A Numerical Method to Improve the Representativeness of Real Microstructure Cut-Outs Applied in Finite Element Simulations

Abstract

To improve the representativeness of a real microstructural cut-out for modeling purposes, a numerical method named as “boundary pixel color alteration (BPCA)” is presented to modify measured 2D microstructure cut-outs. Its physical background is related to the phase growth. For the application, the precondition is that the representativeness of the microstructure is already satisfied to a certain extent. This method resolves the problem that the phase composition of a small cut-out can have a large discrepancy to the real one. The main idea is to change the pixel color among neighboring pixels belonging to different phases. Our process simultaneously maintains most of the characteristics of the original morphology and is applicable for nearly all kinds of multi-phase or polycrystalline metallic alloys, as well. From our axisymmetric finite element (FE) simulations (ABAQUS ) applied with 2D real microstructures, it shows that the volume ratios of microstructural phases, as a function of the structure position to the symmetric axis, converge to phase area ratios in the 2D cut-out, even though the axisymmetric element volume is position dependent. A mathematical proof provides the reason for the aforementioned convergence. As examples to achieve real compositions and to numerically prove the aforementioned convergence, four different materials including multiphase polycrystals are implemented. An improvement of the predicted FE result is presented for the application of a modified microstructure (with a higher representativeness) compared to the original one.