Constraint effect on the near tip stress fields due to difference in plastic work hardening for bi-material interface cracks in small scale yielding

The change in near-tip stress field in Small Scale Yielding (SSY) for crack s located at an inter-face between two materials with different plastic wor k hardening is investigated. The difference in hardening is termed hardenin g mismatch, and is quantified through the parameter An, which is the differ ence in hardening exponent between the two materials. For cracks in elastic -ideally plastic materials the stress level in front of the crack tip is ma inly controlled by the angular extent of the part where the slip lines are curved, often referred to as a centered fan like slip line sector. It is sh own that for an elastic-ideally plastic material coupled to a material with non-zero hardening, an increase in stress is observed due to an extension of this centered fan like slip line sector. The angular extension of the ce ntered fan like sector is dependent on the radial distance from the crack t ip. Further. the change in stress depends strongly on hardening mismatch, i ncreasing as An increases. For the situation with coupling between two non- zero hardening materials it is shown that the full field stress solution de velops in a selfsimilar manner, but differs from the homogeneous case due t o a coupling between the radial and angular stress field dependence. The am plitude of the change in stress field is to a rather good approximation onl y controlled by the hardening mismatch. Deltan, and is more or less indepen dent of the absolute values of hardening exponent of the two materials.