FAILURE ASSESSMENT DIAGRAMS .3. MAPPINGS AND FAILURE ASSESSMENT LINESWHEN THE CRACK DRIVING-FORCE IS A FUNCTIONAL

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 a ssumed that the applied crack driving force J(ep) was obtained by a de formation theory of plasticity and so could be treated as a function o f its arguments. Here the analysis is generalised to consider the situ ation 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 equ ally well for any other parameters describing crack driving force and crack resistance. A unique R-curve image (the RCI) in the FAD can stil l be established in a natural way. Moreover, if this RCI is used as th e failure assessment line (FAL), the treatments of ductile tearing ins tability in R-curve analysis and in the FAD axe still equivalent. The interesting situation then arises, however, that the tangency conditio n can be defined in the FAD but not in R-curve analysis, because in th e latter the usual applied J(ep) curves do not exist. Some difficultie s in using the FAD in this more general situation are discussed. An FA L can be obtained when J(ep) is a function of its arguments by conside ring a sequence of RCI curves for similar structures of ever increasin g 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 whe n 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 considerat ion of increments of crack driving force and fracture resistance and i t is suggested that a fracture mechanics based on the values of these increments rather than on the values of the parameters themselves migh t be developed.