Abstract
A dynamic crack tip shielding model has been developed to describe the brittle-ductile transition (BDT) of precracked crystals in constant strain-rate tests. Dislocations are emitted from a discrete number of sources at or near the crack tip. At the BDT the dislocations are emitted and move sufficiently rapidly to shield the most vulnerable part of the crack, away from the sources, such that the local stress intensity factor remains below Klc for values of the applied stress intensity factor K above Klc. Application of the model to silicon shows that sharp transitions of the type observed are predicted only if crack tip sources are nucleated at values of K≡K0 just below Klc, these sources then operating at values of K≡KN<<K0. Two models for this nucleation process are proposed-one in which existing dislocations in the crystal move to the crack tip and form sources at K0 the other in which slip starts at a few favourable sites along the crack front at K<<Klc, this slip band then spreading along the crack front generating new crack tip sources in this process. In the first of these models the transition temperature Tc is controlled by the distance of the pre-existing dislocations from the crack tip; i.e. the dislocation velocity has to be great enough for the crack tip sources to be formed before K reaches Klc. In the second, Tc is determined by the distance between the initial sources; again the velocity must be high enough for the dislocations to traverse this distance before K reaches Klc. The sharpness of the transition is determined by the density of crack tip sources after the nucleation phase. The model is applied in detail to experiments in precracked silicon and is found to work well. It is shown how pre-stressing at or above Tc can lead to higher fracture stresses at low temperatures, and to a gradual transition below Tc.
