Data-Driven Quantification and Tessellation-Based Modeling of Anisotropy in Polycrystalline Alloys
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The effective mechanical properties of polycrystalline alloys are heavily influenced by their microstructure, including grain morphology, spatial arrangement, and crystallographic orientation. Thermo-mechanical processing methods such as friction extrusion generate microstructures with pronounced anisotropy and complex 3D grain architectures. Direct 3D characterization of polycrystalline materials is experimentally expensive and computationally demanding, which limits the systematic establishment of quantitative structure-property relationships. In this contribution, we present a quantitative analysis of 2D electron backscatter diffraction image data obtained from measurements on orthogonal planes of microstructures arising from friction extrusion. Multivariate grain descriptors that are relevant for effective material properties are evaluated, and their distributions as well as directional dependencies and correlations between neighboring grains are analyzed. Furthermore, we introduce a stereological stochastic 3D tessellation model calibrated using a generative adversarial network (GAN). The model is capable of generating grains with preferred geometrical orientations consistent with those observed in the friction-extruded material. It is based on generalized balanced power diagrams, which generalize Voronoi and Laguerre tessellations and provide a low-parametric, distance-based representation that can capture anisotropy. This representation enables efficient data compression and provides physically interpretable input for micromechanical simulations. The fitting procedure employs a GAN, consisting of a generator that produces 3D generalized balanced power diagrams and a discriminator that distinguishes between measured 2D microstructures and random planar sections of simulated 3D tessellations. This enables the reconstruction of anisotropic 3D grain architectures from limited 2D data.
