Multiscale modelling of titanium aluminides

Arjen Roos (1) , Jean-Louis Chaboche (1) , Lionel Gélébart (2) , Jérôme Crépin (2)

1 ONERA - The French Aerospace Lab [Châtillon]
2 LMS - Laboratoire de mécanique des solides

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.

Mots clés: Multiscale model; Analytic functions; Anisotropic material; Constitutive behaviour; Polycrystalline material

Domaines: Matériaux

Arjen Roos, Jean-Louis Chaboche, Lionel Gélébart, Jérôme Crépin. Multiscale modelling of titanium aluminides. International Journal of Plasticity, 2004, 20, pp.811-830. ⟨10.1016/j.ijplas.2003.08.005⟩. ⟨hal-00111399⟩