Nonlinear dislocation dynamics at ultrasonic frequencies

Abstract

An analytical model of the effects of the Peierls–Nabarro barrier stress on the nonlinear dynamics of dislocation motion in crystalline solids resulting from a perturbative ultrasonic wave is derived. The nonlinearity is quantified by a material nonlinearity parameter β extracted from measurements of the amplitudes of the fundamental and harmonically generated ultrasonic waveforms. The β parameter is found to be functionally dependent on the magnitude of the Peierls–Nabarro barrier stress, the dislocation loop length, the shear modulus, and the Burgers vector of the crystal. The parameter is shown to exhibit a Bessel function oscillatory dependence on the stress amplitude of the fundamental ultrasonic wave resulting directly from the Peierls–Nabarro barrier stress. A sharp increase in the magnitude of β is shown to occur at low ultrasonic amplitudes where the dislocation motion is confined between adjacent lattice planes bounding the unperturbed dislocation. The generalization of the model to polycrystalline solids predicts a significant reduction in the β oscillations that results in a dramatic hooklike shape of the β versus stress amplitude curve at small values of the ultrasonic stress amplitude. Experimental observations of the hooklike shape (known as the Buck hook) have been reported in literature but the phenomenon has been previously unexplained. The present model shows that the Buck hook is a consequence of dislocation dynamics at low ultrasonic drive amplitudes.