Continuum simulations of directional dependence of crack growth along a copper/sapphire bicrystal interface. Part I: experiments and crystal plasticity background

Cracks that exhibit relative amounts of ductility along a copper/sapphire bicrystal interface are simulated within the context of continuum mechanics. The specimen in question exhibits a directional dependence of fracture; that is a crack oriented in one direction along the copper/sapphire interface propagates much more during a given load increment than does the crack oriented to propagate in the opposite direction along the interface. This phenomenon had previously been explained on the basis of an energetic competition between dislocation nucleation and cleavage failure at the two crack tips using both the Rice and Thomson (Philos. Mag. 29 (1974) 73) model as well as the more recent type of dislocation nucleation analysis by Rice (J. Mech. Phys. Solids 40 (1992) 239) based on a Peierls-like stress vs, displacement relationship on the slip plane. However, recent experiments by Kysar (Acta Mater. 48 (2000) 3509) have shown that the orientation of the directional dependence of fracture in the copper/sapphire bicrystal is opposite to that predicted on the basis of dislocation nucleation arguments. The goal of the present work is to attempt to explain the directional dependence of fracture solely on the basis of continuum mechanics. In Part I of this pair of papers we review the main results of the experiments and then set the stage for a series of finite element analyses of the bicrystal specimen by reviewing the fundamentals of single crystal plasticity and the general features of crack tip fields in single crystals. We then discuss two different constitutive hardening models for single crystals and predict that, depending on the hardening model, regions of single-slip around the crack tip may degenerate into regions of triple slip. This leads to a discussion of how the near-tip displacement field can change dramatically with constitutive models. Next the constitutive properties used in the simulations are fit to experimental data. Finally we describe the finite element meshes and procedures for simulating the stationary and quasistatically growing cracks. The simulation results are reported in Part II. (C) 2001 Elsevier Science Ltd. All rights reserved.