1. Gary D. Seidel Virginia Polytechnic Institute and State University Dimitris C. Lagoudas & Piyush R. Thakre Texas A&M University Sarah-Jane V. Frankland & Thomas C. Clancy
National Institute of Aerospace Jiang Zhu
NanoRidge Jaret C. Riddick U.S. Army Research Laboratory
Micromechanics Modeling of the Elastic and Thermal Properties of Carbon Nanotube-Epoxy Nanocomposites and Unidirectional Hybrid Laminates
Gary D. Seidel Virginia Polytechnic Institute and State University
Dimitris C. Lagoudas & Piyush R. Thakre Texas A&M University
Jaret C. Riddick U.S. Army Research Laboratory
Sarah-Jane V. Frankland & Thomas C. Clancy
National Institute of Aerospace
Jiang Zhu
NanoRidge
45th Technical Meeting of the Society of Engineering Science Multiscale Modeling and Characterization of Nano-structured Polymer Composites Session
Urbana-Champaign, Illinois October 12th-15th 2008

2. Aircraft Structural Composites: Potential Applications for Nanocomposites
Aircraft Multifunctional Structural Components:
“Boeing has announced that as much as 50 percent of the primary structure -- including the fuselage and wing -- on the 787 will be made of composite materials.”
“For example, the team is looking at incorporating health-monitoring systems that will allow the airplane to self-monitor and report maintenance requirements to ground-based computer systems.”
Use of nanocomposites for improved fracture toughness, electrostatic discharge, and damage detection in carbon fiber composites
Boeing
Applications of Nanocomposites
Nanocomposites vs Stitching: can’t compute with carbon fiber stiffness, but surface to volume ratio means that you can significantly modify resin material with a small amount of nanomaterial while retaining mechanical properties perhaps adding multifunctionality.
Boeing

3. Motivation For Carbon Nanotube Nanocomposites in Structural Composites
High modulus and strength to weight ratios, large aspect ratio make CNTs attractive as reinforcing material
Boeing 787
Electrical and thermal properties of CNTs has potential to impart multifunctionality to composites
Surface-to-Volume Ratio implies large impact of CNT properties from a small amount of nanomaterial
NASA ARES Mars Aircraft
Applications in terms of engineering design require large scale production and reliable estimates material properties from measurement and modeling
Broad interest, how this pertains to fix wing subsonic. Broad Motivation Nanocomposites (Cheaply explore the design space with reliable models)
q =30o
q=0o q
Grams
SWNT  
90wt%
SWNT
  50wt% 
MWNT
 <8nm
>50nm 10
$1,350
$300
$275
$75
100
$8,500
$2,250
$1,500
$400
1KG
$75,000
$30,000
$3,500
$900

4. Pristine SWCNTs (bundle)
Material System: CNT Nanocomposite Enriched Unidirectional Carbon Fiber Composites
Pristine SWCNTs (bundle)
20 nm
HiPCO Produced Pristine Single-Wall Carbon Nanotubes (Amide-functionalized SWCNTs also considered)
SWCNTs are prepared for dispersion in the toughened epoxy RS47
1μm
CNT bundles
Carbon
Fiber
SWCNTs are sprayed on RS47 prepreg forming CNT-RS47 nanocomposite region around carbon fibers
IM7 Carbon Fiber in micron scale picture, but wanted the idea. Would like more details here (radii, length, spray technique, fiber types, fiber volume fraction)
Carbon Fibers
Obtain Unidirectional Carbon Fiber Composite with Nanocomposite-Coated Carbon Fibers

5. Identifying Relevant Length Scales
Radial distance
rIV
rIII
CNT vol frac Vo
Carbon Fibers
Composite Cylinder Model: Effective Unidirectional Lamina Properties
Carbon
Fiber
Matrix
Lamina RVE
cross-section
Randomly Oriented CNTs in Interphase Regions
CNT
Molecular Dynamics CNT-Epoxy RVE
Molecular Dynamics: Effective Nanotube and Nanotube Polymer Interphase
Micromechanics Orientation Averaging: Randomly Oriented Effective Nanotubes
Top Down Visualization
Bottom Up Modeling

6. Identifying MD Input for Micromechancis Modeling
DGEBA/DDS Epoxy
DGEBF/DDS Taken as approximation of RS47 Epoxy without the toughener. May have some difficulty explaining why shear modulus in nanotube direction is lower than the matrix…infinitely long? Small increase in mu23 demonstrates the weak interaction between nanotube and epoxy? Comes from trying to make results consistent. Factor or 2 not in C44…has 2 Epsilon. The volume fraction of CNT corresponds to an outer radius of 4.58 nm and therefore a 3.58 nm thick epoxy layer surrounding the nanotube (assuming CNT radius of 1nm). Sarah has amide functionalized MD. Sarah wants to do amine.
DGEBA/DDS Epoxy
with Nanotube
MD by Sarah-Jane Frankland
4.76 vol % NT

7. Nanocomposite Layer Effective Nanotube Volume Fraction Distribution
Decreasing Volume Fraction Distributions
Increasing Volume Fraction Distributions
Effective Nanotube Volume Fraction in Lamina
Effective Nanotube Volume Fraction in Lamina
0.9%
2.0%
1.5%
0.4%
1.1%
0.1%

8. Accounting for Random Orientation of Effective Nanotubes
Randomly Oriented CNTs in Interphase Regions
Treating each orientation of K orientations as a separate phase:
If randomly oriented, averaging over all possible orientations:
Where all of the quantities in the local effective nanotube coordinate system have been expressed in the global coordinate system using Euler angle rotations.
And the concentration tensor is determined using a Mori-Tanaka approach
where

9. Material Property Distributions
Distributions Corresponding to Decreasing Volume Fraction Distributions
Distributions Corresponding to Increasing Volume Fraction Distributions

10. Composite Cylinders Property Distribution Approximations
Epoxy Matrix
Nanocomposite Enriched Region
Carbon Fiber
Epoxy Matrix 2.97 GPa
Carbon Fiber 279 GPa
Nanocomposite Enriched Region

11. Composite Cylinders Property Distribution Approximations
Distributions Corresponding to Decreasing Volume Fraction Distributions
Distributions Corresponding to Increasing Volume Fraction Distributions

12. Multi-Layer Generalized Self-Consistent Composite Cylinder: Bulk Modulus
Effective Material
CCA In-Plane Bulk Modulus:
Epoxy Matrix Material
Layer Displacement:
Nanocomposite Interphase
Carbon Fiber
Boundary Conditions:
Radial Displacement
Bounded Displacement at Origin
Matching Conditions:
In-Plane Bulk Modulus:
Energy Equivalency
Hashin and Rosen, J. of Apld. Mech., 1964.
Christensen and Lo, J of Mech & Phys Solids, 1979.
Herve and Zaoui, Int. J. of Eng Sci, 1995.
Carman et al., J. of Comp Mats., 1993.
Seidel and Lagoudas. Mech of Mats 2006.
Point of Slide: Sample boundary value problem
Hashin and Rosen, J. of Apld. Mech., 1964.
Christensen, Mechanics of Composite Materials Krieger Publishing Company, 1979.
G.D Seidel & D.C. Lagoudas. 2005, Mechanics of Materials, In Press.

13. In-Plane Bulk Modulus of Carbon Fiber Laminae
At a Carbon Fiber Volume Fraction of 60%
2.0%
1.5%
Effective Nanotube Volume Fraction in Lamina
1.1%
0.9%
0.4%
0.1%
Would be good to have compared these results to idealized nanotube model with perfect interface.
2.57%
1.19%
0.29%
5.23%
4.19%
2.89%
Also Provided are % Differences Relative to No Nanocomposite Case

14. MD Results for Interfacial Thermal Resistance with Functionalization
Kapitza Resistance:
Identified as large impedance of thermal phonons across an interface as a result of acoustic mismatch
Orders of magnitude difference in elastic properties between CNT and polymer indicative of acoustic mismatch
Defined in terms of a temperature difference across an interface of area A
MD by Tom Clancy

15. Generalized Self Consistent Composite Cylinder for Thermal Conductivity
Assemblage Strain Concentration Tensor:
Total Assemblage
Average Strain Over CNT+Interphase:
Composite Cylinder Assemblage
Average Strain Over Total:
Assemblage BVPs:
Axial Conduction:
Layer Potential:
Boundary Conditions:
Tell for cnt idealized with 2000 W/mK annular conductivity
Transverse Conduction:
Layer Potential:
Boundary Conditions:
Lateral Heat Flow
Insulated Interior

16. Incorporating Interfacial Thermal Resistance in GCCM
Effective Material
Matrix Material
Here we propose treating the Kapitza Resistance in the Generalized Self-Consistent Composite Cylinder Model through the inclusion of a thin interphase region.
Kapitza Layer
CNT
For an N=3 Composite Cylinder Model, layer 1 is the CNT, layer 2, the interphase, and layer 3 the matrix. The interphase conductivity is determined from a flux condition resembling a convection boundary condition:
Where β is the Kapitza Conductivity (i.e., the inverse of the Kapitza Resistance).
The constants (A and B) are determined through the application of the boundary and matching conditions for the entire composite cylinder assemblage.
Seidel and Lagoudas, JAM, 2008

17. End Effects Associated with Interfacial Thermal Resistance
The Axial Conductivity of CNT Annulus is reduced as if capped by an interphase of thickness, t.
Conductivity of caps determined from Lateral Interface Thermal Resistance
The cap thickness t is identical to the Interphase thickness
Thickness goes to zero returns CNT conductivity
Conductivity goes to zero returns fully insulated CNT
Conductivity goes to infinity returns
Seidel and Lagoudas, JAM, 2008

18. Material Property Distributions
Decreasing Vf Distributions Corresponding to Varying Grafting Densities
Increasing Vf Distributions Corresponding to Varying Grafting Densities

19. Composite Cylinders Property Distribution Approximations
Epoxy Matrix
Nanocomposite Enriched Region
Carbon Fiber
Epoxy Matrix 0.16 W/mK
Carbon Fiber 15 W/mK
Nanocomposite Enriched Region

20. Thermal Conductivity of Carbon Fiber Laminae
At a Carbon Fiber Volume Fraction of 60%
140%
57%
52%
25%
22%
11%
Would be good to have compared these results to idealized nanotube model with perfect interface.
Decreasing alpha = 1.45
Increasing alpha = 0.02
2.0%
0.9%
Effective Nanotube Volume Fraction in Lamina
Also Provided are % Differences Relative to No Nanocomposite Case

21. Summary and Conclusions
A multiscale model has been developed which uses input from MD simulations to account for nanoscale interface effects, and is applied toward the prediction of hybrid composite laminate properties.
The model indicates that inclusion of a small amount of nanocomposite material around the carbon fiber can have a small impact on the transverse properties of the lamina
The model indicates that inclusion of a small amount of nanocomposite material around the carbon fiber can have a very significant impact on the transverse conductivity, particularly when the nanotubes are functionalized

22. Acknowledgements
NASA Research Agreement (NRA) #NNX07AB86A - Multiscale Modeling and Characterization of Nano-structured Polymer Composites
Mr. Jeff Cowley – Undergraduate Research Assistant at Texas A&M
Gary Don Seidel Assistant Professor Aerospace and Ocean Engineering Virginia Polytechnic Institute and State University Web:

23. Comparison to Initial Characterization Efforts
2.8-32% 3%
1.6%
11.5%
Bulk Modulus can typically be 20-50% larger than E22; here it is 25%
Sample Preparation and Characterization by Piyush Thakre and Jiang Zhu