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The effect of compressive pre-stress on the thermal expansion behaviour of anisotropic
nuclear grade graphite
M. Haverty, W. Bodel, B.J. MarsdenNuclear Graphite Research Group
The University of Manchestermaureen.haverty@postgrad.manchester.ac.uk
Contents
1. General Methodology used2. Preliminary Study3. Main Study4. Comparison between two studies5. High Resolution images
Motivation
• Previous studies have shown a change in CTE with stress– Gilsocarbon: Applied uniaxial compressive and
tensile stress 1
– Steels: Applied uniaxial tensile stress and pre-stress beyond elastic limit2
• Are these changes observed in PGA?• What causes these changes?
1. Preston, S.D. & Marsden, B.J., 2006. Changes in the coefficient of thermal expansion in stressed Gilsocarbon graphite. Carbon, 44(7), pp.1250–1257
2. Rosenfield, A.R. & Averbach, B.L., 1956. Effect of Stress on the Expansion Coefficient. Journal of Applied Physics, 27(2), pp.154–156.
3. .
CTE MEASUREMENT
Standards and Methodologies Used
• CN821-1 “Advanced technical ceramics-Monolithic ceramics-Thermo-physical properties-Part 1: Determination of thermal expansion” – Provides test method including, sample size;
reference standards and heating rates• Accuracy if followed:
– 5K/min 0.5 x 10-6 K-1
– 2K/min 0.1 x 10-6 K-1
CTE Measurement equipment
• Netzsch Proteus DIL– Pushrod dilatometer– Nitrogen atmosphere
• Al2O3 Reference standard– Glow runs– Filler piece for short samples (Al2O3)
Thermal Expansion Measurements
Al2O3 Sample Holder
Al2O3 Pushrod
Al2O3 Filler Piece
Graphite sample
PRELIMINARY TEST
Method
• Samples were cut in the AG and WG directions • Uniaxial compressive stress applied– Compressive strength: 27 MPa
• Max temp: 250 °CSample No. Stress (%)AG1/WG1 0AG2/WG2 20AG3/WG3 40AG4/WG4 60AG5/WG5 80AG6/WG6 90
Applying Stress
• Universal Load Testing Machine
• Compressive stress• Sample subdivided into
two sister samples• Excess used to face off
to correct tolerance
Φ =12 mm
H =18 mm
Φ =12 mm
H =6 mm
Comparison of unstressed samples with the literature
• Comparing unstressed sample values with Sutton and Howard 3
• Two blocks of PGA, measured in WG and AG directions
• Average CTE for 50°C increments, e.g. 100-150°C
• CTE plotted at midpoint of increment e.g. 125 °C
3. Sutton, A.L. & Howard, V.C., 1962. The role of porosity in the accommodation of thermal expansion in graphite. Journal of Nuclear Materials, 7(1), pp.58–71.
CTE Preliminary Results
• Average CTE plotted• Reference temperature of 50 °C used, e.g.
50-250 °C• CTE plotted at midpoint of temperature
increment
60 80 100 120 140 160 180 2002
2.5
3
3.5
4
4.5
5
AG Average CTE vs Temperature
AG3 (40%)AG2 (20%)AG1 (0%)
Temperature (°C)
CTE
(X 1
0-6
K-1)
60 80 100 120 140 160 180 2002
2.5
3
3.5
4
4.5
5
AG Average CTE vs Temperature
AG5 (80%)AG4 (60%)AG3 (40%)AG2 (20%)AG1 (0%)
Temperature (°C)
CTE
(X 1
0-6
K-1)
60 80 100 120 140 160 180 2002
2.5
3
3.5
4
4.5
5
AG Average CTE vs Temperature
AG6 (90%)AG5 (80%)AG4 (60%)AG3 (40%)AG2 (20%)AG1 (0%)
Temperature (°C)
CTE
(X 1
0-6
K-1)
60 80 100 120 140 160 180 2000
0.5
1
1.5
2
2.5
WG Average CTE vs Temperature
WG1 (0%)
Temperature (°C)
CTE
(X 1
0-6
K-1)
60 80 100 120 140 160 180 2000
0.5
1
1.5
2
2.5
WG Average CTE vs Temperature
WG2 (20%)WG1 (0%)
Temperature (°C)
CTE
(X 1
0-6
K-1)
MAIN STUDY
SamplesΦ =6 mm
H =6 mm
• CTE measured on 10 samples to ascertain sample variability
• Two samples in each direction selected randomly for pre-stressing
Method
• CTE measured• Pre-stress applied (fraction of compressive
strength)• Properties re-measured• Max temp: 450 °C• AG: 0%; 20%; 40%; 90%• WG: 0%; 20%; 40%
Comparison of unstressed samples with the literature
• Comparing unstressed sample values with Sutton and Howard 3
• Two blocks of PGA, measured in WG and AG directions
• Average CTE for 50°C increments, e.g. 100-150°C
• CTE plotted at midpoint of increment e.g. 125 °C
3. Sutton, A.L. & Howard, V.C., 1962. The role of porosity in the accommodation of thermal expansion in graphite. Journal of Nuclear Materials, 7(1), pp.58–71.
Sample VariabilityTemp Range (°C) AG CTE
(x 10-6 K-1)St. Dev (x 10-6 K-
1)
WG CTE (x 10-6 K-1)
St. Dev (x 10-6 K-
1)50-100 0.9 ± 0.1 0.150-150 3.4 ± 0.1 0.1 1.1± 0.1 0.250-200 3.5 ± 0.1 0.1 1.2 ± 0.1 0.150-250 3.6 ± 0.1 0.1 1.3 ± 0.1 0.150-300 3.7 ± 0.1 0.1 1.5 ± 0.1 0.150-350 3.8 ± 0.1 0.1 1.6 ± 0.1 0.150-400 3.9 ± 0.1 0.1 1.7 ± 0.1 0.150-450 4.0 ± 0.1 0.1 1.9 ± 0.1 0.1
0 10 20 30 40 50 60 70 80 90 1000
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Residual Strain vs. Pre-Stress
AG2AG13WG7WG13
Compressive Pre-stress (%)
Resid
ual S
trai
n (%
)
COMPARISON BETWEEN PRELIMINARY AND MAIN STUDY
Observations
• Both preliminary and main studies show good agreement in CTE measurements
• Pre-stress causes increase in CTE– Approximately 20% increase in CTE at 90% Pre-stress in AG
direction– Approximately 10% increase in CTE at 40% Pre-stress in AG
direction• Minimum pre-stress required to cause change has yet
to be determined• Residual strains not directly proportional to pre-stress
What causes change in CTE?
• Crystal re-orientation may be occurring• Other authors have attributed the increase in
CTE in steels to lattice distortion 2 • Elastic limit must be reached in steels before
permanent changes to CTE occur– Residual strains in graphite– Is there a minimum residual strain for permanent
changes in CTE to occur?
Acknowledgements
• This project is funded by EPSRC through the FunGraphite consortium
• The author would like to thank the following for their advice and help with the project: Dr. Marc Schmidt; Gary Harrison; the staff at FEI; David Mortimer; Judith Shackleton
• The SEM images were taken at the Dalton Cumbrian Facility and the author would like to thank DCF for access to the equipment