This research develops a robust experimental procedure to track the evolution of fatigue damage in a nickel-base superalloy with the acoustic nonlinearity parameter, β, and demonstrates its effectiveness by making repeatable measurements of β in multiple specimens, subjected to both high- and low-cycle fatigue. The measurement procedure developed in this research is robust in that it is based on conventional piezoelectric contact transducers, which are readily available off the shelf, and it offers the potential for field applications. In addition, the measurement procedure enables the user to isolate sample nonlinearity from measurement system nonlinearity. The experimental results show that there is a significant increase in β linked to the high plasticity of low-cycle fatigue, and illustrate how these nonlinear ultrasonic measurements quantitatively characterize the damage state of a specimen in the early stages of fatigue. The high-cycle fatigue results are less definitive (the increase in β is not as substantial) due to increased uncertainties involved in the high-cycle fatigue tests, but still show a clear relationship between β and remaining fatigue life. One application of the measured β versus fatigue-life data is to potentially serve as a master curve for life prediction based on nonlinear ultrasonic measurements.

A reliable laser-based ultrasonic technique is developed to measure the second order harmonic amplitude of a Rayleigh surface wave propagating in metallic specimens. Rayleigh waves are experimentally generated with a wedge transducer and detected with a heterodyne laser interferometer. The capability of this system to measure the nonlinear contribution present in Rayleigh surface waves is demonstrated, and these results are interpreted in terms of a parameter developed for Rayleigh surface waves which corresponds to the nonlinear parameter of a longitudinal wave, $\beta$ . The proposed measurement technique is used to assess damage in nickel-base high temperature alloy specimens, and the evolution of material nonlinearity under various loading conditions is quantitatively measured in terms of the increasing amplitude of the second order harmonic. These results show that there is a significant increase in the second order harmonic amplitude at monotonic tensile loads above the material’s yield stress, and that during low cycle fatigue tests, the increase in the second order harmonic amplitude is considerable, although less significant than that in the monotonic loading case. The results from this study show the major role that accumulated plasticity plays in the increase in material nonlinearity, and demonstrate the effectiveness of the proposed experimental procedure to track damage in high temperature alloys.

The objective of this research is to develop an accurate and reliable procedure to measure the second order harmonic of a Lamb wave propagating in a metallic plate. There are two associated complications in measuring these nonlinear Lamb waves, namely, their inherent dispersive and multimode natures. To overcome these, this research combines a time-frequency representation with a hybrid wedge generation and laser interferometric detection system. The effectiveness of the proposed procedure is demonstrated by characterizing the inherent material nonlinearity of two different aluminum plates whose absolute nonlinearity parameters are known from longitudinal wave measurements.

This paper investigates the characteristics of the second harmonic generation of Lamb waves in a plate with quadratic nonlinearity. Analytical asymptotic solutions to Lamb waves are first obtained through the use of a perturbation method. Then, based on a careful analysis of these asymptotic solutions, it is shown that the cross-modal generation of a symmetric second harmonic mode by an antisymmetric primary mode is possible. These solutions also demonstrate that modes showing internal resonance—nonzero power flux to the second harmonic mode, plus phase velocity matching—are most useful for measurements. In addition, when using finite wave packets, which is the case in most experimental measurements, group velocity matching is required for a cumulative increase in the second harmonic amplitude with propagation distance. Finally, five mode types (which are independent of material properties) that satisfy all three requirements for this cumulative increase in second harmonic amplitude—nonzero power flux, plus phase and group velocity matching—are identified. These results are important for the development of an experimental procedure to measure material nonlinearity with Lamb waves.