Theoretical model for adhesive friction between elastomers and rough solid surfaces

Abstract

A theoretical model for the adhesive friction between elastomers and rough solid surfaces is proposed on the basis of opening crack propagation processes at the boundary of the contact interfaces and the rate processes of formation of molecular bonds on the solid surface. This model, which is expressed as a product of the terms related to the two abovementioned processes, requires some measurable and fitted parameters such as the frictional shear strength expressed as a function of viscoelastic dissipation, rate-dependent elasticity, density of bonded molecular chains at a contact junction, critical velocity related to viscoelastic relaxation, and critical velocity related to the rate process of formation of molecular bonds on the solid surface. The friction-velocity relationship exhibits a remarkable fit to previously obtained experimental results for polymers such as engineering rubber, gels, and plastics (glassy polymers), and all fitting parameters are physically reasonable. The viscoelastic index "n" is also related to the "glass-to-rubber transition" of a nanometer-thick polymer layer for frictional behavior. Thus, from a practical viewpoint, this model can be used effectively for fitting the adhesive friction behavior of polymers.

Finger pad friction and its role in grip and touch

“…Momozono et al [115] obtained close agreement with published data for a range of polymers including elastomers. However, Vorvolakos & Chaudhury [118] argued that their data for elastomers sliding on smooth surfaces could be adequately described by the stochastic model without the need to invoke viscoelastic losses.…”

“…However, it is reasonable that similar values of q are obtained for the dry occluded and wet cases since q is a material parameter. In addition, the values are less than the upper limit of unity; for comparison the typical value for elastomers is 0.4 [115].…”

“…On this basis, the values of ' for PP are about 1 and 6 mm in the dry occluded and wet states, and for glass they are about 1 and 3 mm in the dry occluded and wet states. However, Momozono et al [115] argued that this parameter should be of the order of the molecular chain lengths for elastomers (approx. 10 nm).…”

“…The stochastic model predicts frictionless slip at low and high velocities because the energy dissipation is only ascribed to interfacial processes. This limitation is eliminated by considering a fracture mechanics description of sliding friction, which has been developed for elastomers and which accounts for viscoelastic losses at the crack tip [115]. It was formulated for rough surfaces but it could be applied to those that are smooth.…”

On the Friction of Carbon Black- and Silica-Reinforced BR and S-SBR Elastomers

“…G 0 values are selected in the same order for the samples used in this research. For ''high'' crack velocities, G v ð Þ % G 0 22,33]. The ratio of the dynamic modulus in the glassy state to that in the rubbery state,…”