A New Plasticity Index including Size-Effects in the Contact of Rough Surfaces

It is known that contact of rough surfaces occurs over an area much smaller than the nominal contact area, and at asperity scale, increased hardness results in experimentally observed asperity "persistence", namely that it is hard to flatten asperities. Here, we consider Persson's elasto-plastic solution for rough contact together with an hardness equation proposed by Swadener, George and Pharr for spherical indentation, including size effects depending on sphere radius, in particular to define a new plasticity index that defines the tendency to plastic deformation. While the classical plasticity index shows that at sufficiently small scales, there will be plastic deformations unless surfaces are extremely smooth, and with size effects, the small roughness scales the content of spectrum matter in defining the real state of asperities. In particular, what may appear as plastic at a bulk scale returns to an elastic behaviour at a small scale, as suggested by the "asperity persistence" experimental observation. Some illustrative examples are shown, but clearly, our index and elasto-plastic solution are mainly qualitative, as a realistic investigation is much more complex and still computationally too demanding.