Stress Singularities in Composite Materials with an Arbitrary Open Crack Meeting an Interface. (5th Report, Orders of Singularity for Arbitrary Composite Materials).

Abstract

This paper discusses the stress singularities around a crack in the two dimensional elastic materials. Based on Williams' method of the eigenfunction expansions, the crack tip singularities for various open crack and material combinations are computed for plane problems as well as for antiplane problems. The order of singularities is discussed for the cases of modes I, II and III. The intensity of stress singularity and the stress and displacement modes are shown, and the characteristic features of the stress singularities are discussed It is found that stresses have the singularity of the form γi-1, where γis the distance from the crack tip, and the exponent λ lies between 0.0 and 1.0. The characteristic determinant is derived by the various boundary conditions and interface continuity conditions, and is solved directly by using Mullers' method, which computes the algebraic equation of high degree. The theoretical process of analysis and some numerical results represented by figures are given.