Integrated Model of Carbon Fiber

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Figure 1. Visual decomposition of the ICME problem for Graphite/Epoxy

Aerospace structural design is driven primarily by the weight and rigidity of the design. These requirements have led to the wide spread use of light weight high modulus materials such as graphite epoxy composites. Wing structures are particularly vulnerable to vibrational failure. Long thin wings often have natural frequencies that can be excited in flight due to the coupling between aerodynamic loads and structural displacement. In one of these aeroelastic effects, flutter, the wing will vibrate at its natural frequency and causing much higher loads than would be statically predicted. To prevent these vibration driven failures, the higher modulus material or a stiffer design are used. The lighter these structures are, the better the aircraft’s performance or the more fuel or cargo can be carried.

Graphite epoxy composites are composed of two distinct materials: graphite fibers and epoxy matrix. For multiscale analysis, these must be treated as separate materials then “combined” using the connection between the two materials. Since the goal of this analysis is to obtain the material properties for a vibrational and failure analysis, certain information is needed from each of the length scales to gather the full material models. For graphite, the ultimate goal is the elastic moduli, the high rate mechanisms, and the strength of the material. From this the vibrational modes, the material reactions and the failure criteria can be established. For the epoxy, the needed data is the elastic moduli, the high rate mechanisms and the crack nucleation and growth. Because the failure is vibrational, the strength of the epoxy can be ignored as the cyclic loading will fail the epoxy below its ultimate strength. Knowing the end goals each material can be built up through the length scales.

Graphite Scales

Graphite is a carbon based material that is formed from layers of graphene. Graphene is carbon chemically bonded together in a two dimensional lattice that is hexigonal in shape.[1] Graphite is formed by layers of graphene held together by Van der Waals force.[2]


-Using DFT analysis, the Elastic Moduli of the graphite is determined.[2] Bridge to Atomistic -The elasticity as well as the interatomic energies are needed by the atomistic level simulation


-Due to the high percentage of free edges in the graphite a method of analysis that captures edge effects, such as the modified embedded atom method (MEAM), must be used. This analysis yields the material’s High Rate reactions. Note that there is no atomistic level bond between the graphite and epoxy as the protective sizing on the graphite prevents it.[3] Bridge to Extended Graphite ribbons -To perform coarse grain analysis on the fibers, the total energy of each section represented is needed.

Extended Graphite ribbons

-The extended graphite ribbons, layered to form the fiber, are simulated by a coarse grain analysis to determine the ribbon’s strength. The graphite does not contain a grain structure, but coarse grain analysis can predict deflections.[1]

Epoxy Scales


- Using DFT analysis, the Elastic Moduli of the epoxy is determined. Bridge to Atomistic -The elasticity and the interatomic energies are transferred to the atomistic level simulation.


-The epoxy’s high rate effects are obtained by embedded atom simulations or MEAM Bridge to Coarse Graining -The void nucleation and growth in thermoset polymers is driven by crosslinking of the polymer chains.[4]

Coarse Graining

-Using the crosslinking information the Void/ Crack nucleation and growth can be determined by finite element analysis.[5]


Once the material properties are determined for each of the materials, the properties of the combined material can be determined using the volume fraction for each material and the interaction or bridge between the materials.

Graphite/Epoxy Bridge

Bridge between Graphite and Epoxy -The etching on the graphite informs the frictional bond between the Graphite and Epoxy. This interaction defines the material as a whole.[3]


Finite Element vibrational modeling is performed using internal state variables established through previous multiscale techniques. Software packages such as NASTRAN provide aeroelastic analysis which calculates not only the structural response, but the aerodynamics and their interaction to determine flutter, control reversal, or divergence.


  1. 1.0 1.1 Cranford, S., Buehler, M.J., “Twisted and Coiled Ultralong Multilayer Graphene Ribbons.”
  2. 2.0 2.1 Charlier, J.C.,Gronze,X., and Michenaud, J.P. "Graphite Interplanar Bonding: Electronic Delocalization and van der Waals Interaction"
  3. 3.0 3.1 Strong, B. “Practical Aspects of Carbon Fiber Surface Treatment and Sizing.”
  4. Yagyu, H, et al, “Coarse-Grained Molecular Dynamics Simulation of Epoxy-Based Chemically-Amplified Resist for MEMS Application
  5. Riddick, J.C., Frankland, S.J.V., Gates, T.S., “Multiscale Analysis of Delamination of Carbon Fiber-Epoxy Laminates with Carbon Nanotubes.”
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