Numerical modelling of the effects of crystallographic texture and grain structure on the macroscopic behaviour of metals

Abstract

The crystal plasticity theory derives the response of a crystalline material from its structure and the structural defects. This work tries to find this connection. The first part revises the main concepts of the plasticity theory, structure of the crystalline material and its crystallographic texture, and shows how plastic deformations are explained by slip on the slip systems, which in turn is realized through the movement of the dislocations. Then the mathematical relations of the crystal plasticity are introduced, the main of which are Schmid’s law, maximum plastic work principle, Voce law, viscoplastic constitutive relation and Taylor model. Taylor model particularly represents the polycrystal as homogeneous in terms of strains in it. This simplified approach and other relations are used to establish a numerical model of an aluminium sample where texture is represented by a set of Euler angles. This model is then used to derive the yield surfaces of samples with different sharp textures for plane stress situation by two different methods. One of them is the direct Taylor approach, where the load is applied as a deviatoric strain rate tensor. The other is a finite element model with one element. These yield surfaces show a strong unambiguous influence of texture on the plastic properties of the sample. These yield surfaces are analyzed and then represented as analytical yield functions. Finally, the morphology of the sample is introduced into the simulations and some preliminary results, showing its influence, are obtained.