Dislocation Multipoles and Their Role in Strain-Hardening

Abstract

The stress fields of edge dislocation dipoles are able to trap other edge dislocations that pass nearby. The configurations, energies, and trapping stresses of the resulting tripoles are discussed here in some detail. Dipoles may also interact dynamically with approaching dislocations because they cause fluctuating stresses. The decrease in the average velocity of a moving dislocation is given in terms of the fluctuation amplitude and the dislocation's ``mobility parameter.'' On the basis of these results, linear strain-hardening can be accounted for in terms of edge dislocation dipoles. Since dipoles in real crystals tend to be finite in length and their stress fields attenuate rapidly with distance, they act as particles to impede dislocation motions. Thus hardening is proportional to the dipole concentration which is proportional to the plastic strain, so the hardening will be linear in the strain. Through interactions with approaching dislocations, dipoles may become tripoles, then quadrupoles, etc., leading to some of the characteristic residual structures in plastically strained crystals, such as slip bands, deformation bands, and bands of secondary slip. No attempt is made to calculate the strain-hardening coefficients of real crystals because concentrations and distributions of dipoles are not known in sufficient detail. Finally, it is shown that the asymmetric stress fields of dipoles can account in a natural way for the Bauschinger effect.