计算压电材料Ⅲ型裂纹的能量释放率及其强度因子K_Ⅲ和K_ⅣⅡ．刚度微分法

DETERMINATION OF ENERGY RELEASE RATE AND INTENSITY FACTORS KⅢ AND KⅣ OF PIEZOELECTRIC MATERIALS WITH Ⅲ─MODE CRACK Ⅱ.STIFFNESS DERIVATIVE TECHNIQUE

利用压电材料面外剪切问题的有限元数值解作为真实场，用压电材料Ⅲ型裂纹的裂端渐近解作为辅助场，把刚度微分法推广到压电材料Ⅲ型裂纹问题的计算中，并且给出了能量释放率Ｇ和应力强度因子ＫⅢ及电位移强度因子ＫⅣ的计算公式。利用此公式计算了含裂纹长２α的无限压电板面外剪切问题，计算结果的相对误差均小于１．５％。这一方法可广泛应用于压电材料面外剪切情况下的强度因子分析。

By means of the numerical solution to piezoelectric materials obtained by finite element method as actual fields and the asymptotic expressions for the electricmechanical fields in the vicinity of the crack as auxillary fields,a stiffness derivative technique is used to determine energy release rate and intensity factors KⅢ and KⅣof piezoelectric materials withⅢ-mode crack.Numerical examples are presented to demonstrate the accuracy of the proposed approach.This method can be widely used in analyzing intensity factors KⅢ and KⅣ of the an tiplane fracture problem of piezoelectric materials.