Microstructure-based model of nonlinear ultrasonic response in materials with distributed defects

Abstract

Nonlinear ultrasonic technique is one of several promising nondestructive evaluation methods for monitoring the evolution of nanosized defects such as radiation-induced defects in nuclear materials. In this work, a microstructure-based phase-field model of dynamic deformation in elastically nonlinear materials has been developed for investigating the dynamic interaction between distributed defects and a propagating longitudinal sound wave. With the model, the effect of second phase precipitates' size and properties on the nonlinearity parameter β that describes the magnitude of the 2nd harmonic wave was simulated. The results showed that (1) the nonlinearity parameter β increases as the elastic inhomogeneity increases regardless of whether the precipitates are softer or harder than the matrix; (2) β linearly increases with the increase of lattice mismatch strain; and (3) for a given volume fraction of second phase precipitates, β strongly depends on the precipitate size. The predicted precipitate size dependence of β agrees with the experimental data. These results demonstrate that the developed model enables one to predict the contributions of different nonlinear sources to β, to explain the signal physics behind the measured nonlinear ultrasonic response, and to guide the development of nonlinear ultrasound nondestructive detection of material defects in nuclear reactor materials.