Field-theoretical description of the formation of a crack tip process zone

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.