圆柱和平面之间粘-滑接触分析

Analysis of the Stick-Slipping Contact between a Cylinder and a Plane

当圆柱和平面产生粘-滑接触时，在Hertz理论和Mindlin理论基础上，推导了平面内应力分量的计算公式．分析了平面内应力的分布，描述了应力分布的特点．x轴向应力在接触表面的导向边均为压应力，而在拖动边存在拉应力；最大拉应力和最大压应力均出现在接触表面，其中，最大拉应力存在于拖动边的边缘。而最大压应力存在于导向边．z轴向应力均为压应力，最大压应力出现在接触表面的接触中心邻近区域．第一主应力的最大拉应力出现在接触表面的拖动边边缘，而在导向边均为压应力．第三主应力均为压腹力，最大压应力出现在接触表面的导向边．剪应力、主剪应力和VonMises等效应力（当摩擦系数较小时）的最大值均出现在平面内部．因此，第一型裂纹的产生和扩展首先会发生在拖动边的边缘;而塑性滑动开始首先会出现在接触体内，然后扩展到接触表面．这些将为研究接触变形和接触体的失效提供理论基础．

When a cylinder takes place the stick-slipping contact with a plane, the expressions of the stress component in the plane are derived on the base of the Hertz theory and the Mindlin theory ; the stress distributions are analyzed, thus, their characteristics are presented. The x axial direction stress all is compressive at the leading side of the contact surface and there exists the tensile stress at the dragging side; both the maximal tensile stresses and the maximal compressive stresses all occur at the contacting surface; the former occur at the edge of the dragging side, and the latter exists at the area of leading side. The z axial direction stress all is compressive and its maximal compressive stress occurs at the neighborhood of the contact center. The first principal stress reaches the maximum at the edge of the dragging side in contacting surface, and it is always compressive at the leading side; but, its maximal compressive stress occurs at the neighborhood of the contact center. The third principal stress is always compressive and its maximum appears at the leading side of the contacting surface. The maximums of both the principal shear stress and the Von Mises equivalent stress （when the frictional coefficient is small） all occur inside the plane. Therefore, the mode-I crack generation and propagation may firstly take place at the edge of the dragging side; and the plastically slipping inception may firstly occur inside the contacting body, and then, extend to the contacting surface. Those will supply a theory base for researching both the contacting deformation and the failure of the contacting body.