Crack-tip process zone as a bifurcation problem

Stress concentration at a crack tip generates a solid structural transformation in its vicinity, the process zone. We argue that its formation represents a local phase transition described by a multicomponent order parameter. We derive a system of equations describing the dynamics of the order parameter driven by an inhomogeneous, time-dependent stress field in the solid and show that it exhibits a bifurcation. The latter corresponds to the emergence of a process zone characterized by the distribution of the order parameter localized in the vicinity of the crack tip. The emergence temperature T* considerably differs from the temperature of the bulk phase transformation Tc. We demonstrate that T* exhibits a universal behavior T*-Tc∼KI4/3, in terms of the stress intensity factor KI, and that the zone universally vanishes upon achieving a critical velocity. These facts together give rise to a universal dynamic phase diagram.