A loading–unloading elastic–plastic model of contact between three dimensional fractal rough surfaces has been presented in this paper. During loading process, the mechanical properties of a single asperity follow Hertzian theory. During unloading process, the load-area relationships of a single asperity are obtained by EK model. The truncation size distribution functions for different levels of asperities are deduced. And total true contact area and total contact load are obtained during a loading–unloading process. The results show as the rough surface is in elastic deformation, the load-area relationships during loading and unloading process are identical. As the rough surface is in inelastic deformation, the total true contact area during unloading process is greater than that during loading process. An experiment is designed to verify the validity of the present model.

本文提出了三维分形粗糙表面之间接触的装卸弹塑性模型。在加载过程中，单个粗糙体的机械性能遵循赫兹理论。在卸载过程中，通过EK模型获得了单个粗糙物的载荷-面积关系。推导了不同粗糙程度的截断大小分布函数。在装卸过程中，将获得总真实接触面积和总接触载荷。结果表明，由于粗糙表面处于弹性变形状态，装卸过程中的荷载-面积关系相同。由于粗糙表面处于非弹性变形状态，因此卸载过程中的总真实接触面积要大于加载过程中的总真实接触面积。