The scaling of the strength of nuclear graphite

Statistical aspects andImplications for testing

Chris Wheatley

Strength measuresVariability scales in graphiteStrength scaling mechanismsThe Weibull strength theoryStatistical-theoretical basisComparisons with dataConclusions

Outline

2

Non-continuum propertiesContinuum properties

Load configurationSpecimen size & geometryLoad-displacement reference pointSurface finishGlobal & local, scalar stress metrics

Strength measures

3

Material properties

Other

Non-continuum variability Defects Porosity Native particles – ‘grains’ Crystallites …

Continuum variability – intra componentContinuum variability – extra component

Variability scales in graphite

4

Elastic energy source impinges specimen boundaries

Inelastic energy sinks impinge specimen boundaries

Non-continuum dominanceNon-continuum statistics

Strength scaling mechanisms

5

𝐹=1−exp (−∫𝑉 (max (𝜎−𝛾 ,0)/𝛿 )𝛽𝑑𝑉 /𝑉 0)

The Weibull strength theory

6

The Weibull distribution is one of three extreme value distributions

The other two distributions are not applicable

Close analogy with the normal distribution and the central limit theorem

Its validity does not depend on the fracture mechanism when certain conditions are satisfied

Statistical-theoretical basis

7

Comparisons with data

8

9

Neighbour & Wilson - I

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Extrapolated…

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Neighbour & Wilson - II

12

Potter & Olds

Parameter Perpendicular Parallel Units

5.55 5.17 None

4.01 5.42 MPa

7.91 10.02 MPa

Weibull distribution parameters

13

14

Small specimen data - parallel

15

Small specimen data - perpendicular

Non-continuum variability affects macro-scale strength

The Weibull strength theory is applicableThe theoretical basis is sound; it does not apply

to Non-continuum dominance

Very small specimens Steep stress gradients

Small sample sizes Hybrid populations

Comparisons with data are encouraging

Conclusions

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