一致偶应力理论下粗糙表面的接触

Contact of Rough Surfaces under the Theory of Consistent Couple Stress

摘要: 随着现代科技的发展，材料结构在纳米尺度下的力学性能受到研究者的广泛关注。当接触尺寸由宏观缩小到纳米时，尺度效应对接触力学行为的影响将变得非常重要。本文通过理论分析的方法，研究了一致偶应力弹性理论下粗糙表面的接触问题。首先利用数值结果得到了考虑一致偶应力的单个纳米级粗糙度的接触面积和载荷随压痕深度变化的一般关系，然后基于G-W的接触模型提出了一种考虑一致偶应力的粗糙表面接触模型。揭示了一致偶应力和球形粗糙度对粗糙表面的接触载荷、实际接触面积和平均接触压力的影响。结果表明，与间距恒定的经典弹性G-W模型相比，该模型具有更大的法向载荷和更小的实际接触面积。此外，粗糙表面之间的接触载荷随着一致偶应力的增加而增加，但实际接触面积减小；当一致偶应力恒定时，球形粗糙度越大，接触载荷和实际接触面积就越大。

Abstract: With the development of modern technology, the mechanical properties of material structures at the nanoscale have attracted widespread attention from researchers. When the contact size is reduced from the macroscopic scale to the nanoscale, the scale effect on contact mechanics behavior becomes highly significant. This paper investigates the contact problem of rough surfaces under the consistent couple stress elasticity theory through theoretical analysis. First, numerical results are used to establish a general relationship between the contact area and load of a single nanoscale roughness element considering consistent couple stress, as they vary with indentation depth. Then, based on the Greenwood-Williamson contact model, a rough surface contact model incorporating consistent couple stress is proposed. The study reveals the effects of consistent couple stress and spherical roughness on the contact load, real contact area, and average contact pressure of rough surfaces. The results show that, compared to the classical elastic G-W model with constant spacing, the proposed model predicts a larger normal load and a smaller real contact area. Furthermore, the contact load between rough surfaces increases with increasing consistent couple stress, while the real contact area decreases; when consistent couple stress is held constant, larger spherical roughness leads to greater contact load and real contact area.