Equation 9 · Part 6 · Why Materials Fail: Fracture, Flaws and the Inspection Interval
=
=
What this part means
The expressions on both sides represent the same quantity under the stated assumptions.
Its job in the formula
The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.
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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 , the critical remote stress is . 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…
Learn the underlying idea
An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.
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