双压电体界面上的电偶极子和裂纹

ELECTRIC DIPOLE AND CRACK ON BI-PIEZOELECTRIC MATERIAL

求得了压电体双材料界面上的孤立二维电偶极子的解析解，结果表明某点电偶极子激发的应力－电位移场与该点到电偶极子的距离的平方成反比．研究了压电体双材料界面上的电偶极子对裂纹的作用，得到了问题的闭合解．在电偶极子的作用下，界面裂纹裂尖近区应力－电位移仍具有 ｒ－１／２＋ｉεα的振荡奇异性，文中求得裂尖应力强度因子，当电偶极子距裂尖距离ρ很近时，裂尖应力强度因子与 ρ－３／２－ｉεα成比例．

The analytical solution of an isolated electric dipole located on the interface of piezoelectric bi-material is solved and the solution indicates that the stress and electric displacement of a point are reversely proportional to the square of the distance from that point to the dipole. The interaction between electric dipole and crack on interface of piezoelectric bimaterial is also analyzed and the closed form solution and the stress intensity factor are obtained. The stress-electric-displacement fields have oscillatory singularity with index near crack tips. If the dipole is located very near crack tip, the piezoelectric stress intensity factor is proportional to ρ-3/2-iεα where ρ is the distance between dipole and crack tip, i.e. where m is the dipole moment,  and wα are the eigenvalue and eigenvector of [ -e2 H]w= 0, J4 ={0 0 0 1}T and Ω2 is shown in (29) of the text.