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Equation 9 · Part 4 · Why Materials Fail: Fracture, Flaws and the Inspection Interval

Symbol pi

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

What this part means

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

Its job in the formula

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

The passage around this formula

Griffith’s criterion is an accounting statement. Extending a crack by a small increment releases stored elastic strain energy from the material that unloads around the new crack 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 costs…

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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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