尺度相关的分形粗糙表面弹塑性接触力学模型

The Elastic-Plastic Contact Mechanics Model Related Scale of Rough Surface

依据分形理论,研究了粗糙表面间的真实接触状况,建立了粗糙表面间的分形接触模型。考虑微凸体的等级,确定了弹性临界等级、第一弹塑性临界等级和第二弹塑性临界等级的表达式,研究了粗糙表面中单个微凸体的弹性、弹塑性及完全塑性变形的存在条件,推导出各个等级微凸体的临界接触面积的解析式。在此基础上应用微凸体的面积分布密度函数,获得了接触表面上接触载荷与真实接触面积之间的关系。计算结果表明:单个微凸体的临界接触面积是和微凸体的尺度相关,随着微凸体等级的增大而减小;微凸体的变形顺序为弹性变形、弹塑性变形和完全塑性变形,与传统的接触模型一致;在整个粗糙表面接触过程中,粗糙表面变形过程与单个微凸体的变形过程一致;最大微凸体所处的等级范围不同,粗糙表面所表现的力学性能也不相同。

The real contact state between the rough surfaces is studied with fractal theory,a fractal contact mechanics model for rough surfaces is proposed also. Considering the asperity level,the expressions among elastic critical level,the first elastic-plastic critical level and the second elastic-plastic critical level are obtained. The conditions existence of elastic deformation,elastic-plastic deformation and fully plastic deformation of each level asperity are researched on the rough surface,the expressions among the critical contact area in the three regimes are derived respectively. Considering the asperity size distribution function,the analytic expression between the total contact load with the real contact area is obtained. Calculation results show that the critical contact areas of a single asperity are related to its scale,and its reduce while the level of asperity increases. As the load and contact area increase a transition from elastic,elastic-plastic to fully plastic contact model takes place in this order and agreed with classical contact mechanics. During the whole rough surfaces contact,the deformation process of the rough surfaces is consistent with a single asperity. The largest asperity is in different critical levels,mechanical properties of the rough surface are not the same.