Bridging a mesoscopic inhomogeneity to macroscopic performance of amorphous materials in the framework of the phase field modeling

One of the big challenges in materials science is to bridge microscopic or mesoscopic properties to macroscopic performance such as fracture toughness. This is particularly interesting for the amorphous materials such as epoxy resins because their micro/meso structures are difficult to characterize so that any information connecting different scales would be extremely useful. At the process level the polymerization rate, which influences considerably the performance of materials, can be changed experimentally. However, it is known that the maximum toughness does not always appear at the maximum polymerization rate, which suggests that some differences in the micro/meso-scopic structure affect the macroscopic property behind. The goal of this article is to present a framework to bridge between a mesoscopic observation of X-ray CT images and the macroscopic criterion of fracture toughness computed via phase field modeling. First we map the X-ray images with different polymerization rates into several categories using different methods: one is singular value decomposition (SVD) and the other is persistent homology. Secondly we compute a crack propagation of each sample and evaluate a scalar value called the effective toughness (ET) via J-integral, which is one of the good candidates indicating a toughness of materials. It turns out that ET reflects the performance of each sample and consistent with the experimental results.