Resolving the Contradiction of Asperities Plastic to Elastic Mode Transition in Current Contact Models of Fractal Rough Surfaces

The elastic-plastic contact model of fractal rough surfaces offered by Majumdar and Bushan in 1991 (the MB model) is revisited. According to the MB model, the contact mode of a single fractal asperity transfers from plastic to elastic when the load is increased, and the asperity’s contact area grows and becomes larger than a critical area, which is scale independent. This surprising result of the MB model is in contrast with classical contact mechanics where an increase of contact area due to increased load, is associated with a transition from elastic to plastic contact. The present study describes a revised elastic-plastic contact model of a single fractal asperity showing that the critical area is scale dependent, contrary to the MB model prediction. The new model also shows that a fractal asperity behaves as would be expected from classical contact mechanics namely, as the load and contact area increase a transition from elastic to plastic contact takes place in this order.