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Equation 27 · Part 2 · Why Materials Fail: Fracture, Flaws and the Inspection Interval

Symbol V

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

What this part means

V is one of the signed contributions combined to compute the quantity on the left.

Its job in the formula

V is one of the signed contributions combined to compute the quantity on the left.

The passage around this formula

…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 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…

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A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the surrounding passage

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