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The displacement field around an edge dislocation core is examined in an attempt to quantitatively modify the linear elastic Volterra solution. The approach derives from a computer simulation to obtain the equilibrium atomic positions in a dislocated bcc crystallite using Johnson's potential to model α-iron. Unlike many previous calculations of this nature which employ rigid boundary conditions throughout the relaxation, the elastic media bounding the crystallite is here allowed to adjust in response to atomic readjustments within the crystallite. The procedure used to achieve flexible boundaries and its application to this problem is discussed in detail. This scheme permits linear elastic displacements at distances relatively far from the dislocation center. The difference between the computed strain field and the Volterra prescription results from nonlinear effects in the core, and is found to correspond to a net expansion of 0.25b2 per unit dislocation length. This is in accord with findings of experimental studies relating lattice parameters to dislocation densities. The details of this residual field are fairly well described in terms of an elliptical line source expansion center located approximately two Burgers vectors below the tip of the extra half-plane. Thus, these results, while obtained for model material, suggest that an edge dislocation may be characterized by the sum of two linear elastic fields; the Volterra field and an elliptical expansion field. It is found that this result is not explainable by third-order perturbation theories. Finally, we note that the addition of an elliptical dilatation field should have a number of important applications to dislocation theory and specific examples are outlined.
Gehlen et al. (Sun,) studied this question.