XFEM simulation of a mixed-mode fracture experiment in PMMA

Abstract

The eXtended Finite Element Method (XFEM) has become a popular framework for the simulation of fracture phenomena. There has been substantial work to verify the method and expand its formulation for new applications such as hydraulic fracturing; however, there have been limited reports to date which validate XFEM with experimental data. The aim of this paper is to summarize recent efforts to validate a cohesive zone XFEM model with a mixed mode fracture experiment in PMMA. In the experiment, a thin rectangular specimen of PMMA was subjected to axial splitting along its major axis. In order to induce mixed mode crack propagation in the specimen, an initial angled crack was machined into the specimen. The experiment was simulated using an XFEM model with a mixed-mode cohesive traction. Two XFEM models were investigated: one in which the initial crack is idealized with zero initial width; and a second in which the initial crack geometry is explicitly modeled. With these two models, the impacts of the support conditions, geometry, and model parameters were all investigated. The fitted model parameters all fell within the expected range for PMMA. The simulated crack growth was able to capture all of the qualitative behaviour of the experimental crack growth. The simulated and experimental curved crack paths showed excellent agreement throughout the entire loading. Explicitly modeling the initial crack geometry was found to have negligible effects during crack propagation, but exhibited delayed crack initiation compared to the idealized crack. The simulated and experimental force-displacement curves showed excellent agreement in the elastic region, which provides confidence that the support conditions are prescribed correctly. After crack propagation began, the simulated specimen was noticeably stiffer than the experimental specimen. We are able to conclude that the difference in stiffness is not due to differences in the crack path, the crack length, or the model parameters, but we are unable to draw any further conclusions about the root cause of the difference in stiffnesses.