Generating high-fidelity microstructures of polycrystalline materials with prescribed higher-order texture tensors

We introduce an efficient computational procedure for generating polycrystalline microstructures which permits studying the influence of specific texture-tensor orders on the resulting effective mechanical response, both in the linear elastic and the inelastic case. The crystallographic texture of a polycrystalline material is described by the Orientation Distribution Function (ODF). For practical computations, only the Fourier coefficients - called texture coefficients - of the ODF up to a certain order are of interest. In the work at hand, we wish to investigate this microstructure-property relationship. We interpret the task of approximating the texture coefficients of a microstructure realization as a moment-matching, i.e., quadrature, problem, and introduce efficient techniques for generating finite sets of orientations which exactly conform to prescribed polynomial texture terms. First, the microstructure morphology is generated via a well-established Laguerre-tessellation-based approach. Subsequently, the crystal grains are assigned a finite set of orientations which realize prescribed texture coefficients. We exploit the sparse representation of the action of the rotation group SO(3) on higher-order tensors to reduce the computational expense from exponential to cubic in the tensor order. We consider polycrystalline copper as an example material and study the influence of texture terms of different polynomial order on the effective elastic properties and the anisotropy of initial yielding. For a large ensemble of polycrystal microstructures, we find that the elastic properties are mainly influenced by terms up to fourth order, whereas characterizing the yield function accurately requires higher-order texture terms. To encourage further study of the texture dependence of nonlinear material properties, we provide an open-source python implementation of our algorithm.