双材料界面裂纹复应力强度因子的正则化边界元法

双材料界面裂纹渐近位移和应力场表现出剧烈的振荡特性, 许多用于表征经典平方根($r^{1/2})$和负平方根($r^{-1/2})$渐近物理场的传统数值方法失效, 给界面裂纹复应力强度因子($K_{1} +{i}K_{2} )$的精确求解增加了难度. 引入一种含有复振荡因子的新型"特殊裂尖单元", 可精确表征裂纹尖端渐近位移和应力场的振荡特性, 在避免裂尖区域高密度网格剖分的情况下, 可实现双材料界面裂纹复应力强度因子的精确求解. 此外, 结合边界元法中计算近奇异积分的正则化算法, 成功求解了大尺寸比(超薄)双材料界面裂纹的断裂力学参数. 数值算例表明, 所提算法稳定, 效率高, 在不增加计算量的前提下, 显著提高了裂尖近场力学参量和断裂力学参数的求解精度和数值稳定性. 

BOUNDARY ELEMENT ANALYSIS OF COMPLEX STRESS INTENSITY FACTORS OF BIMATERIAL INTERFACE CRACKS

The asymptotic crack-tip field for bimaterial interface cracks exhibits an oscillatory behavior which is quite different from that for cracks in homogeneous materials. Modeling such interface cracks by the conventional solution procedures designed for homogeneous materials is inadequate, and may not lead to accurate solutions. This paper introduces a new set of novel special crack-tip elements for analysis of interface cracks in linear elastic bimaterials by using the boundary element method (BEM). The method can properly describe the oscillatory displacement and stress fields in the vicinity of the interfacial crack-tip. Furthermore, the troublesome nearly-singular integrals, which are crucial in the application of the BEM for ultra-thin structural problems, are calculated accurately by using a nonlinear coordinate transformation. Accurate and reliable BEM results with only a small number of boundary elements can be obtained for interface crack analysis of ultra-thin composite bimaterials.