Frictional elastic contact with periodic loading

Abstract

a b s t r a c tQuasi-static frictional contact problems for bodies of fairly general profile that can be represented as half planes can be solved using an extension of the methods of Ciavarella and Jäger. Here we consider the tangential traction distributions developed when such systems are subjected to loading that varies periodically in time. It is shown that the system reaches a steady state after the first loading cycle. In this state, part of the contact area (the permanent stick zone) experiences no further slip, whereas other points may experience periods of stick, slip and/or separation. We demonstrate that the extent of the permanent stick zone depends only on the periodic loading cycle and is independent of the initial conditions or of any initial transient loading phase. The exact traction distribution in this zone does depend on these factors, but the resultant of these tractions at any instant in the cycle does not. The tractions and slip velocities at all points outside the permanent stick zone are also independent of initial conditions, confirming an earlier conjecture that the frictional energy dissipation per cycle in such systems depends only on the periodic loading cycle. We also show that these parameters remain unchanged if the loading cycle is changed by a time-independent tangential force, provided this is not so large as to precipitate a period of gross slip (sliding).

Frictional systems subjected to oscillating loads

“…Combining these results, we were able to conclude that [4] (1) No slip occurs anywhere in the contact area between B and C in Fig. 13, where the conditions (6) are satisfied.…”

“…These hyperplanes advance and recede as the load varies periodically, but retain the same slope (which is determined by A; B and f. During periods of slip, one or more of the advancing hyperplanes 'push' the point P around the space. For the assumption of complete contact to be satisfied, it is necessary that at all times there exist at least one point that is not excluded by the constraint set (4). If this condition is violated, it is easy to show that the full system will involve one or more nodes in separation.…”

Limiting shape of profile due to dual-mode fretting wear in contact with an elastomer

“…18 This singularity will lead to the appearance of a circular slip zone at the border of the contact area [19][20][21] which leads to wear in this zone 15 while the inner parts of the contact remaining in the state of permanent stick. Note that the existence of the area of permanent stick was shown by Barber et al 22 for arbitrary two-dimensional topographies (with not necessarily connected contact area) under very general assumptions and for three-dimensional topographies under usual assumptions of the Cattaneo-Mindlin theory. In the present paper, we consider only axis-symmetrical profiles; however, the 1 Technische Universität Berlin, Berlin, Germany results of the paper 22 provide a principle possibility of generalization to arbitrary profiles.…”

Numerical simulation of the heat generation process at vibrating contact defects

“…In the case of a periodic normal and tangential loading, a constant hysteretic loop is run through each cycle. It has been shown that the amount of dissipated energy during such a periodic loading corresponds to the area of the hysteretic curve [6]. This property can be used to calculate the energy released by friction during each periodic loading cycle [7].…”