Three-dimensional asymptotic stress field in the vicinity of the circumferential tip of a fiber–matrix interfacial debond

Abstract

A heretofore unavailable asymptotic solution pertaining to the stress field in the neighborhood of the circumferential tip of an interfacial debond, between the fiber or inclusion and the unreinforced plate made of the matrix material, and subjected to far-field extension-bending (mode I), inplane shear-twisting (mode II) and torsional (mode III) loadings, is presented. A local orthogonal curvilinear coordinate system ( ρ, φ, θ), is selected to describe the local deformation behavior of the afore-mentioned plate in the vicinity of the afore-mentioned circumferential line of interfacial debond. One of the components of the Euclidean metric tensor, namely g 33, is approximated ( ρ/ a≪1) in the derivation of the kinematic relations and the ensuing governing system of three partial differential equations. A recently developed eigenfunction approach coupled with a novel local curvilinear coordinate system, is utilized to compute the asymptotic displacement and stress fields. The oscillatory behavior at the debond tip may be considered to be a first-order approximation of the interdiffusion of the component phases followed by molecular entanglement and other similar microscopic phenomena studied by materials scientists.