Fast fracture and crack arrest according to the Dugdale model

Dynamic effects near a propagating crack tip in a ductile material have been investigated on the basis of a model with a strip-zone of yielding. In the analysis of fast fracture the unknown variables are the speeds of the leading and trailing edges of the yield zone, where the latter defines the position of the actual crack tip. Propagation of the crack tip is governed by two conditions: the usual one that the cleavage stress is bounded at the leading edge of the yield zone, and a second condition which involves the yield stress and the stretch of the fiber at the trailing edge of the yield zone. By combining well-known results for transient dynamic stress-intensity factors and crack-opening displacements corresponding to external loads, with steady-state dynamic results for the fields corresponding to the cohesive tractions in the yield zone, the dynamic problem of fast fracture has been analyzed for both the Mode III and the Mode I case. The results can be used to investigate crack arrest when a propagating crack tip enters a region of higher ductility.