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 shear stress vs displacement relation is assumed to hold on a slip plane emanating from the crack tip. Previous results have revealed that the critical G (energy release rate corresponding to the “screened” crack tip stress field) for dislocation nucleation scales with y., (the unstable stacking energy), in an analysis which neglects any coupling between tension and shear along the slip plane. That analysis represents instantaneous nucleation and takes thermal effects into account only via the weak temperature dependence of the elastic constants. In this work, the energy required to thermally activate a stable, incipient 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 prolongation of the crack plane. A first calculation reported is 2D in nature, and 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 activation energy for loads close to the critical load are performed in 2D and in 3D. It is found that the 3D activation energy generally corresponds 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 loading). Implications for the emission of dislocations in copper. K-iron, and silicon at elevated temperature are discussed. The effects of thermal activation are very significant in lowering the load for emission. Also, the appropriate activation energy to correspond to molecular dynamics simulations of crack tips is discussed. Such simulations, as typically carried out with only a few atomic planes in a periodic repeat direction parallel to the crack tip. are shown to greatly exaggerate the (aheddy large) effects of temperature on dislocation nucleation. WE BUILD on recent advances in the modeling of dislocation nucleation at a crack tip based on the PeierlssNabarro concept (RICE, 1992 ; BELTZ and RICE, 199 1, 1992 ; RICE et al., 1992 ; BELTZ, 1992 ; SUN et al., 1991, 1993 ; SUN, 1993). These have provided a consistent description of the genesis of a dislocation, free of core cut-off parameters of earlier approaches, and have predicted a critical load for emission in various materials. The analyses presented thus far, however, have neglected thermal effects, except perhaps through the weak temperature dependence of the elastic constants which enter the analysis. They thus correspond to instantaneous emission without the aid of thermal fluctuations. The purpose of this paper is to extend the Peierls model to calculate the activation energy associated with the nucleation of a