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Estimating Trepanned Strength of AGR Graphites From Inert-Irradiated Young’s Modulus. Ernie D. Eason Modeling & Computing Services Boulder, Colorado, USA eeason@ix.netcom.com Graham Hall Barry J. Marsden
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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
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
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 = CE is attributed to Losty & Orchard (1962) • There is little evidence of S = CE at AGR dose & Tirr 1. CSDMC/P28 (1995), J. Nuclear Materials V. 381 (2008) pp.137-144.
The Losty & Orchard (1962) Evidence Tirr = 60C, dose ≤ 1019 n/cm2
Schematic of AGR Dose Ranges at 370C Losty & Orchard dose range Possible AGR dose range
A Previous Inert E/E0 Model2 Fits Gilsocarbon Data Very Well 2. J. Nuclear Materials V. 381 (2008) pp. 145-151.
Dose Has Little Effect on Inert S/S0 but Strong Effect on E/E0 Above Initial Plateau Test Reactor Irradiations
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.
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
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?
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
Apparent Reason for Poor Fit with E Strength Model Most data above the black dashedE curve Inert Data Trepanned Data Most data below the black dashedE curve
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
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
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
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)
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.