An integrated analytical and experimental study of contact acoustic nonlinearity at rough interfaces of fatigue cracks

This paper presents an analytical model that describes the relationship between interface stiffness and separation of rough interfaces such as fatigue cracks. The contact acoustic nonlinearity at the interface is simulated by a quasi-static model based on Hertzian contact theory. The model is validated using the results of dynamic acoustoelastic testing (DAET) with a Rayleigh wave probe on fatigue cracks in two aluminum alloy samples. One novel aspect of this work is that all the required geometrical parameters for the model are acquired directly from the aperture profile of real cracks extracted from their scanning electron microscopy (SEM) images. Also, the separation of the crack faces during dynamic perturbation is independently measured using a 3D laser Doppler vibrometer (LDV). In addition, using DAET allows for an unprecedented direct comparison between experimental and analytical results. This is because unlike conventional nonlinear ultrasonic tests that are based on measuring the amplitude of higher harmonics, DAET outputs directly the strain-dependency of transmission and time delay of ultrasonic waves propagating across the interface. The model is found in good qualitative agreement with the experimental results, although the predictions tend to underestimate the variation of transmission coefficient and time delay. We conduct a sensitivity analysis to investigate the influence of different assumptions and simplifications on model predictions.