Cubic elasticity and stress distribution at the free surface of polycrystals

Abstract

Crystalline elasticity anisotropy is often neglected in the study of microplasticity mechanisms of polycrystals, even for highly anisotropic metals such as copper and austenite. A finite element evaluation of the effect of cubic elasticity on the stress distribution at the free surface of three-dimesional polycrystals is presented. Commonly studied metals presenting an increased degree of anisotropy are considered (aluminum, nickel, austenite, copper). For anisotropic metals, the distributions of the effective Schmid factors (ratios between the grain mean resolved shear stress computed either with or without neighboring grain effects and the macroscopic tensile stress) are strongly modified with respect to the reference distribution evaluated for isotropic elasticity. The intra-orientation scatters in the axial stress (scatter due to the random crystallographic orientations of the neighboring grains) are higher than the inter-orientation ones (scatter due to the orientation of the grain itself). Finally, free surface effects are discussed by comparing with estimates obtained for bulk grains.