圆片裂纹的应力强度因子

Solution for Stress Intensity Factors in the Penny Shaped Crack Problem

圆片裂纹问题是三维无限弹性体内嵌裂纹的一个经典问题，也是一个重要的理论工作－从Ｆａｂｒｉｋａｎｔ 方程出发，建立了一种特殊的极坐标体系，首先解决了法向载荷下圆片裂纹上特殊点的应力强度因子，并通过坐标系的旋转解决了圆片裂纹上任意点的应力强度因子－ 对于裂纹上作用切向载荷的情况，先单独研究载荷分别沿坐标轴方向的两种情形，然后就一般情形下通过坐标旋转并将载荷沿坐标轴分解后分别求解，再叠加得其应力强度因子－ 从而解决了圆片裂纹上作用幂级数载荷下的三类应力强度因子－ 研究表明，如果圆片裂纹上的载荷是幂级数形式。

The penny shaped crack problem is one of the most important problems in solving the embedded crack problem in three dimensional elasticity.By using Fabrikant's equation ,it has been approached that the stress intensity factors for the penny shaped crack problem can be evaluated in a closed form provided the applied boundary traction takes the power form.The stress intensity factors have been obtained for the particular point in the axle of normal boundary traction case first,then for the general point after rotating the coordinate system.For the shear boundary case ,the problem with the traction along the axle has been studied first,then the preblem with the general traction by resolving the traction and composing the results.The key point is to establish a particular polar coordinate system for the important integral.