Model of contact friction based on extreme value statistics

We propose a model based on extreme value statistics (EVS) and combine it with different models for single asperity contact, including adhesive and elasto-plastic contacts, to derive a relation between the applied load and the friction force on a rough interface. We find that when the summit distribution is Gumbel, and the contact model is Hertzian we have the closest conformity with Amontons law. The range over which Gumbel distribution mimics Amontons law is wider than the Greenwood-Williamson Model. However exact conformity with Amonton's law does not seem for any of the well-known EVS distributions. On the other hand plastic deformations in contact area reduce the relative change of pressure slightly with Gumbel distribution. Elastic-plastic contact mixes with Gumbel distribution for summits. it shows the best conformity with Amonton`s law. Other extreme value statistics are also studied, and results presented. We combine Gumbel distribution with GW-Mc Cool model which is an improved case of GW model, it takes into account a bandwidth for wavelengths of {\alpha}. Comparison of this model with original GW-Mc Cool model and other simplified versions of BGT reveals that Gumbel distribution has a better conformity with Amonton`s law for all values of {\alpha}. When adhesive contact model is used, the main observation is that for zero or even negative applied load, there is some friction. Asperities with height even less than the separation of two surfaces are in contact. For a small value of adhesion parameter, a better conformity with Amontons law is observed. Relative pressure increases for stronger adhesion which means that adhesion controlled friction dominated by load controlled friction. We also observe that adhesion increases on a surface with a lower value of roughness.