Numerical models of orthotropic and lamellar grain structures

In this paper, a method for numerically estimating localized stress concentrations that arise in materials with anisotropic crystalline grains is described. This method is used to quantify stress variations within polycrystals of γ-TiAl, a material system composed of two phases of orthotropic material—lamellar colonies of TiAl/Ti3Al interspersed with small grains of pure TiAl. Effective elastic properties for the lamellar colonies are calculated from the constituent properties using a procedure developed for laminated orthotropic materials. It is postulated that the local anisotropy and differing orientations of adjacent grains of material can lead to microyielding at stresses below the mean yield strength of the material. The effects of local elastic anisotropy on stresses are presented as statistical variations in the stress distributions under simple states of loading. Three-dimensional (3D) and two-dimensional (2D) models are investigated.