Dynamic Fracture in Disordered Media
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Robin L.B. Selinger and John M. Corbett Introduction While it is possible to carry out fracture experiments in single crystals,1 in everyday experience fracture occurs in heterogeneous and often disordered materials. Tear a piece of paper, and the resulting ragged edge shows evidence of the local variation in the paper’s mechanical properties. One might expect the same behavior in fracture of other disordered materials such as polycrystalline solids, fiber composites, and concrete. Engineers interested in estimating failure probabilities often characterize a random heterogeneous material as a stochastic distribution of microcracks, with a mechanical response described by the well-known Weibull distribution.2 But once a crack is initiated, questions remain about the dynamics of the fracture process. For instance, when a crack’s motion is perturbed by interaction with heterogeneity in the underlying material, does the resulting excitation propagate along with the crack, or simply die away as the crack advances? How do we understand the evolution of surface roughness, and the fractal/scaling properties of the crack front and of the fracture surface it leaves behind? Scientists from different disciplines approach fracture of disordered media from vastly different points of view. Statistical physicists classify it among many related problems involving propagation of a front through a forest of obstacles, analogous to the motion of a vortex line through a superconductor containing defects that act as pinning points. Metallurgists and ceramists, by contrast, might view it as one of many instances where microstructure controls macroscopic properties. Computational materials scientists might see it as an opportunity to make quantitative prediction of fracture toughness from atomistic, continuum, or multiscale models. Applied mathematicians see it as a problem that can be approached analytically, at least with a few simplifying approximations. Each of these communities has made useful contributions to the field, although com-
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munication among them is sometimes hampered by variation in terminology, methods, and research goals. Methods used to study fracture of disordered media include models ranging from the nanoscale to the macroscale, from “brute-force” molecular-dynamics (MD) simulation to bond-lattice and continuum models, and even renormalization group methods. It is impossible to survey in a few pages all of the ongoing research in this area, which spans across communities from statistical physics to materials engineering. Instead, we will focus on one aspect of the problem, considering a single dynamic crack front propagating along a heterogeneous planar interface in a threedimensional solid.
Background In quasi-static fracture, an external load or strain is applied to a sample so slowly that the system regains elastic equilibrium between the breaking of individual bonds or elements. Models of fracture in heterogeneous bond lattices under quasi-static loading have been studied extensively since the 1980s; see the
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