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 CO2 and graphite

ionization radiation *2CO CO O

*2CO O CO

Damage in nuclear reactors

*O C CO

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 Methodand Nuclear Graphite

The Finite Element Method

• Numerical technique to solve differential equations• Transforms differential equations to a set of

algebraic equations

{ } { }F K U

External forces

Materialproperties

and geometry

Displacements

s

Probability of failure

Young’s ModulusRandom Field

Top-Down Approach, Local Average Method ProcessAdapted from (Vanmarcke, 1983)

2D Local Average Method Process

Scale of fluctuation

10 mm

10 mm

1 mm

1 mm

The average of a portionof the random field of1x1 mm will return the mean value of the Young’s Modulus μ

1 mm

1 mmμ

Scale of fluctuationof 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 fieldGrey Scale

Density and Young’s

Modulus

CT X-Ray Tomography

Porosity

3D Random Fields from2D Images

Young’s Modulus

Porosity

Compression Tests

Boundary Conditions for Axial Compression tests

Fixed in x,y,z Fixed in zUniform axial

Displacement of 4.2 mm

DeterministicRealization

Random Simulation with a scale of fluctuation (100, 100, 100)

Maximum Value – 82.495

Maximum Value – 64.324

Random Simulation with a scale of fluctuation (500, 500, 500)

Maximum Value – 70.894

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

0fT T Thermal strains

α – Coefficient of Thermal expansionTf – Final temperatureT0 – Reference temperature

Temperature profile for the simulations - ΔT

Random Material Properties for Young’s ModulusRandom PropertiesDeterministic Properties

DisplacementsRandom simulationDeterministic simulation

Random simulationDeterministic simulationStress analysis

Road Map

Compression test

Calibration of theRandom fields and

Creation of a randomField for CTE

ThermomechanicalAnalysis

Creep

Acknowledgements

Thank you!