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Equation 27 · Part 4 · Why Materials Fail: Fracture, Flaws and the Inspection Interval

Symbol sigma_0

Ps=exp⁡[−V(σσ0)m],P_s = \exp\left[-V\left(\frac{\sigma}{\sigma_0}\right)^{m}\right],
σ0\sigma_0

What this part means

the scale parameter.

Its job in the formula

sigma0a_0 occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

Where the article explains it

with m the Weibull modulus and σ0\sigma_0 a scale parameter.

The passage around this formula

…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 σ\sigma is Ps=exp⁡[−V(σσ0)m]P_s = \exp\left[-V\left(\frac{\sigma}{\sigma_0}\right)^{m}\right]. with m the Weibull modulus and σ0\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…

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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the surrounding passage

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