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

Abstract

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.