FAILURE ASSESSMENT DIAGRAMS .2. THE USE OF SINGLE FAILURE ASSESSMENT LINES

In a previous paper a natural mapping was noted from the (a, J(ep)) di agram of R-curve analysis into the (L(r), K(r)) failure assessment dia gram (FAD) of the R6-revision 3 procedure. Assuming that J(ep) is obta ined 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 suffic iently smooth, it may be used to provide an alternative proof that the critical R6-revision 3 load locus touches the R-curve image (RCI) whe n 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 i s illustrated by considering the example of a family of linear R-curve s. The relations between the various other functions used in the FAD a nd R-curve analysis are studied analytically. In particular it is show n how to derive from any single failure assessment line (FAL) on which the assessment point is assumed to move during crack growth, either t he 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 s ingle FAL on which the assessment point is assumed to move during crac k growth, such as those characteristic of level 3 of PD6493 and option s 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 calculatio n of the IAJC requires that the function J(ep) = j(ep)(a, L) of the st ructure be known for a specific restricted range of a and L only. In c ontrast, 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 conse rvatism throughout is not absolute but only relative to the prediction s of R-curve analysis. As in the previous paper, the discussion is giv en in terms of the J based parameters. But the conclusions hold equall y well for an FAD based on any other parameters describing crack drivi ng force and crack resistance.