Continuum simulations of directional dependence of crack growth along a copper/sapphire bicrystal interface. Part II: crack tip stress/deformation analysis

Abstract

The goal of this work is to explain the directional dependence of fracture of interfacial cracks in a copper/sapphire bicrystal in terms of continuum stress and deformation fields. In Part I of this pair of papers, we briefly review the main results of experiments by Kysar (Acta Mater. 48 (2000) 3509) and discuss how the orientation of the directional dependence of fracture is contrary to predictions made on the basis of crack tip dislocation nucleation concepts. We then set the stage for a series of finite element analyses of the bicrystal specimen. In Part II the simulation results are presented. We first conclude that the assumptions which enter into the crack tip dislocation nucleation analyses are valid. Therefore, the orientation of the directional dependence is opposite that of the dislocation nucleation analyses, in spite of the fact that crack tip dislocation nucleation may occur as predicted. We then show that the directional dependence of fracture, at least for the copper/sapphire bicrystal specimen, can be explained by the fact that the quasistatically growing brittle crack has the propensity to generate a significantly higher normal opening stress along its prolongation than does the ductile crack. This conclusion is valid for a wide range of crack growth criteria as well as material constitutive models and parameters. We also present results of the simulated crack opening displacement profiles of the two crack and compare them to experimental measurements. The results do not satisfactorily explain the qualitative features of the normal crack opening displacement profile; however we discuss some possible reasons why the finite element method may not be able to accurately model the crack opening displacement profile.