Theoretical analysis of dry friction in brittle and ductile materials

Abstract

An analysis is proposed to study the mechanical fracture of the microscopic junctions which cause friction and wear in materials. The analysis applies the Griffith energy balance concept and the Rice line integral J to a junction model which is fractured when two opposite cracks advance under an external compressive and shear stress (mode I and mode II fracture). It is found from the model that the friction coefficient is proportional to γ p / Hd, where γ p is the fracture surface energy, H is the hardness of the material and d is the average junction size. For highly brittle materials the predicted junction size is about 10 −9m, suggesting that the heat generated during friction must be due to the direct stimulation of surface atoms into random thermal vibration by the sudden release of elastic energy stored in a junction of molecular dimensions. In the case of ductile materials the predicted junction sizes are of the order of 10 −4–10 −5m, in good agreement with the wear particle diameters determined experimentally.