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

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

3.  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

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

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

6. The Weibull strength theory 6

7.  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

8. Comparisons with data 8

9. 9 Neighbour & Wilson - I

10. 10 Extrapolated…

11. 11 Neighbour & Wilson - II

12. 12 Potter & Olds

13. ParameterPerpendicularParallelUnits 5.555.17None 4.015.42MPa 7.9110.02MPa Weibull distribution parameters 13

14. 14 Small specimen data - parallel

15. 15 Small specimen data - perpendicular

16.  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