fraction

The passage around this formula

If the strength of a brittle body is set by its largest flaw, and flaw populations are random, then strength is a random variable and reporting a mean is an error of category. The standard treatment is the Weibull weakest-link model, in which the probability that a body of volume V survives a uniform stress $\sigma$ is $P_s = \exp\left[-V\left(\frac{\sigma}{\sigma_0}\right)^{m}\right]$. with m the Weibull modulus and $\sigma_0$ a scale parameter. A larger m means tighter scatter. A review of Weibull analysis across ceramics reports moduli of roughly 10 or below for many advanced ceramics such as alumina, hydroxyapatite and silicon carbide, below about 7 for the glass-ceramics and zirconias surveyed, and above 40 for one magnesium-based glass,…

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