ABSTRACT
In the previous chapter we looked into the contact issues in brittle solids. In this chapter, we shall therefore try to understand what the different types of contacts are and how the mechanics change with the type of contact. There are excellent reviews [1-4] available on this subject, particularly in connection with the science of deformation and fracture at the nanoscale, for a truly wide variety of materials. While that knowledge base is of extraordinary importance to the advanced researcher, here, in particular, our approach will be to initiate the understanding of contact mechanics for a beginner. Such an understanding will help us to make a brief scan of the different existing models used to describe the contacts in terms of experimentally measurable physical quantities. As such, there can be many possible types of contact that can happen theoretically in a solid. To start with, it must be borne in mind here that two materials making contact, are involved. One of these is the indenter, and the other is the sample, which is exposed to the indentation by the indenter. There can be situations when the sample is perfectly elastic while the indenter is incompressible and rigid. It may also happen that the sample may be considered as perfectly plastic up to a fixed stress, and the indenter may be still considered as perfectly rigid with a sharp or a worn tip. It may also happen that the indentation process can be likened to that of a physical expansion of an existing cavity in a given solid under the applied contact pressure. There may be many other possible combinations of identities of the idealized indenter and the idealized sample, but for the sake of briefness, we shall deal here with only those three models that are most extensively utilized in the literature [5-7]. These are
1. Elastic indentation model 2. Rigid perfectly plastic model
3. Spherical-cavity expansion model 4. Elastic and perfectly plastic model
The stress-versus-strain behaviors of solids pertinent to these three models are shown in Figures 2.1a-c.
