ON THE BUECKNER WORK CONJUGATE INTEGRAL AND ITS RELATIONS TO THE J-INTEGRAL AND M-INTEGRAL IN PIEZOELECTRIC MATERIALS
压电材料中的Bueckner功共轭积分及和J积分M积分的关系

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.