Materials Science and Engineering A 465 (2007) 238–246 Nonlinear constitutive equation for vapor-grown carbon nanofiber-reinforced SC-15 epoxy at different strain rate Yuanxin Zhou a,∗ , Sajedur Rahman Akanda a , Shaik Jeelani a , Thomas E. Lacy b a Tuskegee University’s Center for Advanced Materials (T-CAM), Tuskegee, AL 36088, USA b Department of Aerospace Engineering, Mississippi State University, MS 39762, USA Received 19 August 2006; received in revised form 2 February 2007; accepted 11 April 2007 Abstract In this study, tensile tests were performed on 0, 1, 2, and 3 wt% vapor-grown carbon nanofiber (CNF)-modified SC-15 epoxy at strain rates ranging from 0.00033 to 0.033 s -1 . Experiment results showed that both the elastic modulus and the tensile strength of the materials increased with higher strain rates, but the failure strain decreased with higher strain rates, indicating that the composite is a strain rate-dependent material. Experiment results also showed an even distribution of CNFs in the 1 and 2 wt% systems and an agglomeration of CNFs in the 3 wt% system. Therefore, the 2 wt% CNF-infusion system exhibited maximum enhancement, compared to other systems. Based on the results, a nonlinear constitutive equation was established to describe the strain rate-dependent stress–strain relationship of neat and nanophased epoxy. The parameters in this model are tensile modulus E, stress exponent n, and stress coefficient σ * . The stress exponent n, which controls the strain rate-strengthening effect and the strain rate hardening effect of the composite, is independent of both strain rate and CNF content. The stress exponent σ * , however, varies with both strain rate and CNF content. © 2007 Elsevier B.V. All rights reserved. Keywords: Strain rate; Tensile properties; Vapor-grown carbon nanofiber; Epoxy 1. Introduction Epoxy resin has been important to the engineering commu- nity for many years. Epoxy-based materials provide outstanding mechanical, thermal, and electrical properties [1]. Using an addi- tional phase, such as inorganic fillers, to strengthen the properties of epoxy resins has become a common practice [2]. These fillers have been proven to improve the material properties of epoxy resins. Because microscale fillers have successfully been syn- thesized with epoxy resin [3–6], nanoscaled materials are now being considered as filler material to produce high performance composite structures with further enhanced properties. Because of the improvements in mechanical, electrical, and chemical properties, many industries, including automotive, aerospace, electronics, and biotechnology [7,8] have become interested in nanocomposite materials. Vapor-grown carbon nanofibers (CNFs), due to their high tensile strength, modulus, and relatively low cost, are drawing ∗ Corresponding author. Fax: +1 334 727 8801. E-mail address: yzhou@tuskegee.edu (Y. Zhou). significant attention for their potential applications in nanoscale polymer reinforcement. They are synthesized through pyroly- sis of hydrocarbons or carbon monoxide in the gaseous state in the presence of a catalyst [9,10]. Vapor-grown CNFs are differ- ent than other types of nanofibers, such as polyacylonitrile or mesophase pitch-based carbon fiber, in their method of produc- tion, physical properties, and structure. Thermoplastics, such as polypropylene [11–16], polycarbonate [17–21], and nylon [22]; thermosets, such as epoxy [23]; and thermoplastic elastomers, such as butadiene-styrene diblock copolymer [24] have been reinforced with carbon nanofibers. Like many other polymer materials, the mechanical responses (deformation, strength, and failure) of nanofiber-modified epoxy, depend on the rate of deformation. It is necessary to know the mechanical behavior of a nanocomposite at different strain rates if a component made of the nanophased epoxy undergoes different loading speeds. The primary purpose of this paper is to describe the effects that different strain rates and the addition of vapor-grown CNFs have on the tensile behavior of epoxy. Based on the experiment results, a nonlinear constitutive equation was developed to describe strain rate-sensitive behavior of neat and nanophased epoxy. 0921-5093/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2007.04.042