Thin Film Exfoliation in the Zone of Trapped Elastic Wave Localization

Abstract

In modern constructions, thin-layer coats are often used as protecting or strengthening elements. Deformations of such constructions may cause significant stresses on the interface between the base and the coat because of the difference in their physical mechanical properties, which leads to the destruction or detachment of the cover. The impact of static or shock loads on the emergence and development of delamination in multilayer constructions has been studied fairly well, but much less is known about destructions of this type under nonstationary (vibrational) loads. The interest in the latter is caused by the fact that even small variable actions may cause the localization of oscillations in a neighborhood of inhomogeneities (such as inclusions, defects, construction elements, etc.) [1] (and lead to the emergence and growth of defects, which strongly affects the reliability and functionality of the whole construction. The possibility of the localization of oscillations near initial delamination and the impact of localization on the growth of the delamination are studied and a model for analyzing conditions under which a detachment zone grows or ceases to grow is suggested. Problem statementTaking into account the fact that the thickness of a thin-layer coat is usually much less than the characteristic size of the substrate, in the first approximation, we replace a coat attached to a substrate by a film on an elastic substrate. It is shown that, if an elastic substrate has an inhomogeneity (the coefficient of the elastic substrate vanishes for some part of the film length), then, under a non-stationary harmonic load, some part of the propagating wave energy is localized near the inhomogeneity. Depending on the parameters of the film and the elastic substrate, various scenarios of the film behavior are possible: the length detachment zone may increase unlimitedly, or it may cease to grow at some time. Note that if there are only propagating waves in the film, then the wave processes only insignificantly affect the behavior of the detachment zone, because the excited wave process rapidly fades out. The situation changes if the waves in the film-waveguide localize near the defect. As is known, in the absence of dissipation, localized oscillations of certain frequencies may not attenuate for an infinitely long time [1], thereby substantially affecting the behavior of the detachment zone. The existence of standing waves localized near the detachment zone means that the corresponding spectral problem has not only continuous but also discrete spectrum of eigenfrequencies. The simplest mathematical model for the behavior of such a film under the action of a transverse non-stationary harmonic load is considered. The film is attached to an elastic Winkler foundation, which models an element of a blade. In the framework of this model, the birth of a detachment is not studied; it is assumed that, at initial moment of time, a film fragment of length 2l 0 is torn away from the elastic substrate. The problem is reduced to t...