The brittle-to-ductile transition in silicon

Abstract

In order to study the brittle-to-ductile transition of a strong solid, silicon was chosen as a model material. Single crystals of silicon with semielliptical surface cracks parallel to the (111) cleavage plane, introduced by indentation, were deformed by four-point bending. The brittle-to-ductile transition is very sharp; brittle failure occurs by cleavage below a critical temperature T c; in the transition region failure also occurs by cleavage, but at a stress intensity considerably greater than that in the low temperature brittle regime. Above the transition region macroscopic yielding of the whole specimen occurs. T c depends on strain rate and this strain-rate dependence is found to be controlled by the activation energy for dislocation velocity. Dislocation mechanisms have been studied at T c by the etch-pitting technique; the observations suggest that ductile behaviour is due to the shielding of the crack by dislocations emitted from a few dislocation sources at favourable sites along the crack front. A model has been developed in which dislocation sources are formed at the crack tip, followed by shielding of the whole of the crack by the emission and motion of dislocation loops from these sources. The dynamics of the shielding process has been simulated by a computer program which assumes mode III deformation. The theory explains the observed relation of the strain-rate dependence of T c with dislocation velocity, accounts reasonably for the sharpness of the transition, and predicts T c and a size effect (observed). The implications of these results on the criteria which control the brittle or ductile response of solids to mechanical stress are discussed.