Effect of Couple-Stresses on Force Transfer Between Embedded Microfibers

Abstract

The present investigation is a continuation of the Weitsman problem, reference 1. The investigation is concerned with the nature of the stress field which develops in the presence of couple- stresses in composite material formed of microfibers embedded in a filler substance. The case is considered when one row consists of an infinitely long microfiber, while the second row is composed of two semi- infinite microfibers. An exact solution, based on a two-dimensional theory of elastic ity with inclusion of couple-stresses is obtained for the stress field which is activated by giving the two semi-infinite microfibers a tangential displacement of separation. The couple-stress theory gives a better representation of the actual physical phenomenon than the classical theory of elasticity. This is especially true and essentially important for bodies having a dimension comparable to the crystal lattice parameter of the material. This is believed to be the case with an elastic microfilm in bond with microfibers. The investigation led to results which are at wide variance with the Weitsman solution near x = 0 and the asymptotic solution shows the same trend as reported previously in reference num bered 2 i.e., bonding layers are dominated by boundary layer behavior throughout their entire thickness.