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

Abstract

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.