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

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

AGR Graphite Moderated Reactors

Fast Neutron Damage Neutron bombardment of graphite Radiolytic Oxidation Chemical reaction between irradiated CO 2 and graphite Damage in nuclear reactors

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

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

Random Finite Element Method and Nuclear Graphite

The Finite Element Method Numerical technique to solve differential equations Transforms differential equations to a set of algebraic equations Externalforces Material properties and geometry Displacements

s Probability of failure

Young’s Modulus Random Field

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

Scale of fluctuation 10 mm 1 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 Scale of fluctuation of 1 mm

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

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

3D Random Fields from 2D Images Young’s Modulus Porosity

Compression Tests

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

Deterministic Realization

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

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

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

Preliminary Results Random Thermoelastic Analysis

Preliminary Thermoelastic Analysis Octant of an AGR brick Free to expand Thermal strains α – Coefficient of Thermal expansion T f – Final temperature T 0 – Reference temperature

Temperature profile for the simulations - ΔT

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

Displacements Random simulationDeterministic simulation

Random simulationDeterministic simulation Stress analysis

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

Acknowledgements

Thank you!