Design-tool representations of strain compatibility and stress-strain relationships for lamellar gamma titanium aluminides

Engineering use of gamma titanium aluminides requires further development of design models of the material. Presently, modeling tools are limited by computational capability, uncertainty in experimental data, and physical accuracy. Lamellar Ti–Al alloys are plastically inhomogeneous and exhibit anisotropic flow. The origin of this behavior is that there are at least four different length scales in the microstructure: the grain size, the domain size, the lamellar thickness and the separation between either dislocations or twins. They range from mm to nm and give rise to strain incompatibilities and internal stresses over a similar range of lengths. Traditional engineering finite-element analysis of plastic deformation ignores all microstructural length-dependent aspects of deformation, but uses instead constitutive equations to describe plasticity. The gap between the scientific and engineering analyses of plasticity might be bridged by using Ashbyʹs strain-gradient arguments. These capture most of the microstructural scale effects and may deliver descriptions of plasticity that are capable of being used in simulations. In this study, strain-gradient arguments are used to interpret experimental stress–strain measurements of both PST (poly-synthetically-twinned) and polycrystalline TiAl.