Random Finite Element Modeling of thermomechanical behavior of AGR bricks

1. Random Finite Element Modeling of thermomechanical behavior of AGR bricks Jose David ArreguiMena, Louise Lever, Graham Hall, Lee Margetts, Paul Mummery

2. Introduction • AGR Reactors • Random Finite Element Method -Young’s Modulus Random Field • Compression Tests • Preliminary Results Random Thermoelastic Analysis

3. AGR Graphite Moderated Reactors

4. Damage in nuclear reactors Fast Neutron Damage • Neutron bombardment of graphite Radiolytic Oxidation • Chemical reaction between irradiated CO2 and graphite

5. Safety Requirements Requirements during normal and fault conditions: • Unimpeded loading and unloading of control rods and fuel rods • An adequate flow of coolant gas • Provide neutron moderation and thermal inertia

6. Hypothesis • Initial, pre-operation spatial variation in the values of the material properties of nuclear graphite have an effect on stress and strain distribution in graphite bricks, which in turn determines the safe operation of a nuclear graphite core

7. Random Finite Element Methodand Nuclear Graphite

8. The Finite Element Method • Numerical technique to solve differential equations • Transforms differential equations to a set of algebraic equations Material properties and geometry Displacements External forces

9. s Probability of failure

10. Young’s ModulusRandom Field

11. 2D Local Average Method Process Top-Down Approach, Local Average Method Process Adapted from (Vanmarcke, 1983)

12. Scale of fluctuation Scale of fluctuation of 1 mm 10 mm The average of a portion of the random field of 1x1 mm will return the mean value of the Young’s Modulus μ 1 mm μ 1 mm 1 mm 1 mm 10 mm

13. Random Fields for Young’s Modulus Correlation length 0.1 Correlation length 100.0 Correlation length 1.0 +Young’s Modulus Mean Value -Young’s Modulus

14. Calibration of the random field CT X-Ray Tomography Grey Scale Density and Young’s Modulus Porosity

15. 3D Random Fields from2D Images Young’s Modulus Porosity

16. Compression Tests

17. Boundary Conditions for Axial Compression tests Fixed in x,y,z Fixed in z Uniform axial Displacement of 4.2 mm

18. Deterministic Realization

19. Random Simulation with a scale of fluctuation (100, 100, 100) Maximum Value – 82.495

20. Random Simulation with a scale of fluctuation (500, 500, 500) Maximum Value – 64.324

21. Random Simulation with a scale of fluctuation (1000, 1000, 1000) Maximum Value – 70.894

22. Preliminary Results Random Thermoelastic Analysis

23. Preliminary Thermoelastic Analysis • Octant of an AGR brick • Free to expand Thermal strains α – Coefficient of Thermal expansion Tf – Final temperature T0 – Reference temperature

24. Temperature profile for the simulations - ΔT

25. Random Material Properties for Young’s Modulus Random Properties Deterministic Properties

26. Displacements Deterministic simulation Random simulation

27. Stress analysis Deterministic simulation Random simulation

28. Road Map Creep Calibration of the Random fields and Creation of a random Field for CTE Thermomechanical Analysis Compression test

29. Acknowledgements

30. Thank you!