A micromechanical model for an interface between two solids in elastoplastic contact is presented to predict the acoustic linear and nonlinear interfacial stiffnesses during loading-unloading cycle. This interface is a representative model for apparently closed cracks and imperfect bonds that are interacting with ultrasonic waves sent for evaluating quality of their interfaces. For a better physical description of the elastoplastic contact behavior of the interface, the previous model [Kim et al., J. Mech. Phys. Solids 52, 1911 (2004)] is improved in two important aspects: the unloading model for unit contact element (asperity) and the geometrical and statistical parameters of the interface. The model is validated with experimental results. The interface parameters are obtained by fitting measured reflection coefficients during loading-unloading cycle with the theoretical model. Using so obtained parameters, the linear and second-order interfacial stiffnesses and the nonlinearity in transmitted longitudinal waves are calculated. The theoretical nonlinear transmission amplitude is in good comparison with the experimental result, demonstrating the capability of the present modeling framework in predicting both linear and nonlinear ultrasonic responses of imperfect interfaces. It is observed that the effect of adhesive force, which is not taken into account in the model, can be important in a certain stage of the unloading phase.
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