纤维增强复合材料轴对称界面端的奇异应力场

Singular stress field at axisymmetric interface wedge of fiber reinforced composite

提出了一种分析横观各向同性纤维增强复合材料轴对称界面端的奇异应力场的特征值法。基于横观各向同性弹性材料空间轴对称问题的基本方程和一阶近似假设,利用分离变量形式的位移函数和无网格算法,导出了关于应力奇异性指数和应力角函数的奇异性特征方程。对于纤维/基体轴对称界面端模型,特征值法给出的应力奇异性指数、相应的位移和应力角函数,与通过有限元分析得到的结果非常吻合。利用有限元计算得到的奇异应力场,结合特征值法给出的应力奇异性指数和应力角函数,通过线性外插得到了相应的应力强度系数。特征值法结合有限元分析,可以完全确定横观各向同性纤维增强复合材料轴对称界面端的奇异应力场。

An eigenvalue method was proposed to study the singular stress field at the axisymmetric interface wedge of the fiber reinforced composites.Based on the fundamental equations of the spacial axisymmetric problem of the transversely isotropic materials and the first-order approximation assumption,a discrete characteristic equation was derived by using the displacement functions with separated variables and the meshless method.The eigenvalue was related to the order of stress singularity,and the associated eigenvector was with respect to the stress angular variations.The fiber/matrix axisymmetric interface wedge model was used to verify the validity of the proposed eigenvalue method.The order of stress singularity,the associated displacement and stress angular variations obtained by this eigenvalue method are in good agreement with those by the finite element method（FEM）.Based on the order of stress singularity and the associated stress angular variations determined by the eigenvalue analysis,as well as the numerical results of singular stress fields by FEM,the stress intensity coefficient was also obtained in terms of the linear extropolation.The singular stress field around the axisymmetric interface wedge can be completely determined by the developed eigenvalue method coupling with the FEM analysis.