裂纹与一类线型扁平夹杂相互干涉的应力强度因子

STRESS INTENSITY FACTORS FOR THE INTERACTION BETWEEN A CRACK AND A FLAT INCLUSION

本文应用奇异积分方程法研究裂纹与一类线型扁平夹杂相互干涉的弹性力学平面问题。将裂纹与夹杂非相交情况推广到在端点以任意角度相交情况。一对位错和一对集中力的格林函数分别被用以形成裂纹和夹杂。通过对所得奇异积分方程组的奇异性分析,确定了裂纹与夹杂在端点以任意角度相交时端点和交点处的应力奇异性指数。最后导出了裂纹与夹杂尖端应力强度因子的计算公式并进行了一些数值计算。结果表明本文的方法对于处理类似的奇异性问题是非常有效的。

In studying the fracture of multi-phase materials and the structures composed of bonded dissimilar solids, special attention must be paid to the two classes of imperfections: one is the geometric discontinuities which may be idealized as cracks, and the other the material inhomogeneities which may be idealized as inclusions. In both cases the tips or ends of the defects are points of stress singularity and, consequently, sources of potential crack initiation and propagation. On this account, the problem of an elastic plane containing a crack and an arbitrarily oriented flat inclusion is considered in this paper. In the formulation of the problem, the Green's functions for a pair of dislocations and a pair of concentrated body forces are utilized to generate the crack and the inclusion respectively. By using the integral equations technique, the stress singularity powers at the tip or end and the intersection point of the crack and the inclusion are defined. Based on this, the formulas of calculating the stress intensity factors at the crack tip and the inclusion end are obtained.