1. Samantha Vaitkunas Rose-Hulman Institute of Technology Parametric Studies of Micromechanics Analyses of Carbon Nanotube Composites Dr. Dimitris Lagoudas, Advising Gary Seidel, Mentor August 6, 2004

2. Texas Institute for Intelligent Bio-Nano Materials and Structures for Aerospace Vehicles Motivation: Nanotechnology - 10 -9 m in size - Intriguing characteristics in regards to its mechanical, thermal, and electrical properties - Varying chirality (angle in which the graphene sheet is “rolled-up”) which determines electrical properties *ZigZag  Semiconducting  = 0 o *Armchair  Metallic  = 30 o - Manufactored by high energy processes: HiPco, Laser Ablation - Measured grams per day production due to small size Copyright Professor Charles M. Lieber Group NANOTUBE MaterialYoung's modulus (GPa)Tensile Strength (GPa)Density (g/cm 3 ) Single wall nanotube1054150~ 1.33 to 1.40 Multi wall nanotube12001502.6 Steel2080.47.8 Epoxy3.50.0051.25 Wood160.0080.6 Copyright 2002-2005 Applied Nanotechnologies, Inc.

3. Texas Institute for Intelligent Bio-Nano Materials and Structures for Aerospace Vehicles Effective Properties of CNT Composites Nanotubes are ideal for use in composites -Stronger than steel with an extremely low density -Long elongation to break -Cannot stand alone…need to be combined with another material Assumptions -Well-aligned (difficult to obtain… nanotubes are attracted to one another and form bundles/ clusters) and parallel -Identical geometry (difficult to form exact nanotubes) -CNT perfectly bonded to matrix Insertion of carbon nanotubes (CNT) in materials alter these materials’ effective properties making these composites multifunctional and useful Modeling these composites is both economically and time efficient Alignment of Carbon Nanotubes within Clusters in a Polypropylene (TEM) *Specimens Provided by Dr. Barrera with TEM Imaging by Piyush Thakre

4. Texas Institute for Intelligent Bio-Nano Materials and Structures for Aerospace Vehicles Objectives Parametric Studies on Stiffness Ratio –Techniques: 1 – Step: Multiphase Composite Cylinders 2 – Step: Generalized Self-Consistent Parametric Studies on Interphase –Stiffness Ratio –Interphase Stiffness –Interphase Thickness Allows for Comparison with Standard Composites Obtains Properties for Varied Thickness and Stiffness Nanotube Polymer Perturbed Polymer or Compliant Interphase Several studies were preformed to determine the effective properties of these carbon nanotube composites to show how fiber/matrix stiffness ratios affect composite properties at various CNT volume fractions. Transform from various properties into a composite of ONE effective property ENEN EIEI EMEM E

5. Texas Institute for Intelligent Bio-Nano Materials and Structures for Aerospace Vehicles 2 – Step Technique Generalized Self-Consistent Transversely Isotropic* Effective Carbon Nanotube Composite Cylinders Model Single Wall Carbon Nanotube Effective CNT Embedded in Matrix Generalized Self-Consistent Effective Composite (Transversely Isotropic*) Step 1: Effective Carbon NanotubesStep 2: The Generalized Self-Consistent Technique or The Mori-Tanaka Method or Mori-Tanaka Polymer Matrix - Same energy stored - Same boundary conditions/geometry  Obtains properties for the transversely isotropic effective carbon nanotube - Assume effective properties are unknown and are solved for iteratively GSC - Assume effective properties are close to matrix and are solved in a single iteration – Mori-Tanaka ***Based on original Eshelby solutions for a single inclusion in a matrix*** *Transversely Isotropic: Property is the same in a plane but different in the direction normal to the plane of isotropy x3x3 x2x2 x1x1

6. Texas Institute for Intelligent Bio-Nano Materials and Structures for Aerospace Vehicles 1 - Step Technique a b c CNT Embedded in Matrix Effective Composite (Transversely Isotropic) Multiphase Composite Cylinder c This application is different in that the matrix and the nanotube have matching boundary conditions. The values for traction and displacement are equal. This method is used for interphase studies with additional boundary conditions to account for the interphase region. Nanotube Interphase Matrix

7. Texas Institute for Intelligent Bio-Nano Materials and Structures for Aerospace Vehicles Parametric Study on Nanotube:Matrix Stiffness Ratio Axial Young’s Modulus: E11 - Tension test performed parallel to the nanotube axis x3x3 x2x2 x1x1

8. Texas Institute for Intelligent Bio-Nano Materials and Structures for Aerospace Vehicles Parametric Study on Nanotube:Matrix Stiffness Ratio Transverse Modulus: E22 - Tension test performed perpendicular to the nanotube axis x3x3 x2x2 x1x1

9. Texas Institute for Intelligent Bio-Nano Materials and Structures for Aerospace Vehicles Conclusion Now have data which sweeps through all reported nanotube properties…present data 200-1000 GPa in literature…entire nanotube spectrum As stiffness ratios decreases –act as standard composite results –higher values of effectives properties occur earlier Showed that indeed it is the very large stiffness difference which causes irregular behavior Change occurs after 60% Volume Fraction