Energy-based method for the assessment of the cumulative slip increment in frictional contacts subjected to cyclic loadings

Abstract

The cumulative slip phenomenon is often observed as a limit state in mechanical assemblies involving interference or press-fits and subjected to cyclic thermomechanical loadings. In engineering structural applications, it may prove very difficult to annihilate completely the occurrence of this phenomenon by targeting a slip-shakedown limit state, due to design and other mechanical constraints. Consequently, the cumulated relative slip magnitude on the contact interface, after a given of applied cycles, should be anticipated to prevent any unexpected contact with other mechanical components that may result in seizure or affect the normal structural behaviour of the assembly. In this paper, a novel theoretical approach is proposed to derive the cumulative relative slip increment from the frictional dissipated energy per cycle. In particular, two independent methods – one based on the rigid body slip property and the other using the unified energy-based approach from fatigue crack growth theory – are considered here to determine the same expression of the expected quantity. The obtained formula is evaluated through various analytical examples with a special focus on bushing migration in interference-fit assemblies. It is shown, in each case, to be in perfect agreement with the incremental displacement calculation of the cumulative slip increment when the cumulative slip phenomenon occurs.