二维复合广义J积分

本文推导出了含复合型裂纹的变厚度板在承受体力和面力、存在非均匀温度场的情况下的能量差率表达式。并由此定义了复合型广义J积分 J=J₁cosφ+J₂sinφ J₁=lim（1/t）{∫Wtdx₂-∫W（t/x₁）d A-∫S_i（u_i/x₁）tds -∫（W/T） （T/x₁）td A-∫Bi（u_i/x₁）tdA} J₂=lim1/t{-∫Wtdx₁-∫W（t/x₂）dA-∫si（u_i/x₂）tds -∫（W/T）（T/x₂）tdA-∫Bi（u_i/x₂）tdA} 在此定义的基础上,我们证明了广义J积分的与路径无关性,并利用其路径无关性和裂纹尖端的应力场奇异性得到了广义J积分与线弹...

A TWO-DIMENSIONAL GENERALIZED J INTEGRAL OF MIXED MODE

An expression of energy difference rate in a plate of non-uniform thickness with a crack of mixed mode under both body force and surface tractions in a non-uniform temperature field is derived.From it a two-dimensional generalized J integral of mixed mode can be defined as following:On the basis of the above definition it is proved that the two-dimensional generalized J integral of mixed mode is independent of integration path.According to the path-independence and the singularity of the stress field in the vicinity of a crack tip,the relation between the two-dimensional generalized J integral of mixed mode and the stress intensity factors in a linear elastic case is deduced as following:When the two-dimensional generalized J integral of mixed mode is calculated by conventional finite element method,the stress intensity factors k1 and k2 in a linear elastic case can be obtained from the above formulas.This paper also demonstrates that the crack tip is not the singular point of temperature field.