Modelling heterogeneous microstructures in superplasticity

Abstract

An approach is presented for the explicit representation of heterogeneity of micro–structure within the constitutive description of superplastic materials. The evolution of inhomogeneous distribution of grain size is modelled, and is fully coupled with the material–s deformation behaviour. The approach is used to model the evolution of initial distributions of grain size during superplasticity and comparisons are made with experimental results. Good comparisons are achieved. The model is used to investigate the effects of different distributions of initial grain size, and their evolution, on subsequent mechanical properties in superplasticity. The experimentally observed dependence of stress–strain–rate behaviour on the distribution of grain size is correctly predicted by the model. Increasing the range of the distribution of grain size is found to lead to increased flow stresses and to reduced strain–rate sensitivities. The effect of the distribution of grain size on strain–rate sensitivity, and the ability of a model to predict it, are technologically important because the properties of superplastically formed components are dependent on strain–rate sensitivity and, in turn, on the distribution of grain size. The model presented therefore provides a step towards the successful design and optimization, by means of process modelling, of superplastic–forming processes.