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Equation 9 · Part 2 · Why Materials Fail: Fracture, Flaws and the Inspection Interval

Symbol E

σf=2Eγsπa.\sigma_f = \sqrt{\frac{2E\gamma_s}{\pi a}}.
EE

What this part means

the modulus.

Its job in the formula

E occurs above the fraction bar. The numerator is divided by the entire denominator below it.

Where the article explains it

For a through-thickness crack of half-length a in a linear-elastic plate with modulus E and surface energy γs\gamma_s , the critical remote stress is σf=2Eγsπa\sigma_f = \sqrt{\frac{2E\gamma_s}{\pi a}}.

The passage around this formula

…faces, and consumes energy in creating those faces. If the release exceeds the cost, extension is spontaneous and the crack runs. For a through-thickness crack of half-length a in a linear-elastic plate with modulus E and surface energy γs\gamma_s , the critical remote stress is σf=2Eγsπa\sigma_f = \sqrt{\frac{2E\gamma_s}{\pi a}}. The structure of this expression matters more than its coefficients. Strength scales as the inverse square root of flaw size, so halving the largest flaw raises strength by roughly forty per cent, and doubling it…

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Learn the underlying idea

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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