轴对称环形片状界面裂纹问题分析

ANALYSIS OF AXIAL-SYMMETRIC RING-SHAPED INTERFACE CRACK PROBLEMS

讨论受拉伸载荷作用的轴对称环形片状界面裂纹问题.该问题归结为求解一组超奇异积分-微分方程.方程中的未知位移间断近似表示为基本密度函数与多项式之积,其中基本密度函数考虑到问题的对称性用二维界面裂纹精确解表示.在圆形片状裂纹的情况下,数值结果与现有理论解作比较的结果表明,数值结果与相应界面圆形片状裂纹和均质体圆形片状裂纹的精确解均吻合得很好.文中以图表形式给出应力强度因子与材料组合和几何条件之间的关系.

The axial-symmetric ring-shaped interface crack problems are discussed under tension loading. The problems are reduced to the solutions of a set of hypersingular integro-differential equations. Unknown displacement jumps in the equations are approximated with the products of the fundamental density tunctions and polynomials, in which the fundamental density functions are expressed with exact solutions of the two-dimensional interface cracks due to axial-symmetries of the problems herein. Comparisons of the present numerical results with the available exact solutions state that the present method gives rapidly converging and accurate numerical solutions for pennyshaped interfacial crack problems in bimaterials as well as ordinary crack problems in homogeneous materials. The stress intensity factors of a ring-shaped interface crack subjected to tension loading are shown in tables and graphics with variations of material combinations and crack dimensions.