New Formulation for Elastic Modulus of Fiber‐Reinforced, Quasibrittle Matrices

Abstract

The main objective of the present research is to develop a rational model to predict the elastic modulus of fiber‐reinforced, quasibrittle matrices such as cement and ceramic matrices. Generally, the elastic modulus of a two‐phase composite is predicted from the mechanical properties and proportions of the two components. Here a new approach is introduced in which the interfacial layer surrounding the fiber, viewed as a third phase with zero volume, is modeled as an imperfect bond with mechanical properties similar to or different from the surrounding matrix. Based on this assumption, new upper‐ and lower‐bound solutions for the elastic modulus of aligned short‐fiber composites are analytically derived assuming either a uniform applied stress or a uniform applied strain; the two solutions are combined to achieve an average modulus of aligned short‐fiber composite. The usual lower‐bound solution for the modulus of elasticity of a fiber composite with the fiber normal to the axis of loading is modified to account for matrix porosity as affected by the presence of fibers. It is finally suggested that the elastic modulus of random short‐fiber composites be taken as an average of the values obtained for the aligned and normal fiber values.