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.
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