Lattice incompatibility and strain-aging in single crystals

A model based on mesoscale field dislocation mechanics is presented for dislocation–solute interaction, and applied to the study of strain-aging related instabilities—the Lüders and Portevin–Le Chatelier phenomena—in single crystals. A dynamical description of dislocation–solute interaction provides local response. Elastic interaction and transport of polar dislocations, a measure of lattice incompatibility, impart spatial coupling. The 3D numerical results provide insight into the distribution of polar dislocations, stress, and strength in the region of the band, and also enable correlation of these quantities with the macroscopic stress–strain curve. The transition from homogeneous deformation to different kinds of propagating bands is captured as the applied strain rate is increased. The dynamical response has been characterized in terms of the correlation dimension of the reconstructed attractor, singular value decomposition and spectrum of Lyapunov exponents, and shown to be consistent with experiment. Other experimental observations, including the relationship of band speed to applied deformation rate, are also retrieved.