Configurational force on a dynamic dislocation with localized oscillation

Abstract

Upon employing the conservation theorem and continuum theory, the configurational force on a singularity, or a defect, is given by a path-independent integral called the J integral. According to the continuum elasticity theory, the J integral around a steadily moving dislocation is equal to the Peach–Koehler force acting on the dislocation and is independent of the integration path. However, using a discrete lattice dynamics method, we theoretically prove that the J integral is not path-independent in practice even under uniform motion. This is because of the generation of phonons during the dislocation motion. In general, phonons are generated upon localized oscillation of the dislocation, and they dissipate energy from the dislocation core; consequently, a drag force is produced. As the drag force disturbs the dislocation motion, the J integral around the moving dislocation is smaller than that around a stationary one, and its deviation from the stationary one corresponds to the drag force. In this study, we analytically derive the drag force for each oscillation mode by adopting dislocation–phonon coordinates. We classify the oscillation mode simply as symmetric or anti-symmetric after assuming the dislocation to be a localized defect having a finite core width. Consequently, the drag force is numerically calculated upon consideration of the discrete nature of the dislocation core. In particular, our study reveals that the anti-symmetric oscillation mode mainly contributes to the drag force in the limit of high dislocation velocity. Furthermore, we show that the resulting relation between the drag force and dislocation frequency can reproduce the dislocation velocity-stress curve. This work is expected to contribute to meso- and macro-scale plasticity when the material is loaded under extreme conditions or transient dislocation motion can be assumed.