Simulation of the brittle-ductile transition in silicon single crystals using dislocation mechanics

A numerical model is developed to characterize the physical process of the brittle-ductile transition (BDT) in Si single crystals. The model considers a symmetric dislocation emission at a crack tip in {110}〈110〉-oriented specimens. The motion of individual dislocations is assumed to be driven by the resolved shear stress and follows an Arrhenius law. Numerical simulations are performed, and the shielding to the crack tip by the emitted dislocations is evaluated. The simulations are terminated either when the crack tip stress intensity reaches the intrinsic fracture toughness (brittle fracture), or when the far field applied stress intensity reaches a critical value significantly higher than the intrinsic toughness (ductile failure). Simulation results show that, when two slip systems are activated simultaneously, a sharp BDT behavior results. The dramatic increase in fracture toughness during the BDT is attributed to the sudden increase in the number of dislocations emitted from the crack tip. The model predictions are consistent with experimental observations. The results also indicate that the number of active slip systems at the crack tip plays an important role in determining the behavior of the BDT. While activation of multiple slip systems gives rise to a sharp transition, a single active slip system will result in a gradual transition. This conclusion may explain some recent experimental observations.