Finite Element Simulation of Chessboard Strain Localization in View of Statistical Spreads in Polycrystal Grain Parameters

The paper presents a finite element simulation for research in the so-called chessboard effect of plastic strain localization. In the simulation, we consider a polycrystal metal strip under uniform tension on the assumption of a normal yield stress distribution over its grains. Using the simplest isotropic model, it is taken that all grains have the same linear hardening coefficient. The simulation results demonstrate that whether the problem statement is two- or three-dimensional the material reveals plastic strain localization in the form of numerous intersecting bands arranged into a chessboard system on the initially flat specimen surface.