This chapter presents some of the existing approaches for describing mathematically the friction and wear behaviour of multi-component systems. The relationship between the size of the reinforcing phase and the asperity size plays an important role in friction and wear phenomena. Depending on this parameter, different types of wear behaviour can occur.
The abrasive wear of particle-reinforced polymer composites can be described by a simple additive equation based on a series model. The apparent filler wear rate in the composite is higher than that measured for the same material in sheet form and this increase is highly dependent on the type of particle-surface treatment. If these composites are, however, subjected to sliding wear against smooth steel counterparts, the simple rule-of-mixtures description does not apply anymore, due to a higher complexity of the wear mechanisms.
From investigations on the unlubricated friction and wear of unidirectionally oriented fibre reinforced polymers (FRP) sliding against carbon steel, the following results were obtained:
(1) The law of mixture for the friction coefficient of FRP was deduced, and the validity of this law was assured by the experimental results.
(2) Carbon-FRP gave a small specific wear rate and a low friction coefficient. By contrast, glass-FRP provided a large specific wear rate and a high friction coefficient.
(3) A model was proposed in which the wear of FRP proceeds by wear-thinning of the fibre with subsequent breakdown of the fibre and by peeling-off of the fibre from the matrix. Using this model, an experimental equation for the wear of FRP was deduced.
Further, work concerning the tribological behaviour of hybrid composites has led to the following conclusions:
(1) The steady-state wear rates of hybrid composites sliding against stainless steel often lie considerably below the values linearly interpolated between those of the single-fibre composites. Thus, wear synergism is exhibited by the hybrid composites.
(2) Fibre orientation affects a composite's wear behaviour, but both the extent of its significance and the optimum orientation for wear resistance depend on the composite's composition.
(3) Using the best wear results achieved with monolithic fibre composites, i.e. with carbon fibres oriented in-plane and parallel to the sliding direction, or with aramid fibres in normal orientation, would lead to a model composite with a 3D-hybrid structure, which is supposed to have optimum wear resistance.
(4) Approaching this model by producing 2D-hybrid composites shows synergistic effects between different fibre materials and directions chosen.
(5) A mathematical, semi-empirical model is suggested that allows one to describe these hybrid effects by (a) starting from a rule-of-mixture prediction on the wear resistance of the hybrid composite, and (b) subtracting a reduction term of the wear rate, resulting from the interactive protection against wear of one component by the other. If the hybrid efficiency factor is negative, the wear of the hybrid composite is, on the other hand, greater than that predicted by the rule-of-mixtures approach.