Surface effect in nano-scale fretting contact problems

The fretting contact behavior of nanomaterials is significantly influenced by surface effect. A model of fretting contact between a nano-sized rigid cylindrical indenter and an elastic half-plane is established based on Gurtin-Murdoch (G-M) surface elasticity theory, with which the surface effects on the stress and displacement distributions and the size of stick region in the contact zone are studied. It is found that the surface effect induces an additional traction besides the external force applied by punch, which leads to smoother stress and displacement distributions. The normal surface-induced traction related to the residual surface stress is opposite to the externally applied compression, which results in a material stiffening in the contact zone so that the contact radius, normal displacement and normal stress decrease compared with classical predictions. The tangential surface-induced traction is opposite to the externally applied frictional stress, leading to reductions of the shear stress and tangential displacement in the contact zone. Furthermore, the surface effect leads to three possible states in the contact zone, including complete slip, partial slip and complete stick, instead of the solely partial slip state in classical fretting contact models. Among them, the complete stick is more beneficial for inhibiting the wear of contact devices, which can be realized by reducing the indenter size. The present research does not only help ones to better understand the physical mechanism in nano-scale fretting contact problems, but should also guide the anti-wear design in nano-electro-mechanical (NEMs) systems.