Equation 9 · Part 11 · Why Materials Fail: Fracture, Flaws and the Inspection Interval
Denominator: pi a
What this part means
The complete quantity below the fraction bar; it must be nonzero for this division.
Its job in the formula
pi a occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.
Full expression→Denominator: pi a→Article meaning
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
A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.
Open the illustrated fractions: division written vertically guide →
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