Based on the stress time histories from the time-domain dynamic analysis, the fatigue damage may be estimated as follows: The fatigue damage is estimated based on the moments of spectra
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maximum value with nearly zero probability of occurrence The calculated stress ranges are
used to evaluate the integral in Eq (20.20) For each sea-state, the fatigue damage associated with each current velocity is multiplied by the probability of occurrence of the current velocity When stress ranges for all sea-states are obtained through the wave force model, the fatigue
damage is calculated using Eq (20.20) The advantage of using the time-domain fatigue for
pipeline ad riser assessment is to account for the non-linearity in the drag forces and structural dynamic response The other benefit is to reduce the conservatism introduced in the boundary condition for spectral fatigue analysis An engineering practice is to derive the ratio of the predicted fatigue life from these two approaches for a few well-selected and performed analyses, and then to apply this ratio to similar fatigue scenarios
20.3.3 Analysis Methodology for Time-Domain Fatigue of Risers
In time-domain analysis, a time domain dynamic analysis is performed for all sea states in the wave scatter diagram, and for each direction with a non-zero probability of occurrence In frequency-domain fatigue analysis of risers, the touch-down point is fixed The time-domain analysis is applied when the soil-pipe interaction needs to be accounted for in order to remove the conservatism introduced in the frequency-domain analysis Besides, the second order (drift) motions of the vessel may significantly affect the result of fatigue analysis It is difficult
to include the second-order motions using stress RAOs to transfer wave spectra into stress
spectra Based on the stress time histories from the time-domain dynamic analysis, the fatigue damage may be estimated as follows:
The fatigue damage is estimated based on the moments of spectra (as those used in the frequency-domain analysis), and the stress-spectra are calculated using the Fast Fourier Transform algorithm
The fatigue damage is calculated directly from the stress time-history using a rainflow counting techniques
The dynamic simulation should be long enough because the dominant period of second order
motions is of the order of 100 seconds
20.3.4 Analysis Methodology for Time-Domain Fatigue of Nonlinear Ship Response
Jha and Winterstein (1998) proposed a "Nonlinear Transfer Function (NTF)" method for efficient prediction of the stochastic accumulation of fatigue damage due to nonlinear ship loads in random seas Nonlinear time-domain ship-load analysis may reveal asymmetry in sag and hog moment at mid-ship The goal of the NTF method is derive accurate prediction using only a limited amount of nonlinear analysis based on regular waves The analysis cost is reduced because expensive time-domain analysis over many cycles of ir-regular sea is replaced by a limited number of regular-wave analysis
The NTF is the generally nonlinear transformation from wave amplitude and period to the load
amplitude measure of interest (e.g., total load range for rainflow-counting) Stochastic process theory is applied to
Identify a minimal set of regular waves @e., wave heights and associated periods) to be applied based on a discretized version of the Foristall (1978) wave height distribution and Longuet-Higgins (1983) model for wave period selection
Assign an appropriate set of "side-waves" to be spatially distributed along the ship based
on probability theory
Trang 2Chapter 20 Spectral Fatigue Analysis and Design 379
Determine how these results should be weighted in predicting statistics of the loads produced in random seas
The prediction of the time-domain fatigue analysis was compared with frequency-domain stochastic fatigue analysis that assumes linear model of ship behavior It was revealed that the nonlinear effect is significant The NTF method may also be applied to any offshore structures
20.4 Structural Analysis
20.4.1 Overall Structural Analysis
Overall structural analyses are usually performed using space frame models and fine FEA models The space frame analyses define the boundary loads for local structural models To get the stress transfer functions for the fatigue damage assessment, these boundary loads are used to factor the results of fine, FEA unit load analysis results
This section presents aspects of modeling, load evaluation, and structural analysis applicable
to the overall structural analysis
Space Frame Model
The space frame model includes all the important characteristics of the stiffness, mass, damping, and loading properties of the structure and the foundation for the structural system
It consists primarily of beam elements The accuracy of the calculated member end forces is influenced by the modeling techniques used
Figure 20.1 shows a space frame model for TLP hull primary structures and deck primary
structures Although not shown in this figure, tendons are included in the model as supporting
structure to provide the proper vertical stiffness Tubular beam elements are used to model the tendons Applied load cases are, in general, self-balancing and should result in zero net load at the tops of the tendons Thus, relatively flexible lateral springs are provided at the tops of all tendons in order to stabilize the analysis model against small net lateral loads
The hull's column and pontoon structures are modeled using beam-column elements Joint and member definitions are interfaced from the global analysis model because interfaced loads from this analysis must be consistent with the model Member properties are determined based
on the member cross-sectional properties and material properties Yield stresses of plate and stiffener components are input, along with the maximum bracket spacing for ring stiffener frames
Additional joints and members are included to ensure that the tendons and deck structure are
structurally stable and as additional load collectors where appropriate Deck members are
modeled using the tubular or AISC (American Institute of Steel Constructions) elements Deck equipment mass locations are determined for each major deck area and specifically included in the model so that proper inertial load magnitudes and centers of action are generated in the analysis
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\
Figure 20.1 Space Frame Model for a TLP
Fine FEA Model
A fine FEA model may be used to analyse the hull structure or a part of the hull structure in detail All relevant structural components shall be included in the model In the fine FEA model, major primary structural components are fully modeled using three- and four-node platelshell elements and solid elements Some secondary structural components may be
modeled as two-node beam elements
Design Loading Conditions
To adequately cover the fatigue environment, fatigue design loading conditions consist of cyclic environmental load components at a sufficient number of wave frequencies These loading conditions include:
Other cyclic loading
The loading components are either explicitly generated or interfaced from the global motion analysis Load summaries are made for each design loading condition and checked for accuracy and load imbalance
Trang 4Chapter 20 Spectral Fatigue Analysis and Design 381
The global motion analysis serves as a basis for dynamic load development The actual
interface from the global analysis to the structural analysis consists of several loading components for each analyzed wave period and direction: the real and imaginary applied unit amplitude, wave diffraction and radiation loads, the associated inertial loads and other cyclic loading such as tendon dynamic reactions The successful interface of these load components
is dependent on a consistent geometric and mass model between the motion and the structural analyses and is also dependent on a consistent generation of the loading components in the motion analysis Consistent modeling is obtained by interfacing the model geometry directly from the motion analysis wherever possible Consistent mass is obtained by interfacing with the same weight control database for both the motions and structural analyses, when available Load combinations are formed for each wave period and direction These combinations consist
of the applied wave load, the generated inertial load, and the associated cyclic loadings such as
tendon dynamic reactions for both real and imaginary loadings of the floating structures These combinations form the total cyclic load condition for each wave period and direction to
be used in the spectral fatigue analysis
Analysis and Validation
Hull structural analyses are performed using linear finite element methods The reaction forces include total force and moment reactions and the analysis results are verified Symmetrical or asymmetrical load conditions are checked to confirm symmetrical or asymmetrical analysis results
20.4.2 Local Structural Analysis
Local structural details are included as a part of the analyses for the entire hull structure The analysis of the structural details may be performed using the finite element program such
as ABAQUS (HKS, 2002) and other software The FEM model is three-dimensional and linear stress analysis is performed The results from the FEA model are interfaced into the fatigue model for additional model validation and subsequent spectral fatigue analysis of the local
structural details The entire model is plotted and revised for accuracy both from the FEA
model and after interface to the fatigue model
Loading conditions for finite element analysis of local structural details should be based on the hull's structural analysis since it includes all cyclic loadings of the structure
The unit loading conditions are frequently applied The resulting stresses for each unit load condition are interfaced to the fatigue model for subsequent combination into fatigue design loads
20.5 Fatigue Analysis and Design
20.5.1 Overall Design
A spectral fatigue assessment should be carried out for each individual structural detail It should be noted that every structural detail, every welded joint and attachment or any other form of stress concentration is potentially a source of fatigue cracking and should be considered individually
The UK DEn procedure or its modified versions are recommended in Europe for the fatigue analysis and design of floating structures since it is the most widely accepted code Design
Trang 5382 Part III Fatigue and Fracture
standards such as AWS (1997) are used in the USA However, it should be noted that different
design standards provide different procedures in the fatigue stress determination and S-N classification, which result in large discrepancies in the predicted fatigue damages Therefore,
a consistent procedure based on one design standard shall be used
The safety factors for fatigue design of floating structures are given by the design standards listed in Section 20.2 based on:
Criticality of the joint
Inspectability and repairability
The criticality of a join is determined based on its structural redundancy A joint is critical if its failure will potentially lead to the failure of the structure
20.5.2 Stress Range Analysis
A stress range analysis is performed using the fatigue software as a precursor to the fatigue
damage calculation The FEA unit load, model geometry and element stress results are interfaced into the fatigue calculation model Loading combinations will then be defined for each fatigue wave load based on the applied boundary loads
Geometry and element properties from the space frame model are plotted and revised for accuracy Any detected errors are corrected in the FEA input file and the FE analysis repeated The finite element model of the specific hotspot region shall be developed based on the procedures, finite element size requirement defined by the design standards
In the FEA model, unit load results will be interfaced into the space fiame model database These unit loads are then appropriately combined based on the applied boundary loads
20.5.3 Spectral Fatigue Parameters
Directional probabilities for fatigue waves are also included in the fatigue assessment It is usually unconservative to ignore any non-uniform distribution in directional probabilities However, in lieu of such information, the wind directional probability may be used to account for the non-uniformity in the wave approaching direction and to provide conservatism in the fatigue damage calculation
Stress Concentration Factors
The determination of the appropriate SCF in the fatigue analysis is a complex task It is also dependent on the S-N classification and stress analysis methods The general rule of thumb is that the stress used in the fatigue analysis should resemble the fatigue stress obtained from the specimen tested when deriving the S-N curves The fatigue stress does not mean the most accurate stress determined by the high-resolution fine mesh FEA It is the pertinent stress, in
Trang 6Chapter 20 Spectral Fatigue Analysis and Design 383
Full penetration welds - T curve Partial penetration welds - W curve
accordance with the chosen S-N curves A discussion of the SCF and S-N classification is given in later Sections
The SCF can be determined based on parametric equations and finite element analysis
S-N Curves
In the United States, the AWS (1997) S-N curves are used to analyze structural details of floating structures Where variations of stress are applied to conventional weld details identified in Figure 9.1 of AWS (1 997), the associated S-N curves in Figures 9.2 or 9.3, should
be used, depending on the degree of criticality Where such variations of stress are applied to situations identified in AWS (1997) Table 10.3 The associated S-N curves are provided in AWS D1.l, Figure 10.6 For referenced S-N curves in AWS (1997), Figures 9.2,9.3 and 10.6, are Class Curves For such curves the nominal stress range in the vicinity of the detail should
be used
In Europe, UK DEn (1 990) S-N curves are used for structural details in floating structures The S-N classification is determined based on the structural configurations, applied loading and welding quality
As discussed earlier, the UK DEn procedure is recommended in this chapter Therefore, the S-
N classification based on UK DEn curves will be discussed in detail, see Table 20.1
X curve is sufficiently devalued to account for thickness/size effect
US Standards (refers to e.g AWS D1.l, 1997) Mean-minus-two-standard deviation Lower bound
curves
One of 8 classes: B, C, D, E, F, F2, G
and W, depending on geometry, stress
direction, and method of fabrication
Or Spectral Fatigue Analysis
Simplified Fatigue - The long-term wave height distribution may be represented by the sum of two Weibull distributions one for noma1 and the other for hurricane conditions
Or Spectral Fatigue Analysis Cathodically protected joints in
Seawater equivalent to joints in air
Unprotected joints in Seawater require S-N curve to be reduced by a factor of 2 on life
Included
S-N curves (X’ and X) presume effective cathodic protection Fatigue provisions of AWS D1.1 apply to members and joints in
atmospheric service Does not recommend further reduction of S-N curve for free corrosion
Not covered Use X curve rather than X’ curve
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Joint Classification
Guidelines on joint classification may be found from the UK DEn (1990) Note that the S-N curves in the UK DEn (1 990) was modified by HSE( 1995)
The UK DEn (1990) guidelines apply only to welded joints that are free from serious defects
or discontinuities Factors such as undercut at the toe, internal or surface breaking defects or cracks, and geometric irregularities may cause a reduction in fatigue strength and should be evaluated separately
The UK DEn (1990) guidelines allocate various types of welded joints into one of nine joint classes To determine the correct classification for a particular weld detail, it is necessary to identify the weld type, the direction of the applied loading, and to consider all potential cracking locations For most types of joint, the weld toes, weld ends, and weld roots are considered the most important locations
The joints with the highest classifications are those that are stressed in a direction parallel to
the weld Fillet or butt weld joints fall into Class C or B in the UK DEn (1990) guidelines depending on whether the manufacturing process is manual or automatic Such joints seldom govern the fatigue strength of a welded details since other joints are likely to fall into lower joint classes
The classification of transverse butt welds is more complex They can fall into Class D or E, depending upon the details of the manufacturing process, position, and location, all of which may influence the weld profile Class C may be justified if the weld overfill is removed by grinding or the weld is shown to be free from significant defects by using non-destructive testing However, if access is limited and the weld must be made from one side only, a lower fatigue strength should be assumed
The UK DEn (1 990) guidelines downgrade butt welds, made onto a permanent backing strip,
to Class F The guidelines also warn against the use of tack welds within small distances of the plates edge, in which case, the classification is lowered to Class G
Tack welds are a controversial topic A number of studies have been conducted for different methods of attaching the backing to the plates prior to making the butt weld Tacking the backing strip to the root preparation, and incorporating this into the final weld, gives small improvement in fatigue strength over joints in which the backing strip is fillet welded to one of the plates However, the increase is not sufficient to warrant a higher joint classification In both cases, failure may initiate at the root of the butt weld
Currently butt welds made onto temporary backing such as glass or ceramic backing strips are
not classified and require further research The availability of electrodes designed specifically for root runs has resulted in an improvement in the quality of single-sided welds made without backing In recognition of this welding quality improvement, such joints can be considered as
Class F2 if full penetration is achieved This classification should be used with caution, because fatigue strength in some areas may be much lower due to lack of penetration at the root
The fatigue strength is seldom governed by butt welded joints, because these joints in general
posses a superior strength over fillet welded joints Fillet welds fall into Class F, F2, or G
depending on their size, orientation, and location in relation to a free plate edge However, recent studies have shown that fillet welds posses a fatigue strength lower than that predicted
by Class G, if the weld is continued over the comer of the plate
Trang 8Chapter 20 Spectral Analysis and Design 385
In addition to the weld toe, which is the most usual site for fatigue cracking to occur, all load carrying fillet welds and partial penetration butt welds must be evaluated to assess possible weld throat failure To avoid this type of failure, it is necessary to ensure that these joints are
adequately dimensioned This may be achieved using the Class W design S-N curve One should note that the maximum shear stress range is associated with the class W design S-N curve
Structural Details
The UK DEn fatigue design and assessment guidelines provide sketches, which provide assistance in the S-N classification of structural details According to UK DEn (1990) guidelines, joints are subdivided into the following types:
Metal free from welding
Transverse butt welds
Details in welded girders
The UK DEn Curves were developed based on small test specimens In the S-N classification
of structural details, the users first carefully relate the fatigue stress in tests with the stress of structural details under consideration For example, the fatigue stress in the test for the weld shown in Figure 20.2a, would be the tensile stress, S, on the cross-section, but for the weld shown in Figure 20.2b, it would be SCF S , where SCF is the stress concentration factor caused by the hole This is due to the fact that at point x, the stress near the weld is SCF S
However, for a small cutout in Figure 20.4c, the stress concentration due to the small hole shall not be included since micro-structural effects have been included in the S-N curves
Continuous welds essentially parallel to the direction of applied stress
Weld attachments on the surface of a stressed member
Load-carrying fillet and T butt welds
t s
C
Figure 20.2 Explanation of Fatigue Stress When Weld is Situated in
Region of Stress Concentration Resulting from Structure’s Gross Shape
Theoretically, structural details should be classified and considered for each loading step throughout the fatigue analysis since different loading steps result in different applied loading
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directions This approach is generally prohibitively complex Therefore, simplified S-N classification is used based on the rule of thumb in engineering applications
When classifylng the weld's structural details in large, complex structural systems from a series of design drawings, it is important to:
Consider each weld individually
Figures 20.3 and 20.4 show two typical examples of details found in a floating structure In the section shown in Figure 20.3, the classifications range from C to F2 and W, depending upon the direction of the applied stress In these examples, stresses in the three principal directions
S, , S, and S, , are not equal Thus the design stress range for each class will differ However, for simple design purposes, the maximum principal stress and F2 classification are assigned for the overall structural details
It is particularly difficult to classify the details that have a hole and to identify potential crack locations Holes in a continuous longitudinal weld are covered in the UK DEn fatigue design
guidelines as Class F, without requirement for an additional stress concentration factor However, a web should be incorporated to this detail The end of a web butt weld at the hole is
a more severe detail that should be ground For the ground detail, Class E or D is recommended Due to the presence of the hole, a stress concentration factor of 2.2 or 2.4 should be included If the end of the butt weld is not ground, a Class F or F2 curve, together with the geometrical stress concentration factor (2.2-2.4), is recommended
Consider each direction of applied stress
Evaluate all possible cracking locations, because each may yield a different classification Consider any possible stress concentration effects
Figure 20.3 S-N Classification of Structural Details Subjected to Triaxial
Loading
Trang 10Chapter 20 Spectral Fatigue Analysis and Design 387
:
Figure 20.4 S-N Classification of Structural Details
If concerns remain about the use of a cope hole, it is possible to improve its fatigue strength by
cutting back and grinding the weld end as shown in Figure 20.3 In such cases, the weld
between the flange and web should be full penetration over the regions on either side of the
cope hole in order to avoid failure through the weld throat (W class)
Figure 20.4 illustrates the third example of S-N classification of structural details It’s the
small bracket between the pontoon and the base node in a TLP structure Based on the UK
DEn (1990) Guidelines and published fatigue test data, the hotspot areas can be classified as F
or F2
S-N classification of the structural details in floating structures is a challenging task During
the design process, there are many structural details, which cannot be classified based on the
UK DEn (1990) guidelines In this case, other design standards such as AWS (1997) or
published fatigue test data may be used to justify the classification
20.5.4 Fatigue Damage Assessment
The fatigue life of structural details is calculated based on the S-N curve approach assuming
linear cumulative damage (Palmgren-Miner rule) A spectral fatigue analysis is used where the
long term stress range distribution is defined through a short term Rayleigh distribution within
each short-term period for different wave directions A one-slope or bi-linear S-N curve may
be assumed
Fatigue lives are determined by the service life and safety factors Additional margin is
desirable due to the uncertainties associated with fatigue assessment procedures
Initial Hotspot Screening
The objective of the initial screening is to identify the fatigue critical areas based on the
experience and the in-service data Fatigue damage is calculated for each element in the group
assuming a conservative S-N curve and upper-bound SCF for each element The calculated
damages are reviewed and all elements with fatigue lives less than the minimum required, are
analyzed in further detail in the specific hotspot analysis
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Specific Hotspot Analysis
Elements that do not pass the initial hotspot screening need to be reanalyzed using SCFs and the associated S-N curves that are more appropriate for the actual structural detail and welding procedure to be used The calculated damages are reviewed and, at least, all elements with fatigue lives less than the minimum required are summarized for further review and potential redesign andor modification of welding procedures, and reanalysis
Specific Hotspot Design
Structural details that do not pass the specific hotspot analysis are redesigned to improve their fatigue strength SCFs and associated S-N curves that are appropriate for the redesigned structural details and welding procedures will be used in the fatigue reanalysis All structural details must meet the minimum fatigue requirements after their re-design and welding procedures are finalized
Detail Improvement
It is clear that the best time to improve the fatigue strength of welded structural details is
during the design stage There are two factors, which need to be specially considered when
improving the fatigue strength of a structural detail:
Nominal stress level
The most efficient approach to improving fatigue strength is to increase the local scantling and
to configure the additional load path within the structure This approach may reduce the nominal stress level and hence the hotspot stress for a given structural detail
Geometrical stress concentration
Adopting a good design of detail configuration by providing softer connections reduces the geometrical stress concentration factor originally caused by the geometric discontinuity It is the most effective technique to improve fatigue strength However, this technique usually requires good workmanship since a soft toeiheel is used
20.5.5 Fatigue Analysis and Design Checklist
Each item in the following checklist should be checked prior to the completion of fatigue analysis:
Computer model topology - the model is plotted in sufficient views to validate model connectivity
Loading conditions - each applied loading condition is checked for accuracy
Analysis and validation - Analysis results are checked step-by-step; discrepancies between expected and obtained analysis results should be documented and explained
Loading combinations - each applied loading combination should be summarized and checked for accuracy
Environmental conditions - wave scatter diagram and directional probability input should
be checked
SCFs - SCFs used in the analysis should be confirmed for validity and applicability S-N curves - S-N curves used in the analysis should be confirmed for validity and applicability
Trang 12Chapter 20 Spectral Fatigue Analysis and Design 389
20.5.6 Drawing Verification
Design drawings corresponding to this design task should be verified according to design results, for correctness and acceptability Non-conforming drawings are to be revised and/or documented depending on their acceptability in the task technical report
20.6 Classification Society Interface
20.6.1 Submittal and Approval of Design Brief
The design brief is submitted to the classification society for review, comments, and approval The classification society’s comments are to be incorporated into the design brief and the revised design brief will be reissued If necessary, the analysis should be repeated to verify and validate the analysis results and design brief revisions
20.6.2 Submittal and Approval of Task Report
A technical task report is issued after the analysis is completed to document the analysis and
design results This report should follow the analysis methodology documented in the design brief and discuss any variations from the design brief The task report includes supporting information, hand calculations and computer output
This task report and supplemental calculations are submitted to the classification society for review, comment, and approval and will be available to the post-design personnel for reference during fabrication
20.6.3 Incorporation of Comments from Classification Society
Comments on the design brief and the task report should be incorporated into the applicable revised document The revised document is issued for record and final approval, if required
API (2001), “API RP 2FPS, Recommended Practice for Planning, Designing and Constructing Floating Production Systems”, First Edition
AWS (1997), “AWS Structural Welding Code - Steel, AWS Dl.1-96”, American Welding Society
Bai, Y (2001), “Pipelines and Risers”, Elsevier Ocean Engineering Book Series, Vol 3 BSI (1993), “BSI 7608-Code for Practice for Fatigue Design and Assessment of Steel Structures”, British Institute of Standards
DNV (2000), “RP-C203, Fatigue Strength Analysis of Offshore Steel Structures”, Det Norske Veritas
Trang 13390 Part Ill Fatigue and Fracture
Fylling, I.J And Larsen, C.M (1989), “TLP Tendon Analysis”, in an ASCE book
entitled “Tension Leg Platforms - A State of the A r t Review” Edited by Demirbilek, Z HKS (2002), “ABAQUS/Standard User‘s Manual, Version 5.6”, Hibbitt, Karlsson & Sorensen, Inc
HSE (1995), “Offshore Installation, Guidance on Design, Construction and Certification”, UK Health and Safety Executives, 4th Edition, Section 21
Jha, A.K and Winterstein, S.R (1998), “Stochastic Fatigue Damages Accumulated Due
to Nonlinear Ship Loads”, Proceedings of OMAE, Lisbon
Longuest-Higgins, M.S (1983), “On the Joint Distribution of Wave Periods and Amplitude in a Random Wave Field”, Proc of Royal Society of London, pp 241-258 Luo, Y.H., Lu, R., Wang, J and Berg, S (2001), “Time-Domain Analysis for Critical Connections of Truss Spar”, Proceedings of ISOPE, Stavanger
MCS, “Flexcorn 3D User’s Manual”, Marine Computational Services
UK DEn (1 990), “Offshore Installations: Guidance on Design, Construction, and Certification”, 3rd Edition, UK Department of Energy (Now UK Health and Safety Executives)
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Fatigue and Fracture
Chapter 21 Application of Fracture Mechanics
21.1 Introduction
21.1.1 General
Applications of the fracture mechanics in marine structural design include:
Assessment of final fracture,
Determination of crack propagation to plan in-service inspection and determine remaining
life of an existing structure,
Fatigue assessment in case S-N based fatigue assessment is inappropriate,
Calibration of fatigue design S-N Curves
In this Chapter, three levels of fracture assessment are outlined, Paris equation is applied to predict crack propagation and the comparison is made between S-N curve based fatigue assessment and fracture mechanics-based fatigue assessment
21.1.2 Fracture Mechanics Design Check
The Fracture Mechanics Design Check of Ultimate Limit-State can be applied in three alternative ways These are evaluation of:
Maximum allowable stress
Minimum required fracture toughness
Maximum tolerable defect size
Maximum Allowable Stress
The fracture mechanics strength criteria can be applied to the derivation of the maximum allowable stress at a given cross section This value is obtained when the material fracture toughness and the defect size are specified If the actual local stress exceeds the maximum allowable stress derived through this procedure, a different local design should be undertaken
in order to reduce the local stress level and fulfill the fracture mechanics criteria
Minimum Required Fracture Toughness
The minimum required fracture toughness should be derived through the fracture mechanics design check when the design geometry is established and a defect tolerance parameter is specified The derived fracture toughness then allows designers to select a suitable material for any particular structure of concern
Trang 15392 Part III Fatigue and Fracture
Maximum Tolerable Defect Size
A maximum tolerable defect size can be derived when the geometry and the fracture toughness
of the selected material are known For statically loaded structures, the maximum tolerable defect size must satisfy the fracture mechanics criteria For dynamically loaded structures, the maximum tolerable defect size represents the critical crack size in a fatigue failure event It may be used to minimise the risk of unstable fracture throughout the operating life of the structure The result also gives direct input to the calculation of fatigue crack growth period There are three levels of procedure that are applied in fracture assessment (Reemsnyder, 1997): Level 1 Utilisation of the Crack-Tip Opening Displacement (CTOD) Design Curve
(explained in Section 2 1.2)
Level 2 The Normal Assessment or Design Safety Format that makes use of the Failure
Assessment Diagram (described in Section 21.3) No practical safety factors need
Utilisation of the Failure Assessment Diagram based on detailed information of stress-strain curves of materials Partial safety factors are applied to the defect size, stress level, etc., see Section 21.4
to be applied here
Level 3
More information may be found from MI 579 (2001), Andersen (1991) and BSI (1999)
21.2 Level 1: The CTOD Design Curve
21.2.1 The Empirical Equations
The CTOD Design Curve may be used to evaluate the resistance against fracture of a wide
range of structures such as pipelines, pressure vessels, ship and offshore structures, buildings
and bridges One of the most commonly used CTOD Design Curves is the one developed by the British Welding Institute (TWI) that relates the CTOD at some critical event, the yield strength cy, nominal strain at a notch E, and flaw size a (Burdekin and Dawes, 1971; Dawes, 1974) This Design Curve was initially included in the first edition of the BSI fitness for purpose guidance (BSI PD 6493, 1980) The BSI (1980) CTOD design curve may be expressed as:
E for -50.5
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(21.4)
where a is the length of a through-crack in an infinite plate equivalent in severity to that of the crack in the element under investigation, and E is Young's Modulus
21.2.2 The British Welding Institute (CTOD Design Curve)
The BSI (1980) CTOD Design Curve shown in Figure 21.1 was constructed relative to the wide-plate test results with a safety factor of 2 on flaw size a
There are three alternative applications for the CTOD Design Curve:
Maximum Allowable Strain: Solving Eqs (21.1) and (21.2) for E I c y , we may define the maximum allowable strain for the given values of material fracture toughness CTOD and crack size a
Minimum Required Fracture Toughness: A material with an adequate toughness CTOD
can be selected for the critical region, given the maximum possible flaw size a and strain level of E I E'
Maximum Allowable Flaw Size: This design curve may be used in the following manner:
Given E I cy in a critical region from a stress analysis of the structure, 0 is determined from the diagram From this value of 0, the maximum allowable flaw size, a, in the critical region may be established given the toughness CTOD of the material
The TWI CTOD Design Curve was also adopted by the American Petroleum Institute in its API 1104 (1983) as a basis for its fitness-for-purpose criteria
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21.3 Level 2: The CEGB R6 Diagram
This Level 2 Assessment provides a simplified method of checking whether particular flaws present in the structure may lead to fracture failure, or whether the flaws can be considered safe without having to go through more complex assessment procedures The approach adopted in this preliminary assessment uses a variable safety factor on flaw size averaging about 2 No additional partial safety factors should be used in Level 2 Assessment
Two normalised parameters are specified and given as follows:
where KR is the fracture ratio,
K = Stress-intensity factor (a function of net section stress c N , crack size a, and geometry) at fracture of the component.,
KMAT = Linear elastic fracture toughness of the component,
SR = Collapse ratio,
c N
crFLow = Flow stress that is defined as the average of yield stress and tensile stress in
= Net section stress in the component at fracture, and
BS 7910 (1997)
1.0 0.8
Trang 18Chapter 21 Application of Fracture Mechanics 395
The original failure assessment diagram (FAD) was developed by the U.K Central Electricity
Generating Board (CEGB) This FAD is shown in Figure 21.2 The CEGB approach (Milne et
al., 1986, 1988; Kanninen and Popelar, 1985) addressed post-yield fracture by an interpolation
formula between two limiting cases: linear elastic fracture and plastic collapse The
interpolation formula, called the failure assessment or R6 curve (see Fig 2 1.2) is:
KR=L? - - I~[s~c(o.~zs,)]
(2 1.7)
The right-hand side of Eq (21.7) is the plastic correction to the small-scale yielding prediction
The CEGB R6 curve in Figure 21.2 may be interpreted as follows: A structural component is
safe if the point W describing its state falls inside of the R6 curve The component fails if the point W is on or above the R6 curve The utilisation factor on load is OW/OF, where point F is
on the R6 curve and point 0 is in the origin
21.4 Level 3: The Failure Assessment Diagram (FAD)
The FAD utilised in Level 3 Assessment is as depicted schematically in Figure 21.3:
The collapse ratio, LR, is the ratio of the net section stress at fracture to the flow stress
The fracture ratio, KR, is the ratio of the crack driving force (including residual stresses) to the material toughness (which could be KMAT or CTOD)
The failure assessment curve defines the critical combination of service loads, material stress- strain properties, and geometry of the cracked member at which failure might be expected Applications of the FAD to design codes include:
CEGB R6 - Revision 3
BSI (1 999) PD 6493
Electric Power Research Institute/General Electric (EPRVGE) model
ASME Section XI Code Case (DPFAD) for ferritic piping
Trang 19396 Part III Fatigue and Fracture
Level 3 is the most sophisticated one among of the three levels and will normally be used in the assessment of high strain-hardening materials andlor stable tearing where the Level 2 approach would prove too conservative In PD 6493 (now BS 7910), Level 3 FAD consists of
two alternative criteria: 1) a general FAD and 2) a material specific FAD in which material stress-strain curves are also input data to the F A D assessment
CTOD is popular in the UK nd European countries, while J-integral is used in the USA, e.g by the nuclear engineering industry
21.5 Fatigue Damage Estimation Based on Fracture Mechanics
21.5.1 Crack Growth Due to Constant Amplitude Loading
The total number of cycle to final fracture is the sum of the number of cycles for the crack initiation phase and crack propagation phase The number of cycles for crack propagation phase, Np, my be estimated using,
(21.8) where a, and a C R are crack depth (or length) at crack initiation and final fiacture respectively The value of acR may be determined using methods for the assessment of fmal fracture, as discussed in Section 21.1 thru Section 21.4 The crack propagation may be predicted using Paris Law Substituting the Pans Law into the above equation, we may obtain that
(21.9)
where F is so-called crack shape factor and S denotes the stress range When the stress range S
is of constant amplitude, the above equation may be re-written as:
The Paris parameters C and m may be found from Gurney (1 979), IIW( 1996), BS 791 0 (1999)
and API 579 (2001) The values of C and m depend on the material, service environment and stress ratio The value of C may also be determined by mechanical tests and the chosen value
is to be the mean value plus two standard deviation of log dddN
The size of initial crack ao, should be determined considering the accuracy of the non-
destructive testing which is used to inspect the defects during fabrication
Trang 20Chapter 21 Application of Fracture Mechanics
Fracture Mechanics
Region I Threshold Region (no crack growth)
397
S-N Curve Fatigue Endurance Limit (infinite life)
21.5.2 Crack Growth due to Variable Amplitude Loading
Region IT Paris Equation
Region III: Final Fracture (yielding)
The equations presented in Section 21.5.1 may be applied to risk-based inspection in which the
crack growth is predicted using Paris Law Predicting the number of cycles for the crack propagation phase for variable amplitude loading is compIex and needs a computer program to
do numerical integration of Eq.(21.9) The number of occurrence ni in a block for stress range
Si for crack depth from a,to a,,, may be estimated as (Almar-Naess, 1985),
S-N Curve (high cycle fatigue) Low-cycle fatigue, failure region
21.6 Comparison of Fracture Mechanics & S-N Curve Approaches for Fatigue
As compared in Table 21.1, the Paris Equation may be transformed to the equation of an S-N
curve Eq(21.10) may be written as