The theory of viscoelastic crack propagation and healing

Classical fracture mechanics applied to a viscoelastic material states that the critical stress-intensity factor at which the crack propagates depends on the instantaneous elastic modulus of the solid, and provides no mechanism for a speed dependence of the apparent surface energy. This suggests that any speed dependence must be because surface energy itself is speed-dependant. Schapery (1975) has explained how by using the Barenblatt concept of fracture mechanics, involving surface forces instead of surface energy alone, a dependence of the apparent surface energy on the crack speed is found. Here, Schapery's principles are applied to the particular case of a Maugis-Dugdale surface force law and a three-element viscoelastic solid to find the complete dependence of the apparent surface energy, both in fracture and in crack healing, on the crack velocity. To a good approximation, the apparent surface energy in crack healing is the reciprocal of the energy for fracture. Simple approximate equations relating the crack speed to the stress-intensity factor are given.