A probabilistic model for quantifying uncertainty of acoustic nonlinearities of lamb waves and its application to the characterization of damage in composite laminates

Nonlinear Lamb wave features are known to be sensitive to microscopic damage, such as fatigue, creep, and material thermal degradation. While previous studies have shown their effectiveness in detecting undersized damage in metallic materials, this study aims to extend the use of the relative acoustic nonlinearity parameter (RANP), a prominent nonlinear feature, to damage characterization in composite materials. First, principles of nonlinear ultrasonics are revisited briefly. Considering operational and measurement uncertainties, it is desirable to quantify the uncertainty of RANP (i.e., its statistics) to facilitate damage characterization. In doing so, an analytical model is established to numerically evaluate the distribution of RANP. Using piezoelectric wafers, continuous sine waves are generated in carbon fiber plate samples. Steady-state responses are acquired and processed to produce the histograms of RANP estimates, in both healthy and damaged conditions, to which the analytical probability model is fit. These distributions are used to enhance the robustness of the parameter, and impact damage in the composite sample is evaluated. The results have shown good agreement between the model and experimental data, and have provided a quantified level of confidence in using RANP for damage state classification in composites.