Multi-scale Rule-of-Mixtures Model of Carbon Nanotube/Carbon Fiber/Epoxy Lamina
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Multi-scale Rule-of-Mixtures Model of Carbon Nanotube/Carbon Fiber/Epoxy Lamina S. J. V. Frankland1, J. C. Riddick2 and T. S. Gates3 1 National Institute of Aerospace, 100 Exploration Way, Hampton, VA 23666, U. S. A. 2 Vehicle Technology Directorate, US Army Research Laboratory, Hampton, VA 23681, U.S.A. 3 Mechanics of Structures and Materials Branch, NASA Langley Research Center, Hampton, VA 23681, U. S. A.
ABSTRACT A unidirectional carbon fiber/epoxy lamina in which the carbon fibers are coated with single-walled carbon nanotubes is modeled with a multi-scale method, the atomistically informed rule-of-mixtures. This multi-scale model is designed to include the effect of the carbon nanotubes on the constitutive properties of the lamina. It included concepts from the molecular dynamics/equivalent continuum methods, micromechanics, and the strength of materials. Within the model both the nanotube volume fraction and nanotube distribution were varied. It was found that for a lamina with 60% carbon fiber volume fraction, the Young’s modulus in the fiber direction varied with changes in the nanotube distribution, from 138.8 to 140 GPa with nanotube volume fractions ranging from 0.0001 to 0.0125. The presence of nanotube near the surface of the carbon fiber is therefore expected to have a small, but positive, effect on the constitutive properties of the lamina.
INTRODUCTION Near term applications of carbon nanotubes (CNT) in materials for aerospace vehicles are most likely to be realized with mechanical or electrical applications that require small quantities of nanotubes. To implement carbon nanotubes as structural members could be accomplished by the selective use of carbon nanotubes in critical areas of traditional composites. For example, carbon nanotubes added between the layers of a traditional carbon fiber/epoxy laminate may well improve the interface strength between carbon fiber and epoxy matrix, and thereby improve fracture toughness of these laminates. The effectiveness of adding carbon nanotubes to laminates can be analyzed with multi-scale models which are capable of incorporating atomistic details. At the atomisticlevel the assumptions of ‘perfect’ bonding between the various contributors to the laminate can be removed in detailed atomistic simulations. With properties at this level established, the micro-scale properties can be accessed with more standard micromechanics methods such as the Mori-Tanaka method or the rule-of-mixtures analysis[1]. Multi-scale models have applied atomistic simulation and micromechanics to the constitutive properties of various functionalized nanotube materials [2-5]. There are some atomistic simulations of epoxy/nanotube composites by other researchers which address nanotube pull-out [6]. Also, a more recent study on nanotubes chemically bonded into the epoxy matrix showed a
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Young’s modulus of up to 160 GPa in the direction of the nanotube axis, and 4-8 GPa in the transverse direction at a nanotube volume fraction of 25 % [7]. In the present w
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