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Electrical Conductivity Modeling andValidation in Unidirectional CarbonFiber Reinforced Polymer Composites
John L. SchmidtDr. Parag Banerjee
Mechanical Engineering and Materials ScienceWashington University in St. Louis, St. Louis, MO
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Background Why electrical conductivity modeling of carbon fiber
reinforced polymer composites? Lightning strike protection of aircraft Electrostatic discharge/electromagnetic interference
Paur, Wired.com (2009)
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Why COMSOL? COMSOL is useful in this study because:
Modeling saves resources It provides a nearly complete suite of software to model:
the current system in three dimensions multiple physics interactions
Electrical
Electrical + Thermal
Electrical + Thermal + Mechanical
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MODEL SETUP
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Basic Model Setup Electric Currents Node within AC/DC Module of
COMSOL Multiphysics (base package)
Potentialapplied ontop surface
Bottom surfacegrounded
Fiberorientation
1 ply
78% fiber loading
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Modeling the Non-Percolation State
Both carbon fiber and polymer are conductive. Carbon fibers contribute very little to the resistance
therefore CF =
Carbonfiber
Polymer resin
ConstantsThermal activation energyElementary chargeTemperatureElectric field
Boggs, et al. , IEEE Trans. Power Del. (2001)
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Modeling the Percolation State
Carbon fiber is the only conductor.
The carbon fiber was considered conductive, and the polymerwas considered virtually non-conductive.
ContactImpedance
Polymer resin
Carbon fiber
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Contact Impedance and Validation
M. Mohiuddin, S. Hoa,Composites Science andTechnology (February 2013)
ExperimentalResult Range
Experimentally, a ply conductivity valueof ~0.04 S/m was found.
Phenomenologically, this indicates acontact resistance exists which is equalto the tunneling distance of 16 ofPEEK.
The resistivity of each node wasapplied from Mohiuddin and Hoa.
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MODELING RESULTS
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The effect of fiber content andverification
A wide range of fiber content was modeled.
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Scaling beyond one ply
1st ply
2nd ply
Interface
Potential applied
Grounded(underneath)
Fiberorientation
Fiberorientation
These verified results can be used to build and analyze larger morecomplicated objects
The number of contacts between two plys was taken into account
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Scaling beyond one ply
Fitting to an equivalent circuit:
Coefficients (R2 = 0.9991):
Rcontact= 1.889e+07 OhmsRblock = 3.534e+05 Ohms Analytical Rblock = 3.37e5 Ohms
These verified results can be used to build and analyze larger morecomplicated objects
The number of contacts between two plys was taken into account
10/10/2013 John L. Schmidt Electrical Conductivity of Composites
Equivalent Circuit
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(0 , 45 , 90 , 45 , 0 ) Composite Example
This kind of compositeis very frequently usedindustrially.
Overall conductivity ofcomposite:0.0323 S/m with~10x10 contacts ateach interface.
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Conclusions COMSOL Multiphysics can be used to model the electrical
conductivity of carbon fiber reinforced polymer composites. Conductivity models were produced for above and below
the percolation threshold.
The percolation model was validated through agreement withexperimentally determined contact resistance between twofibers.
Electrical conductivity was modeled across the entire CF loadingrange.
These basic models were scaled to a more typical industrialcomposite consisting of multiple plies with different contactconfigurations.
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Acknowledgements
Washington University Department of MechanicalEngineering and Materials Science
Boeing Research & Technology Collaborators: Stephen Heinz and Gregg Bogucki
Washington University Start-up funds
Washington University Nanotechnology ResearchFacility, funded by NSF
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