Abstract
A novel method for the 3D reconstruction of a microstructure from limited statistical information provided by 2D cross sections is developed. In the proposed approach, first full-set statistical information (two-point correlation functions) are extracted from 2D cross sections, and then an approximate 3D microstructure is realized based on them. The proposed method relies mainly on conditional probability theorem to establish explicit functional forms between two-point correlation functions extracted from 2D cross sections and full-set 3D statistics. For 3D realization, a novel phase-recovery algorithm is developed that captures prominent attributions of the microstructure. The salient feature of the proposed realization scheme is the ability to fully reconstruct 3D microstructures from statistical information provided by just one cross section for isotropic microstructures and two perpendicular cross sections for anisotropic ones. A number of illustrative examples are provided to demonstrate the accuracy and the versatility of the proposed scheme. The application of the method for the 3D realization of microstructure using an experimental dataset is demonstrated. Finally, the accuracy of the method in capturing and retaining essential features including volume fractions and characteristic attributions as well as the state of anisotropy and percolation of the phases is discussed.
Highlights
Key performance characteristics of the heterogeneous materials is often directly related to their microstructure
Phase recovery algorithms are mostly used for signal processing application, we show that these algorithms can be useful for reconstruction purposes using limited statistical information as well
A new formulation was proposed to obtain a relation between the 3D full set and limited 2D correlation functions of heterogeneous materials
Summary
Key performance characteristics of the heterogeneous materials is often directly related to their microstructure. N-point correlation functions can be exploited directly to characterize effective mechanical, thermal, electrical and permeability properties of a wide range of heterogeneous material systems [1,5,7] Through these functions, characteristic statistics of a microstructure are translated into a set of distributions that systematically provide more information about the microstructure with increasing their order. In order to perform reconstruction from a single digitized cross section image, they developed a hybrid stochastic technique for realizing microstructure from two-point correlation functions that employs colony and kinetic growth algorithms for the realization step and provides a coupled realizationoptimization methodology. Microstructure reconstruction is performed by employing a novel phase recovery algorithm which takes as input approximate two-point correlation functions developed in the initial step. Current study summarizes with a series of experimental and numerical case studies to illustrate the computational efficiency and capabilities of the proposed approach
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