Mechanics of advancing pin-loaded contacts with friction

Abstract

This paper considers finite friction contact problems involving an elastic pin and an infinite elastic plate with a circular hole. Using a suitable class of Green's functions, the singular integral equations governing a very general class of conforming contact problems are formulated. In particular, remote plate stresses, pin loads, moments and distributed loading of the pin by conservative body forces are considered. Numerical solutions are presented for different partial slip load cases. In monotonic loading, the dependence of the tractions on the coefficient of friction is strongest when the contact is highly conforming. For less conforming contacts, the tractions are insensitive to an increase in the value of the friction coefficient above a certain threshold. The contact size and peak pressure in monotonic loading are only weakly dependent on the pin load distribution, with center loads leading to slightly higher peak pressure and lower peak shear than distributed loads. In contrast to half-plane cylinder fretting contacts, fretting behavior is quite different depending on whether or not the pin is allowed to rotate freely. If pin rotation is disallowed, the fretting tractions resemble half-plane fretting tractions in the weakly conforming regime but the contact resists sliding in the strongly conforming regime. If pin rotation is allowed, the shear traction behavior resembles planar rolling contacts in that one slip zone is dominant and the peak shear occurs at its edge. In this case, the effects of material dissimilarity in the strongly conforming regime are only secondary and the contact never goes into sliding. Fretting tractions in the forward and reversed load states show shape asymmetry, which persists with continued load cycling. Finally, the governing integro-differential equation for full sliding is derived; in the limiting case of no friction, the same equation governs contacts with center loading and uniform body force loading, resulting in identical pressures when their resultants are equal.