Very Nice Paper on Fatigue

Platform, Pipeline and Subsea Technology Fatigue Design

Platform, Pipeline and Subsea Technology– Fatigue Design

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INTRODUCTION ....................................................................................................... 3

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STRUCTURAL FATIGUE......................................................................................... 3 2.1 THE NATURE OF FATIGUE LOADING ........................................................................ 3 2.2 FATIGUE BEHAVIOUR OF STRUCTURAL DETAILS ..................................................... 8 2.3 FATIGUE OF WELDED STRUCTURES ....................................................................... 12 2.3.1 Stress Concentrations..................................................................................... 12 2.3.2 Weld Defects................................................................................................... 15 2.3.3 Residual Stress................................................................................................ 16 2.4 FURTHER FACTORS AFFECTING WELD FATIGUE .................................................... 19 2.4.1 Effect of Steel Strength ................................................................................... 19 2.4.2 Effect of Plate Thickness ................................................................................ 20 2.4.3 Effect of Environment ..................................................................................... 20 2.4.4 Effect of Welding Method ............................................................................... 20 2.5 PREDICTING FATIGUE LIFE UNDER VARIABLE AMPLITUDE LOADING.................... 21 2.6 FATIGUE OF TUBULAR JOINTS ................................................................................ 24 2.7 FATIGUE OF OTHER STRUCTURAL DETAILS ........................................................... 34 2.8 WELD FATIGUE LIFE IMPROVEMENT TECHNIQUES................................................. 34

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FATIGUE ANALYSIS .............................................................................................. 36 3.1 3.2 3.3

DETERMINISTIC FATIGUE ANALYSIS ...................................................................... 36 SPECTRAL FATIGUE ANALYSIS............................................................................... 37 RELATIVE MERITS OF DETERMINISTIC AND SPECTRAL FATIGUE ANALYSIS .......... 40

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RISK BASED FATIGUE ANALYSIS AND INSPECTION PLANNING ........... 43

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REFERENCES .......................................................................................................... 47 5.1 5.2 5.3

BOOKS ................................................................................................................... 47 STANDARDS ........................................................................................................... 47 RESEARCH REPORTS AND PAPERS .......................................................................... 47


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1

Introduction

This section of the unit describes the phenomenon of structural fatigue, and discusses the approaches used to design and maintain structures against fatigue failure. It is organized into three sections: the first provides a general background to structural fatigue, the second discusses methods of fatigue analysis used in the design of offshore structures, and the third provides an introduction to risk-based approaches and inspection philosophies.

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Structural Fatigue

In the context of engineering, fatigue is the process by which a crack can form and then grow under repeated or fluctuating loading. The magnitude of the fluctuating loading required to induce fatigue cracking may be much less than that required to cause failure under a single application of the load. In particular, it may be much less than the load corresponding to the allowable static design stress. While some types of structure may be able to tolerate extensive cracking without compromising their load-carrying capacity, other structures may be prone to sudden collapse or excessive deflection if a crack is allowed to progress to some critical size. The initiation and growth of fatigue cracks depends on the number of load cycles, regardless of whether these cycles occur in quick succession, or there are significant periods of time between them. Fatigue performance is therefore often expressed as a life (or period of time before failure) under a particular loading regime. An important corollary of this is that fatigue is a cumulative process. 2.1

The Nature of Fatigue Loading

The definitions commonly used to describing individual fatigue loading cycles are shown in Figure 2-1. Note carefully the definition of stress range which is important in the fatigue analysis of welded structures. Another parameter which is sometimes used to describe fatigue loading cycles is the Stress Ratio, which is defined commonly as the lower limit stress/upper limit stress, or simply as:

Stress Ratio 

Minimum Stress Maximum Stress

(1)

Figure 2-1 shows constant amplitude loading, however, in practice the majority of engineering structures are subjected to some type of variable amplitude, or random loading. Some general examples are shown in Figure 2-2.


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Figure 2-1: Definition of parameters describing constant amplitude fatigue loading cycles.

Figure 2-2: structures.

Some general examples of random loading on engineering


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Some examples of loads which contribute to fatigue damage may be:         

Loads induced during fabrication or construction. Loads induced during transportation. Loads induced during installation (e.g. pile driving) In-place loads induced by waves, current and wind. Pressure variations (for pipelines and pressure vessels). Temperature variations. Weight variations (or live loads). Vortex induced vibrations. Machinery induced vibrations.

In the case of fixed and floating offshore platforms it is usually the in-place environmental loads due to waves which contribute mostly to fatigue damage. Figure 2-3 shows the stress variation in the joint of an offshore platform due to wave loading. Unsurprisingly the stress variation follows the water surface elevation, i.e. the stress fluctuations are associated directly with waves.

Figure 2-3: Example of stress variation in a joint of a fixed offshore platform.

Figure 2-2 and Figure 2-3 show examples of random fatigue loading described in the time domain. It is also possible to represent a time series of water surface elevations (and associated fatigue loads) as the sum of a number of sinusoidal wave components, by a Fourier series: N

x(t )   ai cos( i t   i )

(2)

i 1

Where ai is the amplitude and i is the frequency of the ith wave component. i represents a phase angle


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This concept is shown in Figure 2-4. This permits the random loads to be described in the frequency domain by an energy spectrum, S() which is defined as: S(ω i ) 

ai2 ω 1 2

(2)

where i is a discrete frequency, and ai is the amplitude of the cycles in the frequency band . These definitions are further illustrated in Figure 2-5. This definition of a load spectrum can be useful in spectral fatigue analysis, which will be discussed in a later section of these notes.

Figure 2-4: The relationship between time domain and frequency domain representation of ocean waves.

Figure 2-5: A random load x(t) and its energy spectrum, S(). Platform, Pipeline and Subsea Technology– Fatigue Design

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Spectra are sometimes described as either broad-banded or narrow-banded and these concepts are shown in Figure 2-6. In a broad-banded process, a number of smaller cycles are superimposed on larger cycles, and these smaller cycles may not pass through the mean level. By contrast, in a narrow-banded process most cycles pass through the mean value.

Figure 2-6: Definition of narrow-band and broad-band load spectra.

A further important point is that fatigue loads reflect the dynamic behaviour of the structure. If a structure is excited at close to its natural frequency, dynamic amplification of the loads must be accounted for. A simple way that is sometimes used to correct the results of a quasi-static structural analysis to account for dynamics is to assume that the structure behaves as a single degree of freedom system. A Dynamic Amplification Factor (DAF) is simply applied to the stresses calculated in the quasi-static analysis. The DAF is a function of the system damping and the closeness of the frequency of the excitation force and the natural frequency of the structure. It may be calculated according to the following equation, and the relationship between the DAF and damping, and the excitation frequency is shown in Figure 2-7.

Figure 2-7: Relationship between Dynamic Amplification Factor (DAF), damping ratio() and /N. Platform, Pipeline and Subsea Technology– Fatigue Design

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DAF 

where and

1

(3)

1     2  ζ   2 2

2

  ω ωN  is the damping ratio,  is the frequency of the excitation force, N is the natural frequency of the structure (assuming a single degree of freedom system).

For sway of fixed offshore platforms, a commonly used damping ratio in fatigue analysis is  = 0.02. For dynamically sensitive structures, or sections of structures, a more rigorous approach is often required. An excellent reference is Barltrop and Adams (1991).

2.2

Fatigue Behaviour of Structural Details

In describing the fatigue behaviour of engineering structures, the focus is frequently on structural details. This is because fatigue cracking is highly localized. Therefore, in engineering design the fatigue behaviour of each detail must be considered under the action of local loads. Fortunately, there is now a considerable body of test data covering a wide range of structural details. Figure 2-8 shows a butt welded specimen being tested under constant amplitude loading in a hydraulically powered fatigue test machine. Data from these types of test form the basis for fatigue analysis. The data is usually presented as an S-N curve, which plots Stress Range on the ordinate (y axis) and Number of Cycles to Failure (on a logarithmic scale) on the abscissa (x axis). An example is given in Figure 2-9. It is worthwhile noting the wide range of scatter in the test results (an order of magnitude in cycles to failure in some cases!). Therefore, Design S-N curves usually represent the mean line minus 2 standard deviations to obtain a suitably conservative estimate of the number of cycles to fatigue failure. Some S-N curves include an endurance limit, or stress level below which fatigue failure will not occur irrespective of the number of loading cycles applied to the specimen (see Figure 2-10). To a large extent this is a consequence of the method of fatigue testing. The correct method of dealing with small amplitude load cycles in the fatigue analysis of welded structures remains the subject of ongoing research. However, there is increasing evidence that endurance limits should be ignored, particularly for structures subjected to variable amplitude loading in corrosive environments. However, some engineering guidelines make a compromise by suggesting S-N curves with different slope in the low stress region. Some examples of these are provided later in these notes.


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Figure 2-8: Constant amplitude fatigue test of a butt welded specimen.


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Figure 2-9: Fatigue test data for butt welded specimens.


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Stress

Endurance Limit

S0

Number of Cycles Figure 2-10: The endurance limit represents the stress level below which fatigue failure will not occur in a constant amplitude fatigue test.

One important shortcoming in describing fatigue behaviour using an S-N curve is that the point of “failure” is not always clearly defined. For example, it may be the point at which a detectable crack initiates, the point at which a crack proceeds through the full thickness of a plate, or the point at which a structural specimen breaks in half. A more physically correct approach is to describe the propagation of a crack under cyclic loading using fracture mechanics techniques. Unfortunately, a discussion of fracture mechanics techniques is beyond the scope of this course, however, there are numerous texts on this subject (a good introduction is the book by Broek (1986)). Furthermore, British Standard 7910 provides an excellent engineering guidance for assessing flaws and cracks in engineering structures using fracture mechanics techniques (also known as Engineering Critical Analysis).


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2.3

Fatigue of Welded Structures

Welded joints are particularly susceptible to fatigue failure. Figure 2-11 compares the fatigue performance of welded specimens with plain steel specimens and specimens containing holes.

Figure 2-11: S-N Curves comparing the fatigue behaviour of welded specimens with plane plate and notched specimens.

There are three major factors which contribute to the susceptibility of welded joints to fatigue failure: 1. As joints, welds are subjected to both the stress concentration caused by their location at structural discontinuities, and the stress raising effect of the weld shape itself. 2. Due to the nature of the welding process they are likely to contain defects which act as fatigue crack initiators. 3. High tensile residual stresses frequently exist in the vicinity of the weld as a result of shrinkage during solidification and cooling of the weld metal. These reasons are all important, and influence the way in which engineers carry out fatigue analysis of welded structures, and ultimately design against fatigue failure. They are therefore discussed in more detail in the following sections. 2.3.1 Stress Concentrations

There are two important sources of stress concentration which contribute to the susceptibility of welded joints to fatigue cracking.


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The first source of stress concentration is due to the location of welds at structural discontinuities where there are changes in geometry and stiffness. This leads to a local increase in stress at locations within the joint, and these are sometimes referred to as “hot spots”. Misalignment of joints can also lead to secondary bending moments which can increase stresses locally. The concept of hot spot stress concentration is illustrated in Figure 2-12.

Figure 2-12: Example of hot spot stresses in a tubular nodal joint.


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The second source of stress concentration is the shape of the weld itself. A notch is formed by the toe of the weld and this location is by far the most common initiation site for fatigue cracking in welded structures. However, the root of partial penetration welds and defects introduced during the welding process also represent notches, and therefore potential fatigue initiation sites. Some examples of fatigue crack initiation sites in welds are shown in Figure 2-13 while the influence of the toe radius and flank angle on the fatigue performance of butt welds is shown in Figure 2-14.

(b)

(a)

(c)

Figure 2-13: Fatigue crack initiation sites: (a) at the toe of a butt weld, (b) at the toe of a butt weld containing porosity, (c) at a lack of penetration defect. Percent reduction in fatigue strength

Figure 2-14: Influence of flank angle and toe radius on the reduction in fatigue strength of butt welded joints. Platform, Pipeline and Subsea Technology– Fatigue Design

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The influence of weld shape and defects on fatigue behaviour emphasizes the importance of weld quality in achieving adequate fatigue performance of welded joints. Particular care should be taken with weld quality when joints are subjected to fatigue loading. Another important point is that S-N curves for welded joints are based on experimental data from fatigue tests on welded structural details. Therefore the stress concentration due to the weld itself is included implicitly in the S-N curve and does not need to be considered separately. The stress range on the ordinate (y axis) of the S-N curves of welded details refers to the local, or hot spot stress. This stress must be calculated as part of any fatigue analysis.

2.3.2 Weld Defects

The complexity of the welding process often leads to defects occurring in, or adjacent to, the weld metal. These may be macroscopic defects (such as lack of fusion between weld metal and parent plate, cracking, inclusions, or porosity) which are commonly detected using conventional non-destructive examination techniques. It is common practice to examine critical welds in structures to ensure that any defects present are below an acceptable level. However, even in “sound” welds a range of microscopic defects may occur. These are commonly encountered at the weld toe where melted weld metal meets unmelted parent metal and surface oxides. The rapid cooling of this zone promotes material heterogeneities and the formation of a range of microscopic defects which may include porosity, slag inclusions and sharp undercuts. These defects coincide with the stress concentration of the weld and may ultimately become the initiation sites of fatigue cracks. The nature of these defects is shown diagrammatically in Figure 2-15.

Intrusions at weld toe approx 0.1-0.15 mm deep

Figure 2-15: Microscopic intrusions at the toe of a “sound” weld.


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2.3.3 Residual Stress

The contraction of weld metal during solidification and cooling is responsible for the introduction of “locked-in” residual stresses in welded structures. These stresses exist independent of external loading. Therefore they will be balanced within the structure; in other words there is a system of tensile and compressive components of stress which is in equilibrium. Two systems of residual stress may be produced in a welded structure: global reaction stresses which affect members as a whole, and localized residual stresses in the vicinity of joints. The concept of global reaction stresses is shown in Figure 2-16. Here the assembly procedure may introduce an overall distribution of stresses within the structure. In the simplest cases, tension in some members will be balanced by compression in others.

Tensile load in brace balanced by compression load in adjacent members

Girth weld completed after adjacent welds

Figure 2-16: Concept of global reaction stresses.

The concept of localized residual stresses is shown in Figure 2-17 and Figure 2-18. Most welded joints have sufficient external restraint to lead to tensile residual stresses of similar magnitude to the material yield stress in the vicinity of the joint.


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Figure 2-17: Formation of residual stress as a result of welding: (a) expected longitudinal shrinkage of “unrestrained” weld; (b) longitudinal shrinkage of restrained weld.

Figure 2-18: Typical residual stress distribution in a welded joint.

From the viewpoint of the analysis of welded structures the most important residual stresses are the localized stresses in the joint. To understand the implications of high local Platform, Pipeline and Subsea Technology– Fatigue Design

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tensile residual stress on fatigue, consider Figure 2-19 which shows an alternating fatigue load applied to a welded joint. It is well established that, all other things being equal, compressive stress does not contribute to fatigue crack initiation or propagation. Therefore only the tensile part of the loading cycle contributes to fatigue failure. However, if a tensile residual stress of yield stress magnitude is present at the weld, this combines with the fatigue load to give the stress cycle shown in Figure 2-19(b). Here an elastic-perfectly plastic material behaviour has been assumed so that the stress cycle varies from the yield stress downwards. In this instance the entire stress range is tensile and therefore damaging from the viewpoint of fatigue.

Figure 2-19: When the residual stress is equivalent to a tensile yield stress the actual stress range will vary from yield stress downwards, regardless of the nominal stress ratio.

Therefore, the significance of welding residual stress is that even compressive loads applied to a structure may lead to a net tensile fatigue stress in the vicinity of the welds. For this reason it is the stress range which is usually most important in determining the fatigue behaviour of welded joints. Localized residual stresses can be relieved to some extent by Post Weld Heat Treatment (PWHT). This involves heating the joint in an oven to approximately 600C for a period of some hours. The yield stress of the steel is reduced by the heating and this allows relaxation of the locked-in stresses. Some fatigue analysis guidelines make allowance for a limited benefit from PWHT. If in doubt, a conservative approach is to ignore any beneficial effects which may arise from PWHT. Platform, Pipeline and Subsea Technology– Fatigue Design

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2.4

Further Factors Affecting Weld Fatigue

There are a number of other factors which have some influence on the fatigue behaviour of welded joints and are usually taken into account during fatigue analysis. These are described in this section. 2.4.1 Effect of Steel Strength

One of the most useful features of steel is that its mechanical properties can be significantly altered through alloying and heat treatment. Up to a certain limit, the fatigue strength of smooth steel specimens increases proportionally with tensile strength. However, this relationship does not hold for welded joints. Figure 2-20 shows fatigue test results for welded specimens made from steels ranging in tensile strength from 438 to 753 MPa. The test results fall within a relatively narrow scatter band and there is no correlation between ultimate tensile strength and fatigue strength. Therefore, if an engineering design is limited by its fatigue performance, using a higher strength steel will not improve the situation.

Figure 2-20: Effect of steel ultimate tensile strength on fatigue behaviour (note: 1 tons/in2 = 15.44 MPa).


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2.4.2 Effect of Plate Thickness

It has generally been observed that, all other things being equal, increasing plate thickness results in a decrease in fatigue performance. Figure 2-21 shows the results of fatigue tests on welded specimens in bending. Although the reason for the thickness effect is not universally agreed, one suggestion has been that thinner plates have a higher stress gradient, and therefore the driving force behind fatigue crack growth decreases more rapidly than in thick plates. Most design codes and standards which deal with fatigue design include a correction for the thickness effect.

Figure 2-21: Fatigue test results showing the influence of plate thickness.

2.4.3 Effect of Environment

A corrosive environment, such as seawater, may have the effect of accelerating the growth of fatigue cracks, and therefore reducing overall fatigue performance. The presence of a corrosive environment also effectively removes the endurance limit on the S-N curve. Cathodic protection reduces the impact of this detrimental effect to some extent. In the case of offshore structures different S-N curves are usually specified depending on the prevailing corrosion conditions. It is important to note at this point that cathodic protection is ineffective for joints in the splash zone where electrolyte presence is not continuous. These joints exist under effectively free corrosion conditions. 2.4.4 Effect of Welding Method

There is very little evidence to suggest that, among common welding techniques, different welding methods produce intrinsically different fatigue strengths in welded joints. If


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anything, manual welding techniques produce welds with marginally better fatigue performance compared with automatic welds.

2.5

Predicting Fatigue Life Under Variable Amplitude Loading

It has already been discussed how S-N curves are generated from laboratory tests carried out under constant amplitude fatigue conditions. However, it has also been pointed out that most engineering structures are subject to random, variable amplitude loading. It is therefore necessary to have a method of estimating the fatigue life under a variable amplitude loading regime, but still use S-N curves generated under constant amplitude loading. The method that has achieved the broadest acceptance is the Palmgren-Miner linear cumulative damage hypothesis, commonly known as Miner’s Rule. This states that ni

N

i



n1 n2 n3    ... N1 N 3 N 3

D

(4)

where n1, n2,… are the number of cycles that stresses 1, 2,… are applied to the joint, and N1, N2,… are the corresponding numbers of cycles to failure of a similar joint under constant amplitude loading at those stresses. D is a constant that represents the accumulated fatigue “damage” of the joint. If D = 1.0, the rule may be restated that, under variable amplitude loading, the basic damage fraction caused by each separate loading cycle is equal to that caused by a single cycle of the corresponding constant amplitude loading, and that failure occurs when the sum of these basic damage fractions reaches unity. This concept is shown diagrammatically in Figure 2-22.

1 2 3

Figure 2-22: Definition of Miner’s rule.


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Figure 2-23 shows a comparison of Miner’s Rule with typical experimental fatigue test results under variable amplitude loading. It can be seen that a Miner’s summation (or damage accumulation, D) =1.0 is the most likely result corresponding to failure, however, there is considerable variation in the results.

Frequency of Occurrence

0.35

0.3

0.25

0.2

Corresponding lognormal distribution 0.15

0.1

0.05

0

0

1

2

3

4

5

6

7

8

9

Miner's Sum Figure 2-23: Comparison of calculated Miner’s summation and variable amplitude test results.

There may be instances where a method of turning a time series of stresses into a number of discrete stress cycles is required. A complete discussion of the various methods available is beyond the scope of this course, however it is worth mentioning that the Rainflow, or Reservoir method of cycle counting has gained the broadest acceptance. A discussion of this technique can be found in British Standard BS 7608:1993. In many instances, the fatigue loads in offshore structures are already grouped in a manner which is conducive to fatigue analysis using Miner’s Rule. An example of this is the wave occurrence table shown in Figure 2-24. An alternative is the wave height exceedance diagram of Figure 2-25 which shows Wave height on the ordinate (y axis), and the number of waves exceeding a particular wave height on the abscissa (x axis). An important corollary of the Miner’s Rule calculation is that a large number of small stress cycles can be as equally damaging as a few large cycles. It is therefore important to be able to carry out the Miner’s Rule calculation in order to determine just how damaging a given loading spectrum really is.


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Figure 2-24: Wave occurrence table for fatigue analysis (25 year period). Platform, Pipeline and Subsea Technology– Fatigue Design

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16.0 North West Shelf (typical)

Significant Wave Height, H sig (m)

14.0

Central North Sea (typical) Gulf of Mexico (design)

12.0 10.0

Central North Sea

8.0 6.0 4.0

North West Shelf (shallow water)

2.0 0.0 1.E-02

1.E-01

1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 1.E+08

Number of Waves Exceeding H sig per year

Figure 2-25: Wave height exceedance diagram.

2.6

Fatigue of Tubular Joints

The vast majority of fixed offshore platforms are constructed from a space frame of tubular joints. Considerable research effort has therefore been directed toward characterizing the fatigue performance of this particular class of welded joint. Where tubulars are butt jointed to form members, any eccentricity between adjacent tubulars can lead to the development of secondary bending moments in response to axial loads in the member. For the purposes of fatigue analysis this may be accounted for by assigning a Stress Concentration Factor (SCF) which, when multiplied by the nominal axial stress in the member, describes the increased local stress in the vicinity of the welded joint, i.e. local = SCFnominal

(5)

The various sources of geometric stress concentration which may be encountered in a tubular butt weld are shown in Figure 2-26. For butt welded tubular members, the following formula for eccentricities in flat plates provides a conservative estimate of the SCF at the joints: SCF  1 

3( m ) t

(6)


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A more sophisticated and less conservative method of evaluating the stress concentration factor in butt jointed members can be found in DNV-Recommended Practice C203, along with guidance for joints in pipelines.

Figure 2-26: Sources of geometric stress concentration in butt welded tubular members.

Where tubular members such as jacket braces and legs intersect, a complex geometry is created. In these cases the stress distribution around the joint is not uniform due to the complexity of the localized geometry. Considerable effort has been spent investigating stress concentration factors to be used with tubular joints such as those shown in Figure 2-27. The methods used have included strain gauging and load testing scale models, photoelastic testing, and detailed finite element modelling. These activities have resulted in the availability of parametric equations which are suitable for the analysis of a range of commonly encountered tubular joints. A comprehensive discussion of this subject may be found in HSE (1997). Appendix A provides the parametric equations due to Efthymiou (1988), which are probably now the most widely used of their type. The SCFs for T and Y joints are defined only at the “crown” and “saddle” locations (refer back to Figure 2-12 for the definition of these locations). Therefore there must be some method of interpolation so that the SCFs at the intermediate points can be calculated. The conventional method is to linearly interpolate the SCFs for axial loading, while the SCFs associated with in-plane and out-ofplane loading are sinusoidally distributed. This concept is shown in Figure 2-28.


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Figure 2-27: Geometric parameters describing welded tubular joints.

When carrying out the interpolation described above it is important to understand that the SCFs calculated using parametric equations for tubular joints should be used only with the nominal member stresses. In the case of axial SCFs, the nominal member axial stress should be used in conjunction with the calculated SCF, while in the case of bending SCFs, the maximum (outer fibre) bending stress should be used in conjunction with the relevant bending SCF.

3 4

2

1

5 6

8 7

Figure 2-28: Recommended distribution factors for SCFs in T & Y joints.


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Stresses due to axial, in-plane bending and out-of-plane bending loads may be added using the principle of superposition. The following formula is useful: HSS  SCFaxS  SCFaxC  SCFaxS   θ 90σ ax 





 SCFipC  sin θ σ ip 



(7)



 SCFopS  cos θ σ op 

where

 

HSS is the hot spot stress SCFaxS is the axial SCF at the saddle point SCFaxC is the axial SCF at the crown point SCFipC is the in-plane bending SCF at the crown point SCFopS is the out-of-plane bending SCF at the saddle point ax is the nominal axial stress ip is the nominal (maximum) in-plane bending stress op is the nominal (maximum) out-of-plane bending stress  is the angle around the joint measured from the saddle (see diagram below).

Crown 90

Saddle

0



Figure 2-29: Definition of  in hot spot stress calculation equation.

Note that this method of interpolating the axial SCFs only works in the first quadrant (i.e. for  between 0 and 90 degrees) Symmetry should be used to determine the interpolated axial SCFs in the other quadrants. The fatigue behaviour of tubular joints has been characterized by numerous fatigue tests, and typical results are shown in Figure 2-30. From tests such as these, suitably


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conservative design S-N curves can be derived. As an example, Figures 231 to 233 show the design S-N curves for tubular joints published in the UK Health and Safety Executive’s (HSE) guidance on the design, construction and certification of offshore installations. Different curves are shown for fatigue of joints in air, under free corrosion conditions in seawater, and in seawater with cathodic protection. These S-N curves may also be expressed mathematically as: log10 ( N )  log10 ( K1 )  m log10 ( S B )

(8)

where N is the predicted number of cycles to failure under stress range SB, K1 is a constant and m is the inverse slope of the S-N curve. Details of the basic design S-N curves are given in Table 1 below. S0 and N0 represent the point where the slope of the S-N curve changes, see Figure 2-34. The HSE design S-N curves apply to all joints with plate thicknesses of 16 mm or less. For thicker joints, a thickness correction applies to take account of the thickness effect on welded joints discussed previously. The thickness correction can be incorporated into the mathematical expression of the S-N curves in the following manner:  SB   log10 ( N )  log10 ( K1 )  m log10  q   t B t   where

tB is the reference thickness, = 16 mm t is the thickness of the member under consideration q is the thickness exponent factor, = 0.3 and all other constants are defined as before.


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(9)

Figure 2-30: Experimental results for 16mm thick tubular joints tested in air.

Table 1: Details of thee basic S-N curves in HSE Guidance.

Welded Plates

Tubular Joints


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Figure 2-31: Basic HSE design S-N curves for welded tubular joints and plates in air.


30

Figure 2-32: Basic HSE design S-N curves for welded tubular joints and plates in seawater – free corrosion.


31

Figure 2-33: Basic HSE design S-N curves for welded tubular joints and plates in seawater – cathodic protection.


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Stress

Point where slope of S-N curve changes

S0

N0

Number of Cycles

Figure 2-34: Definition of S0 and N0 on dual slope S-N curve.

It is important to note that different offshore design codes have subtle differences in the elements of fatigue analysis. There are slight differences in S-N curves, thickness corrections, and the required fatigue design life. Once a particular fatigue design code is adopted, it should be followed consistently, and in its entirety. A good example of the differences between design codes is the required fatigue design life. The API offshore design code, RP2A, requires that the calculated fatigue life be at least twice the design life of the structure, whereas the HSE guidance requires that the calculate fatigue life be at least equal to the design life (however, a more conservative S-N curve is used in the latter case). The Norwegian offshore structural design code (Norsok Standard N-004, 1998) suggests an even more sophisticated approach where the calculated design lives also depend on the accessibility of the joint for inspection and repair, and this is described in Table 2. Note that a design fatigue factor of 10 means that the calculated fatigue life must be at least 10 times the design life of the structure.

Table 2: Design fatigue factors (from Norsok Standard N-004, 1998).

Access for Inspection and Repair Classification of structural components based on No access, or in the Accessible damage consequence splash zone Below Splash Zone Above Splash Zone Substantial Consequences

10

3

2

Without Substantial Consequences

3

2

1


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2.7

Fatigue of Other Structural Details

In addition to tubular joints there are, of course, a wide range of other types of welded structural details which occur in offshore structures. These include attachments such as ladders and boat landings, standard weld details in the topsides structure, and ship details in FPSOs and other floating production systems. Where these joints are subjected to fluctuating loading, their fatigue performance must also be assessed. Fortunately, there are a range of design standards and guidelines which describe the S-N curves and analysis methodologies for a range of commonly encountered structural details. These guidelines include: 

British Standard 7608:1993 and DNV Recommended Practice RP-C203 (2001) which provide guidance for the analysis of a range of common structural details, some of which might typically be found in platform topside structures.



DNV Class Note 30.7 (1998) which provides guidance on stress concentration factors and design S-N curves for a range of ship structural details which might typically be found in FPSOs and other offshore structures made up from stiffened panels.

2.8

Weld Fatigue Life Improvement Techniques

Because of the susceptibility of welded joints to fatigue failure, there have been numerous techniques developed to improve their behaviour. Gurney (1979) provides a comprehensive coverage of the different methods which have been tested. However, in practice, the most widely used methods for improving the fatigue behaviour of welded joints are toe grinding and peening. Toe grinding involves using either a disc, or rotary burr grinder to reduce the stress concentration at the toe of the weld as shown in Figure 2-35. To be most effective, toe grinding should extend 0.5–1.0 mm into the parent plate to remove any small undercuts or intrusions which may act as fatigue crack initiators. Peening involves impacting the surface of the weld with a pneumatic hammer fitted with a rounded tool. This induces a compressive residual stress which retards fatigue crack initiation. Peening is usually directed towards the toe of the weld and this may have the added benefit of also improving the shape of the weld toe. The relative benefits of toe grinding and peening are shown in Figure 2-36. Despite the significant benefits which can be achieved through these techniques, they are time consuming and costly, and skill is required to achieve consistently good results. It is for these reasons that these techniques are rarely considered in the design of welded joints (that is, joints are usually designed so that improvement techniques are not relied upon to achieve satisfactory performance). However, they are sometimes used as an added defence against fatigue failure in critical welds.


34

Methods of improving the fatigue performance of a joint at the design stage include modifying the joint geometry to reduce local stresses, or replacing the welded tubular joint with a cast node. Using a casting is an expensive option, but may be cost effective for particularly complex joints.

0.5 mm min

Figure 2-35: It is recommended that toe grinding extend below the plate surface to remove weld defects.

Figure 2-36: Comparison of grinding, peening and some other weld improvement techniques on the fatigue performance of fillet welded specimens.


35

3

Fatigue Analysis

There are two common approaches in the fatigue analysis of offshore structures. Perhaps the most popular is analysis in the time domain, commonly known as deterministic fatigue analysis. However, as will be discussed in a later section, there can be some advantages carrying out fatigue analysis in the frequency domain, and this type of analysis is called a stochastic, or spectral fatigue analysis. The deterministic and spectral approaches to fatigue analysis are described in the following sections, and the relative advantages of each are compared.

3.1

Deterministic Fatigue Analysis

Deterministic fatigue analysis requires fatigue loads to be expressed as a finite number of discrete events. An example of this was provided in Figure 2-24 where a discrete numbers of waves of varying height and period are provided over a 25 year period. The subsequent deterministic fatigue analysis is best summarised as a series of steps: 1. All the physical phenomena which are likely to contribute to fatigue of a structure over its entire life need to be identified. In the case of offshore structures these may include loads imposed during construction, transportation, live loads due to machinery, and, perhaps most importantly, in-place environmental loads due to waves, current and wind. It must be recognized that the stresses at any potential fatigue failure site in the structure will be different for waves coming from different directions and this must be accounted for in the analysis. 2. The physical phenomena need to be translated into loads on structural members. The use of specialized offshore structural computer analysis packages can often be used for this step. The effect of dynamics should also be accounted for. 3. Loads in structural members need to be translated into localized joint stresses. Member loads must firstly be translated into member stresses and, in the case of tubular joints, hot spot stress concentration factors can be used to determine the localized stresses at various points around the joint. Typically 8 locations around the joint on both the chord and brace would be considered. Remember that it is the stress range which is important in determining fatigue behaviour, and so the maximum and minimum hot spot stresses need to be determined. 4. A S-N curve describing the relevant structural detail must be chosen. Appropriate codes and standards provide a range of S-N curves. 5. A Fatigue Damage calculation must be carried out using Miner’s Rule. The calculation must be carried out for expected loads over the design lifetime of the structure. Remember that Miner’s Rule is cumulative, therefore the fatigue damage due to one set of loads can be added directly to the fatigue damage caused by other loads. In particular the fatigue damage may be summed for each wave direction.


36

6. The fatigue life of each detail (or hot spot) of interest can be compared with the design life after appropriate factors of safety have been accounted for.

3.2

Spectral Fatigue Analysis

Spectral fatigue analysis recognizes the underlying random nature of the wave height occurrence table (as given in Figure 2-24) and models the process statistically. It has already been discussed in S ection 2.1 of these notes that a random series (of for example wave heights) may be expressed as an energy spectrum. Figure 2-5 is reproduced below:

The energy of a harmonic wave is proportional to the square of its amplitude, and the energy in each frequency band is given by the following equation: S (ω i ) 

ai2 ω

1 2

(10)

Using Fourier analysis techniques, a random process such as a wave history may be represented by a superposition of a large number of sinusoidal components. If one component of the excitation process is given by x(t )  ai  cos(ω i t   i )

(11)

then the component of the response at the same frequency is given by y (t )  Tω  x(t )

(12)


37

This provides the definition of the transfer function, T(). The excitation process is typically the wave height spectrum. The response function is typically the hot spot stress range at a particular joint location. The energy spectrum of the response may therefore be related to the energy spectrum of the excitation by using the relationship

S y (ω)  Tω  S x (ω) 2

(13)

The relationship between the excitation spectrum, the response spectrum and the transfer function is illustrated in Figure 3-1.

Figure 3-1: The transfer function T(f) relates the excitation spectrum Sx(f) and the response spectrum Sy(f).

The excitation and response functions, as well as the transfer functions may equally be expressed as functions of frequency in Hz, instead of radians/sec. The definition of the transfer function would then be given by:

S y ( f )  T f   S x ( f ) 2

(14)

where f represents frequency expressed in Hz. The remainder of this section of the notes will assume that the functions are expressed in Hz. In passing, it is important to note that care should be taken to properly define the shape of the loading spectrum and transfer function, particularly around the natural frequencies of the structure. Once a fatigue stress spectrum has been developed (i.e. a plot of Sy( f )) then the fatigue damage may be calculated by firstly calculating the zero and second order moments of the stress spectrum. The moments of an energy spectrum are defined as:


38



m n   S x  f   f n df

(15)

0

Therefore the zero order moment is: 

m 0   S x  f df

(16)

0

and this represents the area under the spectral curve. The second order moment is: 

m 2   S x  f   f 2 df

(17)

0

In practice, these integrals can be evaluated by numerical integration using for example the trapezoid rule. This concept is shown in Figure 3-2.

Figure 3-2: Definition of zero order and second order moments of response spectrum.

For a narrow-banded process, and where the frequency in the response spectrum is expressed in Hz, the mean zero upcrossing period may be approximated as: Tz 

m0 m2

(18)


39

[ Note that this equation will be slightly different if the input, output and stress transfer functions are expressed in rad/sec. rather than Hz. ] The number of stress cycles, n, in a total time of T seconds is therefore given by: n

T Tz

(19)

The complete derivation of spectral fatigue damage under a narrow banded process is beyond the scope of this course. Interested readers are referred to Barltrop and Adams (1990). However, assuming that the stress range within each short term seastate can be described by the Rayleigh distribution, the fatigue damage for each seastate may be calculated as: D T 

where

m 2 (8m 0 ) m 2  2  m      m0 K  2 

(20)

T is the time period in seconds m0, m2 are the zero and second order spectral moments (defined above) m and K are constants describing the S-N curve (see Section 2.6 of these notes) 

 is the incomplete gamma function: ( g )   x ( g 1) e x dx 0

The fatigue damage may be summed linearly over all seastates and all wave directions. If T is the number of seconds in 1 year, then the fatigue life of the hot spot in years will be 1/D. The spectral fatigue analysis approach is illustrated schematically in Figure 3-3.

3.3

Relative Merits of Deterministic and Spectral Fatigue Analysis

An important aspect of spectral fatigue analysis is that, via the transfer function, it can account for dynamic effects more completely than deterministic fatigue analysis. Provided that appropriate software is available to develop the transfer function between the excitation spectrum and the response spectrum spectral analysis is usually more computationally efficient than deterministic analysis. However, an important implicit assumption in the development of the transfer function is that it applies to each wave component irrespective of its amplitude. This means that there must be a linear relationship between the excitation (wave height) and the response (hot spot stress range). In practice, this is a reasonable approximation for large jacket type structures in moderate to deep water depth, although effort is sometimes put toward modifying the transfer functions to account for the non-linear nature of the drag force in Morison’s equation and the non-linear kinematics associated with higher order wave Platform, Pipeline and Subsea Technology– Fatigue Design

40

theories. These effects may be particularly important for smaller structures in shallow water, and spectral fatigue analysis may not be appropriate. It is also important to recognize that deterministic and spectral fatigue analyses require the wave height distribution to be expressed differently. Deterministic analyses require a table describing the occurrence rate of waves of a specific height and period (such as that shown in Figure 2-24). Spectral analyses, on the other hand require a table describing the occurrence rate of individual seastate conditions (described typically by the significant wave height and zero upcrossing period). It should be apparent from the previous sections that both deterministic and spectral fatigue analysis are computationally intensive. In practice, it would be commonplace to carry out a damage summation for 8 locations on both the brace and chord side of all critical tubular joints for a range of range of wave heights and periods over 8 directions for a fixed offshore structure. For this reason, specialised offshore analysis packages such as SESAM, SACS and StruCAD*3D all have fatigue analysis modules which carry out the numerous repetitive calculations required. Despite the convenience of analysis software, a sound understanding of the fundamentals of fatigue remains an essential prerequisite for obtaining reliable results.


41

Figure 3-3: Frequency domain spectral fatigue analysis.


42

4

Risk based fatigue Analysis and Inspection Planning

It is apparent from the previous discussion that there are several sources of uncertainty, or variability in fatigue analysis. The practice adopted by most engineers when faced with such uncertainty is to adopt conservative approaches (for example using the mean S-N curve minus two standard deviations for design). While there is nothing wrong with this, an alternative approach is to consider the uncertainties explicitly along with the inherent conservatisms, and carry out a reliability analysis. The concept behind fatigue reliability analysis is illustrated schematically in Figure 4-1. Here, Tmean represents the best estimate of fatigue life, T represents the standard deviation (or variability) associated with the estimate of fatigue life, and Ts represents the required service life. The shaded area therefore represents the probability of fatigue failure.

Tmean

Probability Density

Ts

T

Fatigue Life (Years) Figure 4-1: Concept of fatigue reliability analysis: Tmean and T represent the calculated distribution of fatigue lives, Ts represents the required service life, and the shaded area represents the probability of fatigue failure.

A crucial aspect of any engineering reliability assessment is quantifying the uncertainties associated with the analysis. In estimating the fatigue life of welded structures there are three principal sources of uncertainty: 1. Uncertainty in estimating the fatigue loads and hot spot stresses on the structure. 2. Uncertainty associated with fatigue test data which is apparent as scatter on the S-N curve (refer back to Figure 2-9). 3. Uncertainty associated with the exact value of Miner’s summation which will result in fatigue failure of the joint (refer back to Figure 2-23).


43

A detailed description of the calculation of probability of fatigue failure taking into account the uncertainties listed above is beyond the scope of this course, however, Appendix B provides a general introduction. The calculation can be carried out using either S-N data, or by using a fracture mechanics approach. Although Figure 4-1 illustrates the concept of the probability of fatigue failure at the end of a service lifetime, Ts, it is not difficult to imagine that the probability of fatigue failure can be calculated at other times. This enables the probability of fatigue failure to be plotted as a function of time, an example is shown in Figure 4-2. This figure shows how the probability of fatigue failure increases with the amount of time that a joint is subjected to a certain loading environment. An extension of Figure 4-2 also demonstrates one of the important uses of probabilistic fatigue analysis. The results of inspections can be used to update the probability of fatigue failure using Bayesian statistics. Figure 4-3 illustrates schematically the effect of inspection after 10 years with no crack being detected. In this way, inspection can be used to maintain the probability of failure below some acceptable level. The results of the analysis can also be used to determine optimum inspection intervals on a risk basis. This is known as Risk Based Inspection (RBI) planning.

Probability of Fatigue Failure, PF

1.0E+00

1.0E-01

1.0E-02

1.0E-03

1.0E-04

1.0E-05

1.0E-06

1.0E-07

0

5

10

15

20

Service Life (years)

Figure 4-2: Typical results of a probabilistic fatigue analysis: Time in Service vs. Probability of Fatigue Failure.


44

Probability of Fatigue Failure, PF

1.0E+00

Effect of Inspection at 10 years no crack detected

1.0E-01

1.0E-02

1.0E-03

-4

P F = 2.2 x 10 1.0E-04

1.0E-05

1.0E-06

1.0E-07

0

5

10

15

20


Figure 4-3: The probability of fatigue failure can be updated through inspection.

Another use for probabilistic fatigue analysis is in design optimization studies. Here, the total cost of a structure may be defined as: Total Cost = CAPEX + OPEX + RISKEX where

(21)

CAPEX is capital expenditure, including the cost of fabricating and installing a structure or structural element. OPEX is operating expenditure, including fatigue inspection. RISKEX is risk related expenditure, defined as the probability of failure multiplied by the cost of failure.

In many engineering designs there is a trade-off between these types of expenditure. Figure 4-4 shows the results of probabilistic fatigue analysis on a joint in an offshore structure. Increasing the thickness of the chord in the joint will increase CAPEX, however, this will be offset by decreased OPEX (because the inspection intervals have been increased) and decreased RISKEX (because the probability of failure has been reduced).


45

1.0E-01

Probability of Fatigue Failure

Minimum Joint Design Thickness

1.0E-02

1.0E-03

Increasing Joint Thickness = Increasing CAPEX

1.0E-04

Increasing Inspection Interval = Decreasing OPEX

1.0E-05

41mm 44mm 47mm 50mm

1.0E-06 0

5

10

15

20


Figure 4-4: Increasing joint thickness in an offshore structure may increase CAPEX, but may also decrease OPEX and RISKEX.


46

5 5.1

References Books

Almar-Naess A. (1985) Fatigue Handbook – Offshore Steel Structures, Tapir, Trondheim. Barltrop N.D.P. and Adams A.J. (1991) Dynamics of Fixed Marine Structures, 3rd Ed., Butterworth-Heinemann, Oxford. Broek D.B. (1986) Dordrecht.

Elementary Engineering Fracture Mechanics, 4th Ed., Kluwer,

Gurney T.R. (1979) Fatigue of Welded Structures, 2nd Ed., Cambridge University Press, Cambridge. Maddox S.J. (1991) Fatigue Strength of Welded Structures, 2nd Ed., Abington Publishing, Cambridge. UEG (1985) Design of Tubular Joints for Offshore Structures, UEG. 5.2

Standards

API (2000) Recommended Practice for Planning, Designing and Constructing Fixed Offshore Platforms – Working Stress Design, 21st Ed., American Petroleum Institute. BS 7608:1993 Fatigue Design and Assessment of Steel Structures, British Standards Institute. BS 7910:1999 Guide on Methods for Assessing the Acceptability of Flaws in Metallic Structures, British Standards Institute. DNV RP C203 (2001) Fatigue Strength Analysis of Offshore Steel Structures, Det Norske Veritas. DNV Classification Note 30.7 (1998) Fatigue Assessment of Ship Structures, Det Norske Veritas. HSE (1990) Offshore Installations: Guidance on Design, Construction and Certification, 4th Ed., United Kingdom Department of Energy / Health and Safety Executive. Norsok (1998) Design of Steel Structures, Rev.1, Norsok Standard N-004, Norwegian Petroleum Directorate. 5.3

Research Reports and Papers

Efthymiou (1988) Development of SCF Formulae and Generalized Influence Functions for use in Fatigue Analysis, Offshore Tubular Joints Conference, Surrey UK. HSE (1997) Stress Concentration Factors for Simple Tubular Joints, Offshore Technology Report OTH 354, United Kingdom Health and Safety Executive. HSE (1999) Background to New Fatigue Guidance for Steel Joints and Connections in Offshore Structures, Offshore Technology Report OTH 92 390, United Kingdom Health and Safety Executive.


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APPENDIX A


48

APPENDIX B


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Very Nice Paper on Fatigue

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