The phase-field approach as a tool for experimental validations in fracture mechanics

Abstract

In a phase-field approach to fracture crack propagation is modeled by means of an additional continuous field. In this paper, two problems of linear elastic fracture mechanics are studied experimentally and numerically in order to evaluate the practicability of the phase-field approach and to validate the measured parameters. At first, a three-point bending experiment of silicon dies is simulated assuming static plate bending. Then, wave propagation and spallation in a Hopkinson bar test are analyzed in a dynamic regime. The simulations show that phase-field fracture reproduces the experimental results with high accuracy. The results are comparable to other fracture simulations, e.g., the cohesive element technique. In total, the phase-field approach to fracture is capable of tracking crack evolution in a very convenient and quantitatively correct way.

Gradient damage modeling of brittle fracture in an explicit dynamics context

“…In this work, we will fully exploit the variational nature of the damage problem, and (10) will be numerically solved by a direct mathematical optimization procedure at the structural scale. For the equivalent local conditions of the damage criterion (10) and the energy balance condition (8), readers are referred to [12]. While other sophisticated constitutive functions exist (for instance those proposed and analytically studied in [14,15]), in this work, we will consider two particular damage constitutive laws.…”

“…Crack tip singularities automatically disappear because of regularization, and the classical finite element method can be used throughout the domain, as long as the regularized crack geometries are correctly captured by a relatively small mesh size. Because of these advantages, phase-field models can be used to explore numerous dynamic fracture phenomena in particular crack instabilities [7] or as a tool for experimental validations [8]. Given arbitrary admissible displacement, velocity and damage fields .u t ; P u t ;˛t /, the energetic quantities needed in the variational formulation are defined as follows.…”

Modeling and numerical simulation of crack growth and damage with a phase field approach

“…However, also with such a rather coarse mesh a quantitative agreement to cohesive element simulations was obtained, cf. [9]. The mobility parameter in equation (38) is set to M = 10 6 /s.…”

Numerical investigation of dynamic brittle fracture via gradient damage models

“…Concerning local damage dissipation, a quadratic function w(α) = α 2 originally proposed in [19] is widely used among the phase-field community [8,[13][14][15]. It can be regarded as the Ambrosio and Tortorelli elliptic regularization of the Griffith functional based on their work on image segmentation.…”

“…The formulation of dynamic gradient damage models that extends the original quasi-static ones [1] is sketched in [12]. The governing equations derived from the variational principles resemble those of other phase-field models originated from the computational mechanics community [8,[13][14][15], with a particular choice of damage constitutive law. These models settle down a unified and coherent numerical framework covering the onset and the space-time propagation of cracks with possible complex topologies and have been successfully applied to study various real-world dynamic fracture problems.…”