高阶奇异项及J积分表达式

HIGHER ORDER SINGULAR TERMS AND J -INTEGRAL FORMULATIONS

从４种典型裂纹情况的特征展开式出发，运用其微分性质和伪正交性质得到了含有高阶奇异项的Ｊ积分表达式．它们是通用的显函数表征的．本研究支持了Ｈｕｉ和Ｒｕｉｎａ的杰出研究和重要观点，即高阶奇异项和非奇异项一样在小范围屈服描述中扮演着重要角色．研究表明，常规柔度方法确定的Ｊ积分已隐含了高阶奇异项的贡献．

This paper starts from the eigenfunction expansion forms(EEF) in four typical crack problems taking into account the higher order singular terms(HOST). Using the differential properties and the pseudo-orthogonal properties of EEF's, the universal and explicit formulations of the J -integral are given. The present investigation does support the significant conclusion derived recently by Hui and Ruina that the HOST's do play an important role in the small scale yielding description. It is shown that the first term in the J -integral formulations is the contribution arising from the traditional r -1/2 (or r -1/2-i ε ) singularity, while the second is a summation contributed by the interaction of the HOST's and the regular terms in the EEF's. This means that the traditional compliance methods which were commonly used to estimate the J -integral imply the contributions induced from the existence of the HOST's. Thus, the stress intensity factors derived by using these methods should be suspected.