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

Abstract

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.