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