The quasistatic approximation for a cracked interface between a layer and a substrate

Heuristic in nature, the quasistatic approximation (QSA) describes the interaction of ultrasonic waves with imperfect interfaces by modeling the interfacial imperfection as distributions of springs and masses. The QSA does not provide any relationship between the interfacial stiffness constants and the micromechanics of the defects. The aims of this paper are threefold. First, a derivation from first principles of the QSA boundary conditions on a cracked interface is presented. Relationships linking the interfacial constants to the mechanical and geometrical properties of the distributed cracks are also obtained. Second, the stiffness dependence of a cracked interface between a layer and a substrate on the layer thickness is investigated. It is shown that the interfacial stiffnesses cannot be regarded as intrinsic properties of the interface, but they may also depend on the structural properties of the hosting system. Finally, the effect of the thickness dependence of the interfacial stiffnesses on the phase velocity of the lowest mode supported by the layered structure is investigated.