Multiscale modelling of titanium aluminides

Abstract

In this work a three-scale model of the mechanical behaviour of titanium aluminides is presented. The first scale transition between the macroscopic length scale and the scale of an individual α 2, γ or lamellar α 2 + γ grain is made using elastically self-consistent transformation field analysis (TFA) with anisotropic elasticity. The constitutive equations of the α 2 and γ-phases are obtained through the framework of crystal plasticity. The effective behaviour of the lamellar α 2–γ phase, however, necessitates a second scale transition. This transition, derived from a system of linear equations for a multilayer, is obtained and shown to be equivalent to the formalism of transformation field analysis. Some simple simulations are presented to show the viability of the method.