Mechanistic studies of the acoustic nonlinearity in metallic crystals [electronic resource]
Keywords: Mechanical Engineering.

Fatigue is a prevalent failure mechanism of metals caused by progressive damage resulting from repeated stressing. It is one of the most common and costly causes of mechanical failures that affects nearly every solid material. Traditional detection techniques require costly inspections for the presence of macrocracks. Advances in the field of nonlinear ultrasonics are enabling researchers to monitor in-situ the fatigue damage associated with evolution of microstructures. The acoustic nonlinearity parameter beta is known to progressively grow in magnitude from the earliest cycles of fatigue to final fracture. Unfortunately, the dislocation mechanisms giving rise to this increase are not well understood. An orientation-dependent line energy model of beta arising from a pinned dislocation monopole bowing out in its glide plane is developed using a quasi-static loading assumption. A strong dependence on Poisson's ratio and the orientation of the Burger's vector relative to the initial line direction is found to be missing in the previously accepted model. A negative dislocation contribution to beta is predicted for the first time and is a possible explanation for decreases in beta that have been measured experimentally. Discrete dislocation dynamics (DD) simulations are used for the first time to predict beta and compared with the model. The techniques are extended to the long-range interactions between straight dislocations to better describe fatigue microstructures. An analytic model of an isolated dislocation dipole's beta is derived and beta is found to be primarily dependent on the residual glide stress acting on the dipole, which has not been predicted before. beta of multipolar interactions in an infinite dipole train and an infinite Taylor lattice is shown arise only under the presence of a residual glide stress and not a simple aggregation of dipoles as previously predicted. Agreement with two-dimensional DD simulations is shown for glide stresses well below the critical stress that causes dissolution of the dipole structure. Several finite sections of the Taylor lattice commonly used to approximate fatigue microstructures are modeled with DD and are found to have anomalous scaling behaviors with increasing number of dislocations. Finally, the validity of the quasi-static loading assumption is evaluated using cyclic DD simulations. This assumption has been the foundation of numerous models of beta, but its applicability to various dislocation microstructures has never been verified. The effect of dislocation drag on energy dissipation and the second harmonic is modeled using an overdamped first-order viscous drag mobility law. In addition to the drag on an individual dislocation, the interaction between remote dislocations has an appreciable impact on the measured beta, which has been overlooked in previous attempts to justify the quasi-static assumption. The assumption is predicted to break down in BCC metals due to the significant barriers to dislocation motion and the low mobility of screw dislocations. Even in materials where drag is important, the quasi-static limit provides an upper bound on the magnitude of the acoustic nonlinearity.