Abstract
The crack tip process zone is regarded as a region where the solid physical properties are altered due to high stress. They are controlled by the solid degrees of freedom existing within the zone and vanishing outside, and can be divided into two classes: (1) zones always existing at the tip and (2) those emerging as soon as certain conditions are met. We focus on the zones of the second kind and argue that they can be described analogously to phase transitions taking place locally. We report both a numerical and an analytical solution for the process zone. We find that the zone can only exist within a limited domain of the dynamic phase diagram, at one side of the phase transition line. We describe this domain and establish its dependence on the crack velocity. We show the existence of a critical crack velocity above which the zone cannot exist.
Highlights
1.1 Mechanics of a propagating crackTo a great extent, the acute interest presently focused on the problem of the fracture of solids is related to high precision experiments that have recently revealed a number of reproducible instabilities in the high-speed dynamics and morphology of an isolated crack
The acute interest presently focused on the problem of the fracture of solids is related to high precision experiments that have recently revealed a number of reproducible instabilities in the high-speed dynamics and morphology of an isolated crack
Following the great achievements of the linear elastic fracture mechanics, it came to its limitations, being unable to determine the direction of the crack propagation in isotropic materials, correctly predict the terminal crack velocity, explain the mechanisms of the observed instabilities in the dynamics and morphology of a fast crack, in solids of various origins, both inorganic and organic, calling for its modification
Summary
The acute interest presently focused on the problem of the fracture of solids is related to high precision experiments that have recently revealed a number of reproducible instabilities in the high-speed dynamics and morphology of an isolated crack. It is especially intriguing that the instabilities often look similar in materials as different as glasses, PMMA and brittle polyacrylamide gel [1] This has given rise to the hope that the crack dynamics may be considered within the context of the rapidly developing science of pattern formation, and has engendered a number of theoretical attempts, both analytical and numerical, to predict and describe such instabilities. No approach to correctly introduce dissipative processes in a deterministic form at a truly atomistic scale has been proposed [11] This suggests that the universal description of the experimental facts of the crack dynamics fails within the tractable lattice models. It should be expected that this phenomenon would have an impact on the static and dynamic properties of a fracture
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