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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.1548

The effect of varying both the aspect ratio and the coefficient of friction of contacts with elliptical geometry on their elastic shakedown performance has been examined theoretically for surfaces with two types of subsurface hardness or strength profiles. In stepwise hardening the hard layer is of uniform strength while in linear hardening its strength reduces from a maximum at the surface to that of the core at the base of the hardened layer. The shakedown load is expressed as the ratio of the maximum Hertzian pressure to the strength of the core material. As the depth of hardening, expressed as a multiple of the elliptical semi-axis, is increased so the potential shakedown load increases from a level that is appropriate to a uniform half-space of unhardened material to a value reflecting the hardness of the surface and near-surface material. In a step-hardened material, the shakedown limit for a surface`pummelled' by the passage of a sequence of such loads reaches a cut-off or plateau value, which cannot be exceeded by further increases in hardening depth irrespective of the value of the friction coefficient. For a linearhardened material the corresponding plateau is approached asymptotically. The work confirms earlier results on the upper bounds on shakedown of both point and line contacts and provides numerical values of shakedown loads for intermediate geometries. In general, the case depth required to achieve a given shakedown limit reduces in moving from a transversely moving nominal line load to an axisymmetric point load.

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Background: The iliofemoropopliteal artery significantly changes path length during normal hip and knee flexion. Prosthetic bypass grafts, such as polytetrafluoroethylene (PTFE) grafts, are relatively stiff and thus can subject graft anastomoses to high tension when the path length increases. The aim of this study was to examine the influence of length redundancy and twist on the biomechanical properties of PTFE bypass grafts. Methods: Unreinforced and ring-reinforced PTFE grafts were loaded in an axial mechanical testing machine to measure the tensile and compressive axial forces with varying levels of length redundancy and axial twist. Results: Adding 5-15% length redundancy to a graft decreases the force to cause 5% extension by > 90% without substantially increasing shortening forces. Adding 4.5 /cm of axial twist imparts a corkscrew shape to the graft without increasing extension or shortening forces in the presence of length redundancy. Ring-reinforced PTFE grafts require more length redundancy to experience these reductions in forces especially in the presence of axial twist. Conclusions: A modest amount of length redundancy and twist (i.e., a corkscrew condition) confers improved biomechanical properties in a PTFE graft, especially in ring-reinforced grafts. This should be taken into consideration when fashioning an arterial bypass graft in the iliofemoropopliteal segment.