Dislocation nucleation from a crack tip: A formulation based on anisotropic elasticity

Abstract

The analysts of dislocation emission from a crack tip within the Peierls framework [Rice (1992) J. Mech. Phys. Solids 40, 239–271; Rice et al. (1992) Topics in Fracture and Fatigue, pp. 1–58; Sun et al. (1993) Mater. Sci. Engng A170, 67–85], heretofore developed for isotropic solids, is generalized to take into account elastic anisotropy. An incipient dislocation core, represented in terms of a critical configuration at the crack tip, is determined numerically (most simply in the shear-only version of the model, but also for a combined tension-shear version that includes tension-shear coupling constrained by atomic modeling). These solutions improve upon approximations based on an effective shear stress intensity. For fcc crystals and intermetallics, the nucleation event analysed is that of a set of partial dislocations emitted sequentially. The anisotropic formulation accounts for corrections as large as 30% in the critical value of the stress intensity factor for atomic decohesion, or cleavage. The anisotropic critical crack extension force for dislocation emission may be greater or less than its isotropic counterpart. For an embedded-atom-method (EAM) model of bcc α-Fe, the anisotropic values can be as large as 2.4 times the isotropic ones in one crack orientation; in another crack orientation, the values are as much as 40% less than the isotropic analogs. For fcc structures (EAM nickel, aluminum and Ni 3Al), the difference is within a ± 10–25% range. For silicon, the isotropic formulation is good, with less than a 14% difference from the anisotropic counterpart. The anisotropic effects are found to increase with a standard ratio of elastic anisotropy, and are important for predicting intrinsic ductile versus brittle response.