Quasi-periodic variation of Peierls stress of dislocations in face-centered-cubic metals

Abstract

The Escaig stress, i.e. the shear stress perpendicular to the Burgers vector, modulates the stacking fault area between two partials of a full dislocation, in turn, affects the mobility of the dislocation. In this paper, using the newly improved semi-discrete variational Peierls-Nabarro (SVPN) model we studied the variation of Peierls stress (τ p) of dislocations in face-centered-cubic crystals with respect to the Escaig stress. We found that τ p quasi-periodically oscillates and the oscillation gradually decreases with the increase of Escaig stress. This quasi-periodic variation of τ p can be mathematically described by the combination of a sinusoidal and an exponential function, and further accounted for by the variation of the stacking fault width (SFW) between two partials during their movement under applied stress. For the maximum τ p , SFW is about integral multiples of the Peierls period. For the minimum τ p , SFW is around half-integral multiples of Peierls period. The variation of τ p is associated with the oscillation magnitude of SFW from half-integral multiples to integral multiples of the Peierls period and then back to integral multiples of Peierls period caused by the Escaig stress. Molecular dynamics (MD) simulations further examined quasi-periodic variation of τ p , validating the SVPN model's capability of predicting sophisticated behavior of dislocation under applied stress.