Continuous Distributions of Dislocations and Energy Dissipation of Metals

Abstract

The theory of continuous distribution of oscillating dislocations has been joined with Zener's thermoelastic effects to give a possible estimate of the energy dissipation in metals. This approach to the question of energy dissipation was considered first by Eshelby. In this work, Eshelby made the following simplifying approximations: the inertia of the material was neglected, the interaction effect between the dislocations was not considered, and the inside of the dislocation core was not considered, only the medium outside the dislocation bounded by a “cutoff” length l was considered. Also, difficulties appeared in Eshelby's work because of the singularity of the stress field at the center of a dislocation. With the above restricting assumptions Eshelby was able to obtain that the energy dissipation should increase with frequency. This result disagrees with the limited experimental data available. We attempt to improve upon the basic thesis proposed by Eshelby by considering a continuous distribution of dislocations instead of a discrete dislocation. Also, the inertia of the material is included in the analysis.