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Equation 9 · Part 1 · Why Materials Fail: Fracture, Flaws and the Inspection Interval

Symbol sigma_f

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

What this part means

the critical remote stress.

Its job in the formula

sigmafa_f is part of the quantity the equation computes from the expression on the right.

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

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 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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