An Analysis of Plastic Deformation in Rolling Contact

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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.