Accurate modeling and reconstruction of three-dimensional percolating filamentary microstructures from two-dimensional micrographs via dilation-erosion method

Heterogeneous materials are ubiquitous in nature and synthetic situations and have a wide range of important engineering applications. Accurate modeling and reconstructing three-dimensional (3D) microstructure of topologically complex materials from limited morphological information such as a two-dimensional (2D) micrograph is crucial to the assessment and prediction of effective material properties and performance under extreme conditions. Here, we extend a recently developed dilation–erosion method and employ the Yeong–Torquato stochastic reconstruction procedure to model and generate 3D austenitic–ferritic cast duplex stainless steel microstructure containing percolating filamentary ferrite phase from 2D optical micrographs of the material sample. Specifically, the ferrite phase is dilated to produce a modified target 2D microstructure and the resulting 3D reconstruction is eroded to recover the percolating ferrite filaments. The dilation–erosion reconstruction is compared with the actual 3D microstructure, obtained from serial sectioning (polishing), as well as the standard stochastic reconstructions incorporating topological connectedness information. The fact that the former can achieve the same level of accuracy as the latter suggests that the dilation–erosion procedure is tantamount to incorporating appreciably more topological and geometrical information into the reconstruction while being much more computationally efficient.