Effects of interfacial imperfections on nanoscale adhesive contact for layered medium

Depending on processing technologies and working conditions, imperfect bonding at the layer-substrate interface may occur, resulting in diverse mechanical responses compared to a perfectly bonded layer-substrate system. This study focuses on an imperfect interface under force-like conditions and incorporates it into a nanoscale adhesive contact model to explore the influences of interfacial imperfection on the adhesive contact behaviors of the layered medium. The adhesive contact model is formulated based on the Lennard-Jones (LJ) potential and the Hammaker summation method. The adhesive contact problem is addressed by solving the nonlinear surface gap equations between the contact bodies. The deformation within the gap equations, accounting for the influence of imperfections, is computed using the fast Fourier transform (FFT) algorithm. This study explores the influence of three stress jumping coefficients $t_1$, $t_2$ and $t_3$, which quantitatively characterize the interfacial imperfection, and their coeffects with material parameters, including imperfection depth (layer thickness), adhesion work, and elastic modulus, on the adhesive contact behaviors of the layered medium. The findings underscore that the normal stress jumping coefficient $t_3$ exerts the most significant impact, wherein a higher $t_3$ value corresponds to a smaller adhesive force and a larger absolute contact approach, while tangential stress jumping coefficients $t_1$ and $t_2$ exhibit negligible influence. Decreasing $t_3$ values correspond to varying interaction force-contact approach responses and contribute to alleviating contact stability in cases with large Tabor parameters. Interfacial imperfections manifest their influence by modifying the pressure-displacement response, with noticeable effects only within a specific imperfection depth range $\overline{h}<40$. While the introduction of interfacial imperfections does not alter the fundamental impact of material parameters—such as imperfection depth, adhesion work ratios, and elastic modulus ratios—on adhesive force and contact approach, it does modify the magnitude of these effects. Furthermore, imperfections alter stress distribution, increasing maximal von Mises stress and causing stress concentration within the layer and at the interface. In summary, force-like imperfections reduce surface displacement, resulting in a smaller region of positive pressure and ultimately contributing to a larger adhesive force. However, this effect is accompanied by increased stress concentration at the imperfect interface. This heightened stress level poses a potential risk to the system's reliability.