论M积分和Bueckner功共轭积分之间的关系

ON THE RELATION BETWEEN THE M INTEGRAL AND THE BUECKNER WORK CONJUGATE INTEGRAL

摘要

摘要:对均质各向同性材料、各向异性材料和两相各向同性材料中的裂纹问题各提出一种辅助的位移应力场，证明Ｍ积分和Ｂｕｅｃｋｎｅｒ功共轭积分之间有一种固有的简单关系．这个关系与材料特征根无关，也不受界面裂纹尖端应力振荡奇性的影响．由此证明，Ｍ积分在上述三种情况下，从本质上说来源于Ｂｅｔｉ功互等定理．正像Ｊ积分的本质来源于功互等定理一样．只是辅助的位移应力场不同而已，这说明，Ｂｕｅｃｋｎｅｒ由Ｂｅｔｉ功互等定理提出的功共轭积分是更为一般的路径无关积分．因为，由Ｂｕｅｃｋｎｅｒ积分加上不同的辅助位移应力场可推出任何一种已发表的路径无关积分来．

Abstract:The path independent integrals in the field of fracture mechanics have received considerable attention in recent years since Rice proposed the well known J integral in 1968. On the one hand, Herrmann and Herrmann (1981) pointed out that the integrals L and M provide a more natural description of energy release rate associated with plane cracks than the integrals J 1(≡J) and J 2 . On the other hand, Chen (1985), Chen and Hasebe (1994,1995) found that there is a simple and inherent relati...