Constitutive relation, deformation, failure and strength of composites reinforced with continuous/short fibers or particles

Abstract

Various issues on the constitutive relation, deformation, failure, and strength of a composite reinforced with either continuous or short fibers, or particles are systematically addressed based on Bridging Model and the true stress concept. The internal stresses in the fiber (standing for the reinforcement) and matrix obtained by Bridging Model or any other micromechanics model are homogenized quantities. They must be converted into true values. The conversion details are summarized in the paper. A constitutive relation of the composite outside an elastic region is affected by constituent plasticity, true stress effect and relative slippage displacement between debonded fiber and matrix interfaces, and has been established in the paper. Using the true stresses, various composite failures including ultimate strengths of a laminated composite can be predicted mainly against the fiber and matrix properties. Only the prediction for a processing dependent failure, either interface debonding, laminate delamination or fiber kinking failure, needs additionally an ultimate data of a unidirectional laminate measured upon existing standards. One of the best advantages of this paper is in that probably a minimum effort is needed to prepare the input data for a composite design. Another advantage is in that all of the involved formulae are analytical and in closed form, making the analysis for a composite structure comparable in computational amount to that made of an isotropic material.