Reconstruction of random two-phase polycrystalline solids using low-order probability functions and evaluation of mechanical behavior

Abstract

The phase distribution in a multi-phase material can affect its material properties and mechanical behaviors significantly. Because multi-phase materials even with the same volume fraction can have different phase distributions, a method to describe the phase distribution is needed. For this purpose, contiguity and low-order probability functions are investigated for representing the phase distributions of microstructures. The virtual samples for evaluating the mechanical properties of the two-phase materials with random phase distribution are reconstructed using the low-order probability functions (two-point correlation and lineal-path functions), and the mechanical behaviors are evaluated using the finite element method based on the restricted slip system. Macro-scale mechanical response (stress–strain curve) and lattice strains for sets of crystal families, as well as characteristics of the probability functions, are almost the same between the original and reconstructed virtual samples. It is confirmed that the virtual microstructures of random isotropic and anisotropic phase distributions reconstructed from the low-order probability functions exhibit high potential for investigating the mechanical behavior such as lattice stress and strains through simulations, which can be used to supplement diffraction experiments.