Estimating Trepanned Strength of AGR Graphites From Inert-Irradiated Young’s Modulus

1. Estimating Trepanned Strength of AGR Graphites From Inert-Irradiated Young’s Modulus Ernie D. Eason Modeling & Computing ServicesBoulder, Colorado, USA eeason@ix.netcom.com Graham Hall Barry J. Marsden Nuclear Graphite Research Group, School of Mechanical, Aerospace & Civil Engineering, University of Manchester, UK graham.n.hall@manchester.ac.uk barry.J.marsden@manchester.ac.uk Presented at INGSM-14 Seattle, Washington, USA September 16, 2013

2. Topics • Background on estimating strength, S, from inert-irradiated Young’s Modulus, E • Counter-examples from test reactor S and E data • 2009 trepanned strength model based on weight loss • No statistical justification for including any function of E • Incorporating E degrades the fit to trepanned strength data • 2013 trepanned strength model based on irradiated density • No statistical justification for including any function of E • Incorporating E degrades the fit to trepanned strength data • Conclusion: Estimating trepanned strength from inert- irradiated Young’s Modulus is not appropriate

3. Background on Estimating S from Inert-irradiated E • Various models1 in the UK have estimated oxidised strength of Gilsocarbon graphite from inert-irradiated Young’s modulus • The square root dependence S = CE is attributed to Losty & Orchard (1962) • There is little evidence of S = CE at AGR dose & Tirr 1. CSDMC/P28 (1995), J. Nuclear Materials V. 381 (2008) pp.137-144.

4. The Losty & Orchard (1962) Evidence Tirr = 60C, dose ≤ 1019 n/cm2

5. Schematic of AGR Dose Ranges at 370C Losty & Orchard dose range Possible AGR dose range

6. A Previous Inert E/E0 Model2 Fits Gilsocarbon Data Very Well 2. J. Nuclear Materials V. 381 (2008) pp. 145-151.

7. Dose Has Little Effect on Inert S/S0 but Strong Effect on E/E0 Above Initial Plateau Test Reactor Irradiations

8. Test Reactor Counter-examples to S = CE

9. Trepanned Bending Strength 2009 Model3 • 2009 strength model based on weight loss • Se = 0.15 (measured as S/S0) or 3.84 (measured as S) on 424 calibration points • Good fit, with no significant residual trends in any variable • Model includes no effect of dose or E/E0 3. J. Nuclear Materials V. 436 (2013) pp. 208-216.

10. No Justification For Including a Function of Inert E or E/E0 in 2009 Strength Model No significant residual trend implies no need for inert E/E0 in the 2009 model

11. Testing the Inert E Modelling Concept • If the idea of using Einert is valid, a model including such a term should fit better to the trepanned data • In the 2009 model, let with no other changes • Does the strength model with Einert fit better or not?

12. The Model Using Einert (dashed curve) is a Significantly Worse Fit to Trepanned Data unconservative Note the wrong shape when Einert is used(dashed curves) The Einertmodel is above the data at long exposure

13. Apparent Reason for Poor Fit with E Strength Model Most data above the black dashedE curve Inert Data Trepanned Data Most data below the black dashedE curve

14. Trepanned Bending Strength 2013 Irradiated Density Model • Model form • Se = 0.05026 measured as log(S) (or 3.99 MPa measured as S) on 1831 calibration points • Good fit, with no significant residual trends in any variable (see presentation 9/18/2013) • Model includes no effect of dose or E/E0

15. No Justification For Including a Function of Inert E or E/E0 in 2013 Strength Model No significant residual trend implies no need for inert E/E0 in the 2013 model

16. Testing the Inert E Modelling Concept • If the idea of using Einert is valid, a model including such a term should fit better to the trepanned data • In the 2013 density-based strength model, let with no other changes • Best-fit value over 1831 data points is n = 0, i.e., no effect of E • If we impose (inert E/E0)0.5 in the density-based model, the fit is degraded significantly • Significantly higher standard error • Significant residual trends with dose, inert E/E0, trepanning year

17. Significant Residual Trends if Inert-Irradiated Young’s Modulus is Imposed Including (inert E)0.5 in the density-based model seriously degrades the fit Unconservative (model S > actual S) Conservative (actual S > model S)

18. Conclusions • The test reactor strength data over the AGR range of dose and Tirr do not support estimating strength from inert-irradiated Young’s modulus (instead use inert strength = constant) • The trepanned strength data do not justify using inert Young’s modulus to estimate strength • Two models using different oxidation functions both show no residual error with inert E/E0, so no need for inert E/E0 in model • The best-fit exponent on (inert E/E0)n over 1831 trepanned data points is n = 0, i.e., no Young’s modulus effect • Estimating trepanned bending strength from (inert E/E0)0.5 is not appropriate. Imposing an (inert E/E0)0.5 term: • degrades the fit of trepanned strength models based on either weight loss or irradiated density, • causes incorrect shape of strength vs. weight loss and irradiated density curves compared to trepanned data, and • produces an unconservative strength estimate at long exposure.