Analysis and Detection of the Pit Formation under Rolling/Sliding Contact Loading

研究了滚动/滑动接触应力场作用下的表面裂纹问题。为了从断裂力学的角度探讨表面裂纹的扩展，准确地分析了表面裂纹的应力强度因子，准确地检测了内部裂纹的形状。可以得出如下结论。（1）讨论了三维表面裂纹分析中基于体积力法的奇异积分方程的数值解法。为了获得精确的数值结果，满足边界条件的体积力密度未知函数用基本密度函数与多项式的乘积近似。在这里，基本密度函数被选择来精确地表达由于无限体中的嵌入椭圆裂纹引起的应力场。结果表明，该方法能很好地满足边界条件，并给出了沿着裂纹前缘的精确应力强度因子。（2）在确定了裂纹位置和表面长度的情况下，利用裂纹附近的应变测量数据，确定了半无限体中倾斜表面裂纹的内部形状。未知参数，表面裂纹的深度和倾角，确定通过最小的条件之间的残差平方和的测量和计算的一个假设的裂纹的应变分布。由于施加在裂纹体的自由表面上的垂直力的应变被用作主要信息。数值实验表明，通过可切换地选择两个应变测量点，可以很好地确定裂纹形状。

This study dealt with a problem of surface crack under rolling/sliding contact stress field. In order to discuss the surface crack propagation on the basis of fracture mechanics, stress intensity factors of the surface crack were analyzed exactly and the internal crack shape was detected accurately. The conclusions can be made as follows.(1)The numerical solution of singular integral equations on the basis of the body force method was discussed in the analysis of 3-D surface crack. To obtain the numerical result accurately, the unknown functions of the body force densities which satisfy the boundary conditions were approximated by the products of the fundamental density function and polynomials. Here, the fundamental density function was chosen to express exactly the stress field due to an embedded elliptical crack in an infinite- body. The boundary condition was found to be highly satisfied and very accurate stress intensity factors along the crack front were given by the present method.(2)The Internal shape of an inclined surface crack in a semi-infinte body was detected from data of strains mesured around a region of the crack when the location and the surface length of the crack were already identified. The unknown parameters, the depth and the inclination angle of the surface crack, were determined through the condition which minimizes the squre sum of residuals between measured strain distributions and computed ones for an assumed crack. The strains due to the vertical force applied on the free surface of the cracked body were used as the primary information. The numerical experiment showed that the crack shape was determined with good accuracy from switably chosen two measuring points of the strain.