Dependence of friction coefficient on the resolution and fractal dimension of metallic fracture surfaces

The paper studies the friction mechanism that is developed between metallic fracture interfaces of fractal geometry. The main purpose of the paper is to investigate how both the resolution and the fractal dimension of the interface affect the friction mechanism. Friction is assumed to be the result of the involving phenomena and the gradual plastifications of the fractal interface asperities. For that, a fractured body with an elastic–plastic behaviour is assumed, in which the fracture interface has fractal geometry. Three different cases are considered, corresponding to fractal interfaces f ( m ) with different fractal dimensions. For each fractal interface, a number of classical problems is considered, corresponding to different values of the resolution δ n . In the limit of the finest resolution useful conclusions are derived for the friction coefficient for the scale ranges studied here. Finally, the influence of the applied normal loading to the friction mechanism is investigated with respect to the fractal dimension and the fractal resolution of the interfaces.