Modeling size effects on fracture toughness by dislocation dynamics

The effects of grain size and of crack-tip blunting radius on the fracture toughness of tungsten polycrystals are studied by using a combined dislocation dynamics/cohesive zone model (CZM). Two-dimensional dislocation dynamics are employed to analyze crack-tip plasticity and crack propagation is characterized by a CZM. The geometry of the crack and the corresponding boundary conditions are described by means of a boundary element method with dislocation dipoles as fundamental solution. Grain boundaries are introduced as obstacles for dislocation motion. Numerical experiments reveal that the fracture toughness decreases with grain size, because grain boundaries confine the plastic zone. This effect is particularly pronounced at small loading rates, where the unconfined plastic zone is large. Our results also show that fracture toughness scales with the tip radius as the stress concentration at the crack tip is reduced and the plastic zone is enlarged.