The Theory of the Change in the Conductivity of Metals Produced by Cold Work

An attempt is made to calculate the increase in the residual electrical resistance of cold-worked metals by attributing the effect to an elastic distortion similar to that produced by the presence of edge type dislocations. It is shown that, in single crystals, the direction of the dislocation axes, the slip direction and the direction normal to the slip plane represent a set of principal axes of the conductivity tensor. The dislocation resistance parallel to the dislocation axes is zero, while the resistance in the slip direction exceeds the resistance normal to the slip plane by a factor which depends upon Poisson's ratio and which lies between 1 and 3. The mean density of dislocations in a highly cold-worked polycrystalline specimen of copper is estimated from the observed resistance change and is found to be in reasonable agreement with the value derived from the energy stored during work hardening. The formulation of the present theory follows the lines of a recent paper by J. S. Koehler; the results differ considerably from Koehler's, however, and it is shown that his treatment cannot be regarded as satisfactory.