A High-Fidelity Texture Discretization Method for Polycrystalline Aggregates Considering Grain Size Distributions

Accurate discretization of the orientation distribution function (ODF) is essential for reliable microstructural modeling of polycrystalline aggregates. This work proposes a novel texture discretization method that achieves high-fidelity ODF approximation even with a small number of orientations using only grain volume information. The core idea is to extend conventional inverse transform sampling by reconstructing the source samples before inversion. This reconstruction suppresses discretization errors induced by random sampling fluctuations and improves adaptability to non-uniform grain size distributions (GSDs). To preserve texture diversity under the same ODF, spatial shuffling and subsequent unscrambling of grain positions are introduced. The total variation distance (TVD) is adopted as a global metric to quantify discretization errors, and key influential factors are systematically analyzed, particularly the binning strategies. Error comparisons demonstrate that, within the typical range of grain numbers (10²-10³), the TVD of the proposed method is one order of magnitude lower than that of the conventional method, with its standard deviation two orders of magnitude smaller. The randomness and periodicity of discretized textures are further investigated, thereby elucidating the underlying mechanisms for the newly introduced advantages. This method provides a robust and efficient framework for texture modeling with consideration of GSDs.