平行于异材界面的三维椭圆平片裂纹分析

ANALYSIS OF AN ELLIPTICAL CRACK PARALLEL TO A BIMATERIAL INTERFACE UNDER TENSION

讨论了拉伸载荷作用下平行于两相材料界面的椭圆平片裂纹问题 .首先 ,使用有限部积分概念和两相材料界面完全接合时的点力基本解导出了一组以裂纹表面位移差为未知函数的超奇异积分方程组 .该组方程表明 ,此时三种裂纹模型同时存在 ;其次 ,在数值求解该组方程的过程中 ,未知函数裂纹表面位移差被近似为位移差的基本密度函数与多项式之积 .基本密度函数反映了裂纹前沿应力奇性性态 ;最后 ,以拉伸载荷为例 ,讨论了椭圆平片裂纹与界面的距离、裂纹形状比和不同材料组合对应力强度因子的影响 ,并以图表形式给出 .

An elliptical crack parallel to a bimaterial interface under tension is analyzed. Firstly, the concept of finite-part and the point-force fundamental solutions for bimaterials with an interface bonded perfectly are used to formulate a system of hypersingular integral equations with displacement differences on crack surfaces as unknown functions. It is shown that three kinds of fracture modes are coupling. Then these equations are solved numerically by approximating the unknown displacement difference to a product of the fundamental density function and polynomials. Finally, the effects of the aspect of crack shape, its distance from the interface and the elastic constants on stress intensity factors for the elliptical crack are discussed and illustrated in the form of tables and figures.