Plasticity Analysis of Fibrous Composites

Abstract

The elastic-plastic behavior of composites consisting of aligned, continuous elastic filaments and an elastic-plastic matrix is described in terms of constituent properties, their volume fractions, and mutual constraints between the phases indicated by the geometry of the microstructure. The composite is modeled as a continuum reinforced by cylindrical fibers of vanishingly small diameter which occupy a finite volume fraction of the aggregate. In this way, the essential axial constraint of the phases is retained. Furthermore, the local stress and strain fields are uniform. Elastic moduli, yield conditions, hardening rules, and overall instantaneous compliances, as well as instantaneous stress concentration factors are derived. Specific results are obtained for the case of a Mises-type matrix which obeys the Prager-Ziegler kinematic hardening rule. Any multiaxial mechanical load may be applied. Comparisons are made between the present results and certain other theories.