Discrete dislocation dynamics simulation of crack-tip plasticity

The fracture toughness of transition metals or semiconductor crystals strongly depends on loading tate 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 temperature exists where the material behavior undergoes a transition from brittle to ductile. In our investigations we conducted two-dimensional discrete dislocation dynamics simulations to study semi-brittle fracture, where a plastic region around the crack tip starts to develep, but cannot shield the crack completely, such that the material still fails by fracture. The simulation show that in the semi-brittle regime crack-tip plasticity and fracture toughness are thermally activated with a constat activation energy. By means of a theoretical analysis of the numerical data an Arrhenius-like relation is derrived for loading rate and temperature at points of constant fracture toughness. This scaling relation is also in complete agreement with experimental data of three-point bending tests of tungsten single crystals. Thus, the proposed scaling relation can be used to predict fracture toughness in a wide range of temperatures and loading rates, based on only a small number of experiments.