Analysis of Singularity Characteristics and Intensities of Axisymmetric V‐Notches Under Variable Boundary Conditions

ABSTRACT A detailed linear‐elastic stress state analysis around the vertex of an axisymmetric V‐notch depends on the understanding of stress singularity orders, eigenangular functions, and generalized stress intensity factors. This study introduces a numerical method for determining the stress singularity state of an axisymmetric V‐notch. The displacement field near the axisymmetric V‐notch tip is expanded asymptotically and substituted into the equilibrium equations of the axisymmetric structure, yielding a system of characteristic singularity equations that govern the stress singularity orders. The interpolating matrix method is introduced for solving the established characteristic equations, which simultaneously determine the stress singularity orders and their associated eigenangular functions under different radial boundary conditions. Generalized stress intensity factors of axisymmetric V‐notches are computed using the finite element method by postprocessing the stress results. The effects of material properties and notch geometry on singularity orders and generalized stress intensity factors are discussed in detail.