A new model for the determination of optimum fiber volume fraction under multi-axial loading in polymeric composites

Abstract

Mechanical properties of composite materials are a function of fiber volume fraction. Based on the existing micromechanical models, the in-plane shear strength of these materials is decreased as their fiber volume fraction is increased. However, their compressive strength is initially increased and then it is dropped as the fiber content increases. The fiber content in the composite of maximum compressive strength was referred to as the optimum fiber volume fraction. Experiments performed in this study revealed that in-plane shear strength variation versus fiber volume fraction was to some extent similar to that of compressive strength. Moreover, different optimum fiber volume fractions for in-plane shear strength and compressive strength were observed. Consideration of both in-plane shear strength and the compressive strength in combined loading was proposed to find the optimum fiber volume fraction. The modified Hashin failure criterion by Lessard was employed to relate the longitudinal and transverse compressive stress and strength to in-plane shear stress and strength. A safe region predicted by this failure criterion was represented by plotting longitudinal compressive and in-plane shear stress relation for different fiber contents. The fiber content corresponding to the maximum safe region was introduced as the optimum fiber volume fraction. Axial compressive and in-plane shear tests were conducted for obtaining the variation of longitudinal compressive and in-plane shear strengths with fiber volume fraction. To identify the capability of the model for multi-axial state of stress, a unidirectional off-axis test was also performed. The test results on the unidirectional and off-axis composite specimens confirmed the predictions by the theoretical model.