Failure assessment diagrams. III. Mappings and failure assessment lines when the crack driving force is a functional

1994 ◽  
Vol 444 (1922) ◽  
pp. 497-508 ◽  
Keyword(s):  
Driving Force ◽  
Curve Analysis ◽  
General Situation ◽  
Crack Driving Force ◽  
Tearing Instability ◽  
Tangency Condition ◽  
Theory Of Plasticity ◽  
Failure Assessment ◽  
Natural Way ◽  
Flow Theory Of Plasticity

In two previous papers a natural mapping was noted between the ( a, J ep ) diagram of R-curve analysis and the ( L r , K r ) failure assessment diagram (FAD) of the R6-revision 3 procedure. In these papers it was assumed that the applied crack driving force J ep was obtained by a deformation theory of plasticity and so could be treated as a function of its arguments. Here the analysis is generalised to consider the situation where J ep is not a function but a functional of its arguments, as in the flow theory of plasticity. As in I the discussion has been given in terms of the J based parameters. But the conclusions hold equally well for any other parameters describing crack driving force and crack resistance. A unique R-curve image (the RCl) in the FAD can still be established in a natural way. Moreover, if this RCl is used as the failure assessment line (FAL), the treatments of ductile tearing instability in R-curve analysis and in the FAD are still equivalent. The interesting situation then arises, however, that the tangency condition can be defined in the FAD but not in R-curve analysis, because in the latter the usual applied J ep curves do not exist. Some difficulties in using the FAD in this more general situation are discussed. An FAL can be obtained when J ep is a function of its arguments by considering a sequence of RCl curves for similar structures of ever increasing size and this procedure can be extended to the situation where J ep is a functional. The R-curve plays a central role in the argument when J ep is a function and even more so when J ep is a functional. In the latter situation, the analysis rests essentially on the consideration of increments of crack driving force and fracture resistance and it is suggested that a fracture mechanics based on the values of these increments rather than on the values of the parameters themselves might be developed.

Failure assessment diagrams. II. The use of single failure assessment lines

1994 ◽  
Vol 444 (1922) ◽  
pp. 483-496 ◽  
Keyword(s):  
Crack Growth ◽  
Deformation Theory ◽  
Curve Analysis ◽  
Alternative Proof ◽  
Crack Driving Force ◽  
Ductile Tearing ◽  
Natural Mapping ◽  
Tearing Instability ◽  
Failure Assessment ◽  
Level 3

In a previous paper a natural mapping was noted from the ( a, J ep ) diagram of R-curve analysis into the ( L r , K r ) failure assessment diagram (FAD) of the R6-revision 3 procedure. Assuming that J ep is obtained by a deformation theory of plasticity, the analytical expression for this mapping is given and used to derive the images in the FAD of the applied J ep curves and of the R-curve. If this mapping is sufficiently smooth, it may be used to provide an alternative proof that the critical R6-revision 3 load locus touches the R-curve image (RCI) when the crack extension and the load are the same as those predicted by R-curve analysis. The natural mapping may not always be 1:1 and this is illustrated by considering the example of a family of linear R-curves. The relations between the various other functions used in the FAD and R-curve analysis are studied analytically. In particular it is shown how to derive from any single failure assessment line (FAL) on which the assessment point is assumed to move during crack growth, either the implied R-curve (IRC) or, alternatively, the implied applied J ep curve (IAJC). Further comments are made on the internal consistency or conservatism of analyses of ductile tearing instability which use a single FAL on which the assessment point is assumed to move during crack growth, such as those characteristic of level 3 of PD6493 and options 1 and 2 of R6-revision 3. The method for testing the consistency or conservatism of an FAD with a single FAL which involves the calculation of the IAJC requires that the function J ep = j ep ( a, L ) of the structure be known for a specific restricted range of a and L only. In contrast, the deduction of the IRC requires a knowledge of the j ep ( a, L ) over a wider domain. It is emphasized that the assessment of conservatism throughout is not absolute but only relative to the predictions of R-curve analysis. As in the previous paper, the discussion is given in terms of the J based parameters. But the conclusions hold equally well for an FAD based on any other parameters describing crack driving force and crack resistance.

Failure assessment diagrams. I. The tangency condition for ductile tearing instability

1994 ◽  
Vol 444 (1922) ◽  
pp. 461-482 ◽  
Keyword(s):  
Crack Growth ◽  
Maximum Load ◽  
Crack Size ◽  
Curve Analysis ◽  
Ductile Tearing ◽  
Tearing Instability ◽  
Tangency Condition ◽  
Failure Assessment ◽  
Analytical Proof ◽  
Assessment Procedures

Until now no analytical proof has been given to show that the tangency conditions used to define ductile tearing instability in the failure assessment procedures R6 and PD6493 are equivalent to R-curve analysis, although for R6 such an equivalence has been widely claimed. The failure assessment line (FAL) specified in R6-revision 3-option 3 is actually a family of lines when ductile tearing is involved. With this option the use of the tangency condition specified in R6-revision 3-category 3 analysis does not give a treatment of ductile tearing instability which agrees with that of R-curve analysis. The only reliable way of obtaining such an agreement when this failure assessment line family is used is by the solution of simultaneous equations or by some equivalent procedure such as the identification of a maximum load. However, an alternative FAL along which the assessment point moves during crack growth can be constructed. This has been called a ‘failure assessment curve for changing crack size’ but is referred to here as the R-curve image (RCI) because it is an image of the R-curve in the failure assessment diagram (FAD). When this RCI is used as the FAL the tangency condition does give the same predictions as R-curve analysis. Because the R6 diagram explicitly includes a plastic collapse parameter while R-curve analysis does not, this agreement is at first sight rather surprising. Although the use of the tangency condition specified in R6 does not give predictions in accord with R-curve analysis, it is confirmed analytically that it does give a more conservative estimate of the critical load for instability, provided that a conservative choice of the failure assessment line is made and that the RCI lies wholly above it. Thus this work not only throws light on the structure of R6 but suggests that it may be conservative relative to R-curve analysis. This is demonstrated qualitatively by two examples; whether it is a general result is a matter for further study. PD6493 and some options of R6 involve procedures for assessing ductile tearing instability which use the tangency condition combined with a single failure assessment line along which the assessment point moves during crack growth. Some preliminary comments on the implications of such combinations are made and it is suggested that when these combinations are used, checks on the internal self consistency of the assessment procedures are available.

ECAs, FE and Bi-Axial Loading: A Critique of DNV-OS-F101, Appendix A

2015 ◽  
Author(s):  
Andrew Cosham ◽  
Kenneth A. Macdonald
Keyword(s):  
Finite Element ◽  
Driving Force ◽  
Longitudinal Strain ◽  
Axial Loading ◽  
Limit Load ◽  
Fe Analysis ◽  
Plastic Limit ◽  
Crack Driving Force ◽  
Failure Assessment ◽  
Plastic Limit Load

Controlled lateral buckling in offshore pipelines typically gives rise to the combination of internal over-pressure and high longitudinal strains (possibly exceeding 0.4 percent). Engineering critical assessments (ECAs) are commonly conducted during design to determine tolerable sizes for girth weld flaws. ECAs are primarily conducted in accordance with BS 7910, often supplemented by guidance given in DNV-OS-F101 and DNV-FP-F108. DNV-OS-F101 requires that finite element (FE) analysis is conducted when, in the presence of internal over-pressure, the nominal longitudinal strain exceeds 0.4 percent. It recommends a crack driving force assessment, rather than one based on the failure assessment diagram. FE analysis is complicated, time consuming and costly. ECAs are, necessarily, conducted towards the end of the design process, at which point the design loads have been defined, the welding procedures qualified and the material properties quantified. In this context, ECAs and FE are not an ideal combination for the pipeline operator, the designer or the installation contractor. A pipeline subject to internal over-pressure is in a state of bi-axial loading. The combination of internal over-pressure and longitudinal strain appears to become more complicated as the longitudinal strain increases, because of the effect of bi-axial loading on the stress-strain response. An analysis of a relatively simple case, a fully-circumferential, external crack in a cylinder subject to internal over-pressure and longitudinal strain, is presented in order to illustrate the issues with the assessment. Finite element analysis, with and without internal over-pressure, are used to determine the plastic limit load, the crack driving force, and the Option 3 failure assessment curve. The results of the assessment are then compared with an assessment using the Option 2 curve. It is shown that an assessment based Option 2, which does not require FE analysis, can potentially give comparable results to the more detailed assessments, when more accurate stress intensity factor and reference stress (plastic limit load) solutions are used. Finally, the results of the illustrative analysis are used to present an outline of suggested revisions to the guidance in DNV-OS-F101, to reduce the need for FE analysis.

Probabilistic Failure Assessment of a Complex Nozzle Structure With Flaw Defect Based on FITNET Procedure

2016 ◽  
Author(s):  
Yan Wang ◽  
Yan-Wei Wang ◽  
Hanxin Chen ◽  
Linwei Ma
Keyword(s):  
Crack Growth ◽  
Failure Probability ◽  
Driving Force ◽  
Complex Geometry ◽  
Crack Depth ◽  
Initial Crack ◽  
Structural Safety ◽  
Crack Driving Force ◽  
Failure Assessment ◽  
Nozzle Structure

A probabilistic failure assessment based on the fracture and fatigue modules of European FITNET procedure is presented in this work. Analysis of the leak probability of a complex nozzle structure with postulated flaw defect under thermal mechanical loading is performed. Crack growth is calculated using FITNET fatigue module, in which the crack driving force ΔKeq considering mixed-mode load is applied. For the structural safety evaluation, the failure assessment diagram (FAD) within the frame of FITNET fracture module is utilized with the parameter Keff combing KI and KII. The fracture mechanical parameters are calculated using finite element (FE) method because of the complex geometry and load conditions. To meet the needs of probabilistic analyses, formulas calculating crack driving force are developed specific for this nozzle structure through nonlinear regression based on the FE results. With an initial crack depth of 5 mm, the nozzle failure probability in form of leak comes to 1.84×10−4 in next fifty years. The good agreement of the results of Monte Carlo simulation and stratified sampling technique confirms that the crack growth parameter C and the initial crack shape ratio c/a have considerable effect on the structural failure probability.

Development of the BS 7910 Failure Assessment Diagram for Strain Based Design With Application to Pipelines

2012 ◽  
Author(s):  
Simon Smith
Keyword(s):  
Yield Strength ◽  
Driving Force ◽  
Critical Assessment ◽  
Complex Structures ◽  
Crack Driving Force ◽  
Failure Assessment ◽  
Proposed Modification ◽  
Force Data ◽  
Suitable Modification ◽  
J Estimation

Engineering Critical Assessment (ECA) uses J estimation schemes to derive the crack tip loading of complex structures to determine their tolerance to crack-like flaws. The methods currently being used were derived in the 1980s for structures with primary stresses below the material yield strength. These are now being extensively used for loads beyond this level for what has been called Strain Based Design (SBD). Some papers have shown the standards BS7910:2005 and R6 Revision 4 can be unconservative when used for SBD. A possible reason has been identified and a suitable modification proposed. The proposed modification is briefly reviewed in the present paper together with a comparison of the method with suitable crack driving force data.

Application of the strain-based FAD to failure assessment of surface cracked components

2015 ◽  
Vol 6 (6) ◽  
pp. 689-703
Author(s):  
Igor Varfolomeev ◽  
Michael Windisch ◽  
Gerben Sinnema
Keyword(s):  
Boundary Conditions ◽  
Strain Hardening ◽  
Driving Force ◽  
Design Methodology ◽  
Surface Cracks ◽  
Crack Driving Force ◽  
Content Type ◽  
Failure Assessment Diagram ◽  
Aerospace Applications ◽  
Failure Assessment

Purpose – The purpose of this paper is to validate the strain-based failure assessment diagram (SB-FAD) approach for surface cracks in components subjected to displacement controlled boundary conditions. Design/methodology/approach – Numerical analyses are performed for several crack geometries and materials representative for aerospace applications. The performance of the SB-FAD is judged by comparing numerically calculated J-integrals to respective analytical estimates, using both Options 1 and 2 approximations. Findings – In the most cases, both Options 1 and 2 SB-FAD method results in reasonably conservative J-estimates. Exceptions are for surface cracks in a pressurized vessel made of a material with low-strain hardening, for which Option 2 assessment produces non-conservative results. In contrast, Option 1 assessment is conservative for all geometries considered. In general, Option 1 results in a considerable overestimation of the crack driving force, whereas Option 2 produces rather accurate results in many cases. Originality/value – The results demonstrate both the potential of the SB-FAD method and needs for its further improvements.

Failure assessment diagrams. IV The inclusion of constraint parameters

1995 ◽  
Vol 448 (1933) ◽  
pp. 281-291 ◽  
Keyword(s):  
Crack Extension ◽  
Crack Tip ◽  
Curve Analysis ◽  
General Situation ◽  
Two Dimensional ◽  
Growth Path ◽  
Constraint Function ◽  
Independent Variables ◽  
Failure Assessment ◽  
Crack Tip Constraint

Recent discussions of the relation between R-curve analysis and failure assessment diagrams of the type used in R6 and PD6493 are generalized to the situation where the material resistance is defined by a function depending not only on the crack extension but also on other parameters which measure the constraint at the crack tip. There is thus a resistance surface if only one other parameter in addition to the crack extension is involved. The analysis is formulated for any number of generic constraint parameters which can be defined in terms of a generic constraint function which depends on the independent variables used in the characterizing parameter functions. These variables are here taken to be the crack length a and the load L on the structure. The analysis is developed in detail for the parameter T . It is shown that, provided the R-curve image (RCI) of the previous work is generalized to a curve called the projected growth path image (PGPI) the relations between R-curve analysis and the failure assessment diagram (FAD) can be extended to this more general situation while still retaining a two dimensional fad. The methods previously developed for testing the consistency or conservatism of an engineering fad can thus be extended to generalized diagrams which allow for crack tip constraint. An illustrative example showing the effect of including constraint is given and some general implications are considered.

Crack Driving Force in Anisotropic Media due to Non-Elastic Deformation

2004 ◽  
Vol 261-263 ◽  
pp. 75-80
Author(s):  
G.H. Nie ◽  
H. Xu
Keyword(s):  
Elastic Deformation ◽  
Driving Force ◽  
Strain Energy ◽  
Elastic Stress ◽  
Complex Function ◽  
Crack Driving Force ◽  
Special Cases ◽  
Degree Of Anisotropy ◽  
Minimum Strain Energy ◽  
Orthotropic Media

In this paper elastic stress field in an elliptic inhomogeneity embedded in orthotropic media due to non-elastic deformation is determined by the complex function method and the principle of minimum strain energy. Two complex parameters are expressed in a general form, which covers all characterizations of the degree of anisotropy for any ideal orthotropic elastic body. The stress acting on the long side of ellipse can be considered as a crack driving force and applied in failure and fatigue analysis of composites. For some special cases, the resulting solutions will reduce to the known results.

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