The process of shear band formation in plane strain compression of fcc metals: Effects of crystallographic texture

Abstract

The recent advances in the development of constitutive equations for large deformations of ductile single crystals and the development of robust finite element procedures for solving non-homogeneous boundary-value problems using these constitutive models, provide a foundation for understanding and predicting many features of the localization of deformation into shear bands. This paper presents the results of a numerical simulation of the effects of crystallographic texture evolution on the process of shear band formation in plane strain compression of initially isotropic OFHC polycrystalline copper. An aggregate of single crystals is used to represent a polycrystal. The calculations are two-dimensional plane strain at the macroscopic level, but they use the actual slip system structure for fee materials with twelve {111} 110 type slip systems. In the calculations an element of the finite element mesh represents either a single crystal or a part of a single crystal, and the constitutive response at an integration point is given by the single crystal constitutive model. The calculation procedures enforce equilibrium and compatibility throughout the polycrystalline aggregate in the weak finite element sense. No initial material or geometric imperfections are prescribed, but the initial lattice orientations are different from one grain to the next. The localization of deformation in the simulations is found to be a natural outcome of large deformation processes in ductile polycrystalline materials, and associated with the concurrent evolution of crystallographic texture. Comparison of results from the numerical simulations against experimental measurements shows that the resolution of grain-scale micro-shear bands requires very fine finite element meshes. The limitations of our computers are such that at present even very refined finite element meshes are too coarse to capture grain-scale shear bands. However, our simulations do capture the major features that are observed experimentally. In particular, the averaged global stress-strain behavior, the crystallographic texture, and the orientation of macroscale shear bands predicted by our simulations are close to those measured in our experiments.