Repeated Loading, Residual Stresses, Shakedown, and Tribology
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Repeated loading, residual stresses, shakedown, and tribology J. A. Williams Engineering Department, Cambridge University, Trumpington Street, Cambridge, CB2 1PZ, United Kingdom
I. N. Dyson and A. Kapoor Mechanical Engineering Department, Sheffield University, Sheffield S1 3JD, United Kingdom (Received 23 March 1998; accepted 3 September 1998)
Protective residual stresses may be developed in the near surface layers of tribological contacts which enable loads sufficiently large to cause initial plastic deformation to be accommodated purely elastically in the longer term. This is the process of shakedown and, although the underlying principles can be demonstrated by reference to relatively simple stress systems, the situation is complex under a moving Hertzian pressure distribution. Bounding theorems can be used to generate appropriate load or shakedown limits not only for uniform half-spaces but also those with plastic and/or elastic properties which vary with depth. In this way, shakedown maps, which delineate the boundaries between potentially safe and unsafe operating conditions, can be generated for both hardened and coated surfaces.
I. INTRODUCTION
When two engineering surfaces are loaded together there will always be some distortion of each of them. These deformations may be purely elastic or may involve some additional plastic, and so permanent, changes in shape. In the case of nonconformal contacts, whether on the macro- (i.e., component) or micro- (i.e., asperity) scale, it is conventional to model the stress situation as one of Hertzian conditions which is equivalent to supposing that, over the extent of the contact patch, the distribution of pressure between the two surfaces is semielliptical. It also means, at least in material that is initially free of stress and in contacts involving traction or friction coefficients less than about 0.3, that the most heavily loaded element of material, and thus the location of first yield, is not actually at the surface but a little way below it, as illustrated in Fig. 1. This region of first plasticity is thus completely surrounded by material that remains elastic; in consequence, the initiation of yield will not be immediately apparent to the superficial observer as the scale of the plastic strain must be of the same order as the elastic limit of the material which, in metals, is only a fraction of a percent. An additional complication is the fact that the manufacturing process which generated the surface itself (machining, grinding, etc.) leaves its imprint not only in the shape or topography of the surface but also in the pattern of residual stresses in the material at, and near, the surface. While these stresses play a role in influencing the loading conditions that lead to first yield, under conditions of repeated loading, the steady-state situation is predominantly dependent on the stress field generated by the subsequent imposed loads. 1548
http://journals.cambridge.org
J. Mater. Res., Vol. 14, No. 4, Apr 1999
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