Contact-area-based FEA study on conical indentation problems for elastoplastic and viscoelastic-plastic bodies

The authors discuss the contact-area-based indentation contact mechanics instead of the conventional penetration-depth-based analysis. In time-independent elastoplastic regime, the indentation load P versus contact area A relationship for a cone indentation is linear both for the loading and the unloading paths. The slope of the loading path directly yields the Meyer hardness H-M, and the slope of the unloading path, i.e., the unloading modulus M, is related to the elastic modulus E' through the relation of M = E'tan beta/2. The relation of the total contact area A to the purely elastic and the purely plastic contact areas of A(e) and A(p) are theoretically as well as numerically examined. The normalized relationship between A(p)/A versus A(p)/A(e) is equivalent to the Johnson's hardness plot of H-M/Y versus E'tan beta/Y. By extending the concept of A(e) and A(p) to time-dependent viscoelastic-plastic regime, a detailed discussion is made how to eliminate the plastic deformation/flow from the total contact area A(t) to yield the viscoelastic contact area A(ve)(t) prior to determining the linear-viscoelastic parameters and functions.