The critical stress in a discrete Peierls–Nabarro model

Abstract The Peierls stress is calculated for a discrete Peierls—Nabarro model of a dislocation. Unlike the original continuum model where a continuous distribution of infinitesimal dislocations was considered, the discreteness of the slip plane is maintained throughout the calculation, and the Peierls stress τp is determined as the critical applied stress beyond which the stability of the system breaks. Results for three types of interatomic shear potential are well approximated by the relation τp G∞ exp(−Ah/b), as predicted by the continuum model, G being the shear modulus, b the spacing between slip planes, b the length of the Burgers vector and A a constant depending on the potentials. The magnitude of τp of the discrete model is larger than that of the continuum model for the same sinusoidal potential. Long-range potentials give low τp although they are still larger than experimental values.