On nonlinear behavior in brittle heterogeneous materials

Abstract

Many modern fiber-reinforced composite materials are ‘brittle’, in the sense that their strain to failure under quasi-static loading is typically of the order of 1% when loaded in directions generally controlled by fiber fracture, and the energy-to-failure under the quasi-static loading curve is typically small. For this reason, analysis of these materials is typically done under assumptions of linear elasticity, usually for homogeneous materials or material layers in a laminate. This is in contrast to ‘ductile’ metal behavior in which elastic–plastic behavior is widely discussed. What is most remarkable is the fact that for long-term behavior, the situation is nearly reversed in many cases. For design-level stresses, nonlinear behavior in ductile materials is often minor (even high temperature structures are often designed with linear analysis) but heterogeneous brittle materials may show changes of the order of 10–30% in stiffness and strength for long-term behavior under design loads that are quite safe. One cannot properly describe or model the behavior of composite laminates, therefore, without an understanding and representation of nonlinear behavior. The present paper will focus on some of these nonlinear behaviors, and will present some recent interpretations of them, for both long-term and quasi-static loading of continuous fiber reinforced composite laminates. The paper begins with a discussion of the effect of temperature on fiber-direction stiffness of unidirectional carbon reinforced PPS composite laminates. Micromechanical models are used to estimate the changes in stiffness, strength, and life. Quasi-static and cyclic behavior of woven laminates is then considered. Data and predictions are presented.