Phonon scattering during dislocation motion inducing stress-drop in cubic metals

Abstract

This work proves that scattering of elastic waves in the dislocation core induces an unusual behavior called stress-drop, which is defined for the first time in this study as a phenomenon where an externally applied stress drops inside a nano-sized cubic metal during dislocation motion. We develop a theoretical phonon scattering model based on discrete lattice dynamics and derive simple analytical equations to quantify the magnitude of the stress-drop. The proposed model is supported by atomistic simulations of perfect dislocations in bcc iron, where the stress-drop resulting from bond breaking is inversely proportional to the square of the dislocation speed. The derived equation is in excellent agreement with direct atomistic simulations for edge and screw dislocations. Next, we extend the equation to the edge dislocation in fcc aluminum where the dislocation exists as a stacking fault ribbon surrounded by two Shockley partial dislocations and thus the interaction between them is important. The extended equation accurately predicts the phonon scattering, resulting in the stress-drop by the oscillation of the two partials as well as bond breaking. In addition to the discussion on the validity of our model and equations at absolute zero, we investigate the temperature and size effects on our equations. As temperature increases, the magnitude of the stress-drop decreases and converges to zero even at very low temperature because of the extremely small Peierls barrier. Moreover, the magnitude of the stress-drop decreases, as the thickness of the nanoplate increases, which shows that the stress-drop is a mechanical behavior that is prominent on the nanoscale.