. Conductors, conductor frames and risers are deleted. The joint and cone dimensions are as follows: Chord : outside radius wall thickness gap Brace: outside radius wall thickness inclination angle Cone: outside radius, upper outside radius, lower wall thickness length Geometrical parameters:
a)
The braces between levels 0 and +35 transfer the largest axial waveand current load forces. Due to a rather small P ratio, it shall be checked if the fatigue joint design at +35 m is acceptable.
b)
At level +35 the fluctuating stresses in the chords are also large, and the designer wants to know if the fatigue design of the cone transition in this region can be accepted.
Dynamic analysis. The structure in Fig. 11.8 is rather slender and it must be checked that its natural period is not too close to the wave period. The structure is therefore
Section 1 1.4
xi 35000
4
$+
C)
Plan .Levatton
@-
9
@-Kmy p I a n
Elevation a t row A,B,land2
Fig. 1 1.8 Geometry of steel structure.
140.00
Section 1 1.4 modelled for a computer analysis accounting for' its stiffness and mass. A suitable computer program such as SESAM 80 (Ref. 1191) is used. This calculation shows that the first natural period is 2.8 s, and is so low that a deterministic fatigue analysis is appropriate (Chapter 2). It is seen in Fig. 10.22 c that the Weibull shape parameter h is nearly constant up to a natural period of 3 s. Force and moment ranges. Due to symmetry only the four wave directions in Fig. 11.9 are considered. We shall look at direction 2 in more detail. The wave loading is calculated by an appropriate computer program, for example SESAM 80 (Ref. 1201). The program gives the forces on the structure according to Morison's equation (Section 2.6). A drag coefficient CD = 0.87 is assumed, accounting among other things for anodes for cathodic protection. Also the marine growth on the members must be considered, and a growth thickness of 100 mm is assumed. To calculate the maximum force range in the lower brace (Fig. 1 1.1 O),
4
'
Joint to analysed
be
Fig. 11.9 Wave directions to be considered. 474
Fig. 1 1-10. Definition of forces.
Section 11.4 appropriate waves are stepped through the structure as explained in Section 10.5.3. Maximum and minimum axial force in the brace occur for respectively maximum and minimum base shear. The axial force and the moments at the brace end are calculated for these loading conditions using a suitable computer program (Ref. 1191). We now assume that the calculation has been performed for the maximum wave height H = 3 1 m and for H = 7 m. Waves with heights around 7 m are giving the largest contribution to fatigue damage as explained in Section 10.5.2. These wave heights correspond to wave periods of respectively 17.3 s and 9.8 s (Section 2.7.4). The resulting force ranges are shown in Table 11.3. Table 11.3 Force and moment ranges, direction 2 in Fig. 11.9. Force and moment range ANb A"ipb
aMopb
1
H = 31 m, T = 17.3 s 1.2 1.7
1.2 6.7 2.9 3.5
'
107 N lo6 Nrn lo6 Nm lo7 N lo6 Nm lo6 Nm
H = 7.0 m, T = 9 . 8 s 0.15 0.20 0.15 0.80 0.30 0.45
lo7 N lo6 Nm lo6 Nm lo7 N lo6 Nm lo6 Nm
AN, AMipc AMV, The table values serve to illustrate the calculation procedure and are not a result of a detailed computer simulation.
According to Section 2.7.4 the wave height is given as: log n H = Hmu(l - 1 log no where no is the number of stress cycles in 100 years. With a wave period of 6 s, no = 5.26 10' = 1o ~. The . number ~ ~ of waves exceeding a wave height of 7 m is: logn = logno(l - -)H = 8.72(1 - -)7 = 6.75 Hm, 31 Calculation of the Weibull parameter. The Weibull parameter h may now be determined, using Equation 10.19 in Section 10.2.2, and the procedure outlined in Section 10.5.3.
Section 1 1.4 Aa and Aao can be calculated, using the force- and moment ranges in Table 11-3: Cone cross section area A, r 2 n R, T = 2 n 1750 90 = 98.96 lo4 mm2 Cone cross section modulus Wc =
Resulting bending moment range AM =
JAM^^^ +
2 AMopb
This is approximately the same value which may be derived from Fig. 10.22 c for a drag dominated structure, taking into account the reduction of h due to the position of the joint in the structure (Fig. 10.22 b). Stress concentration factors, SCF. The stress concentration factors are calculated, using the recommended parametric formulas in Chapter 8, Table A4.
Chord side Axial load : SCF, = 1-51 .y0.67. P-0.59. T1.lO. 0.067. sin1.52e
P = 1 - 5 1 23-30.67. 0.43-0.59. 0.441.10. 0.390.067. sin1-52450
.
= 4.60
Section 1 1.4 In-plane bending: S C F ~= 1.82 70.3 8. ~ 0 . 0 6 T0-94. . sin0.9e
.
= 1-82 23.30-38 0,430.06. 0,440.94* sin0.945~ = 1.94
Out-of-plane bending :
-
SCF, = [ l .O1 - 3 . 3 6 ~ 0.641~1 = [1.01 - 3.3610.43
rl-l8 * ~ i n l . ~ ~ f 3
- 0.641~1 23.3°.95*
450
= 3.79
Brace side
Axial load : SCF, = 0.92 .r0.16. P-0.44. T0.56. P 0.058. ,1.45*sin8 = 0.92. 23.30.16. 0.4~-0.44. 0.440.56*0.390.058. ,1.45*sin45O = 3.68
In-plane bending: S C F ~= 2-83 p-0.3 5. T0.35. sin0.58
. = 2-83 .0.43-0.35* 0.440.35. sin0.545~ = 2.40
Out-of-plane bending :
.
T ~ sin2-03f3 . ~ ~ SCFz = [0.76 - 1.92(P - 0.72)~] = [0.76 - 1.92(0.43 - 0.721~1 23.30eg9*0 . 4 4 O . ~ ~ sin2-0345~ -
= 3.32
The greatest SCF values are found on the chord side, therefore, further calculations are limited to that side. Hot spot stresses. The cross section area and cross section modules for the braces are respectively : A b z 2 * n m r * t = 2 - n * 9 0 O 9 4 022.60 = 1o4mm2 w ~ = T * ~ ~ * ~ = T * ~102o o 106mm3 ~ * ~ o =
Section 1 1.4 The extreme hot spot stress range Aoo can now be calculated by Equations 8.7, Section 8.3.7. We have for wave direction 2 : Aao= SCF,
mi b mb + SCFy --.-P-
Ab
= 244
+ 32 + 4 4 =
Wb
+ SCF, . AMopb Wb
320 MPa
Question a. Total number of stress cycles with a period of 6 s in direction 2 in 40 years:
Accumulated damage ratio for wave direction 2 can now be calculated using Equation 10.20, Section 10.2.2. Values of Z and m for the T-curve are found in Table 1 1.2 and for the gamma function in Table 10.2.
A similar procedure is followed t o determine the damage ratios associated with the other wave direction, and we get for the total damage ratio:
Since the chord thickness is much greater than 32 mm, the damage ratio should be corrected for the thickness effect as explained in Section 10.6: (-)
Dthickness effect included =
m/4
= D .(--) 90
3 2.
32
314 = 2-17
.D
Alternatively, the thickness effect can be considered by reducing the ii value
of the T-curve:
-
-
32 mi4 = a
athickness effect included = a (-1t
. ( 3 ) 3 / 4 = 0.46 . a 90
Section 11.4 The allowable damage ratio q is discussed in Ref. 1211. For critical members below water level which are regularly inspected, r) = 0.33. It can be seen in Fig. 1 1.9 that waves of direction 3 will produce larger axial forces in the considered brace than those of direction 2. We can therefore conclude, without further calculation, that D > q for the brace, and that the geometry must be modified. According to Section 8.3.4.4, the SCF's can be reduced by decreasing y increasing 0 The wall thickness of the chord is already rather high, so the second alternative may be the best choice. 0 may be increased by increasing the brace radius over the total brace length or by inserting a cone, thus locally increasing the radius. Question b. The maximum fluctuating stresses in the considered chord occur for wave direction 2, for which the data in Table 11.3 apply. The stress concentration factor at the chordlcone transition may be calculated based on elastic shell theory, see e.g. Ref. 1221. The stress at the transition can also be calculated by the following formula (Ref. 1131):
where: R = radius of the chord cylinder at the transition T = chord wall thickness Tc = cone wall thickness - T for calculation of stresses in the chord Te- Tc for calculation of stresses in the cone o, = axial stress due to axial load ub = global bending stress a = cone angle (Fig. 1 1.lo) We assume that the transition chord/cone is welded from both sides. According to Appendix A, Chapter 11, the joint belongs to class 7.6, SNcurve E with log Z = 12.02 and m = 3. The highest stress concentration factor is found for the transition with the lowest R:
Section 1 1.4 tga = 2100 - 17'0 = 0.167 (Fig. 11,lO) and 2100
The accumulated damage ratio D2 from waves in direction 2 can now be calculated. We will first correct Ti for the thickness effect:
A similar procedure is followed for the other wave directions. As direction 2 is giving the largest contribution t o the fatigue damage, it can be concluded that the total damage
A damage ratio of 0.33 is allowed, therefore the cone transition design is acceptable with respect to fatigue.
Comments on Example 4. The example shows how fatigue lives may be predicted at an early design stage. It is noted that even a small check involved numerous calculations. The calculation of fatigue lives is therefore best suited for computers using efficient preprocessors for handling of geometrical data and postprocessors for automatic calculation of SCF's and fatigue lives. During the last years a large effort has been made to make efficient programs for deterministic and stochastic fatigue analyses. At the same time the efficiency of the computers has increased and the costs associated with large analyses have been largely reduced. In many cases it is therefore preferable to let the computer do the work even at an early stage of the design as described in Section 10.5.3. Never-the-less it is important that the designer understands how fatigue lives are computed in the program. It is also important that he understands which factors influence the fatigue life. That enables him to make the best modifications to the design if the calculation results in unacceptable fatigue lives.
Section 11.5.1 - 11.5.2 11.5 FATIGUE DESIGN REGULATIONS BASED ON CRACK GROWTH RATE TESTS AND FRACTURE MECHANICS 11.5.1 General
In this section a review is made of the new fatigue design regulations based on crack growth rate tests and fracture mechanics as outlined in Classification Note no. 30.2, Det norske Veritas, Ref. 181. Normally, weld connections contain several defects, both surface defects and internal defects. Fatigue cracks may propagate from both types, dependent on such factors as the size of the defect, the type of the weld connection, and the geometry of the weld. The defect which most rapidly leads to unstable fracture, shall be decisive. In Section 10.3.4, Eq. (1 0.34), it was shown that the number of cycles to failure could be expressed as:
with
when failure was defined as crack growth through the thickness. The different parameters in Eqs. (1 1.5) and (1 1.6) are as follows:
C = crack growth coefficient, Table 11.4 m = crack growth exponent, Table 11.4 W = width of. plate Aa = stress range Ui = ai/W ai = initial crack depth F = geometry correction factor 1 1.5.2 Crack growth parameters
If documentation on relevant crack propagation parameters is lacking, the values in Table 11.4 may be used. If fatigue analysis based on fracture mechanics is used for design purpose, the C-value given as the mean plus 2 standard deviations should be used in order to comply with the safety of the corresponding SN-curve.
Section 1 1.5.3 Table 11.4 Crack growth parameters. C
-
[(MP,">m)m]
Mean + 2 st.dev.
m
Mean value
Welds in air
3.1
1.1 10-l3
3.3 -10-I
Welds subjected to seawater
3 -5
3.4*10-l
1.6- 10-I
11.5.3 Crack growth calculation for butt welds, cruciform joints and tubular joints The integral I defined in Section 11.5.1 has been calculated for a buttweld, a cruciform joint and a tubular joint assuming infinitely long cracks. The results are shown in Figs. 11.1 1 - 11.19 (Ref. /8/). The values apply to crack propagation from an initial crack depth, ai, to a depth af equal to the plate thickness, i.e. a = 1. The number of stress cycles to failure follows from Eq. (1 1.5). If the crack grows from a, to a,, the answer results when the difference between I(a,) and I(az) is inserted as numerator in Eq. (1 1.5). Figs. 11.1 1-1 1.19 are based on local tension stresses as defined in Chapter 10, Section 10.2.4. If the stresses are mainly due to bending, I must be calculated according to Eq. (1 1.6). The appropriate F function may be derived by finite element analyses of the considered structure, see e.g. Ref. 1151 and Chapter 3 in this book. For surface cracks the integral I is shown for two values of the crack growth exponent m. m = 3.1 is relevant for non-corrosive environments or corrosive environments with an effective corrosion protection system. Without corrosion protection and especially for high values of the stress ratio R, m = 3.5 is relevant. Residual stresses should be considered when R is determined. In Figs. 1 1.1 1-1 1.16 the integral is shown for two different strain conditions marked: No restriction to bending and restriction to bending. The former means that the plate is free to bend as the crack propagates and the crack opens, the latter that bending is rendered impossible. The values of the integral in Figs. 1 1.1 1-1 1.19 refer to infinitely long cracks. For internal defects close to the surface in cruciform joints, the number of cycles to fracture is calculated in two steps: First Fig. 11.17 is used for growth to the surface, thereafter Fig. 11.15 or Fig. 1 1.16 until complete fracture takes place. In the first step, equal growth at both crack
Section 1 1.5.3
Fig. 11.1 1 Butt welds in air. Toe defects. No restriction against bending. m = 3.1. Ref. /8/.
Section 1 1.5.3
Fig. 11.12 Butt welds in air. Toe defects. Restriction against bending. m = 3.1. Ref. 181.
Section 1 1.5.3
Fig. 11.13 Butt welds in seawater. Toe defects. No restriction against bending. m = 3.5. Ref. /8/.
Section 11.5.3
Fig. 11.14 Butt welds in seawater. Toe defects. Restriction against bending. m = 3.5. Ref. /8/.
Section 1 1.5.3
.
.
.
. .
. .
.
.
. . . .
.
-
. . . . . .
.
.
.
.
.
. . ....
.
.
.
.
.. .
.
.
.
. ..
.
.
.
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. .
. ..
0.001
.
.
.
. . . . .
..
....
.
....
...
.
. ..
.
.
.
.
0.01
..
..
..
0.1
Fig. 11.15 Cruciform joints in air. Toe defects. m = 3.1. Ref. /8/.
1 .o a/w
Section 1 1.5.3
Fig. 11.16 Cruciform joints in seawater. Toe defects. m = 3.5. Ref. 181.
Section 1 1.5.3
Fig. 1 1.1 7 Cruciform joints. Embedded defects. m = 3.1. Ref. 181.
Section 1 1.5.3
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1
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a
-
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1
Fig. 11.18 Tubular joints in air. Surface cracks at the weld toe. m = 3.1. Ref. /8/.
1
1
1
Section 1 1.5.3
Fig. 1 1.1 9 Tubular joints in seawater. Surface cracks at the weld toe. m = 3.5. Ref. 181.
Section 11.6 tips is assumed. Cracks situated less than 0.15 B from the weld toe should be treated as surface cracks and evaluated by the curves in Figs. 1 1.15 or 11.16. Welded tubular joints may be of varied designs. Figs. 11.18 and 1 1.19 are based on upper bound values for crack growth in simple unstiffened T-, Y- and IS-joints and are relevant for growth of surface cracks in the thickness direction in the hot spot region. Hot spot stresses shall be used in Eq. (1 1.5).
11.6 EXAMPLES OF CRACK GROWTH CALCULATION BASED ON CRACK GROWTH RATE TESTS AND FRACTURE MECHANICS
EXAMPLE 5
1
2
3
S h a r p under c u t
Fig. 11.20 Fatigue life as a function of undercutting. Consider the cross-joint in Fig. 1 1.20. The throughgoing plate is subjected to an equivalent stress range Ao = 20 MPa. A fatigue crack is assumed to develop from an initial defect of depth ai at the weld toe. Calculate the number of stress cycles to fracture!
Section 11.6
Solution. We presume a long crack and that the length of the loaded plate is large compared with its thickness. This way, the plate is free to bend as the crack develops and the graph in Fig. 11.15 with e/W = 0 and "no restriction to bending" applies. a/W = 0.1130 = 0.0033 yields: I = 0.53 and from Eq. (1 1.5):
For different values of the initial defect ai, the curve in Fig. 11.20 results, showing the fatigue life in relative units as function of the initial defect depth. EXAMPLE 6
j~s-T+-
A6
-7
Fig. 11-21 Butt welded plates. Two plates with thickness W = 25 mm are joined by an X weld, Fig. 11.21. After fabrication, undercuts at the weld toe of 1 mm depth and a misalignment between the plates of e = 2 mm are detected. The joint operates in sea water without cathodic protection, and is exposed to cyclic loading with No = lo6 cycles at an equivalent stress range Ao = 30 MPa. Accidental events may produce stresses equal to the yield strength of the plate. Material properties: Re = 340 MPa, KIC = 60 MPafi. It shall be checked if the design can be accepted under the given conditions. Solution.
It is assumed that the plates are long, so that bending stresses due to crack opening are limited and Fig. 1 1.13 applies. The relative misalignment e/W = 0,08. Since the nomograph in Fig. 11.13 is not drawn for this value, we calculate the local stress range at the
Section 11.6 weld toe (Chapter 10, Section 10.2.4): Aulocal = Ao(1 + 3 e ) = 30(1 + 3 00.08)= 37.2 MPa W
We have for the critical crack length af at fracture:
KIC = R , d n . a f * F where F is the geometry correction factor, dependent on af (Chapter 3):
By trial and error procedure it has been found that af r 5 mm and F satisfy the two equations:
1.4
We then read in Fig. 11.13 for 0 =30°, e/W = 0, and a/W = 1/25 ~ 0 . 0 4 : I. = 4.2
lo-'
and for a/W = 5/25 = 0.2:
If = 6.0 lo-' In Table 1 1.4, m = 3.5 and C = 1.6 10-I for the mean-plus-two-standarddeviations. We then obtain for the number of stress cycles to fracture, Eq. (1 1.5):
For a structure in sea water without cathodic protection, the codes generally recommend a usage factor of q = 0.3 when the fatigue life calculation is based on SN-curves. Logically, the same factor must apply in crack growth calculations. The design life of the joint is therefore:
Conclusion: The designlfabrication is not acceptable under the given condi-
Section 11.7 tions. An increase of the design life might be obtained by grinding of the weldlplate transition as explained in Chapter 6. With reference to the calculation, grinding leads to a reduction of the undercut depth and therefore an increase of I. .
11.7 FATIGUE FAILURE CRITERIA IN CONNECTION WITH REPAIR
OF DEFECTS Each crack or defect not complying with the code requirements must be individually considered, when the question of possible repair comes up. First, a detailed investigation of the structural strength with regard to static and fatigue loading will have to be performed. The following items should be considered : Importance of structural member. Consequences associated with a possible unstable fracture. Uncertainties about present size of defect or crack. Reliability of inspection method. Maximum static stress and stress range during fatigue cycling. Uncertainties associated with fatigue crack growth parameters and material toughness. Number of cycles to next inspection or to end of life. The importance of the member may be determined by a simple inspection of the collapse mechanism. For more complex geometries and redundant structures it may be advisable to remove the considered element and calculate the redistributed forces in order to get more information on the probability of a progressive collapse. The consequences of a progressive collapse should be evaluated with respect to:
-
-
-
loss of human lives pollution cost of structure and equipment
In order to perform a most reliable crack growth analysis, it is necessary to establish a good description o f the defect geometry. In this connection the accessibility for inspection of the detail in question must be considered; further the reliability and sensitivity of the inspection method are important elements. If deterministic analyses are used in crack growth calculation, conservative estimates of the defect size should be applied.
Section 1 1.8.1 Due considerations should be made to uncertainties in calculated stresses. As fatigue lives are inversely proportional to the stress range raised to a power of 3, deterministic fatigue calculations should be based on conservative estimates of stresses. Strain gauge equipment at the defective regions may improve the reliability of stress estimates. When probabilistic methods are applied, each coefficient defining the stress function should be accounted for. Possible bias should be on the safe side. Bias is defined and discussed in Ref. 1181. Crack growth calculations with reference to possible repair of defects are much influenced by the crack growth parameters m and C. There is a great scatter in the values as can be seen by comparing the mean and the mean-plus-two-standard-deviation values in Table 11.4. As is previously discussed, the fracture toughness of the plate or weld material only slightly influences the fatigue life of simple joints. For tubular connections the situation is different, and the fracture toughness value may be important. The number of cycles to the next inspection or to the end o f the structure life is important. Also the reliability of the inspection must be considered. Cost of repair is essential, and the cost effectiveness of different repair solutions should be evaluated. The extent and costs of analyses and investigations connected with repair of defects should comply with the consequences of a possible failure. When consequences are large, fracture mechanics analyses based on probabilistic methods may pay and prove conclusive, in addition to the deterministic analyses described in Sections 1 1.4 and 1 1.5. 11.8 NOTES ON DAMAGES AND METHODS FOR MAKING REPAIRS
1 1.8.1 General As a general rule, offshore platforms will require repair or maintenance during their lifetime, due to causes such as unfavourable shapes of structural details, inaccurate design analysis, occurrence of unforeseen load combinations, falling objects, ship impacts, explosions, fire, misuse, corrosion and other deterioration. In most cases the recorded damages are of less serious character. Nevertheless, in each particular case, the following aspects will have to be reviewed:
- Cause of the damage.
-
-
Possibility of other undetected damages on the structure due to the same cause. Possible need for further inspection.
Section 11.8.2
-
Need for repair. Time for repair. Possible consequences of postponement of repair. Possible limitations in the operation of the platform before, during and after the repair has been completed. Quality and suitability of repair methods adopted.
11.8.2 Repair and reinforcing methods The following repair and reinforcing methods have been proposed or used for offshore steel structures:
-
-
-
-
-
Underwater wet welding. Dry welding in habitat. Clamping of prefabricated parts to the structure. Grouting of confining sleeves. Grouting between insert pipe and original member. Grouted body inside tubular member. Grouting and auxiliary welding. Grinding and drilling.
Underwater welding performed by divers in a wet environment has been and is being utilized, but with all the obvious difficulties involved, the results are not promising in structural repair. The main problems are of metallurgical nature. Hydrogen and oxygen produced by dissociation of water lead to increased risks for porosity and cracking as well as reduced ductility and fracture toughness. The high cooling rate tends to raise the hardness of the heat affected zone and to produce internal stresses. Habitat welding is the preferred underwater welding technique for structural welds. Besides access and space in a watertight hyperbaric environment, power for preheating, welding and drying of steel surfaces is required. Provisions must be made for shielding gas for welding, inert gas in the habitat and breathing gas for the welder. Non-destructive testing should be used for checking the weld homogeneity. Habitat welding may be difficult to apply to complex joints, and if the cracks are caused by inadequate material properties, repair is not likely to be successful. Compared to wet welding, hyperbaric welding yields superior quality, but at a considerably higher cost. Clamping methods may be used to replace the functions of a damaged part by adding members adjacent to the damage. The problems are related to the tight fit needed to transfer the forces, and that the bolts tend to loosen. These difficulties may be overcome, but it requires rigorous checking
Section 1 1.8.2 during installation and service. Accurate alignment and rigging generally call for a considerable amount of expensive underwater operation. Repair - and reinforcement methods based on grouting technique appear promising, mainly because a moderate amount of underwater work is needed and because cracks and unfavourable residual stresses are not introduced in the structure. The application of grouted confining sleeves around defective joints, as shown for a T-connection in Fig. 11 2 2 , is however not without practical problems, such as the varying and complicated geometry of the joints, and the rather difficult task of securing tightness of the assembly during grouting.
Fig. 11.22 Grouting of defective T-connection. Grouting between an insert pipe and the original member is shown in Fig. 11.23. It is a possible way of reinforcing a leg, but placing an insert pipe inside a brace is complicated. Full internal grouting is an alternative method in this case.
'Gr o u l
Seal
'
Fig. 11.23 Grouting between insert pipe and original member.
Section 11.8.2 The combination of grouted sleeve with welded sealing proves a less attractive method because it involves most of the disadvantages of both methods. Grinding and drilling are two methods that can be used to stop a crack from propagating. Grinding smoothens the sharp ends of a crack, thereby reducing the stress concentration factor. A hole drilled at each end of the crack has a similar effect. Cold working of the inside surface of the hole by drawing through it a slightly overdimensioned bar or wire, produces an additional reduction of the local tensile stresses. EXAMPLE 7 - Jacket repair of cracked tubular joint at 20 m depth.
During the annual NDT-survey, a 900 mm long crack was detected in a tubular joint by magnetic particle inspection. The crack was located in the fusion line between weld and leg. It was decided to repair by dry welding. A habitat was made to fit around the node. The water inside the habitat was displaced by compressed air which allowed the diver to carry out the welding under dry conditions. Before the welding took place, all cracks and crack indications were removed by grinding and gouging. Magnetic particle testing was then applied to ensure that no cracks were left. After preheating to 100°C by electric heating elements, the welding was completed manually with gas shield and flux cored wire. Visual - and magnetic particle inspection followed.
EXAMPLE 8 - Repair of crack in jacket leg at 15 m depth. A doubler plate had been welded to a jacket leg during installation for fastening one of the temporary float chambers. The weld between the plate and the leg had cracked, and the crack had propagated into the leg, and through the wall for a length of about 4 m. The leg had been grouted on the inside. When the crack was discovered, the doubler plate was removed and holes were drilled at all crack ends to prevent further propagation. A habitat for dry rewelding of the cracked area was fitted around the leg. The cracks were ground out and bevelled, the grout underneath removed and magnetic particle inspection was applied to the area to ascertain that all cracks had been completely removed. The leg was then preheated for 15 hours to remove moisture from the underlying grout. After completed repair, the welds were inspected visually, with ultrasonics and magnetic particles.
Chapter 1 1 . References REFERENCES 1. Gurney,T.R.: Fatigue of Welded Structures. Cambridge University Press, Second edition, 1979. 2. Gurney, T.R.: Fatigue Design Rules for Welded Steel Joints, The Welding Institute Research Bulletin. Volume 17, Number 5, May 1976. 3. Regulations for the structural design of fixed structures on the Norwegian Continental Shelf, Norwegian Petroleum Directorate, 1977.
4. Offshore installations: Guidance on Design and Construction, Department of Energy, 1977. Her Majesty's Stationary Office, London. 5. Rules for the Design, Construction and Installation of Offshore Structures, Det norske Veritas, 1977. 6. BS 5400 Part 10, 1980. Code of Practice for Fatigue. Steel, Concrete and Composite Bridges. British Standard Institution. 7. Offshore Installations: Guidance on Design and Construction. New Fatigue Design Guidance for Steel Welded Joints in Offshore Structures. Recommendations of the Department of Energy "Guidance Notes" Revision Drafting Panel. August 1983, Issue N.
8. Classification Note No. 30.2. Fatigue Strength Analysis for Mobile Offshore Units. Det norske Veritas, 1984. 9. NS 3472 Design rules for steel structures, 1984. Norges Standardiseringsforbund. 10. AWS (1972) Structural Welding Code. American Welding Society. 11. AWS D l .1 (1980) Structural Welding Code. American Welding Society. 12. AWS D l .1 (1983) Structural Welding Code. American Welding Society. 13. API RP 2A Recommended Practice for Planning, Designing and Constructing Fixed Offshore Platforms. Thirteenth Edition, January 1982. American Petroleum Institute. 14. Peterson, R.E.: Stress Concentration Factors. John Wiley & Sons, Inc., 1974. 15. Aarnodt, B.: Application of the Finite Element Method to Problems in Linear and Nonlinear Fracture Mechanics. Thesis. Division of Structural Mechanics. NTH, The University of Trondheim, 1973. 16. Publication Document 6493: 1980. Guidance on Some Methods for the Derivation of Acceptance J evels for Defects in Fusion Welded Joints. British Standard Institution.
Chapter 1 1 . References 17. Hellan,K.: Introduction to Fracture Mechanics, McGraw-Hill, New York, 1984. 18. Fjeld, S.:
Reliability of Offshore Structures, OTC paper 3027, 1977. 19. SESAM' 80. SESTRA. Super Element Structural Analysis. User's manual. Computas Report No. 82-6102,1983. 20. SESAM' 80. WAJAC. Wave and current loads on Fixed Rigid Frame Structures. User's manual. Computas Report No. 82-6108,1983.
21. Oljedirektoratetsforskrift for baerende konstruksjoner. Utkast nr. 12. Oljedirektoratet. Stavanger. 1984.
22. Tirnoshenko, S.P. and Woinowsky - Krieger, S.: Theory of Plates and Shells. McGraw-Hill. 1959.
rn 0
Appendix A. Joint Classification (Gurney, T.R.: Fatigue of Welded Structures, Cambridge University Press, 1979).
N
*
Cd
%3
g
Type 1. Material free from welding Notes on potential modes of failure In plain steel, fatigue cracks initiate at the surface, usually either at surface irregularities or at corners of the cross-
section. In welded construction, fatigue failure will rarely occur in a region of plain material since the fatigue strength of the welded joints will usually be much lower.
In steel with rivet or bolt holes o r other stress concentrations arising from the shape of the member, failure will usually initiate at the stress concentration.
Type number, description and notes on mode of failure
Class Explanatory comments
Examples, including failure modes
1.1 Plain steel (a) With all surfaces machined and polished, and of uniform o r uniformly varying cross-section.
A
(b) In the as-rolled condition, o r with cleaned surfaces but with no flame-cut edges o r re-entrant corners
B
Beware of using class B for a member which may acquire stress concentrations during its life, e.g. as a result of rust pitting. In such an event class C would be more appropriate
(c) A s (b) but with any flame-cut edges subsequently ground o r machined t o remove all visible sign of the drag lines
B
Any re-entrant corners in flame-cut edges should have a radius greater than the plate thickness
(d) As (b) but with the edges machine flame-cut by a controlled procedure t o ensure that the cut surface is free from cracks
C
Note, however, that the presence of a re-entrant corner implies the existence of a stress concentration so that the design stress should be taken as the net stress multiplied by the relevant stress concentration factor
9
Type 2. Continuous welds essentially parallel to the direction of applied stress Notes o n potential modes of failure With the excess weld metal dressed flush, fatigue cracks would be expected to initiate at weld defect locations. In the as-welded condition, cracks might initiate at stopstart positions or, if these are not present, at weld surface ripples.
continuous, and (b) if they are attached by welding those welds must also comply with the relevant class requirements (note particularly that tack welds, unless subsequently ground out or covered by a continuous weld, would reduce the joint to class F, see joint type 6.5.
General comments 1. Backing strips. If backing strips are used in making these joints: (a) they must be
2 . Edge distance. An edge distance criterion exists to limit the possibility of local stress concentrations occurring at
unwelded edges as a result, for example, of undercut, weld spatter, or accidental overweave in manual fillet welding (see also notes on joint type 4). Although an edge distance can be specified only for the 'width' direction of an element, it is equally important to ensure that n o accidental undercutting occurs on the unwelded corners of, for example, cover plates or box girder flanges. If it does occur it should subsequently be ground smooth.
2.1 Full or partial penetration butt welds, or fillet welds Parent or weld metal in members, without attachments, built up of plates or sections, and joined by continuous welds.
tn
0 W
(a) Full penetration butt welds with the weld overfill dressed flush with the surface and finish-machined in the direction of stress, and with the weld proved free from significant defects by non-destructive examination.
B
The significance of defects should be determined with the aid of specialist advice andlor by the use of fracture mechanics analysis. The NDT technique must be selected with a view to ensuring the detection of such significant defects.
(b) Butt or fillet welds with the welds made by an automatic submerged or open arc process and with no stop-start positions within the length.
C
If an accidental stopstart occurs in a region where class C is required remedlal action should be taken so that the finished weld has a similar surface and root profile to that intended.
(c) As (b) but with the weld containing stopstart positions within the length. This class includes welds made manually.
D
For situation at the ends of flange cover plates see joint type 6.4.
-
*
'a
3E X
3
u
P
Type 3. Transverse butt welds (i.e. essentially perpendicular to the direction of applied stress) Notes on potential modes of failure With the weld ends machined flush with the plate edges, fatigue cracks in the aswelded condition normally initiate at the weld toe, so that the fatigue strength depends largely upon the shape of the weld overfill. If this is dressed flush the stress concentration caused by it is removed and failure is then associated with weld defects. In welds made on a permanent backing strip, fatigue cracks initiate at the weld metallstrip junction, and in partial penetration welds (which should not be used under
Design stresses In the design of butt welds of types 3.1 or 3.2 which are not aligned the stresses must include the effect of any eccentricity. An
Type number, description and notes on mode offailure
Class Explanatory comments
3.1. Parent metal adjacent to, o r weld metal in, full penetration butt joints welded from both sides between plates of equal width and thickness or where differences in width and thickness are machined to a smooth transition not steeper than 1 in 4.
fatigue conditions), at the weld root. Unless made on a permanent backing (type 3.3) welds made entirely from one side are not classified for fatigue purposes, since adequate control cannot be exercised over the profile of the root bead which is where fatigue cracks would be likely to initiate.
Note that this includes butt welds which do not completely traverse the member, such as circular welds used for inserting infilling plates into temporary holes.
approximate method of allowing for eccentricity in the thickness direction is to multiply the nominal stress by (1 + 3elt), where e is the distance between centres of thickness of the two abutting members (if one of the members is tapered, the centre of the untapered thickness must be used); and t is the thickness of the thinner member. With connections which are supported laterally, e.g. flanges of a beam which are supported by the web, eccentricity may be neglected.
Examples, including failure modes
a ?? X
>
(a) With the weld overfill dressed flush with the surface and with the weld proved free from significant defects by nondestructive examination.
C
The significance of defects should be determined with the aid of specialist advice and/or by the use of fracture mechanics analysis. The nondestructive testing technique must be selected with a view to ensuring the detection of such significant defects.
(b) With the welds made in the shop, either manually o r by an automatic process other than submerged arc, provided all runs are made in the flat position.
D
In general welds made positionally, or on site, o r by the submerged arc process tend to have a poor reinforcement shape, from the point of view of fatigue strength. Hence such welds are downgraded from D to E.
(c) Welds made other than in (a) or (b).
E
In both (b) and (c) the corners of the cross-section of the stressed element at the weld toes should be dressed to a smooth profile. Note that step changes in thickness are, in general, not permitted under fatigue conditions, but that where the thickness of the thicker member is not greater than 1.15 x the thickness of the. thinner member, the change can be accommodated in the weld profile without any machining. Step changes in width lead to large reductions in strength (see joint type 3.3). Continued.
7jpe nrtmber, descrlprion and r ~ o t eon . ~ rr~odeof failure
Class E~ylannroryc o n ~ m e r ~ t s
3.2. Parent metal adjacent to, or weld E metal in, full penetration butt joints made on a permanent backing strip between plates ot equdl width and thlckneqs or wlth d~tferences In wldth and th~ckness machlned to a smooth transition not steeper than 1 in 4
Note that ~t the b a c k ~ n gstrlp is flllet welded or tack welded t o the member the joint could be reduced to class G (joint type 4 2)
3.3. Parent metal adjacent to, or weld metal in, full penetration butt-welded joints made from both sides between plates of unequal width, with the weld ends ground to a radius not less than 1.25 x the thickness r .
Step changes in width can often be a v o ~ d e dby the use of shaped transition plates, arranged so as to enable butt welds to be made between plates of equal width.
F?
Examples, including failure modes
-- ;- I
-
0 No t a c k we!ds
ru'ote that for this detail the stress concentration has been taken into account in the joint classification.
Type 4. Welded attachments on the surface or edge of a stressed member Nores on [rotenrial modes of failure When the weld is parallel to the direction of the applied stress fatigue cracks normally initiate at the weld ends, but when it is transverse to the direction of stressing they usually initiate at the weld toe; for
attachments involving a single as opposed to a double weld, cracks may also initiate at the weld root. The cracks then propagate into the stressed member. When the welds are on or adjacent t o the edge of t h e
stressed member the stress concentration is increased and the fatigue strength is reduced; this is the reason for specifying an 'edge distance' in some of these joints (see also note o n edge distance in joint type 2)
a 2> 5
E X
*
Type number, description and notes on mode of failure
Class Explanatory comments
4.1. Parent metal (of the stressed member) adjacent to toes or ends of bevel-butt or fillet-welded attachments, regardless of the orientation of the weld to the direction of applied stress, and whether or not the welds are continuous round the attachment.
Examples, including failure modes
Butt-welded joints should be made with an additional reinforcing fillet so as to provide a toe profile similar to that which would exist in a filletwelded joint.
(a) With attachment length (parallel to the direction of the applied stress) < 150 mm and with edge distance LlOmm.
F
(b) With attachment length (parallel to the direction of the applied stress) > 150 mm and with edge distance a 10 mm.
F2
4.2. Parent metal (of the stressed member) at the toes or the ends of butt- or fillet-welded attachments on or within 10 mm of the edges or corners of a stressed member, and regardless of the shape of the attachment.
G
The decrease in fatigue strength with increasing attachment length is because more load is transferred into the longer gusset, giving an increase in stress concentration.
distance
Note that the classification applies to all sizes of attachment. It would therefore include, for example, the junction of two flanges at right angles. In such situations a low fatigue classification can often be avoided by the use of a transition plate (see also joint type 3.3).
Continued.
* Sc
0 00
Type number, description and notes on mode of failure
Class Explanatory comments
4.3. Parent metal (of the stressed member) at the toe of a butt weld connecting the stressed member to another member slotted through it.
Note that this classification does not apply to fillet-welded joints (see joint type 5.lb). However it does apply to loading in either direction (L o r T in the sketch).
(a) With the length of the slotted-through member parallel to the direction of the 0 and with edge applied stress ~ 1 5 mm distance 310 mm.
F
(b) With the length of the slotted-through member parallel to the direction of the applied stress >I50 mm and with edge distance 210 mm.
F2
(c) With edge distance < I 0 mm.
G
Type 5. Load-carrying fillet and T butt Notes on potential modes of failure Failure in cruciform o r T joints with full penetration welds will normally initiate at the weld toe, but in joints made with load-carrying fillet or partial penetration butt welds cracking may initiate either at the weld toe and propagate into the plate
Examples, including failure modes
welds or at the weld root and propagate through the weld. In welds parallel to the direction of the applied stress, however, weld failure is uncommon; cracks normally initiate at the weld end and propagate into the plate perpendicular t o the direction of applied
stress. The stress concentration is increased, and the fatigue strength is therefore reduced, if the weld end is located on or adjacent to the edge of a stressed member rather than on its surface.
Type number, description and notes on mode of failure
Class Explanatory comments
Examples, including failure modes
-
Member Y can be regarded as one with a non-load-carrying weld (see joint type 4.1). Note that in this instance the edge distance limitation applies.
5.1. Parent metal adjacent to cruciforrn joints o r T joints (member marked X in sketches).
(a) Joint made with full penetration welds and with any undercutting a t the corners of the member dressed out by local grinding.
F
(b) Joint made with partial penetration o r fillet welds with any undercutting at the corners of the member dressed out by local grinding.
F2
In this type of joint, failure is likely to occur in the weld throat unless the weld is made sufficiently large (see joint type 5.4).
-/71
P
'a
z
3
wl 0 \O
E
X
Continued.
P
Appendix A
Type 6. Details in welded girders Notes on potential modes of failure Fatigue cracks generally initiate at weld toes and are especially associated with local stress concentrations at weld ends, short lengths of return welds, and changes of weld direction. Concentrations are Type number, description and notes on mode of failure
enhanced when these features occur at o r near an edge o f a part (see notes on joint type 4).
General comment Most of the joints in this section are also
Class Explan arory comments
6.1. Parent metal at the toe of a weld connecting a stiffener, diaphragm, etc. t o a girder flange. (a) Edge distance 3 l O m m (see joint type
shown, in a more general form, in joint type 4; they are included here for convenience as being the joints which occur most frequently in welded girders.
F
4.2). (b) Edge d~stance< 10 mm.
G
6.2. Parent metal at the end of a weld connecting a st~ffener,diaphragm, etc. t o a girder web in a region of combined bending and shear.
E
~3
Examples, including failure modes
Edge distance refers t o distance trom a free, i.e. unwelded, edge. In this example, therefore, it is not relevant as far as the (welded) edge of the web plate is concerned. For reason for edge distance see note on joint type 2.
(
)'
-
G
/-
-z-
--
4
Y'
--(
Edge d~stance
This classification Includes attachments to girder webs.
all
Continued.
*
9
'dl
+
w
Type number, description and notes on mode of failure
'a Class Explanatory comments
Examples, including failure modes
2
EL
-e--
6.3. Parent metal adjacent t o welded shear connectors. (a) Edge distance 210 mm.
F
(b) Edge distance <10 mm (see type 4.2).
G
6.4. Parent metal at the e n d of a partial length welded cover plate, regardless of whether the plate has square o r tapered ends a n d whether o r not there are welds across the ends.
G
This class includes cover plates which are wider than the flange. However, such a detail is not recommended because it will almost inevitably result in undercutting of the flange edge where the transverse weld crosses it, as well as involving a longitudinal weld terminating on the flange edge a n d causing a high stress concentration.
6.5. Parent metal adjacent t o the ends of discontinuous welds, e.g. intermittent web-to-flange welds, o r tack welds unless subsequently buried in continuous runs.
E
This also includes tack welds which are not subsequently buried in a continuous weld. This may be particularly relevant in tack-welded backing strips.
As above, but adjacent to cope holes.
F
Note that the existence of the cope hole is allowed for in the joint classification; it should not be regarded as an additional stress concentration as far as the web-to-flange welds are concerned.
Edge distance
SUBJECT INDEX
acrylic model 333 added mass 50 added mass coefficient 63 added mass force 63 "Alexander L. Kielland" 25,27 allowable cumulative damage format 440 allowable stress format 438 API 460 API X SN-curve 340 applying improvement methods 283 articulated tower 5 assessment of defects 252 autocorrelation function 44 AWS improved profile weld 270 basic crack shape factor 109 Basquin curve 193 beachmarks 169 block loading 197 brittle fracture 372 brittle fracture design 395 BS 5400 SN-curves 285 burr grinding 264, 279 calcareous deposit 293 cast steel node 359 casting defects 24 1 cathodic polarization 293 cathodic polarization level 304 cathodic protection 29 1,293,306 cathodic protection, effects on crack growth 300 fatigue life 304 SN data 294
Charpy toughness 374 classification of defects 237 classification of SN data 225 cleavage instability 373 clipping level 199 closed form fatigue equation 409 Cnoidal wave theory 55 COD 375 compact tension test 377 complex joint 353 constant amplitude fatigue life 125, 136 constant amplitude loading 423 constant amplitude SN testing 176 definition of terms 177 failure criteria 185 fatigue limit 186 notched specimens 197 real structures vs test specimens 187 relation to crack growth testing 176 structural components 185 types of loading 178 types of tests 182 welded joints 183 conversion table 142 corrosion effects on crack growth 300 fatigue life 304 SN data 294 corrosion fatigue 292 corrosion fatigue mechanisms 293 corrosion pits 24 1,293 corrosion protection measures 296 crack growth 161 crack growth calculation 424,482,492
crack growth coefficient 1 15, 1 17,481 crack growth exponent 1 15,117,48 1 crack growth in tubular joints 173 crack growth integrals 425,455,483-491 crack growth rate 115 crack growth rate curves 162,174, 175 crack growth rate relations 114 crack growth regions 164, 165 crack initiation 124,212 crack modes 95 crack propagation 124 crack propagation prediction 135,422,454 crack shape 122 crack shape factor 108, 122 crack tip stress field 95 crest factor 199 critical defect size 384, 39 1 critical value of K 1 15 cross sectional ovalization 336 CTOD 375 CTOD design curve 386,395,453 CTOD testing 380 cumulative damage 208 cumulative damage hypothesis 434 cumulative damage ratio 438 cumulative probability function 43,46 cycle counting 199 cyclic strain 174, 176, 189, 191,192 damage 17 damage calculation 45 1,478 damage ratio 409,4 13 damping 50,5 1 defect severity 254 defects 237 deformation load 4 1 DEn T SN-curve 340 Department of Energy 440,460 design chart 443
design criteria 2 14 design format 437 design guide-lines 308 design precautions 32 dime test 271 dimensionless CTOD 386 disc grinding 264,279 drag coefficient 63 drag force 63,83 ductile collapse 10 dynamic amplification 50 dynamic analysis 48, 50,472 eddy current inspection 248 effects of geometry on fatigue 2 15 elastic stress concentration factor 97, 194 elastic superposition principle 105 elastic-plastic behaviour 373 elastic-plastic fracture mechanics 94 elliptical crack 155 endurance limit 260 energy spectrum 44 engineering crack growth curve 166 engineering strain 190 engineering stress 190 environmental corrosion factors 296 environmental load 4 1 equivalent stress range 210,413,454 equivalent stress range approach 128 error function 46 examples : crack growth integration 135, 137,423, 426,454,492,493 critical defect size 383,384,391 CTOD calculation 3 8 1 damage ratio calculation 4 15,418,451,480 dynamic stress analysis 472 equivalent stress range calculation 4 15, 448,468
examples cont. : fatigue life calculation 408,448,470, 471,472
hot spot stress 477 long-term stress range distribution 80,87 maximum allowable crack size 387,388, 396,453
maximum allowable stress range 439, 444,468
probability of failure 435 short term stress range distribution 84 SN-curve selection 419,449 stress concentration factor 476 stress intensity factor 133, 134,379 stress relief treatment 448 vortex induced oscillations 74 Weibull parameter 475 Weibull stress range distribution 468 weld repair 499 exceedance spectrum 200 expected value 43
fatigue crack growth threshold 167 fatigue damage 4 19 fatigue design calculation 468 fatigue design check 14 fatigue design regulations 462,481 fatigue ductility coefficient 193 fatigue evaluation 346 fatigue failure 10,24 fatigue failure characteristics 168 fatigue failure criteria 185,495 fatigue initiation 160 fatigue life prediction 124,406 fatigue limit 186,29 1 fatigue limit region 132 fatigue load spectra 207 fatigue mechanisms 159 fatigue notch factor 196 fatigue of welded joints 157,2 12 fatigue strength coefficient 193 fatigue strength exponent 193 fatigue strength improvement methods 262, 283
fabrication defects 238 fabrication precautions 34 fabrication tolerances 433 failure criteria 185,344,433,495 failure modes 37 1 failure region 132 fatigue building codes 459 American Petroleum Institute 440 American Welding Society 440,460 BS 5400 459 Department of Energy 440,460 Det norske Veritas 440,460 Norwegian Petroleum Directorate 440, 460 NS 3472 460
fatigue capacity 174 fatigue crack growth parameter 167
comparison of methods 278 cost of methods 282 grinding techniques 264 hammer peening 273 improved profde 270 inspection 285 plasma dressing 269 shot peening 275 special electrodes 27 1 TIG dressing 266 weld toe remelting 266 fatigue testing 167,174,185,339 finte element analysis 326 finite life region 132 finite thickness factor 108, 109 finite width factor 108,109 fitness-for-purpose approach 252
fracture mechanics 9 1, 382 fracture mechanics calculation of SN-curves 130 fracture toughness 382,396 effects of metallurgy 399 effects of strain rate 398 effects of temperature 397 effects of thickness 396 fracture toughness testing 376 free corrosion 306 frequency effect 299,302 front face factor 108, 109 Froude-Krylov force 63 Fuchs' theory 66 gamma function 17,410,415,438 gap parameter 352 gaussian distribution 244 gaussian process 45 geometry function 425 geometric parameters 3 18,350 Gerber relation 181 Gibstein7sformulas 334,370 global stress 320,4 17 Goodman relation 181 gravity platform 4 Green's function 105, 146, 150, 153 grinding techniques 264 grout reinforced tubular joints 356 grouting 498 guyed tower 5 Haigh diagram 179, 180 hammer peening 273,280 harmonic component 47 heavy duty tubular joints 349 high-cycle fatigue 15, 130,2 14 histogram 244 hot spot 321
hot spot instrumentation 33 1 hot spot location 323 hot spot stress 171,321,323,417,477 hydrodynamic damping 5 1 hydrodynamic forces 63 hydrodynamic response deterministic calculation 69 spectral calculation 70 hydrogen crack 240,262 hydrogen embrittlement 293 hydrogen sulphide concentration 303 improved profile electrode 271 improved profile weld 270,280 improvement methods 259 improvement methods comparison 278 incomplete penetration 238 inertia coefficient 64 inertia force 64,82,83 influence function method 105 initial crack depth 424 in-service defects 241 inspection reliability 249 intermediate fatigue region 132 internal defects 245 irregular loading 197 irregular waves 55 irregularity factor 198 jacket 4,22,28 jack-up 4,24 J-integral375 joint classification 42 1,463,502-5 12 joint design 345 joint fabrication 345 JONSWAP spectrum 56
K,, testing 377
KQ 378 Keulegan-Carpenter number 64 Klesnil-Lukas equation 304 Kuang's formulas 333,366,367 lack of fusion 238,262 lack of penetration 262 lamellar tearing 240 large-scale fatigue testing 185 level crossing counting 201 linear elastic fracture mechanics 94 linear system 47 linear wave theory 53,82 liquid penetrant inspection 247 live load 4 1 load calculation 428 loading buoy 448 loading variables 299 loads 39 local nominal stress 2 18 local stress 4 17,422 local stress range 421 log N distribution 435 long range stresses 188 long-term stress range distribution 78,412 deterministic analysis 78,80 simplified analysis 87 stochastic analysis 84 long-term wave statistics 59 low-cycle fatigue 15, 2 14 magnetic particle inspection 247 marine environment 29 1 maximum allowable defect size 388 maximum allowable stress range 439 maximum stress intensity factor 423 maximum stress range 4 15 McCamy theory 66
mean crossing 198 mean stress 177 Miner summation 208 Miner-Palmgren formula 406 misalignment of joining plates 2 18,242, 419 monotonic loading 179 monotonic stress and strain 189 Morison's equation 63,82,429 narrow band loading 198 natural frequency 52 non-destructive inspection 247 Norwegian Petroleum Directorate 460 occurrence spectrum 199 overlappingjoints 350,35 1 oxygen concentration 303 parametric stress concentration formula 333 Paris' equation 116 Paris-Erdogan crack growth law 164 peak counting 202 permanent load 4 1 Peterson's formula 196 phase angle 50 photo elasticity 333 Pierson-Moskowitz wave spectrum 56,85 plasma dressing 269,280 plastic zone size 98 PMBSHELL 328 post weld heat treatment 447 pre-engineering design check 443 probability density distribution 43,45, 244 probability of failure 434 progressive failure 18 properties of welded joints 157 prototype testing 174
radiographic inspection 248 rainflow counting 204 random loading 197 range counting 203 "Ranger I" 25 Rayleigh distribution 46, 58,86 regular wave approach 7 1 regular waves 53 reinforced tubular joints 3 56 reinforcement angle 243 reinforcing methods 497 reliability index 435 repair methods 496 residual stresses 188,223 response process 47 Reynolds number 64 Rice distribution 46 root-mean-cube stress range 129, 198 root-mean-square stress range 129, 198 R6 failure assessment diagram 389 sea water corrosion 293 seastate 59 "Sedco 135" 24 semi-submersible 1, 19,24 sensitivity analysis 427 short range stresses 188 shot peening 275,280 significant wave height 56,59 simple tubular joints 3 18 single-degree-of-freedom 48 size effect 187,220,408,443,451,465 slag inclusions 238 slamming 73 Smedley's formulas 334, 368,369 Smith diagram 182 SN weld classes 502-5 12 SN-curve selection 4 19,449 SN-curves 17, 130,174,339,407,421, 43 1
SN data 464 SN data for welded joints 224,502-5 12 SN design curves 227,460,466,467 consistency of data 228 residual stresses 229 selection of data 227 slope of curves 23 1 statistical analysis 227 stress range philosophy 230 soil damping 5 1 solidification cracks 240 solitary wave theory 55 spectral density 44 spectral moment 58 spectral width 45 spectrum loading 197 stability parameter 74 static failure region 132 stiffened plate 172 stiffened tubular joint 355 stochastic loading 197 Stoke's wave theory 55 strain concentration factor 324,333 strain gage instrumentation 332 strain gage measurement 330 stream function wave theory 5 5 stress amplitude 177 stress calculation 429 stress concentration 16, 1 17 stress concentration factor 120,215,321, 469 stress concentration factor calculation 476 stress concentration formulas 364 Gibstein 370 Kuang 366,367 Wordsworth/Smedley 368,369 stress corrosion cracks 242 stress distribution 335 stress gradient correction factor 108, 1 13, 120
stress intensity correction factor 383,422 stress intensity factor 94,96 boundary problems 102 compendium of 144-1 56 compounding technique 104 compressive stresses 102 equivalence of 100 hybrid method 108 influence function 104 superposition of 99 stress intensity factor range 115,422 stress intensity of welded joints 117 stress interaction 2 11 stress peak 197 stress range 177, 197,407 stress range exceedance function 410 stress range intensity factor 115,422 stress range philosophy 230 stress range probability distribution 409 stress ratio 115, 177,299,301 stress relieving consideration 447 stress reversal 197 stress spectral moment 86 stress valley 197 striations 169 Strouhal number 73 structural damping 5 1 structural geometry 2 15 structural mass 50 structural redundancy 188 structural stress concentration 2 16 subsurface pressure 54 surface profile 54 surface roughness 64 Soderberg relation 181
T curve 467 template platform 4 tension leg platform 22
thickness effect 187,220,408,443,451, 465 threshold region 132 threshold value 115, 162 TIC dressing 266,280 time history simulation 72 toe grinding 264 toughness parameter 374 transfer function 47,85 tripod platform 5 true strain 190 true stress 190 tubular brace 171 tubular joints 7,172,313,315 cast steel 359 complex 353 crack growth 342 definitions 3 18 design and fabrication 345 fatigue evaluation 346 fracture mechanics analysis 349 geometrical parameters 318,337,350 load cases 319,347 overlapping 350 repair 348 simple 3 18 SN-curves 339 stress analysis 326 stress concentration factor 321,333,338 stress concentration formulas 364 types 3 15 TUJAP 329 Ultimate strength design check 13 ultrasonic inspection 249 uncertainty analysis 427 undercut 240,262 unstable fracture 10,372,382 usage factor 443
variable amplitude fatigue life 127 variable amplitude loading 17, 196,302, 425 variance 45 Veritas Rules 440,460 VERITAS X SN-curve 340 vortex shedding 73 water particle acceleration 54 water particle velocity 54 wave exceedance diagram 62 wave force calculation 474 wave kinematics 54 wave length 54 wave spectrum 56 waves 53 Weibull distribution 59,87, 207,410,438 Weibull parameter 208,413,415,430,444 Weibull parameter calculation 475 Weibull parameter consideration 445 weld defect distribution 247 weld defects 213 weld geometry 2 1 , 217 weld notch effect 321 weld quality 244 weld toe remelting 266 welded joints 8 Wordsworth's formulas 334,368,369 Zero crossing wave period 46,56,59 zero order moment 4 5,58
