Models for fracture toughness in the semi-brittle regime
The fracture toughness of transition metals or semiconductor crystals strongly depends on loading rate and temperature in such a way that the fracture toughness increases with temperature or with decreasing loading rate. For a given loading rate a more or less well-defined termperature exists where the material undergoes a transition from brittle to ductile behavior. In our investigations we employed the two-dimensional discrete dislocation dynamics method to study the semi-brittle regime, where a plastic region around the crack tip starts to develop, but cannot shield the crack completely. Thus, in this regime the material still falls by final fracture. Based on gernal findings of the numerical simulations an Arrhenius-like relation between loading rate and temperature at points of constant fracture thoughness is derived. This scaling relation shows the dominance of dislocation mobility as 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.