An Analysis of Plastic Deformation in Rolling Contact

Abstract

When two metal cylinders roll together under a contact pressure sufficient to cause yielding, a surprising mode of plastic deformation occurs. The surface of each cylinder is progressively displaced in the forward direction of rotation relative to the core by plastic shearing in a thin subsurface layer. This phenomenon was first observed by Crook (6) in 1957 and the results of a more complete experimental investigation are reported by Hamilton (9) in an accompanying paper. In this paper an attempt is made to explain the mechanism of ‘forward flow’ by an approximate numerical analysis of the elastic-plastic stress cycles to which the material is subject in repeated rolling contact. On the basis of an idealized material which is elasticperfectly plastic and isotropic, it is shown that a forward displacement of the surface would be expected as a result of the complex cycle of stress and strain encountered in rolling. It is also shown that residual compressive stresses are introduced into the immediately subsurface layers during the first few cycles of the load. If the load does not exceed the elastic limiting load by more than 66 per cent further plastic deformation would then cease. At higher loads a steady pattern of plastic deformation is predicted which in its principal features is consistent with the observed behaviour.

A note on Merwin’s measurements of forward flow in rolling contact

“…Peak pressures of the order of 1 GPa or higher are currently encountered, so that not only the elastic limit is passed, but actually also the elastic shakedown and plastic shakedown. Classical experiments on twin-disk rigs such as Crook [1], Merwin [2] (see also [6]), and Hamilton [7], typically used "soft" materials such as copper. This choice was probably suggested to amplify (and therefore make more easily measurements) plastic deformations, but at the same time copper has a quite marked cyclic hardening behaviour and the mechanism of ratchetting in this material is very different from that of rail steel, ultimately more important for railway industry.…”

Review of Fatigue of Coatings/Substrates

“…Examining the nature of the damage during cyclic contact displacement, Madlin [22][23] has shown that under contact pressure, the shear stress required to overcome the static frictional resistance will have a maximum at the center of the circular contact area. While Madlin's analysis assumes elastic conditions, the three-dimensional nature of the problem and local plasticity effects have been considered recently using numerical techniques [24][25][26][27][28]. There are three conditions -stick, partial slip and general slip [29][30][31][32].…”

Integrated approach to advanced machining

“…The approach is to first determine the elastic stresses in the half space, use these as the initial conditions for determining the plastic stresses, then elastically unload the material to determine the residual stress state. This procedure was first used by Menvin and Johnson [9] to analyze stresses induced by rolling contacts and is provided in flow chart form by Suh [lo].…”