Partial slip incomplete contacts under constant normal load and subject to periodic loading

• Asymptotic approach for solving incomplete partial slip contact problems is investigated.
• The stick slip behaviour during the steady state cyclic loading is presented.
• The quantification of the range of the singular shear asymptote is obtained for different combinations of periodic loading and phase angles.
• An extensive analysis on the limitations of asymptotic methods and the quality of the approximations is presented.

We present a general formulation for the stick slip behaviour of incomplete contact under oscillating loading, but with a constant normal load. An asymptotic description of the contact traction very close to the contact edges is used. The slip zones present in the steady state with cyclically varying bulk tension and shear force (with an arbitrary phase shift) are found. The range of the variation of the state of stress near both of the contact edges and the respective slip zone sizes are defined in terms of the loading parameters, including the phase angle. The quality of the approximations used by the asymptotic approach and the range of applicability of the method is also analysed in detail in this paper.