Modelling of dislocation-mobility-controlled brittle-to-ductile transition

Abstract

The phenomenon of brittle-to-ductile transition (BDT) is known to be controlled by the competition between cleavage fracture and dislocation activity at crack tips. The transition can be determined by one of two successive processes--dislocation nucleation and dislocation motion. In this thesis two models are developed to study the various aspects of a dislocation-mobility controlled BDT. The finite-element method and the elastic-zone concept are used to capture the crack-tip stress intensity. In the elastic-zone concept, a small circular elastic region surrounds the crack tip with the material outside the zone being governed by one of the two models given in this thesis. In one model, the outer material is assumed to undergo an elastic--rate-dependent-plastic deformation with constant dislocation density and a plastic strain rate proportional to the dislocation velocity. The constitutive model derivation is given along with the numerical results for several loading rates. The constant-dislocation-density material is capable of predicting the BDT temperature at different loading rates. However, the constant-dislocation-density material cannot capture the sharp transition seen in the experimental data. In the second case, the model material is still assumed to undergo an elastic--rate-dependent-plastic deformation but the dislocation density is allowed to evolve with the loading. The constitutive model is given, including the form of the dislocation-density evolution equation. The evolving-dislocation-density model not only predicts the BDT temperature at different loading rates, but also captures the sharpness of the transition. The numerical results of each model are compared with experimental results.