On the role of anisotropic expansion and yield stress on crack tip precipitates

Abstract

This pilot study uses a Landau-Lifshitz phase field model to study the growth of a precipitate originating from a crack tip. A boundary layer giving a remote square root singular elastic stress field is applied. The materials are assumed to be elastic-plastic with linear strain hardening. The precipitate is assumed to expand in a simplified anisotropic manner, meaning that the hydride is assumed to grow with an orientation giving maximum expansion perpendicular to the crack plane. The results show that the anisotropic expansion has a strong effect on the shape of the hydride. For anisotropic materials the hydride becomes wedge like. The resulting shapes for the anisotropic cases are in line with observations of internal crack tip hydrides in zirconium. The shapes resemble earlier results for Einstein-Smoluchowski stress driven diffusion using discrete models and simplified modelling of the growth process. The crack tip shielding caused by both precipitation and plastic yielding is examined using the J integral. It shows that the near tip value is a around a quarter of its remote value for elastic isotropic materials and around a half for anisotropic materials.