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.
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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.