Investigation on Physics-based Multi-scale Modeling of Contact, Friction, and Wear in Viscoelastic Materials with Application in Rubber Compounds

This dissertation aims to contribute towards the understanding and modeling of tribological phenomena of contact, friction, and wear in viscoelastic materials with application in rubber compounds. Tribiological properties of rubber compounds are important for many applications such as tires, shoe heels and soles, wiper blades, artificial joints, O-ring seals, and so on. In all these applications, the objective is to maximize the friction coefficient to avoid slipping and reduce the wear rate to improve the life expectancy and performance of the products.

The first topic in this study focuses on a novel multiscale contact theory proposed by Persson and explains the advantages of this theory over other classical contact theories. The shortcomings of this theory are also investigated, and three methods are proposed to improve Persson's original contact model by correcting the approximation of deformation in the contact area. The first method is based on the original Greenwood and Williamson (GW) contact theory, which neglects the effect of elastic coupling between asperities. The second method is based on an improved version of GW theory, which considers the elastic coupling effect of asperities in an approximate way. The third method is based on the distribution of local peaks of asperities, which is particularly suitable to determine the fraction of a skewed height profile involved in tribological processes. This method can be implemented within the framework of other proposed methods. Since the height profiles of rough surfaces studied in this dissertation are approximately normally distributed, the second correction method is applied to the original contact model to calculate the real contact area and friction coefficient.

The second topic addresses the theoretical model of hysteresis friction in viscoelastic materials. The multiscale temperature rise of the rubber surface due to hysteresis friction is also modeled and the effect of flash temperature on the real contact area and friction coefficient is studied. Since the hysteresis friction is not the only mechanism involved in the rubber friction, a semi-empirical model is added to the hysteresis model to include the contribution of adhesion and other processes on the real contact area. Based on the improved multiscale contact theory, a pressure-dependent friction model is also developed for viscoelastic materials, which is in good agreement with experimental results.

The third topic deals with the theory of stationary crack propagation in viscoelastic materials and the effect of crack tip flash temperature on the instability of crack propagation observed in some experimental results in the literature. Initially, a theoretical model is developed to calculate the tearing energy vs crack tip velocity in a Kelvin-Voigt rubber model. Besides, two coupled iterative algorithms are developed to calculate the temperature field around the crack tip in addition to the tearing energy as a function of crack tip velocity. In this model, the effect of crack tip flash temperature on the tearing energy is considered to update the relation between tearing energy vs crack tip velocity, which also affects the flash temperature. A theoretical model is also developed to calculate the contribution of the hysteresis effect to the tearing energy vs crack tip velocity using the dynamic modulus master curve of a rubber compound. Then, the low-frequency fatigue test results are compared with the theoretical predictions and used in the framework of powdery rubber wear theory to calculate the stationary rubber wear rate due to fatigue crack propagation.

Moreover, a sliding friction and wear test set-up, with both indoor and outdoor testing capability, is developed to validate the theoretical models. The experimental results confirm that the theoretical model can successfully predict the friction coefficient when there is no trace of thermochemical degradation on the rubber surface. Investigating the wear mechanism of rubber samples on three different surfaces reveals that the contribution of fatigue wear rate is less important than other wear mechanisms such as abrasive wear due to sharp asperities or thermochemical degradation due to a significant rise of temperature on the contact area. Finally, the correlation between friction coefficient and wear rate on different surfaces is studied, and it is found that the relation between friction and wear rate strongly depends on the dominant wear mechanism, which is determined by the surface characteristics, sliding velocity, normal load, and contact flash temperature.