Extraction of singular stress fields using the axisymmetric single-fiber micromechanics model

Abstract

The stress distributions near the points of singularity in a single-fiber micromechanics model as obtained by local asymptotic methods and global (numerical solutions to full-field boundary value problem) methods are described. While the numerical/analytical solutions (without special treatment of the singularity) can capture higher order terms and are sufficiently accurate away from points of singularity, the solutions are approximate in the neighborhood of the singularity due to the inherent assumptions (single-valued at the point of singularity) about the nature of the stress fields. The study focuses on a methodology for accurate determination of generalized stress intensity factors from the “approximate” methods of stress analysis with relatively coarse discretizations and without any special modeling of the singularity. The approach adopted entails the comparison of the angular distribution of the stress components at varying radial distances near the point of singularity and identifying a region in which the numerical/analytical solutions have the best ability to determine the stress intensity factor. Determination of the generalized stress intensity factors is illustrated for a penny-shaped crack in a homogeneous medium and for a crack in fiber terminating at the fiber-matrix interface (fiber-break problem).