Incomplete contacts in partial slip subject to varying normal and shear loading, and their representation by asymptotes.pdfVIP

J. Mech. Phys. Solids 99 (2017) 178–191 Contents lists available at ScienceDirect Journal of the Mechanics and Physics of Solids journal homepage: /locate/jmps Incomplete contacts in partial slip subject to varying normal and shear loading, and their representation by asymptotes R.M.N. Fleurya,?, D.A. Hillsa, R. Ramesha, J.R. Barberb a Department of Engineering Science, University of Oxford, Parks Road, OX1 3PJ Oxford, UK b Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109-2125, USA MARK ARTICLE INFO Keywords: incomplete contacts partial slip asymptotic methods ABSTRACT We develop a method for the solution of partial slip contact problems su?ering complex loading cycles where, generally, the normal load, shear force and, potentially, di?erential bulk tensions are all functions of time, using an edge-asymptote approach. The size of the slip zone and local shear traction distribution are revealed as functions of time. The results are then re-worked in asymptotic form, so that they do not hinge on inherent symmetry and anti-symmetry conditions for the contact overall, and are of general applicability. The multipliers on the local solutions (generalised stress intensity factors) are also appropriate as a means of taking laboratory tests quantifying fretting fatigue and employing them to wholly di?erent prototypical problems. 1. Introduction Fretting fatigue, the accelerated nucleation of cracks caused by small amounts of di?erential movement between components pressed together, is conveniently divided into two phases; the nucleation of cracks and their propagation. Here, a rigorous quanti?cation of the edge slip conditions for incomplete (convex) contacts is sought. The results to be derived are applicable to any geometry of contact which is capable of local idealization using half-plane analysis, i.e. to almost any contact which advances as the normal load is increased; it is necessary neither to have a closed form solution for the conta