samantha vaitkunas rose-hulman institute of technology parametric studies of micromechanics analyses...
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Samantha VaitkunasRose-Hulman Institute of Technology
Parametric Studies of Micromechanics Analyses of
Carbon Nanotube Composites
Dr. Dimitris Lagoudas, AdvisingGary Seidel, Mentor
August 6, 2004
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 = 0o
*Armchair Metallic = 30o
- Manufactored by high energy processes: HiPco, Laser Ablation - Measured grams per day production due to small size
Copyright Professor Charles M. Lieber Group
NN
AA
NN
OO
TT
UU
BB
EE
Material Young's modulus (GPa) Tensile Strength (GPa) Density (g/cm3)
Single wall nanotube 1054 150 ~ 1.33 to 1.40
Multi wall nanotube 1200 150 2.6
Steel 208 0.4 7.8
Epoxy 3.5 0.005 1.25
Wood 16 0.008 0.6Copyright 2002-2005 Applied Nanotechnologies, Inc.
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
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
NanotubePolymer
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
EN
EI
EM
E
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 CNTEmbedded in Matrix
Generalized Self-Consistent
Effective Composite(Transversely Isotropic*)
Step 1: Effective Carbon Nanotubes Step 2: The Generalized Self-Consistent Technique
or The Mori-Tanaka Method
or
Mori-TanakaPolymer 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
x3
x2
x1
Texas Institute for Intelligent Bio-Nano Materials and Structures for Aerospace Vehicles
1 - Step Technique
ab
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 InterphaseMatrix
Texas Institute for Intelligent Bio-Nano Materials and Structures for Aerospace Vehicles
Parametric Study on Nanotube:Matrix Stiffness Ratio
Normalized Axial Young's Modulus Comparison of 1-Step and 2-Step CC/SC Trends For Various CNT: Matrix Stiffness Ratios
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Volume Fraction of CNTs
No
rma
liz
ed
E1
1
1 Step - Ratio: 1100:3
1 Step - Ratio: 697:3
2 Step - Ratio: 697:3
2 Step - Ratio: 1100:3
Axial Young’s Modulus: E11 - Tension test performed parallel to the nanotube axis
x3
x2
x1
Texas Institute for Intelligent Bio-Nano Materials and Structures for Aerospace Vehicles
Normalized Transverse Modulus Comparison of 1-Step and 2-Step CC/SC Trends For Various CNT: Matrix Stiffness Ratios
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Volume Fraction of CNTs
Nor
mal
ized
E22
1 Step - Ratio: 1100:3
1 Step - Ratio: 697:3
2 Step - Ratio: 697:3
2 Step - Ratio: 1100:3
Parametric Study on Nanotube:Matrix Stiffness Ratio
Transverse Modulus: E22 - Tension test performed perpendicular to the nanotube axis
x3
x2
x1
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