The influence of repeated loading, residual stresses and shakedown on the behaviour of tribological contacts

Most tribological pairs carry their service load not just once but for a very large number of repeated cycles. During the early stages of this life, protective residual stresses may be developed in the near surface layers which enable loads which are of sufficient magnitude to cause initial plastic deformation to be accommodated purely elastically in the longer term. This is an example of the phenomenon of 'shakedown' and when its effects are incorporated into the design and operation schedule of machine components this process can lead to significant increases in specific loading duties or improvements in material utilization. Although the underlying principles can be demonstrated by reference to relatively simple stress systems, when a moving Hertzian pressure distribution in considered, which is the form of loading applicable to many contact problems, the situation is more complex. In the absence of exact solutions, bounding theorems, adopted from the theory of plasticity, can be used to generate appropriate load or shakedown limits so that shakedown maps can be drawn which delineate the boundaries between potentially safe and unsafe operating conditions. When the operating point of the contact lies outside the shakedown limit there will be an increment of plastic strain with each application of the load - these can accumulate leading eventually to either component failure or the loss of material by wear. © 2005 Elsevier Ltd. All rights reserved.

The impact of sand slugs against beams and plates: Coupled discrete particle/finite element simulations

The impact of a slug of dry sand particles against a metallic sandwich beam or circular sandwich plate is analysed in order to aid the design of sandwich panels for shock mitigation. The sand particles interact via a combined linear-spring-and-dashpot law whereas the face sheets and compressible core of the sandwich beam and plate are treated as rate-sensitive, elastic-plastic solids. The majority of the calculations are performed in two dimensions and entail the transverse impact of end-clamped monolithic and sandwich beams, with plane strain conditions imposed. The sand slug is of rectangular shape and comprises a random loose packing of identical, circular cylindrical particles. These calculations reveal that loading due to the sand is primarily inertial in nature with negligible fluid-structure interaction: the momentum transmitted to the beam is approximately equal to that of the incoming sand slug. For a slug of given incoming momentum, the dynamic deflection of the beam increases with decreasing duration of sand-loading until the impulsive limit is attained. Sandwich beams with thick, strong cores significantly outperform monolithic beams of equal areal mass. This performance enhancement is traced to the "sandwich effect" whereby the sandwich beams have a higher bending strength than that of the monolithic beams. Three-dimensional (3D) calculations are also performed such that the sand slug has the shape of a circular cylindrical column of finite height, and contains spherical sand particles. The 3D slug impacts a circular monolithic plate or sandwich plate and we show that sandwich plates with thick strong cores again outperform monolithic plates of equal areal mass. Finally, we demonstrate that impact by sand particles is equivalent to impact by a crushable foam projectile. The calculations on the equivalent projectile are significantly less intensive computationally, yet give predictions to within 5% of the full discrete particle calculations for the monolithic and sandwich beams and plates. These foam projectile calculations suggest that metallic foam projectiles can be used to simulate the loading by sand particles within a laboratory setting. © 2013 Elsevier Ltd.