Tangential loading of general three-dimensional contacts

A general three-dimensional contact between elastically similar half-spaces , is considered. With a fixed normal load, we consider a pure relative tang ential translation between the two bodies. We show that, for the case of ne gligible Poisson's ratio, an exact solution is given by a single component of shearing traction, in the direction of loading It is well known that, fo r full sliding conditions, the tangential force must be applied through the center of the pressure distribution. Instead, for a full stick case the ta ngential force must be applied through the center of the pressure distribut ion under a rigid flat indenter whose planform is the contact area of the p roblem under consideration Finally, for finite friction a partial slip regi me has to be introduced. It is shown that this problem corresponds to a dif ference between the actual normal contact problem, and a corrective problem corresponding to a low-er load, but with same rotation of the actual norma l indentation. Therefore for a pure translation to occur in the partial sli p regime, the point of application of the tangential load must follow the c enter of the "difference" pressure. The latter also provides a complete sol ution of the partial slip problem. In particular, the general solution in q uadrature is given for the axisymmetric case, where it is also possible to take into account of the effect of Poisson's ratio, as shown in the Appendi x.