Singular stress and displacement fields around the corner point of a fiber end in short fiber reinforced composites

Abstract

Singular elastic stress and displacement fields around the comer point of a fiber end are examined. Using the eigenfunction expansion method, the elastic fields are determined for the three fundamental problems, which are (I) the stress-free edges of the corner, (II) the fixed displacement edges, and (III) the stress-free edge and fixed displacement edge. On the fundamental problems (I) and (II), singular stress and displacement fields are determined with two kinds of singularity order, λ = λ + and λ = λ −, respectively; also, it is found that, for λ = λ +, the stress field is symmetrical with respect to the bisector angle of the corner point of the fiber end and, for λ = λ −, the stress field is antisymmetrical. For the fundamental problem (III), the stress field without symmetry with respect to the bisector angle of the corner point of the fiber end is determined. Also, the singular stress and displacement fields around the corner point of the fiber end are obtained for equivalent Poisson's ratio, K.