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.

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This article presents a theoretical model of the kinetic friction characteristics for sliding velocity under mild wear condition, assuming a simple effective hardness at asperity contacts. The proposed model depends on the surface temperature distribution obtained by using Jaeger's estimation for a moving homogeneous heat source with an infinitely long band on a semi-infinite solid and a relation between steel hardness and temperature measured by Tominaga. Further, the model takes into consideration the stochastic model of a rough surface contact that was proposed by Greenwood and Williamson. The calculation results show that the surface temperature increases and the surface hardness and the friction coefficient decrease as the sliding velocity increases. However, the variation in the friction coefficient is less than that in the surface hardness. The initial value of the friction coefficient and the contact pressure has a great influence on the relation between the friction coefficient and the sliding velocity. In contrast, the standard deviation of the asperity summit heights has little influence on the relation.

The tribological properties under abrasive wear conditions, the tensile properties, the thermal properties and the structure have been investigated on the polyamide 6 (PA6) fibers dispersed with vapor-grown carbon fibers (VGCF's) in order to analyze the effects of dispersing VGCF's on the wear resistance of PA6 fibers. The wear resistance of the fibers have been determined using a method previously proposed by the present authors. The coefficient of friction decreased by dispersing a small amount of VGCF's but increased with increasing VGCF fraction at large VGCF fractions. The wear resistance increased with increasing VGCF fraction. Under the experimental conditions adopted in this study, the dispersion of VGCF's more effectively increased the wear resistance of PA6 fibers than the heat treatment. These experimental results have been analyzed based on a model with which the coefficient of friction (μ) and the wear rate (W s) have been related to the microhardness (H), the resistance against sliding (σ s), the fracture probability (f) the shape factor (g) and a constant (k) as μ = gσ s /(kH) and W s = gf/(kH).

This paper describes a modification of the theoretical model presented by Nakahara for estimating the static friction coefficient of the contact between rough surfaces and a boundary film. The theoretical model is modified from Halling's friction model for soft thin metallic films. The effective hardness in Halling's model is transposed with a new model, which is modified from Bhattacharya-Nix's equation for a conical indenter, in order to apply it to a spherical indenter on the basis of Johnson's cavity model. Nakahara's model takes into consideration the effect of pressure on the shear strength of the boundary film, which was suggested by Briscoe et al., and it can elucidate the effects of the following factors on the friction coefficient: apparent contact pressure, film thickness, the three parameters of roughness in Greenwood-Williamson's model, and the ratio of film bulk hardness to substrate hardness.This study elucidates the effects of the following factors on the new model of static coefficient of friction proposed by Nakahara: the difference between parabolic and spherical indenters, elastic deformation under the condition of contact with a substrate, i.e. film breakdown, and the adhesion force at the contact.