A non-equilibrium thermodynamic model for the crack propagation rate

A non-equilibrium thermodynamics-based evolution model describes the nonsteady, crack propagation rate for both brittle fracture and for viscoplastic behavior at the crack tip. This model for dynamic crack propagation under dynamic or quasi-static loading is developed from an energy functions viewpoint and extends a non-equilibrium thermodynamics construction based on a instantaneous maximum dissipation criterion and a thermodynamic relaxation modulus that permits multi-scale modeling. The evolution equations describing the non-equilibrium fracture process are generated from a generalized energy function whose zero gradient manifold gives the assumed quasi-static crack propagation equations. The class of models produced includes the classical Freund model and a modification that is consistent with the experimental maximum crack velocity. In unstable propagation, the non-equilibrium process is repelled from the quasi-static manifold. If the initial state is stable, then the crack growth process approaches the quasi-static manifold and eventually the crack is arrested. 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.