Hertz contact at finite friction and arbitrary profiles

On indenter boundary effects at elastic contact

“…However, it was shown in [Storåkers and Elaguine 2005] for the case of monotonically increasing loading that history dependence is only fictitious and that the stick-slip contour relative to the external contact contour will be invariant for any contact profile provided that it is smooth and convex and the loading is axisymmetric and monotonically increasing. In the same paper a consistent and robust method was described to solve frictional normal contact problems at smooth and convex but otherwise arbitrary profiles with special emphasis put on the presence of finite friction causing partial slip between dissimilar solids.…”

“…Storåkers and Elaguine [2005] analyzed the present problem, depicted in Figure 1, and the corresponding one for a cone indenter with a rounded tip. In this investigation a reduced incremental problem was laid down based on a flat stationary boundary and modeled by finite elements.…”

“…It has been shown, however, by Mossakovskii [1963] and Spence [1975b], that a half-space solution will still suffice to determine surface values. As explained in [Storåkers and Elaguine 2005], following [Spence 1975b], the stress state in the contact region between two elastic bodies is equivalent to that arising from contact between a rigid indenter and an elastic half-space with material parameters modified according to the relations:…”

“…Thus, the resulting contact tractions may be directly determined by aid of a half-space solution procedure described in [Storåkers and Elaguine 2005]. As a result, two uncoupled problems pertinent to dissimilar half-spaces with prescribed normal and tangential stress distributions are obtained and the complete internal stress fields may be subsequently generated by two harmonic potentials as explained in detail in e.g.…”

“…In this context substantial progress was made by Spence [1975a;1975b], who showed that under monotonic loading a single stickslip contour will evolve being independent of the contact profile provided it has a polynomial shape. More recently (see [Ciavarella and Hills 1999;Ciavarella 1999;Argatov 2002;Jaffar 2002;Storåkers and Elaguine 2005]], contact of various nonstandard profiles such as blunted cones and flat indenters with rounded edges, has been investigated. Besides a more general contact law behavior, the main intention has been to predict initiation of plastic flow or the occurrence of brittle fracture (also the contact behavior at nanoindentation is an interesting feature in this context; see [Fu 2006;Fu and Cao 2009]).…”