Robert Spatschek

Phase field modeling of crack propagation

Fracture is a fundamental mechanism of materials failure. Propagating cracks can exhibit a rich dynamical behavior controlled by a subtle interplay between microscopic failure processes in the crack tip region and macroscopic elasticity. We review recent approaches to understand crack dynamics using the phase field method. This method, developed originally for phase transformations, has the well-known advantage of avoiding explicit front tracking by making material interfaces spatially diffuse. In a fracture context, this method is able to capture both the short-scale physics of failure and macroscopic linear elasticity within a self-consistent set of equations that can be simulated on experimentally relevant length and time scales. We discuss the relevance of different models, which stem from continuum field descriptions of brittle materials and crystals, to address questions concerning crack path selection and branching instabilities, as well as models that are based on mesoscale concepts for crack tip scale selection. Open questions which may be addressed using phase field models of fracture are summarized.

Phase Field Modeling of Fast Crack Propagation

We present a continuum theory which predicts the steady state propagation of cracks. The theory overcomes the usual problem of a finite time cusp singularity of the Grinfeld instability by the inclusion of elastodynamic effects which restore selection of the steady state tip radius and velocity. We developed a phase-field model for elastically induced phase transitions; in the limit of small or vanishing elastic coefficients in the new phase, fracture can be studied. The simulations confirm analytical predictions for fast crack propagation.

Phase field modeling of fracture and stress-induced phase transitions

We present a continuum theory to describe elastically induced phase transitions between coherent solid phases. In the limit of vanishing elastic constants in one of the phases, the model can be used to describe fracture on the basis of the late stage of the Asaro-Tiller-Grinfeld instability. Starting from a sharp interface formulation we derive the elastic equations and the dissipative interface kinetics. We develop a phase field model to simulate these processes numerically; in the sharp interface limit, it reproduces the desired equations of motion and boundary conditions. We perform large scale simulations of fracture processes to eliminate finite-size effects and compare the results to a recently developed sharp interface method. Details of the numerical simulations are explained, and the generalization to multiphase simulations is presented.

Comparison of phase-field models for surface diffusion

The description of surface-diffusion controlled dynamics via the phase-field method is less trivial than it appears at first sight. A seemingly straightforward approach from the literature is shown to fail to produce the correct asymptotics, albeit in a subtle manner. Two models are constructed that approximate known sharp-interface equations without adding undesired constraints. Numerical simulations of the standard and a more sophisticated model from the literature as well as of our two models are performed to assess the relative merits of each approach. The results suggest superior performance of the models in at least some situations.

On the velocity‐strengthening behavior of dry friction

The onset of frictional instabilities, e.g., earthquakes nucleation, is intimately related to velocity-weakening friction, in which the frictional resistance of interfaces decreases with increasing slip velocity. While this frictional response has been studied extensively, less attention has been given to steady state velocity-strengthening friction, in spite of its potential importance for various aspects of frictional phenomena such as the propagation speed of interfacial rupture fronts and the amount of stored energy released by them. In this note we suggest that a crossover from steady state velocity-weakening friction at small slip velocities to steady state velocity-strengthening friction at higher velocities might be a generic feature of dry friction. We further argue that while thermally activated rheology naturally gives rise to logarithmic steady state velocity-strengthening friction, a crossover to stronger-than-logarithmic strengthening might take place at higher slip velocities, possibly accompanied by a change in the dominant dissipation mechanism. We sketch a few physical mechanisms that may account for the crossover to stronger-than-logarithmic steady state velocity strengthening and compile a rather extensive set of experimental data available in the literature, lending support to these ideas.

Phase-field-crystal study of grain boundary premelting and shearing in bcc iron

We use the phase-field-crystal (PFC) method to investigate the equilibrium premelting and nonequilibrium shearing behaviors of

Amplitude equations for polycrystalline materials with interaction between composition and stress

[001]

Instabilities at frictional interfaces: Creep patches, nucleation, and rupture fronts

symmetric tilt grain boundaries (GBs) at high homologous temperature over the complete range of misorientation

Fast crack propagation by surface diffusion

0<\theta<90^\circ

Velocity-strengthening friction significantly affects interfacial dynamics, strength and dissipation

in classical models of bcc Fe. We characterize the dependence of the premelted layer width