Dynamic crack propagation with a variational phase-field model: limiting speed, crack branching and velocity-toughening mechanisms

We address the simulation of dynamic crack propagation in brittle materials using a regularized phasefield description, which can also be interpreted as a damage-gradient model. Benefiting from a variational framework, the dynamic evolution of the mechanical fields are obtained as a succession of energy minimizations. We investigate the capacity of such a simple model to reproduce specific experimental features of dynamic in-plane fracture. These include the crack branching phenomenon as well as the existence of a limiting crack velocity below the Rayleigh wave speed for mode I propagation. Numerical results show that, when a crack accelerates, the damaged band tends to widen in a direction perpendicular to the propagation direction, before forming two distinct macroscopic branches. This transition from a single crack propagation to a branched configuration is described by a well-defined master-curve of the apparent fracture energy Γ as an increasing function of the crack velocity. This Γ (v) relationship can be associated, from a macroscopic point of view, with the well-known velocity-toughening mechanism. These results also support the existence of a critical value of the J. Bleyer · C. Roux-Langlois · J-F. Molinari Ecole Polytechnique Fédérale de Lausanne Department of Civil Engineering Department of Materials Science 1015 Lausanne, Switzerland Tel.: +41 21 69 32413 ∗ Corresponding author: J. Bleyer E-mail: jeremy.bleyer@{epfl.ch,enpc.fr} C. Roux-Langlois University of Rennes 1 Institute of physics of Rennes Mechanics and Glasses Department, UMR UR1-CNRS 6251, Campus de Beaulieu, 35042 Rennes Cedex, France energy release rate associated with branching: a critical value of approximately 2Gc is observed i.e. the fracture energy contribution of two crack tips. Finally, our work demonstrates the efficiency of the phase-field approach to simulate crack propagation dynamics interacting with heterogeneities, revealing the complex interplay between heterogeneity patterns and branching mechanisms.