Stable crack growth along a brittle\ductile interface—II. Small scale yielding solutions and interfacial toughness predictions

The problem of a crack growing steadily and quasi!statically along a brittle:ductile interface under plane strain\ mixed mode\ and small scale yielding conditions is considered[ The ductile material is assumed to be characterized by the J1!~ow theory of plasticity with linear strain hardening\ while the brittle material is assumed to be linear elastic[Adisplacement!based _nite element method\ exploiting the convective nature of the problemis utilized to solve the relevant boundary value problem[ In Part I of this work\ the corresponding asymptotic problem was solved[ This paper addresses the full!_eld problem in order to validate the asymptotic solutionsand to explore the physical implications of the results[ The numerical full!_eld results are found to be in good agreement with the analytical asymptotic solutions[ In particular\ the full!_eld results strongly suggest that the stress _elds in the vicinity of the crack tip are variable!separable of the power singular type^ and also that the mode mix of the near!tip stress _elds is\ to a large extent\ independent of the applied elastic mode mix[ The amplitude "the plastic stress intensity factor# and the regions of validity of the asymptotic _elds are estimated from the full!_eld results\ and are observed to be strongly dependent on the applied mode mix[ The remote elastic loading _elds appear to in~uence the near!tip _elds\ primarily\ through the plastic stress intensity factor[ The present work also explores the suggestion made by Bose and Ponte Castan eda "0881# that the solutions to the small scale yielding problem may be used in the context of a standard crack growth criterion\ requiring that continued growth take place with a _xed near!tip crack opening pro_le\ to obtain theoretical predictions for the dependence of interfacial toughness on the applied mode mix[ Based on the numerical results\ predictions for mixed mode toughness of the brittle:ductile interface are reported[ The results\ which are in qualitative agreement with available experimental data and also with some recent theoretical results\ predict a strong dependence of interfacial toughness on mode mix[ This suggests that ductility provides the main operating mechanism for explaining the dependence of interfacial toughness on the mode mix of the applied loading _elds\ during steady crack growth[ 0887 Elsevier Science Ltd[ All rights reserved