Atomic Displacements around Dislocation Loops

Abstract

The displacement field around a ``penny‐shaped'' inclusion or void in an isotropic elastic medium has been computed by the methods outlined by Sneddon. The boundary conditions for such a loop are that in the plane of the loop z = 0, the displacement is = ±| b |/2 for r less than the loop radius c, and zero outside the loop, and that the shear stress in the r direction across this plane is zero everywhere. We assume that the actual atomic displacements are represented by this displacement field beyond a few atomic diameters of the loop. The solutions for the r and z components of the displacment field are given in series from, and contour plots for these components have been generated by a CDC‐6600 computer for Poisson's ratio, σ = 0.30. At large distances from the loop the series expressions for the displacement field converge to that of a single doublet force without moment oriented in the z direction plus a point singularity at the center of the loop. The strengths of these two singularities are expressed in terms of the dimensions of the loop, | b | and c, and σ. From these strengths the lattice dilatations including image effects have been calculated for a finite medium with a uniform distribution of loops. We obtain the results that the only dilatation is normal to the plane of the loop, and that the strain is simply the fraction of atoms contained in the loops.