A 3D benchmark problem for crack propagation in brittle fracture

TL;DR

This paper introduces a comprehensive 3D benchmark problem for brittle fracture using experiments and phase-field modeling, enabling detailed comparison of crack propagation, failure loads, and fracture surfaces in complex mixed-mode loading scenarios.

Contribution

It presents a new 3D benchmark problem for brittle fracture based on experiments, validated with phase-field models, facilitating standardized testing of numerical methods.

Findings

Phase-field model accurately reproduces complex crack surfaces.

Benchmark allows quantitative comparison of failure loads.

Experimental and numerical results show good agreement.

Abstract

We propose a full 3D benchmark problem for brittle fracture based on experiments as well as a validation in the context of phase-field models. The example consists of a series of four-point bending tests on graphite specimens with sharp V-notches at different inclination angles. This simple setup leads to a mixed mode (I + II + III) loading which results in complex yet stably reproducible crack surfaces. The proposed problem is well suited for benchmarking numerical methods for brittle fracture and allows for a quantitative comparison of failure loads and propagation paths as well as initiation angles and the fracture surface. For evaluation of the crack surfaces image-based 3D models of the fractured specimen are provided along with experimental and numerical results. In addition, measured failure loads and computed load-displacement curves are given. To demonstrate the applicability of the benchmark problem, we show that for a phase-field model based on the Finite Cell Method and multi-level hp-refinement the complex crack surface as well as the failure loads can be well reproduced.