A comparison of homogenization approaches for modelling the mechanical behaviour of pearlitic steel
In this paper different homogenization approaches are adopted for two micromechanical based models of elasto-plasticity in pearlitic steel. Both models are based on the assumption that the yielding is primarily caused by shear of the ferrite between the cementite lamellae. The orientation distribution of the cementite lamellae determines the macroscopic anisotropy characteristics of pearlitic steel. Properties of the cementite and the ferrite are determined from microcompression tests where the orientation of the cementite lamellae is varied. This is done for both of the micromechanical based models. The first of these models is a micromodel where cementite and ferrite are modeled individually. The second model is a mesomodel where a homogenization approach of a cementite lamella together with the surrounding ferrite is proposed. The anisotropy evolution is assumed to be governed by the re-orientation of the cementite lamellae during the deformation. The most fundamental model that is studied is a 3D grain structure where the fluctuating displacement field within the grain structure is solved by using Finite Element Method (FEM). The re-orientation of the cementite lamellae is governed by the deformation of the grain structure. In the analytically homogenized models the re-orientation is assumed to follow the areal affine assumption where the normals of the cementite lamellae are convected with the macroscopic deformation gradient. Numerical results for the different models, when subjected to simple shear loading, are given and comparisons of stress-strain response are shown.