Resolving the contradiction of asperities plastic to elastic mode transition in current contact models of fractal rough surfaces

The paper suggests a revision to the asperities plastic to elastic mode transition in the elastic–plastic contact model of fractal rough surfaces, offered by Majumdar and Bushan [A. Majumdar, B. Bushan (MB model) J. Tribol. 113 (1991) 1–11.]. According to the MB model, the contact mode of a single fractal asperity transfers from plastic to elastic when the load increases and the growing contact area exceeds a certain critical value, which is scale independent. This surprising result of the MB model is in contrast with classical contact mechanics where increasing 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, contrary to the MB model prediction, the critical contact area is scale dependent. The revised 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 mode takes place in this order.