压电材料中的Bueckner功共轭积分及和J积分M积分的关系

研究横观各向同性压电材料中裂纹问题,提出了Bueckner功共轭积分在这类材料中的表达式：并通过引出两类辅助的应力-位移-电位移-电势场,证明功共轭积分和这类材料中的J积分和M积分仍然存在简单的两倍关系由此,各类在脆性材料断裂问题中已广泛应用的权函数方法可顺理成章地推广到压电材料的研究中来．这对独立地确定电位移强度因子和经典的I、II型应力强度因子提供了有力的数学上的工具．进而通过计算机械应变能释放率对压电材料中裂纹的稳定做出判断．

ON THE BUECKNER WORK CONJUGATE INTEGRAL AND ITS RELATIONS TO THE J-INTEGRAL AND M-INTEGRAL IN PIEZOELECTRIC MATERIALS

This paper deals with crack problems in transversely isotropic piezoelectric material. The formulations of Bueckner work conjugate integrals in these kinds of materials are presented. Furthermore, by introducing two kinds of supplementary "stress-displacement and electricdisplacement-electric field potential" fields, it is proved that are simple but universal relationsbetween the Bueckner work conjugate integral and the J--integral and between the Bueckner workconjugate integral and the M-integral in these kinds of materials. Therefore, the weight functionmethods whiCh are widely used in fracture mechanics for brittle elastic materials could be extendedto treat the crack problems in piezoelectric materials. The methods could then be adopted to findthe electric displacement-intensity factor as well as the traditional Mode I and Mode II stress intensity factors, distinctively, at a crack tip in piezoelectric materials, from which the well--knownmechanical strain energy release rate could be given and the stability or growth of the crack insuch materials could be determined.