Multiscale Approach to Analysis of Composite Joints Incorporating Nanocomposites Zeaid Hasan, * Aditi Chattopadhyay, † and Yingtao Liu ‡ Arizona State University, Tempe, Arizona 85004 DOI: 10.2514/1.C032652 This study focuses on the benefits of using nanocomposites in aerospace structural components to prevent or delay the occurrence of unique composite failure modes, such as delamination. A three-scale approach was considered to determine the mechanical properties of the nanocomposites. First, the effective carbon nanotube properties were calculated based on the composite cylinder assemblage method. Second, the effective properties of the carbon nanotube embedded in an epoxy matrix were obtained using the Mori–Tanaka method. Finally, the effective properties of the composite lamina were also acquired using the Mori–Tanaka method assuming that the nanocomposite obtained in stage two was the matrix of that lamina surrounding the fibers. These properties were then used to analyze the structural response of a T-section stringer using detailed finite element models. The stringer was analyzed under different loading conditions and assuming different flaw types in the structure. Initial damage was detected via the virtual crack closure technique implemented in the finite element analysis, and it was assumed to be the characteristic variable to compare the different behaviors. It was found that the use of nanocomposites in the manufacturing process of composite stringers would improve the overall performance against unique composite failure modes. Nomenclature C = effective stiffness tensor E = Young’ s modulus G = shear modulus G I = mode 1 strain energy release rate G II = mode 2 strain energy release rate G III = mode 3 strain energy release rate G Ic = mode 1 toughness allowable G IIc = mode 2 toughness allowable G IIIc = mode 3 toughness allowable K = stiffness matrix L = concentration tensor L m = concentration matrix S = Eshelby tensor v = volume fraction W = volume-averaged strain energies κ = bulk modulus λ = failure index ν = Poisson’ s ratio I. Introduction C OMPOSITE materials such as graphite epoxy are ideal candidates for many applications, including aerospace and automotive, due to their high strength-to-weight ratios [1]. However, composite laminates are extremely susceptible to crack initiation and propagation along the laminar interfaces. In fact, delamination is one of the most common life-limiting crack growth modes in laminated composites, as their presence may cause severe reductions in the in- plane strength and stiffness, leading to catastrophic structural failure [2]. Delaminations may be introduced during the manufacturing process or in service. Many useful techniques have been successfully employed to improve the delamination resistance in composite structures such as three-dimensional (3-D) weaving [3], stitching [4], braiding [5], Z-pin anchoring [6], and the use of short fibers or microscale particles in the polymer matrix [7]. These methods enhanced the interlaminar properties, but at the cost of in-plane mechanical properties [8]. Extensive research has been performed on the use of carbon nanotubes (CNTs) in various applications due to their unique and superior physical and mechanical properties. In particular, the superior Young’ s modulus of CNTs combined with their flexibility and lightness makes them ideal fillers for high-performance nanocomposites. Thus, single-walled carbon nanotubes (SWCNTs) or multiwalled CNTs (MWCNTs) incorporated inside a polymer matrix could significantly improve the properties of polymeric materials. Since the nanocomposite is a macrocontinuum scale, whereas the individual phases can range from the continuum down to the nanometer scale, this creates challenges while attempting to model them analytically or numerically. Therefore, multiscale analysis is the tool necessary to analyze such nanocomposites. Several research articles and book chapters can be found in the literature that discusses multiscale analysis in the context of nanomaterials [9–20]. A significant amount of research has been conducted to predict the properties of nanocomposites that include CNTs embedded in polymer matrix [21–23]. Mechanical properties of nanostructured materials can be determined by a select set of computational methods. One of the most widely used approaches for determining the stress or strain concentration tensors, for use in determining the effective properties of composite materials, is the Mori–Tanaka method [24]. This method was originally developed for calculating the average internal stress in matrix materials with inclusions. This generated a significant amount of work in the analysis of composite materials based on the idea of equivalent inclusions [25]. This method was used to compute the effective properties of the constituents in micromechanics. Other applications, such as crack effects and void growth in viscous metals, were also investigated [26]. The application of the Mori–Tanaka method in micromechanics modeling of nanocomposites has also been reported [27,28]. The composite cylinder assemblage (CCA) method is also a well-known approach that is used to determine the bounds and expressions for the effective elastic moduli of materials reinforced by parallel hollow circular fibers [29,30]. The CCA method uses the direct strain energy equivalency between the response of concentric circular fiber Received 8 October 2013; revision received 14 December 2013; accepted for publication 3 January 2014; published online 30 April 2014. Copyright © 2013 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. Copies of this paper may be made for personal or internal use, on condition that the copier pay the $10.00 per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923; include the code 1542-3868/14 and $10.00 in correspondence with the CCC. *Graduate Student, School for Engineering of Matter, Transport and Energy; zeadnws@hotmail.com. † Professor, School for Engineering of Matter, Transport and Energy; aditi@ asu.edu. ‡ Research Associate, School for Engineering of Matter, Transport and Energy; yliu158@asu.edu. 204 JOURNAL OF AIRCRAFT Vol. 52, No. 1, January–February 2015 Downloaded by UNIVERSITY OF OKLAHOMA on August 5, 2019 | http://arc.aiaa.org | DOI: 10.2514/1.C032652