The Effect of Mode Mix on Interfacial Toughness: A Ductile Mechanism

Abstract

This paper deals with the problem of a plane strain crack growing steadily and quasi-statically along the interface between a brittle and a ductile material, under small scale yielding and mixed-mode conditions. Previously determined asymptotic near-tip solutions are used in conjunction with a variational statement of compatibility to obtain approximate solutions for a sequence of small scale yielding problems with different values of the phase angle (or mode mix) of the remotely applied elastic singularity fields. As suggested by Bose and Ponte Castaneda [3], such full-field solutions may be used in the context of a standard crack growth criterion, requiring that continued growth take place with a fixed near-tip crack opening profile, to obtain theoretical predictions for the dependence of interfacial toughness on phase angle. The results, which are in qualitative agreement with available experimental data, and also with some recent theoretical results by Tvergaard and Hutchinson [9], predict a strong dependence on mode mix, and also on material properties, particularly, on the hardening parameter. In addition, it is found that this increased mixed-mode interfacial toughness phenomenon also occurs for crack growth in homogeneous ductile materials, if it is assumed that the crack is somehow (say, by scratching the surface of the specimen) constrained to grow straight ahead of the crack tip, regardless of the mode mix of the applied loading fields. This suggests that ductility provides the main operating mechanism for explaining the dependence of interfacial toughness on the mode mix of the applied loading fields, during steady crack growth.