Three-dimensional microstructure reconstruction for two-phase materials from three orthogonal surface maps

Abstract

Introduction: A full three-dimensional (3D) microstructure characterization that captures the essential features of a given material is oftentimes desirable for determining critical mechanisms of deformation and failure and for conducting computational modeling to predict the material’s behavior under complex thermo-mechanical loading conditions. However, acquiring 3D microstructure representations is costly and time-consuming, whereas 2D surface maps taken from orthogonal perspectives can be readily produced by standard microscopic procedures. We present a robust and comprehensive approach for such 3D microstructure reconstructions based on three electron backscatter diffraction (EBSD) maps from orthogonal surfaces of two-phase materials.Methods: It is demonstrated that processing surface maps by spatial correlation functions combined with principal component analysis (PCA) results in a small set of unique descriptors that serve as a representative fingerprint of the 2D maps. In this way, the differences between surface maps of the real microstructure and virtual surface maps of a reconstructed 3D microstructure can be quantified and iteratively minimized by optimizing the 3D reconstruction.Results: To demonstrate the applicability of the method, the microstructure of a metastable austenitic steel in the two-phase region, where austenite and deformation-induced martensite coexist at room temperature, was characterized and reconstructed. After convergence, the synthetic 3D microstructure accurately describes the experimental system in terms of physical parameters such as volume fractions and phase shapes.Discussion: The resulting 3D microstructures represent the real microstructure in terms of their characteristic features such that multiple realizations of statistically equivalent microstructures can be generated easily. Thus, the presented approach ensures that the 3D reconstructed sample and the associated 2D surface maps are statistically equivalent.

Scattering transform in microstructure reconstruction

“…In contrast, for arbitrary material different approaches exist, for example, combinations of spatial correlation functions and principle component analysis [9] or using matching Wang tiles [10]. Another big class of random media reconstruction approaches are based on machine learning algorithms, which arose since a lot of research is available in the field of image processing and image recognition using neural networks [27].…”

Fast descriptor-based 2D and 3D microstructure reconstruction using the Portilla-Simoncelli algorithm

“…In cases where the morphology is too complex to be described by Voronoi cells, ellipsoids or cylinders, it can still be sensible to simplify the geometry for computational efficiency [50]. Finally, the optimization problem may be solved by a black-box shooting method based on arbitrary descriptors, as long as efficient generators are available [51].…”