Instability in dynamic fracture

J. Fineberg and M. Marder



The fracture of brittle amorphous materials is an especially challenging problem, because the way a large object

shatters is intimately tied to details of cohesion at microscopic scales. This subject has been plagued by conceptual

puzzles, and to make matters worse, experiments seemed to contradict the most "rmly established theories. In this review,

we will show that the theory and experiments "t within a coherent picture where dynamic instabilities of a crack tip play

a crucial role. To accomplish this task, we "rst summarize the central results of linear elastic dynamic fracture mechanics,

an elegant and powerful description of crack motion from the continuum perspective. We point out that this theory is

unable to make predictions without additional input, information that must come either from experiment, or from other

types of theories. We then proceed to discuss some of the most important experimental observations, and the methods

that were used to obtain the them. Once the #ux of energy to a crack tip passes a critical value, the crack becomes

unstable, and it propagates in increasingly complicated ways. As a result, the crack cannot travel as quickly as theory had

supposed, fracture surfaces become rough, it begins to branch and radiate sound, and the energy cost for crack motion

increases considerably. All these phenomena are perfectly consistent with the continuum theory, but are not described by

it. Therefore, we close the review with an account of theoretical and numerical work that attempts to explain the

instabilities. Currently, the experimental understanding of crack tip instabilities in brittle amorphous materials is fairly

detailed. We also have a detailed theoretical understanding of crack tip instabilities in crystals, reproducing qualitatively

many features of the experiments, while numerical work is beginning to make the missing connections between

experiment and theory. ( 1999 Elsevier Science B.V. All rights reserved.

J. Fineberg, M. Marder / Physics Reports 313 (1999) 1}108 3