Thermal activation of crack-tip plasticity: The brittle or ductile response of a stationary crack loaded to failure

Metals with a body centered cubic crystal structure, like tungsten, exhibit a pronounced semibrittle regime at intermediate temperatures. In this regime their fracture toughness strongly depends on loading rate and temperature. Crack-tip plasticity has been studied with two-dimensional numerical simulations on different length scales. The method of discrete dislocation dynamics has been employed to test various assumptions made on the deformation mechanisms and the origin of the strong loading rate and temperature dependence of fracture toughness in this regime. A continuum elasticity-viscoplasticity model capable of describing larger plastic deformations yields complementary information with respect to the discrete dislocation method. Despite of their fundamental differences, both simulations consistently show that crack-tip plasticity can be described as a time-dependent microplastic deformation with well-defined activation energy and that the blunting of the crack tip plays an important role for the transition from semibrittle to ductile behavior. Based on general findings of the numerical simulations an Arrheniuslike relation between loading rate and temperature at points of constant fracture toughness is derived. This scaling relation shows the dominance of dislocation mobility as the rate limiting factor for fracture toughness and for the brittle-to-ductile transition itself. The results of our simulations are also consistent with experimental data gathered on tungsten single crystals. Thus, the proposed scaling relation can be used to predict fracture toughnesses in a wide range of temperatures and loading rates, based on only a small number of experiments.