目的 用理论方法来求解复杂工况下的次表面裂纹问题，并分析裂纹尖端的力学行为。方法 利用叠加原理将主问题分成两个子问题，基于弹性力学集中力的Flamant解求解子问题一，基于分布位错技术求解子问题二。进一步建立关于位错密度的积分方程，利用Gauss-Chebyshev数值求积法求解此奇异积分方程，得到相关的力学参量。结果 得到了裂纹尖端的应力强度因子和靠近上表面裂纹尖端附近产生局部粘着的临界摩擦系数，并分析了裂纹长度、裂纹埋入深度对裂尖应力强度因子及临界摩擦系数的影响。在裂纹埋入深度一定时，两个裂尖的应力强度因子都随裂纹变长而先增加后减小。靠近表面的裂尖更容易发生粘着，裂纹长度越短，裂纹埋入深度越小，越容易粘着。临界摩擦系数随着裂纹长度的增加而缓慢增加，随裂纹埋入深度的增加，近似呈线性增加。结论 在赫兹压力作用下，当裂纹长度较短时，裂纹更容易往内部扩展；而当裂纹较长时，裂纹更容易往表面扩展。

The work aims to solve the subsurface crack by theoretical solution and analyze the mechanical behaviors of crack tips. The problem was divided into two sub-problems based on the superposition principle. The first sub-problem was solved by Flamant’s solution of the concentrated force in the elastic mechanics and the second sub-problem was solved by the distributed dislocation technique. Further, the singular integral equations about dislocation density were established. The numerical solution of the equations was presented by Gauss-Chebyshev quadrature method and the relevant mechanical parameters were obtained. The stress intensity factor at crack tips (SIF) and the critical friction coefficient (CFC) for the upper surface crack tip adhesion were obtained, and the effects of crack length and crack embedding depth were investigated. From the results, SIF first increased and then decreased with the crack length increasing when the depth of the crack was constant. The crack tip close to the surface was easier to adhere. The smaller the crack length and depth are, the more likely the crack plane is to adhere. CFC increased slowly as the crack length increased. There was an approximate positive relationship between CFC and the crack depth. Under the Hertz pressure, the crack propagates to the material interior when the crack length is relatively small, while the crack propagates toward the surface when the crack length is relatively large.