THE ACTIVATION-ENERGY FOR DISLOCATION NUCLEATION AT A CRACK

THE ACTIVATION energy for dislocation nucleation from a stressed crack tip is calculated within the Peierls framework, in which a periodic s hear stress vs displacement relation is assumed to hold on a slip plan e emanating from the crack tip. Previous results have revealed that th e critical G (energy release rate corresponding to the ''screened'' cr ack tip stress field) for dislocation nucleation scales with gamma(us) (the unstable slacking energy), in an analysis which neglects any cou pling between tension and shear along the slip plane. That analysis re presents instantaneous nucleation and takes thermal effects into accou nt only via the weak temperature dependence of the elastic constants. In this work, the energy required to thermally activate a stable, inci pient dislocation into its unstable ''saddle-point'' configuration is directly calculated for loads less than that critical value. We do so only with the simplest case, for which the slip plane is a prolongatio n of the crack plane. A first calculation reported is 2D in nature, an d hence reveals an activation energy per unit length. A more realistic scheme for thermal activation involves the emission of a dislocation loop, an inherently 3D phenomenon. Asymptotic calculations of the acti vation energy for loads close to the critical load are performed in 2D and in 3D. It is found that the 3D activation energy generally corres ponds to the 2D activation energy per unit length multiplied by about 5-10 Burgers vectors (but by as many as 17 very near to the critical l oading). Implications for the emission of dislocations in copper, cc-i ron, and silicon at elevated temperature are discussed. The effects of thermal activation are very significant in lowering the load for emis sion. Also, the appropriate activation energy to correspond to molecul ar dynamics simulations of crack tips is discussed. Such simulations, as typically carried out with only a few atomic planes in a periodic r epeat direction parallel to the crack tip, are shown to greatly exagge rate the (already large) effects of temperature on dislocation nucleat ion.