This document discusses multiscale modeling of liquid crystalline polymer (LCP) and carbon nanotube composites. It motivates using LCP and CNTs due to their high strength, stiffness, and thermal conductivity. The research aims to develop the composite forming process and optimize mechanical and thermal properties using a mathematical modeling approach. It describes using a Mori-Tanaka model with Eshelby's tensor to predict elastic properties based on nanotube orientation, volume fraction, and interfacial conditions. It shows accomplishments in modeling elastic properties and relationships between moduli and fiber volume fractions. Future work includes optimizing the model with different fiber orientations and aspect ratios.

1. Multiscale modeling of Liquid
Crystalline/Nanotube composites
Sharil Patrale
Guided by:
Dr. Gregory Odegard

2. Outline
• Introduction
• Motivation
• Application
• Method
• Accomplishments
• Current work
• Future work

3. Introduction
• Composite material is a material composed of
two or more distinct phases.
• Types of composites
– Metal matrix composites
– Ceramic matrix composites
– Polymer matrix composites

4. Polymer Matrix Composites
• Material consisting of a polymer matrix combined
with a reinforcing phase of fibers.
• Exhibit high strength and stiffness
• Light in weight.
• Show directional strength properties
• Carbon fiber reinforced polymer composites.

5. Liquid crystalline polymer
• Obtained by dissolving a polymer in solvent or
heating to its melting point
• High mechanical strength
at high temperatures
– High strength to weight ratio
when combined with
nanotubes
Material : Liquid Crystal
Polymer LCP 304T40
• Used for electrical
and mechanical parts

6. Why Carbon Nanotubes?
• Very high strength-
Stronger than the sp3
bonds in Diamond
• High stiffness
• High thermal conductivity
• Extremely light weight-
about 1/5th of the weight
of steel

7. Motivation
• Ability of LC molecules (matrix) to be oriented in
preferred direction using electric or magnetic
fields
• Surface tension aligns the nanotubes
• Resulting mechanical and thermal properties

8. Applications
• Vehicle and aircraft components
– Surfacing, engine components
• Sport goods
– Racquets, Helmets, Bikes
• Electronic sensor components
• High temperature applications

9. The Research
• To develop the nano-composite forming
process.
• To optimize the mechanical and thermal
properties of the nano-composites.
→ To implement a mathematical modeling
approach for efficiently predicting the
composite’s mechanical properties.

10. Mechanical/elastic properties
• E1 – longitudinal young’s modulus
• E2 – transverse young’s modulus
• v12 – longitudinal poisson’s ratio
• v23 – transverse poisson’s ratio
• G12 – longitudinal shear modulus

11. Micromechanics
• Analysis of a composite at the level of its individual
constituent
• Can predict the multi-axial properties of anisotropic
composites
• Typically based on continuum mechanics
– Response of anisotropic materials
→ Focus on Mori-Tanaka modeling approach

12. Mori-Tanaka modeling approach
• Calculating the average internal stress in the
material
• More efficient than any other method with
anisotropic matrix
• Predicting elastic properties as a function of
– Nanotube orientation
– LC orientation
– Nanotube volume fraction
– Interfacial conditions

13. Eshelby’s Tensor
• Fourth order tensor, Sijkl ( ij = ji)
• Relates the average fiber strain to the average
matrix strain.
c=S T
ij ijkl kl
• Depends on the properties of the matrix material

14. Numerical integration using Gaussian Quadrature:

15. Accomplishments
• Mathematical model to determine elastic
properties of LaRC-SI/nanotube composite.
• Relationship between various moduli and fiber
volume fractions at different aspect ratios.
• Model to calculate Eshelby’s tensor for
anisotropic matrix
• Corresponding graphs are shown.

16. Moduli for various nanotube lengths

17. Aligned fibers

18. Randomly oriented fibers

19. Future work
• Searching for properties of LC polymer (RM-
257)
• Using various fiber/matrix orientations and
aspect ratios
• Optimizing the model

20. Thank you