Image-based modelling of carbon/carbon composites

Image-based modelling of
carbon/carbon composites
J. Ali and P. M. Mummery
School of Materials,
University of Manchester, UK
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The Victoria University of Manchester

Introduction
Objective of study
2D woven composites
Methodology of image-based (IB) modelling
– X-ray
Microtomography to FE meshes.
3D Unit cells
FE modelling of mechanical and thermal behaviour
– Nanoindentation for input mechanical data
– Micro-thermal properties from literature
– Compression test (validation)
– Laser flash test (validation)
Future work on irradiation
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Objective
Predicting mechanical and thermal properties
– Function of architecture, irradiation and temperature (end goal)
– Greater focus on the complex material architectures
– Framework for all classes of material with similar structures
ExtreMat
– European Integrated programme
– New materials for extreme environments
Irradiation, temperature, heat flux
C/C Composites
– Restraints and control rods in fission reactors
– Divertor structures in fusion reactors
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2D Woven C/C Composites
Toyo Tanso CX-27
Graphitised & Un-graphitised conditions
Lamina (X)
(Ishihara, JAEA)
Perpendicular (Y)
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What is X-ray X
Microtomography?
Non-destructive technique for imaging the
internal structure of samples in 3D
Set of radiographs of sample at many
orientations obtained by rotating it within beam
Read by reconstruction software
3D attenuation contrast image of object using
standard filtered back-projection algorithm
[1]
[1] Babout et al.: Carbon, 2005, 43, 765-774.
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What is X-ray X
Microtomography?
3-D D data set
Ability to visualise internal
features non-destructively
Characterise structures
– “Virtual” metallography
Study deformation
processes in situ
FE Modelling
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Tooth and Filling

X-ray Microtomography Data
Imaging conditions at a low voltage of ∼60-70kV and
90-210
210µA, with pixel resolution of ~20µm
Graphitised C/C:
Grey Scale image
Porosity
Transverse
shrinkage cracks
Matrix
Fibre(s)
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200µm

Creating IB FE Meshes
Deduce volume fraction of composite phases:
Porosity % - Pore-Master (Porosimeter(
Porosimeter)
– Archimedes (water) displacement test - compared
Fibre % and matrix % - SEM Images
Work out image threshold representative to
volume fraction of phase(s)
Mesh generated via Simpleware LTD
Mechanical properties of fibres and matrix
determined by Nanoindentation
Thermal properties taken from literature
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[2]
[2] Ali et al.: ‘Image-based modelling of stress/strain behaviour
in carbon/carbon composites’, Energy Materials, 2006.

Microstructural Representation
Transverse
Un-graphitised
C/C composite
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FE Mesh
Red = Porosity, Blue = Matrix, Yellow = fibres
1mm
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Unit-cell for comparison
Upgraded to curve architecture [3]
0.5mm
[3] Farooqi et al.: Comp. Mater. Sci., 2006, 37, 361-373.

Micromechanical data
Properties of fibres and matrix:
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GRAPHITISED
Region Indented
Side-of-fibres
End-of-fibres
Matrix
UN-GRAPHIT.
Region Indented
Side-of-fibres
End-of-fibres
Matrix
No. of Indents
11
3
3
No. of Indents
10
3
3
Mean Modulus
(GPa)
7.1 (±1.6)
24.9 (±1.9)
11.4 (±2.7)
Mean Modulus
(GPa)
5.5 (±1.0)
22.8 (±2.1)
7.5 (±1.1)

Images of Indents
Matrix less elastic recovery compared to fibres
End-of-fibres
(parallel)
Indent marks
in matrix
(Remaining)
Atomic Force Microscope
(AFM)

Compressive Testing
Validate the models with experimental data
Loading
Extensometer
Platen 1
Platen 2
Sample
Cubic samples:
6mm x 6mm x 6mm
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Stress/strain results
Graphitised C/C composite – lamina direction
80
70
60
Stress (MPa)
50
40
30
20
10
0
Experimental
Image-based
Analytical
Unit-cell
0 0.001 0.002 0.003 0.004 0.005
Strain

Stress/strain results
Graphitised composite – perpendicular direction
100
90
80
70
Stress (MPa)
60
50
40
30
20
10
0
Experimental
Image-based
Analytical
Unit-cell
0 0.04 0.08 0.12 0.16 0.2
Strain

Stress/strain results
Un-graphitised C/C composite – lamina direction
70
60
50
Stress (MPa)
40
30
20
10
0
Experimental
Image-based
Analytical
Unit-cell
0 0.001 0.002 0.003 0.004 0.005 0.006
Strain

Stress/strain results
Un-graphitised composite – perpendicular direction
160
140
120
Stress (MPa)
100
80
60
40
20
0
Experimental
Image-based
Analytical
Unit-cell
0 0.03 0.06 0.09 0.12 0.15
Strain

Shear failure
Lamina direction
Perpendicular direction

Analysis of stress/strain curves
Predictions of Young’s s modulus, E (GPa(
GPa):
Derived from stress/strain curves
Loaded
Direction
Graphitised
lamina
Graphitised
perpendicular
Un-graphitised
lamina
Un-graphitised
perpendicular
Experimental
22.0
0.6
15.4
1.3
Image-based
16.3
0.5
13.2
1.1
Unit-cell
16.7
2.3
13.0
1.5
Analytical
13.3
8.7
11.2
6.2
Best predictions highlighted in red
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Summary of stress/strain results
Good correlation between both FE models and
experimental curves (valid)
Image-based models better than analytical and
unit-cells
Unit-cell comparable in lamina direction but
linear – neglect of porosity
Comparison of image-based predictions:
– Un-graphitised model gave better agreement with
experiment than graphitised
– More representative area chosen for mesh
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Computational power

Thermal Conductivity:
Measurement Principle
Thermal conductivity:
λ = α ρ C p
– α: : thermal diffusivity (Laser flash)
– : : average density
[4]
– C p
: specific heat
Laser flash
– heat pulse on a sample front face
– temperature raise recorded on rear face
T (ºC)
T max
α =
0.136* L
t
1/ 2
[4] Chawla: ‘Ceramic Matrix
t 1/2 time (s) Composites’, Chapman & Hall, 1993.
2

Schematic of
Laser Flash Rig

Thermal Analysis
Thermal diffusivity measurements converted to
thermal conductivity
– Used to validate FE predictions
Best representative input data taken from
literature
[3]
Steady state FE analysis
Fourier’s s law
Heat flux marks thermal conductivity
Predictions made using:
– Image-based models
– Unit-cells
Sub-models for 4 classes of porosity (A-D) designed by
Farooqi et al.
[3] Farooqi et al.: Comp. Mater. Sci., 2006, 37, 361-373.

Porosity classes
4 Classes of porosity identified by optical and
scanning electron microscopy
[5]
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[5] Puglia et al.: Composites Part A: Applied Sci.
and Manufac., 2004, 35, 223-230.

Thermal results
Graphitised C/C
Composite
Experimental
results (Wm -1 K -1 )
Image-based
model (Wm -1 K -1 )
Unit-cell model
(Wm -1 K -1 )
Un-graphitised C/C
Composite
Experimental
results (Wm -1 K -1 )
Image-based
model (Wm -1 K -1 )
Unit-cell model
(Wm -1 K -1 )
Lamina direction
13.94
15.31
16.81
Lamina direction
9.42
11.32
11.47
Perpendicular
direction
5.04
5.85
7.01
Perpendicular
direction
2.85
3.44
3.95

Optimisation
Optimum input data
Material direction
Graphitised composite:
Lamina
Perpendicular
Average:
Un-graphitised composite:
Lamina
Perpendicular
Average:
Thermal conductivity, k (Wm -1 K -1 )
Fibre parallel
33.50
35.44
34.47
21.92
18.57
20.25
Fibre transverse
3.35
3.54
3.45
2.19
1.86
2.03
Matrix
8.38
8.88
8.63
5.48
4.64
5.06
Input data should be the same for both directions
– Therefore best representative input data is in theory
average of the above values for each constituent

Comparison of input data
Literature based input data versus optimised
Graphitised C/C
Composite
Expt. . (Wm -1 K -1 )
Literature (Wm -1 K -1 )
Optimised (Wm -1 K -1 )
Lamina direction
13.94
15.31
13.22
Perpendicular
direction
5.04
5.85
4.90
Un-graphitised C/C
Composite
Expt. . (Wm -1 K -1 )
Literature (Wm -1 K -1 )
Optimised (Wm -1 K -1 )
Lamina direction
9.42
11.32
8.70
Perpendicular
direction
2.85
3.44
3.10
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Summary of thermal results
Image-based models showed superior agreement with
experimental data
– Slight over-prediction
– Literature input data questionable, optimised input data better
Image-based models gives truer representation of
composite structure
Unit-cell based on idealisations of composite
microstructure
Difference lies in consideration of porosity
Unit-cell main weakness in perpendicular direction
– Thin laminate structure

Application of framework
Materials under investigation:
NB-31 3D C/C Composite
B0-27 2D SIC/SIC Composite
SGL 2D C/C Composite
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Conclusion
Comparison of FE techniques for woven composites
Providing useful initial results
Overall results indicate image-based models better at
predicting mechanical & thermal behaviour
Image-based meshes account for complex network of
pores in structure
FE analysis complicated due to stress shielding large pores
More difficult to assign truer properties
Unit-cells based on idealisations of composite
microstructure
Truer properties
Thinness main weakness

Future work
Un-irradiated predictions completed
Shows potential for predicting irradiation
behaviour using IB FE meshes
Tomography scans of irradiated materials
Other alternatives similarities with thermal oxidation
Need irradiation input data:
Fibres & Matrix
History
Porosity and constituent dimensional changes
under irradiation already accounted
Irradiation sub-routine developed for graphite
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May eventually be applicable to carbon composites

References
[1] L. Babout, , P. M. Mummery, T. J. Marrow, A. Tzelepi,
P. J. Withers: Carbon, , 2005, 43, , 765-774.
774.
[2] J. Ali, C. Berre and P. M. Mummery: ‘Image-based
modelling of stress/strain behaviour in carbon/carbon
composites’, , accepted for publication in Energy
Materials
[3] J. K. Farooqi, , M. A. Sheikh: Comp. Mater. Sci., , 2006,
37, , 361-373.
373.
[4] K. K. Chawla, ‘Ceramic Matrix Composites’, , Chapman
& Hall, 1993.
[5] P. Del Puglia, M .A. Shiekh, , D. R. Hayburst:
Composites Part A: Applied Sci. . and Manufac., , 2004,
35, , 223-230.
230.
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Acknowledgements
EPSRC - Funding
AMEC NNC - Funding
Dr Ishihara, JAEA - Supplying samples
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