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The scaling of the strength of nuclear graphite

The scaling of the strength of nuclear graphite. Statistical aspects and I mplications for testing Chris Wheatley. Outline. Strength measures Variability scales in graphite Strength scaling mechanisms The Weibull strength theory Statistical-theoretical basis Comparisons with data

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The scaling of the strength of nuclear graphite

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

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

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

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

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

  6. The Weibull strength theory

  7. Statistical-theoretical basis • 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

  8. Comparisons with data

  9. Neighbour & Wilson - I

  10. Extrapolated…

  11. Neighbour & Wilson - II

  12. Potter & Olds

  13. Weibull distribution parameters

  14. Small specimen data - parallel

  15. Small specimen data - perpendicular

  16. Conclusions • 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

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