Elasto-plastic micromechanical model for determination of dynamic stiffness and real contact area from ultrasonic measurements

The interaction of ultrasonic waves with rough surfaces in contact is sensitive to the micromechanics of the contacts and to the topography of the surfaces. A continuous effort to develop a link between ultrasonic measurements and interfacial properties has evolved to the extent that elasto-plasticity occurring during loading can now be taken into account. Here, a state-of-the-art model is critically revisited in light of recent results on the micromechanics of elasto-plastic asperities in contact during unloading. A new probability density function of the asperity height is derived, which takes into account plastic deformation. This function is used to evaluate the pressure during unloading as a function of the relative approach between the mean planes of the surfaces. It is also shown that this relation can be cast in terms of the probability density function prior deformation, provided that a suitable transformation variable is utilized. These results are used to obtain a new expression for the dynamic stiffness of the elasto-plastic interface which determines the response of the latter to an incident wave. Finally, some results illustrating the behavior of the static and dynamic interfacial stiffness during a complete loading–unloading cycle are presented.