\-dw

Critique of instability predictions. It is clear that a variety of methods now exist for predicting unstable ductile tearing, all broadly compatible, though following different analyses. It is not yet clear whether one will emerge as universally preferable or whether all will have strengths or weaknesses in particular problem areas. The underlying point is the acceptance of a J-R-curve that is either unique for the material or a lower bound to the problem with respect to orientation and configuration. It is not now clear whether the severe restrictions of the original T theory to (J) p I and Aajb very small are essential. In part this may be overcome by choice of R-curve analysis as discussed in Chapter 2, Section 2.4.1.3, but in the present example the modified analyses have not in fact been used. Of course prediction with an R-curve from one configuration to instability in another has not here been made: the example with its implied selfconsistent data is merely used to illustrate the various methods. However, it seems possible that the near-Prandtl field discussed in connection with the

work of Rice, Drugan and Sham (Section 2.4.1.2) is more nearly maintained in cases where tearing occurs prior to net section limit load than would be the corresponding monotonic HRR field with gross or general yield so that restriction to small amounts of growth is not necessary. An alternative more practical view is that where tearing occurs near limit state, the prediction of load is a relatively insensitive criterion and all that different theories or indeed different R-curve values would show, would be different amounts of tearing before instability, again a not very critical or well-known quantity in many practical cases. At least in this example this is reflected in the T or dJ methods, and 1= J r statement, being rather uncertain predictors whereas the comparison with lor J and dw/ B da gives a more certain answer, less sensitive to the R-curve data.