The brittle-ductile transition in silicon. II. interpretation - Hirsch, P; Roberts, S; Samuels, J (Royal Society, 1989)
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 anddollar; emitted and move sufficiently rapidly to shield the most vulnerable parts of the crack, furthest away from the sources, such that the local stress intensity factor remains below K$_{Ic}$ for values of the applied stress intensity factor K above K$_{Ic}$. Computer simulations of the dynamics of dislocation generation from the crack tip sources, assuming mode III loading, suggest that a sharp transition as observed in silicon is predicted only if generation starts at $K \equiv K_0 \thickapprox K_{Ic},$ but then continues at $K \equiv K_N \ll K_{Ic}$. Dislocation etch pit studies reported by Samuels and Roberts (Proc. R. Soc. Lond. A 421, 1-23 (1989)) (hereafter called I) confirm that generation begins at $K_0 \thickapprox K_{Ic}.$ It is suggested that K$_0$ corresponds to the value of K at which a crack tip source is nucleated by movement of an existing dislocation in the crystal to the crack tip. The model accounts quantitatively for the strain-rate dependence of the transition temperature T$_c$ reported in I, and predicts a dependence of T$_c$ on dislocation density, in qualitative agreement with (unpublished) experiments. Calculations of the stress field around the crack tip of a semicircular precrack, suggest that the ends of the half loops emitted by crack tip sources undergo multiple cross slip to follow the crack profile. The predicted dislocation configurations agree with etch pit observations reported in I.