Session: 12-23-02: Symposium on Multiphysics Simulations and Experiments for Solids

Paper Number: 146516

146516 - Investigating Fracture Behavior in Porous Media Using Phase Field and Asymptotic Homogenization 

Porous media make up many of the most important materials around us. Our bones transport blood through pores. The safety of the water we drink is dependent on porous wafer filters. The bridges and buildings we occupy are made of porous concrete. When these materials structurally fail, the results are often catastrophic. Researchers and engineers aim to constantly improve the process of predicting failure in engineering structures. One important failure mode is fracture. The prediction of fracture in porous media is still an open topic of research as capturing the effects of its microscale heterogeneity presents challenges. Voids in the vicinity of a crack can act as an arresting mechanism; drilling holes ahead of a crack is used in numerous industries as a means of fatigue mitigation. However, such features also create stress concentrations and could potentially initiate, or propagate, a different crack. Empirically determining such behavior requires testing in numerous loading directions and ascertaining a microstructure's orientation relative to the loading direction. A material's microstructure is usually orders of magnitude smaller than the dimensions of the body it aggregates. Capturing all features of a body by numerical discretization is computationally exhaustive and, for most intents and purposes, not practical. Although numerous studies have examined crack propagation at the local level, we argue that geometric variation in microscale pore morphology affects course-scale crack propagation. To provide accessible tools for researchers and establish a standardized framework that anyone can freely utilize and contribute to the study of fracture in porous media, we use open-source software, FEniCSX. We develop a framework that first calculates an effective continuum-level constitutive tensor based on asymptotic homogenization theory. Specifically, using this methodology, representative volume elements of single void-filled microstructures are meshed, constrained with periodic boundary conditions, and perturbed with uniform strain loading conditions. Then, we use the resulting displacement field to derive an effective constitutive tensor, which serves as an input to a linear elastic brittle fracture mechanics model. As opposed to sharp interface models such as peridynamics or XFEM, this work implements the phase-field variational formulation based on Griffith's classical energy balance. In addition to propagation, this numerical scheme has demonstrated a robust ability to capture crack coalescence, branching, and turning. Numerous physical characteristics can augment the stress field around a void, thereby increasing the strain energy contributing to crack initiation. This work analyzes pore shapes of varying topological complexity to capture a wide range of pore morphology. Here, we analyze cases with circular, rectangular, and a few irregular pore shapes. The macroscale crack propagation and path for a 2D classical tensile loading problem can then be compared when using effective constitutive tensors corresponding to different pore-shape indices.  Preliminary results show that crack advancement is appreciably altered even when porosity is held constant for pore morphologies with differing shape indices. Specifically, a 20 percent change in the ratio of pore perimeter to area corresponded to a 13 percent change in crack onset force of the 2D tensile loading problem. The results link a porous media's morphology at the microscale to its fracture behavior at the macroscale.

 

Presenting Author: Ryan Nielsen University of Utah

Presenting Author Biography: Ryan Nielsen is currently a PhD student in the Mechanical Engineering program. He received his Bachelor of Science from the University of Utah in Mechanical Engineering with an emphasis in Solid Mechanics. He currently works in the aerospace industry as an engineer for gas turbine engine manufacturer, Williams International.

Authors:

Ryan Nielsen University of Utah
Pania Newell University of Utah