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
10
Extrapolated…
11
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
16