Fracture

Abstract

Non-steady crack propagation is a non-equilibrium thermodynamic process. The application of the maximum dissipation construction to fracture mechanics provides an example in which the critical manifold represents neither thermostatic nor steady states. In this case, it is a set of states satisfying a critical condition or event, and the set may be either an attractor or a repeller depending on whether the crack propagation is stable or unstable. In unstable propagation, the non-equilibrium process is repelled from the quasi-static critical manifold. If the initial state is stable, then the crack growth process approaches the quasi-static critical manifold and eventually the crack is arrested. The maximum dissipation non-equilibrium evolution model describes the non-steady, crack propagation rate for both brittle fracture and for viscoplastic behavior at the crack tip. The class of models produced includes the classical Freund model and a modification that is consistent with the experimental maximum crack velocity. Further, the thermodynamic relaxation modulus for brittle fracture has a physical interpretation in terms of the microscopic response of the material. An application of the construction gives the craze growth in PMMA. A simple viscoplastic model for metals predicts the change in temperature at the crack tip as the crack grows.