On The Stress Singularities At The Axisymmetric Interface Wedge Of Fiber-reinforced Composites

Interfaces are important microstructures of composites and axisymmetric interface wedges or axisymmetric cylindrical interface cracks are common. There may appear multiple stress singularities at axisymmetric interface wedges as well as oscillatory singularities at axisymmetric cylindrical interface cracks, which usually lead to the failure of composites. Therefore the comprehensive understanding of the singular behaviors should be the preconditions for the strength and reliability criterions of composites. The parameters fully describing the singular behaviors include the order of stress singularity, the stress angular variations, and the stress intensity coefficients.An eigenvalue method was proposed to study the singular stress field at the axisymmetric interface wedge of the fiber reinforced composites. The major work of this paper is as follows:1. Based on the fundamental equations of the spacial axisymmetric problem of the transversely isotropic materials and the first-order approximation assumption, the discrete characteristic equation was derived by using of the displacement functions with separated variables and the meshless method. The eigenvalue is relative to the order of stress singularity, and the associated eigenvector is with respect to the stress angular variations. The order of stress singularity, the associated displacement and stress angular variations obtained by eigenvalue method are in good agreement with those by FEM.2. 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 extrapolation. The singular stress field around the axisymmetric interface wedge can be completely determined by the developed eigenvalue method coupling with the FEM analysis.3. The influences of dimensionless parameterδ, which denoting the ratio of the fiber's radius to the singular dominated region, are discussed. The results show that, when the ratio is more than two orders of magnitude, the parameters obtained by eigenvalue method are in good agreement with those by first-order approximation; when the ratio is less than two orders of magnitude, the parameters obtained by first-order approximation can not describe the singular stress field near the singularity points, and then the influences ofδmust be considered.