Tessellation growth models for polycrystalline microstructures

Abstract

Abstract This work proposes novel models to represent and parametrize random morphology of polycrystalline microstructures. The reliability of high-fidelity mechanical analysis of polycrystalline microstructures depends upon the morphological representation of the virtual model. Two models addressed in this work are spherical growth and ellipsoidal growth tessellations in which grains grow as spheres (or ellipsoids) with random velocities which initiate from random nucleation sites represented by a spatial point process. All of the stochastic parameters can be represented by a marked point process random field model, for which simulation algorithms exist. Probability distributions of the model parameters are estimated by obtaining best-fit realizations of the models to a data set of a reconstructed microstructure specimen. The accuracy to which these tessellation models can represent real microstructures is evaluated using two example data sets by computing numerous microstructure features as well as the mismatch volume between the best-fit realizations and the data. The spherical growth and ellipsoidal growth tessellations demonstrate very significant improvements over the Voronoi tessellation, while remaining low dimensional representations of the microstructure. Realizations generated from a marked point process random field model show very good agreement in grain size, aspect ratio, and nearest neighbor distributions compared to an example data set. Thus, subsequent realistic instantiations of microstructures having the same statistical characteristics of the data can be trivially obtained, which are necessary to propagate the uncertainty associated with morphological randomness on response quantities of interest in mechanics-based applications.