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

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 (τp) of dislocations in face-centered-cubic crystals with respect to the Escaig stress. We found that τp quasi-periodically oscillates and the oscillation gradually decreases with the increase of Escaig stress. This quasi-periodic variation of τp 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 τp, SFW is about integral multiples of the Peierls period. For the minimum τp, SFW is around half-integral multiples of Peierls period. The variation of τp 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 τp, validating the SVPN model's capability of predicting sophisticated behavior of dislocation under applied stress.