Singularity evaluation for single material and bi-material propagating V-notches

Abstract

By introducing displacement asymptotic expansion around the vertex of a propagating V-notch into elasticity governing equation, radial boundary conditions and interfacial continuity conditions, the singularity eigen analysis for a propagating V-notch is transformed into solving a set of eigen ordinary differential equations. The singularity orders and corresponding eigen angular functions for a propagating V-notch can be obtained after applying interpolating matrix method in order to solve the established eigen equation. The singularities for single material and bi-material propagating V-notch are respectively analyzed under different material properties, propagating directions and propagating velocities. It is found that the relationship between stress singularity and propagating velocity depends on the propagating direction as well as the singularity variation with respect to propagating velocity is not monotonous. For a single material V-notch, the singularity will be the weakest when the propagating direction is along the bisector of V-notch, and it will be the strongest when the propagating direction is perpendicular to the notch bisector. For a bi-material V-notch, the strongest singularity for a bi-material V-notch occurs when the propagating direction is along the harder material.