Data-driven texture design for nearly-isotropic elastic and plastic properties in titanium-based materials

Abstract

Polycrystalline titanium and its alloys exhibit anisotropic elastic and plastic mechanical properties, which hinder their extensive application as structural components. Designing a nearly-isotropic material by purely experimental or computational methods is challenging due to the elastic and plastic anisotropy intrinsic to the constituent Ti crystal, the complexity of texture evolution during Ti processing, and the high dimensionality of the texture space. Here, we discover a linear relationship between the elastic modulus or plastic flow and the Orientation Distribution Function used to represent texture, and, using this, we formulate a set of convex optimization problems that simultaneously minimize anisotropy in the elastic and plastic regimes. We obtain textures that exhibit remarkably nearly-isotropic properties, while simultaneously maximizing stiffness or strength. Sparsity promoting algorithms are then employed to produce texture solutions with minimal number of orientations, proving that, rather counter-intuitively, strong textures can produce nearly-isotropic properties. Furthermore, we identify optimal textures that are likely to be obtained from common metal forming processes, such as rolling, with minimal changes compared to those that are typically generated. Finally, we show that these anisotropy-minimizing textures can be effectively used for minimizing anisotropy in other Ti-based materials, without the need to repeat the data-collection and optimization processes.