The scaling of the strength of nuclear graphite Statistical aspects and Implications for testing Chris Wheatley

 Strength measures  Variability scales in graphite  Strength scaling mechanisms  The Weibull strength theory  Statistical-theoretical basis  Comparisons with data  Conclusions Outline 2

 Non-continuum properties  Continuum properties  Load configuration  Specimen size & geometry  Load-displacement reference point  Surface finish  Global & local, scalar stress metrics Strength measures 3 Material properties Other

 Non-continuum variability  Defects  Porosity  Native particles – ‘grains’  Crystallites  …  Continuum variability – intra component  Continuum variability – extra component Variability scales in graphite 4

 Elastic energy source impinges specimen boundaries  Inelastic energy sinks impinge specimen boundaries  Non-continuum dominance  Non-continuum statistics Strength scaling mechanisms 5

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

ParameterPerpendicularParallelUnits None MPa 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 applicable  The 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