Published: 21 July 2014
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This paper will discuss four mechanisms for scale effects in the strength of graphite, two of which originate from the amorphous structure of graphite. The main focus of the paper will be a theoretical investigation into one of these: the case when the micro-scale structure affects the scaling of the strength of macro-scale specimens. The theoretical analysis is based on the Weibull strength theory and comparisons with published data. The paper concludes that there is a sound theoretical basis for the Weibull strength theory but its limitations must not be overlooked. In summary, it does not apply to very small specimens (a micro-scale limitation), to regions of very high stress gradient (a second micro-scale limitation), to small sample sizes (i.e., numbers of specimens—a convergence limitation of asymptotic statistics), and to hybrid populations of material (a statistical population limitation). Three kinds of extrapolation of the theory were discussed in this paper: with gage length, with gage cross section, and with load configuration. Empirical evidence presented in the paper illustrates how the Weibull strength theory is able to correlate data at different scales and can be applied to flexural strength data obtained from macro-scale specimens to obtain an estimate of flexural strength at larger scale. It was found that the reduction in mean flexural strength due to the scale effect was slight and the minimum flexural strength can be quite large. Other comparisons in the paper were inconclusive about whether the Weibull theory can unify flexural and tensile strength data in the macro-scale region because the specimen sizes were too small. The primary conclusion of this paper is that the Weibull strength theory can, with the provisos noted above, explain the scaling of the mean and variance of strength with specimen volume.
nuclear graphite, strength, scaling, weibull, extreme value statistics
Wheatley, C. J.