Normal dynamic adhesion of an infinite elastomer layer on a statistically rough substrate

Abstract

The dynamic adhesion properties under different pulling speeds on rough substrates have potential value in practical applications. Our primary objective is to ascertain the influence of the pulling speed on the normal stress required for delamination when an infinite elastomer layer delaminates from a statistically random rough rigid substrate. We decouple the interface delamination velocity from the pulling speed based on the deformation of the elastomer during pull-off procedure. Based on the balance of interface stress and elastomer stress, we obtain the varying interface delamination velocity with constant pulling speed. By combining the Greenwood-Williamson statistical model of rough substrate with Muller theory of dynamic adhesion, we obtain a dynamic adhesion model to describe the adhesion force between the elastomer and the rough substrate under various interface delamination velocities, and deduced the pull-off stress σ_pull-off as a power function of the pulling speed v_U, that is σ_pull-off ∝ $v_U^{k_{\text{exp}}}$. The exponential k_exp of the above power function is studied as the pulling speed range of 0.01 ∼ 10 mm/s, the elastomer modulus range of 49.4 ∼ 4000 kPa and the RMS roughness range of 10⁻⁴ ∼ 10⁻⁷ m. Through the experimental verification when the RMS roughness of substrate Z_rough and the modulus of elastomer E satisfy 20×(z_rough/z_k) < (E/E_k)^−0.354 (here z_k = 1 mm, E_k = 1 kPa), the exponential is constant and independent of roughness or modulus. High roughness or high modulus will result in this exponential increase due to the change of the pressing depth probability density function. This finding is expected to simplify the analysis of the dynamic adhesion on the rough substrate and provide ideas for the rough substrate adaptive design of adhesive materials.