Some aspects of forces and fields in atomic models of crack tips
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M. S. Daw Sandia National Laboratories, Livermore, California 94551-0969 J. P. Hirth Washington State University, Pullman, Washington 99164-2920 (Received 29 April 1991; accepted 18 July 1991)
This paper examines the stresses and displacement gradients in atomistic models of cracks based on an EAM potential devised for aluminum. Methods for computing these quantities are described. Results are presented for two models differing in terms of the orientations of the crack relative to the crystal, a [100] (010) orientation that behaves in a brittle fashion and a [111] (110) orientation that emits partial dislocations prior to extending. Both models display lattice trapping. The stresses in the brittle crack model are compared with the linear elastic prediction and found to be in remarkably good agreement to within distances of about one lattice parameter of the crack tip and at the free surface where contributions from sources other than strain energy (e.g., surface tension) influence the results. Similar results are observed for the ductile model until dislocation emission occurs. The largest stresses that develop just prior to crack extension or dislocation emission are used to estimate the ratio of theoretical tensile strength to shear strength in this material. Eshelby's conservation integrals, F and M, are also computed. F is found to be essentially contour independent and in agreement with the linear elastic prediction in both models until dislocation emission occurs, at which point a large screening contribution arises from the emitted partials. The contour size dependence of M reveals some interesting features of the crack tip including a slight wobble of the crack tip inside its potential well with changing applied K and the existence of forces acting to move the crack faces apart as blunting occurs. I. INTRODUCTION This paper is concerned with the micromechanics of the atomic structure of a crack tip when that tip is on the verge of either extending or emitting dislocations. The relative ease or difficulty with which these two events occur establishes a material as intrinsically ductile or brittle. In order to characterize this "ease or difficulty" and, hence, understand the origins of toughness, one needs to be able to describe, at a minimum for an atomically sharp crack: (a) the generalized forces available either to extend the crack or to emit a dislocation, and (b) the resistance offered by the material to the operation of these two mechanisms. Kelly, Tyson, and Cottrell1 and Rice and Thompson2 have examined this issue using essentially continuum fields based on linear elasticity to determine the interaction between a crack tip and nearby dislocations. While providing solutions to the generalized forces and therefore insight into effects that might influence the balance one way or the other, such solutions may not be very accurate when the crack tip and dislocation are so close together that their nonlinear cores overlap. In addition, and for similar reasons, there are uncertainties in describing the res
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