Rapid detachment of a rigid sphere adhered to a viscoelastic substrate: An upper bound model incorporating Maugis parameter and preload effects

For a typical adhesive contact problem, a rigid sphere initially adhered to a relaxed viscoelastic substrate is pulled away from the substrate at finite speeds, and the pull-off force is often found to depend on the rate of pulling. Despite significant theoretical advancements in this area, how the apparent adhesion enhancement is affected by the Maugis parameter and preload remains unclear, and existing models are sometimes contentious. In this work, we revisit this adhesive contact problem and propose a theoretical model to predict the upper bound detachment behavior when the pulling speed approaches infinity. Our analysis reveals that the apparent work of adhesion can always be enhanced, regardless of the Maugis parameter, when the initial contact radius exceeds a critical threshold. Conversely, when the initial contact radius is below this critical value, the adhesion enhancement becomes limited and depends on both the Maugis parameter and the preload condition. Further model calculations suggest that the critical initial contact radius is dependent on the Maugis parameter. In the JKR-like regime, this critical radius converges to a constant value, whereas in the DMT-like regime, it diverges rapidly following an inverse power law with respect to the Maugis parameter. As a result, observing adhesion enhancement is generally more challenging in DMT-like contacts compared to JKR-like contacts. In the meantime, our model also suggests that the adhesion enhancement arises from the expansion of the cohesive zone area due to the viscoelastic properties of the material not only within the cohesive zone but also in the intimate contact zone. Overall, our findings offer a more comprehensive understanding of viscoelastic effects in adhesive contacts, which can be used to rationally predict or optimize adhesion strength in viscoelastic interfaces.