Crack propagation pattern and trapping mechanism of rolling a rigid cylinder on a periodically structured surface

Abstract

Recent experiments on the rolling of a cylinder with a poly-dimethylsiloxane (PDMS) film-terminated ridge-channel surface structure against a flat rigid plate have shown significant enhancement in rolling resistance. For rolling perpendicular to the ridges, the rolling resistance initially increases with the ridge spacing. Treating the trailing edge of the rolling interface as an opening crack, this increase has been explained quantitatively by a crack-trapping model. However, beyond a critical value of spacing, the rolling resistance reaches a maximum value and observations suggest that its subsequent decrease is due to two factors. First is the nucleation of cavities ahead of the opening interfacial crack. Second is the growth of these defects parallel to the ridge. These two phenomena limit and eventually attenuate the effect of crack trapping, the primary mechanism of rolling resistance enhancement. Cavitation of the interface is a critical phenomenon limiting rolling resistance, and its mechanism is modeled in this work. We have developed a finite element method (FEM) to simulate the rolling process. Specifically, we developed a special cohesive element and numerical scheme to study how cavities nucleate and grow during rolling. Our simulation captures qualitatively the key experimental observation that cavitation is controlled by ridge spacing. However, our numerical model under-predicts the rolling resistance enhancement due to finite cohesive zone size effects.