Numerical Analyses of Non-Uniform Deformation during Plane Strain Compression of Polycrystalline Material Using Second-Order Homogenization Method

Abstract

A second-order homogenization method, in which strain gradient in macroscopic region is considered, has been proposed to evaluate the size effect on the macroscopic deformation. In this study, plane strain compression of a polycrystalline material is numerically investigated using an FE-based second-order homogenization method, and effects of size of macrostructure and friction on macroscopic non-uniform deformation is discussed. In the simulation of plane strain compression, the friction between an anvil and a specimen causes non-uniform deformation on the macroscopic region and the size of the specimen affects the compressive force and the macroscopic distribution of strain when the friction force works. The results find that under deformation with the strain gradient caused by the friction the compressive force becomes larger and the macroscopic distribution of strain becomes more inhomogeneous as the size of the specimen becomes larger. These size effects on the macroscopic region are related to deformation in microstructure that depends on the strain gradient in the macrostructure.