Lecture 9 14.5 Release
Fatigue Analysis
Introduction -
This This lectu lecture re provid provides es only only the the basic basic ide ideas as of fatigue fatigue.. Som Some e discus discussion of the background to to the checking methods methods is included as well.
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The The main main purpo purpose se of thi thiss lect lecture ure is to to demo demonst nstrate rate the the imp imple lemen mentat tation ion of ANSYS ANSYS technology in studying fatigue in fixed f ixed marine structures.
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Joint Joint fatigue fatigue assessme assessment nt (FATJA (FATJACK) CK) is inclu include ded d in Design Design Asses Assessme sment nt and can be connected to Static Structural, Transient Structural and Harmonic Response analyses.
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In order order to use FATJAC FATJACK K in the the most most efficie efficient nt way, way, glob global al mode models ls are often ften studied first. Although such models contain approximations, they have the benefit of giving a good insight into the structural behaviour. At a later stage local models models may need need to be solved (see ( see submodeling). submodeling).
Nomenclature -
Attribute Groups define the input data to FATJACK
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DA result objects define the output. They can be requested either before or after the analysis
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Inspection Points are the positions to check for fatigue around the brace where it connects to the chord
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As WB is geometry-based the user needs to select bodies rather than individual elements
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Elements that do not have results will be semi transparent in the graphics window
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Stress Concentration Factors can be returned for the brace or the chord side
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As always the results can be parameterised!
Stress Concentration Factors -
The distribution of stresses across the section of a member may be abrupt due to stress raiser in the region (bolt holes, notches, welds). When the variation is abrupt so that within a very short distance the stress intensity increases greatly, the condition is described as stress concentration.
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The term is vague and it implies some sort of irregularity not inherent in the member.
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In short, SCF is the ratio σact/σ, i.e. actual stress divided by nominal stress. The nominal stress is based on the net section ignoring any stress redistribution caused be the irregularity. Consider the following example:
Sample subjected to uniform bending My moment, the no m , which for the current I 6 M geometry becomes no m
b( D h) 2
But the actual stress is much higher because of the stress concentration that occurs at the
Stress Concentration Factors (cont.) -
SCFs relate hot spot stresses to the nominal stresses in a member computed from the axial forces and in-plane and out-of-plane bending moments.
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FATJACK provides facilities for both defining explicit SCF values and for automatically generating the SCF values using one or more established empirical formulations. Explicit and generated SCF values may be mixed as necessary to achieve the desired result.
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Some default values exist in FATJACK, e.g. for tubular section: brace side SCF for in-plane bending=3.5 brace side SCF for out-of-plane bending=3.5 chord side SCF for axial force=3.0 chord side SCF for in-plane bending=3.5 chord side SCF for out-of-plane bending=3.5
Fatigue Assessment -
When a steel member is subject to a sufficiently large fluctuating tensile stress, small crack-like defects will grow in size and eventually reach a big enough size to cause the member to fail.
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Most marine structures are subject to chaotic stress fluctuations during their design life making any approach based on endurance limit stress impractical. Random operation loads (wind, wave, earthquake, VIV) make the use of S-N curves necessary in this case.
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The use of S-N curves is an alternative approach for the assessment of inservice cracks. Based on specimens subject to fluctuating loading the number of cycles to failure N is inversely proportional to the stress range S to the power m of 3 to 4. This is expressed by the following relationship:
N AS m where A and m are obtained experimentally -
The method used within FATJACK to carry out the fatigue assessment is based upon the use of S-N curves
Fatigue Assessment (cont.) -
The environment is also important, fatigue life is reduced in freely corroding conditions (Bradshaw et al. 1984).
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Tubular joints are used throughout fixed marine structures and a number of different S-N curves already exist in the public domain.
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Crack propagation is mostly driven by tensile stresses but high tensile residual stresses in the material exist creating tensile stresses even when the applied stress is compressive. This compression-tension cycle requires the use of the full stress range in fatigue calculation. A typical S-N curve is shown below.
Miner’s Rule -
Miner’s rule is based on the concept of fatigue damage. For variable amplitude environmental load, Miner’s rule allows for the number of different amplitude stress cycles to be considered.
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The S-N curve only provides information for constant amplitude loading.
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The fatigue damage for a joint that is subject to n number of cycles/year of constant amplitude loading when it could take N AS m cycles is simply n/N. If the same joint is subject to a variable amplitude loading the load cycles can be divided into groups of approximately an equal stress range. Thus, if there are G groups with stress range Sg and number of cycles ng in each group, the fatigue damage, per group, is m N g AS g D g n g / N g where
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Miner’s rule states that failure, under variable amplitude loading, is to G occur when D g 1 g 1
Miner’s Rule (cont.) ni
N
Miner’s Damage Rule:
i
amp
n1 N 1
n2
N 2
N1 n1
N 3
n4 N 4
n5 N 5
Damage =1.0
N2 n2
n3
N3
n3
N3
n4
N4
n5
N5
log N
Since the calculation is based on the number of cycles/yr for the constituent waves, the resulting damage is that associated with one year of operation. The fatigue life is simply the reciprocal of damage, that is life=1/D
Added Mass When dealing with marine structures, two important additions to the normal structural mass have to be considered: -
The added (entrained) mass of water, which moves with submerged or partially submerged structural members.
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The increase in mass due to marine growth (which varies over the life of the structure). It must be remembered that the added water is external to the structure and is over and above any water contained within a hollow structure. For example a hollow pipe has an effective mass equal to:
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The mass of the member
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The mass of the water contained within the pipe
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The added mass
Added Mass (cont.) In theory added mass (mass/unit length) is determined by potential flow theory but added mass values for common sections are widely documented. Closely with added mass are the drag and inertia coefficients (OCTABLE) Added mass is defined in OCDATA as, the ratio of added mass of the external fluid over added mass for a circular cross section
Obviously the added mass can have a profound effect on modal and dynamic analyses and should be calculated as accurately as possible.
Rainflow Counting -
Consider the stress-time history recorded at a probe as shown in Fig. A. Questions like “what stresses are significant, what counts as a cycle, and what is the measure of damage incurred spring into mind!
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Consider the first fully reversed cycle a nd the second fully reversedcycle.
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It is clear that to impose the stress-time history on a part, it is necessary that the time trace look like the solid line plus the dashed line.
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Fig. B begins and ends with the max stress-time history.
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Acknowledging the existence of a single stress-time history is to discover a “hidden” cycle as shown in the dashed line.
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To ensure that the hidden cycle is not lost, start the curve with the largest (or smallest) stress and add previous history to the right side as shown in Fig. B.
Rainflow Counting (cont.) -
Imagine we flood the curve with water and we gradually drain it to monitor the valleys that are formed.
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Valley #1 has σmax=80Pa, σmin=-60Pa, σav=70Pa, σm=10Pa
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Valley #2 has σmax=60Pa, σmin=40Pa, σav=10Pa, σm=50Pa
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Valley #3 has σmax=-20Pa, σmin=-40Pa, σav=10Pa, σm=-30Pa
Rainflow Counting (cont.) •
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Based on ASTM E1049-85 (2005) Standard Practices for Cycle Counting in Fatigue Analysis Reduces spectrum of varying stress into simple stress reversals Allows the application of Miner’s rule to assess fatigue life of structure subject to complex loading
It is possible to use results from up to 1000 different transient dynamic analyses and loading (i.e., multi-directional wave spectra) Results can be combined using a probabilistic approach, output includes: •
fatigue life (based on Miner´s rule)
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usage factors
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damage per wave (history)
ANSYS - Code Checks (FATJACK/BEAMST) • Joint Code & Member Code checks including: – AISC 10th edition working stress and 2nd edition LRFD
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API RP2a-WSD 21st edition working stress RP2A-LRFD 1st edition BS5950 part 1 1992 NORSOK 2000 NORSOK NS3472 1984 NPD 1992 DS449 1984 (with 1994 amendments) DS412 1984 (with 1994 amendments) ISO 19902 implementation started
• Easy-to-use code check facilities including:
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Code checks on time histories Code checks on combined load cases Visualization of code checks Ability to use them in combination with ANSYS calculations
ANSYS - Fatigue Assessments FATJACK module offers both deterministic and spectral fatigue capabilities •
for tubular frame structures subjected to waves and current or wind including wind gusts
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can be used in frequency and time domain
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sea states: JONSWAP, Pierson-Moskovitz, Occhi-Hubble, Scot-Weigel and Shell New Wave, or user-defined wave spectra
FATJACK includes explicit SCF definitions •
SCFJ – if crown & saddle SCF is known e.g. from empirical formulae
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SCFA – if SCF is known at specific locations e.g. from FE
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SCFB – if SCF is constant across a section
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SCFP – if SCF values vary with location
Automatic (empirically derived) SCF definitions based on •
Efthymiou, Wordsworth, Kuang or DS449
Analysis Type Selection At v14 support for spectral fatigue was added:
Analysis Type Selection (cont.) The following types of fatigue analysis are supported in Workbench: -
Time History: enables the selection of joints to be included, along with the definition of the cycles for rainflow counting and target life. Upstream systems are usually transient analyses with random ocean loading coming from different wave directions
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Stress History: enables the selection of joints to be included, along with the definition of the target life. Wave conditions (heights, periods, directions) are automatically determined with OCEAN commands in the upstream system(s). Wave occurrence data can be provided with attribute groups. Upstream systems can be either static or transient structural
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Spectral (static/dynamic): Enables the selection of joints, along with definition of the peak stress, wave spreading and target life of the analysis. Wave transfer function, spectrum, and additional frequency data should be provided in a text file containing the FATJACK commands. Wave load cases are automatically determined using the HROCEAN command provided in upstream system(s) in the order that they are defined. Upstream systems are usually of the Harmonic Response type; note that both the static and harmonic options of the HROCEAN command can be used when performing a spectral analysis
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Deterministic: Enables the selection of joints, along with definition of the target life. Wave load cases are automatically determined using the harmonic ocean wave procedure provided in upstream system(s). Upstream systems should be of harmonic response type; only the static option of the HROCEAN is appropriate here (HROCEAN,STATIC)
Deterministic Methods -
Deterministic methods apply Miner’s rule directly
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The ocean environment is idealised by representative wave cases, with a defined number of loading cycles (occurrences/year). MAPDL commands will be used to produce a series of wave cases. The structure is then analysed to determine the stress state and then the fatigue life
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In deep waters (D>0.5λ) where the structure responds sinusoidally to the load, the wave loading generates a loadcase pair for each wave case analysed. The pair of loadcases represents the real and imaginary parts of a solution which retains both magnitude and phase information
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The above is achieved by undertaking a harmonic response analysis
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FATJACK uses this data to generate the stress ranges directly from the incoming member forces for the loadcase pairs
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In shallow waters linear theory is invalid and a more detailed analysis needs to be adopted, i.e. stress-history approach (not covered here)
Harmonic Ocean Wave Procedure (HOWP) •
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Standard harmonic analysis logic with ocean loading includes the added mass of the water outside the pipe. A damping matrix must be added separately if one is needed. The load vector is computed based on the loads at a given time, but the standard analysis method usually misses some important effects, as all peak loads rarely occur at the same time So that all relevant ocean wave loading effects are accounted for, a specialized variation of the harmonic analysis is available. The harmonic ocean wave procedure (HOWP) applies to regular waves only (Airy and Wheeler one-component waves, as well as Stokes and Dean’s Stream Function waves), and works only with the full-solution harmonic analysis method (HROPT,FULL)
Harmonic Ocean Wave Procedure (HOWP) (cont.) -
HOWP is implemented with the HROCEAN command. The frequency is obtained by the wave period defined via OCDATA & OCTABLE when HROCEAN, HARMONIC.
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Ocean loads are calculated with the assumption that the structure is stationary
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ANSYS calculates the forces on each load component of each element at NPHASE solutions, spread evenly over one wave cycle. Then, the minimum and maximum, and the phase between them, are calculated. The command uses the resulting information to generate the real and imaginary loads.
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For every component of every element, special calculations are performed to obtain real and imaginary loads. All loads are sinusoidal at the given frequency, but the magnitude and phase angle of every component of every element needs to be determined, as follows:
Harmonic Ocean Wave Procedure (HOWP) (cont.) -
First, assume that the wave profile is represented as a simple cosine wave, as shown below:
Harmonic Ocean Wave Procedure (HOWP) (cont.) -
A series of static analyses is performed ranging from 0 to 360 degrees. The number of these analyses is controlled via the HROCEAN command. The result is a roughly sinusoidal force pattern, as shown below:
Harmonic Ocean Wave Procedure (HOWP) (cont.) -
From this force history, the maximum and minimum forces are calculated by fitting the highest and lowest points. Then: A
(Y max Y min )
( X max
2 X min 180)
( X max
2 X min 180) 2
if X max X min if X max X min
Y A cos( X ) A cos cos X A sin sin X
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Acosφ is the coefficient on the real load vector and Asinφ is the coefficient on the imaginary load vector
Harmonic Ocean Load HROCEAN, Type, NPHASE Type Specifies how to include ocean wave information in a harmonic analysis:
HARMONIC — (default) Performs a harmonic analysis using both real and imaginary load vectors (calculated via HOWP). This behaviour is the default. This option works by performing a harmonic analysis running at a frequency determined by the wave period (specified via OCTABLE). STATIC — Performs a static analysis using both real and imaginary load vectors (calculated via HOWP). This option works by performing a harmonic analysis running at a frequency of 0.0. OFF — Deactivates a previously activated HOWP and performs a standard harmonic analysis. NPHASE Positive number specifying the number of phases to calculate forces. This value must be at least 8 (defaults to 20)
Further Reading Salmon C.G. & Johnson J.E. (1980) Steel structures design and behaviour, Harper and Row, New York Gurney T.R. (1979) Fatigue of welded structures, Cambridge Uni Press Knott J.F. (1973) Fundamentals of fracture mechanics, Butterworths UK Lalani, M. & Teddett, I.E. (1985) Design of tubular joints for offshore structures, UEG, London Barltrop, N. & Adams, A.J. (1991) Dynamics of Fixed Marine Structures, Butterworth-Heinemann Bishop, N & Sherratt, F. (2000) Finite Element Based Fatigue Calculations, NAFEMS
Workshop 7 – Fatigue Analysis • Workshop 7 – Fatigue Analysis • Goal:
– Learn how to set up a Design Assessment system with FATJACK – Learn about Solution Selection and analysis factorization – Define input in DA – Request output from DA – Study the results
