Intergranular mechanical equilibrium during the rolling deformation of polycrystalline metals based on Taylor principles

Abstract

Taylor principles indicate that the Taylor strain tensor is identical to the macroscopic strain tensor during plastic deformation and prevails everywhere inside polycrystalline aggregates, in which real grain behaviors generally differ. These principles have been modified in many deformation models while considering strain and stress equilibria in local areas, e.g., grains, grain pairs or grain clusters. However, the Taylor strain tensor is still valid in the surrounding matrix of local areas. In this paper, a reaction stress model based on intergranular mechanical interactions is proposed for rolling deformation caused by penetrating slips and additional local slips while keeping reaction shear stresses below certain top limits. Both stress and strain equilibria are reached in entire rolling sheets in the model, and the same Taylor texture is predicted without the Taylor strain tensor anywhere inside the polycrystalline matrix, regardless if the isotropic matrix is rigid or elastic. Rolling-texture formation in experimental polycrystalline metals could be simulated based on the model if the relaxation effects of additional slips on reducing the top limits of reaction shear stresses are included.