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 cracks located at an interface between two materials with different plastic work hardening is investigated. The difference in hardening is termed hardening mismatch, and is quantified through the parameter n, which is the difference in hardening exponent between the two materials. For cracks in elastic-ideally plastic materials the stress level in front of the crack tip is mainly 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 shown 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 centered fan like sector is dependent on the radial distance from the crack tip. Further, the change in stress depends strongly on hardening mismatch, increasing as n increases. For the situation with coupling between two non-zero hardening materials it is shown that the full field stress solution develops in a selfsimilar manner, but differs from the homogeneous case due to a coupling between the radial and angular stress field dependence. The amplitude of the change in stress field is to a rather good approximation only controlled by the hardening mismatch, n, and is more or less independent of the absolute values of hardening exponent of the two materials.