分形粗糙表面弹塑性接触力学模型

Mechanical model of elastic-plastic contact between fractal rough surfaces

为了建立更为精准的粗糙表面接触模型,基于分形理论提出一种修正的弹塑性接触模型,该模型同时考虑了微凸体的弹性、弹塑性、完全塑性三种变形状态;建立了临界第一弹塑性接触面积、临界第二弹塑性接触面积与临界弹性接触面积之间的关系,分别推导出三种变形阶段的接触载荷与接触面积之间的关系式;结合海洋岛屿面积分布密度函数,获得了接触表面上总接触载荷与真实接触面积之间的表达式。计算结果表明:单个微凸体的临界弹性接触面积不但与材料属性和分形参数有关,也与微凸体的尺寸有关;分形参数一定时,随着接触载荷的增大,真实接触面积也在增大,弹性接触面积与真实接触面积的比值逐渐减小。该模型的建立为进一步研究粗糙表面的摩擦、磨损、润滑提供了理论依据。

To establish a contact mechanical model of rough surface with better accuracy, based on fractal theory, an improved analytical model for elastic-plastic contact of rough surfaces is developed. The problem can be considered in three separated phases:the elastic phase,the mixed elastic-plastic phase, and the fully plastic phase. The relations between the first and the second critical elastic-plastic contact area with the elastic critical contact area are established, respectively. The expressions between the contact load with the contact area in the three regimes are derived. Considering the size distribution function, the fractal model of elastic-plastic contact between rough surfaces is built up. The analytic expression between the total contact load and the real contact area is obtained. Calculation results show elastic critical contact area of single asperity relates not only with the material properties and the fractal parameters, but also with the size of asperity. The bearing capacity of the rough surface is proportional to the fractal dimension and is inversely proportional to the characteristic length scale for constant contact area. This model provides a foundation for researching friction, wear and lubrication of rough surface.