Modeling Considerations and Material Properties Evaluation in Analysis of Carbon Nano-Tubes Composite F. KARIMZADEH, S. ZIAEI-RAD, and S. ADIBI This article presents a computational modeling approach for predicting the mechanical behavior of polymer carbon nano-tubes (CNTs). The CNT’s interaction with matrix material was modeled using the continuum mechanics theory and finite element approach. The effective mechanical properties of CNTs were then evaluated by using the finite element method (FEM) models. Two different models were constructed. The first model was a two-dimensional (2-D) axisymmetric nano-scale on a cylinder representative volume element (RVE). The second model considers a three-dimensional (3-D) finite element on a square representative volume element. Several numerical examples were carried out to investigate the stress distribution and to dem- onstrate the load carrying capacities of the CNT. Having known the stress and strain distri- butions, the material properties of the CNT can be easily calculated from the standard theory of elasticity. The computed results were compared with those obtained from the simple rule of mixture for validity. The results indicate that cylindrical RVEs tend to overestimate the effective Young’s moduli of the CNT-based composites while the obtained results from square RVEs are more reliable. DOI: 10.1007/s11663-007-9065-y Ó The Minerals, Metals & Materials Society and ASM International 2007 I. INTRODUCTION NANO-TECHNOLOGY can be broadly defined as, ‘‘the creation, processing, characterization, and utiliza- tion of materials, devices, and systems with dimensions on the order of 0.1 to 100 nm, exhibiting novel and significantly enhanced physical, chemical, and biological properties, functions, phenomena, and processes due to their nano-scale size.’’ Current interests in nano-tech- nology encompass nano-biotechnology, nano-systems, nano-electronics, and nano-structured materials, of which nano-composites are a significant part. In the last decade or so, the field of computer simulation of nano-materials has advanced extremely rapidly for several reasons. The first is the tremendous increase in computing resources (along with simulation techniques) that has occurred in this time span, making the simulation of nano-scale arrays possible. The second is that atomic scale simulations (such as molecular dynamics) are ideally suited to explore nano-scale phenomena at a time when experimental exploration and theoretical understanding of nano-materials has become of intense interest. In fact, several regularly published journals are now devoted to articles illustrat- ing simulations of new material properties spanning length scales from the subatomic to the macroscopic. [1] Carbon nano-tubes (CNTs), discovered by Iijima in 1991, possess exceptionally high stiffness, strength, and resilience, as well as superior electrical and thermal properties. [2] Many believe that CNTs may provide the ultimate reinforcing materials for the development of a new class of nano-composites. [3,4] It has been demon- strated that with only 1 pct (by weight) of CNTs added in a polymeric matrix material, the stiffness of a resulting composite film can increase between 36 and 42 pct and the tensile strength by 25 pct. [5] The article’s studying scope, i.e., mechanical-load carrying capacities of CNTs in nano-composites, has also been demonstrated in some experimental work [5–8] and simulations. [9] All of these studies show that the CNT-based composites have the potential to provide extremely strong and ultralight new materials. However, enormous challenges remain in the development of such nano-composites. Computational method can play a significant role in the development of the CNT-based composites by providing simulation results to understand, analyze, and design nano-composites. At the nano-scale, analyt- ical models are difficult to establish or too complicated to solve, and tests are extremely difficult and expensive to conduct. Modeling and simulations of nano-compos- ites, on the other hand, can be achieved readily and cost effectively on even a desktop computer. Characterizing the mechanical properties of CNT-based composites is just one of the many important and urgent tasks that simulations can accomplish. However, much work still needs to be done before the potentials of the CNT-based composites can be fully realized in real engineering applications. Evaluating the effective material properties of such nano-scale materials is one of the challenging tasks for the development of nano-composites. F. KARIMZADEH, Assistant Professor, Material Engineering Department, and S. ZIAEI-RAD, Associate Professor, and S. ADIBI, Research Assistant, Mechanical Engineering Department, are with the Isfahan University of Technology, 84156, Isfahan, Iran. Contact e-mail: karimzadeh_f@cc.iut.ac.ir Manuscript submitted March 30, 2006. Article published online July 7, 2007. METALLURGICAL AND MATERIALS TRANSACTIONS B VOLUME 38B, AUGUST 2007—695