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 loadPversus contact areaArelationship for a cone indentation is linear both for the loading and the unloading paths. The slope of the loading path directly yields the Meyer hardnessHM, and the slope of the unloading path, i.e., the unloading modulusM, is related to the elastic modulusE′ through the relation ofM=E′tanβ/2. The relation of the total contact areaAto the purely elastic and the purely plastic contact areas ofAeandApare theoretically as well as numerically examined. The normalized relationship betweenAp/AversusAp/Aeis equivalent to the Johnson’s hardness plot ofHM/YversusE′tanβ/Y. By extending the concept ofAeandApto time-dependent viscoelastic-plastic regime, a detailed discussion is made how to eliminate the plastic deformation/flow from the total contact areaA(t) to yield the viscoelastic contact areaAve(t) prior to determining the linear-viscoelastic parameters and functions.