Stress and Dilatation Fields of the 〈111〉 Dislocation in Cubic Crystals

Abstract

Exact expressions of the stress components and dilatation of a straight dislocation, lying in a 〈111〉 direction in a cubic crystal, have been obtained analytically. The transitions in the contours of stress and dilatation fields are found to be controlled by an elastic anisotropy parameter R. For bcc crystals, the transition of σ₂₃ contours of a screw dislocation takes place at$\mathrm{R=(}\frac{3}{2}{)}^{\text{1/2}}$ and that of σ₁₃ contours at R=3 (for W, Ta, V, Cr, Mo, Nb, and Fe,$\mathrm{R<(}\frac{3}{2}{)}^{\text{1/2}}$ ; for Na, K, Li, $(\frac{3}{2}{)}^{\text{1/2}}\text{<R<3}$ ). The results of the stress analysis are useful in treating the dissociation of screw dislocations in the bcc lattice. The dilatation contours of a [111] dislocation of the mixed type with Burgers vector a/2[111̄] are illustrated. The differences in shape of the contours for the anisotropic and isotropic cases are greater for the pure edge dislocation than for the mixed‐type dislocation.