Equation 10 · Why Materials Fail: Fracture, Flaws and the Inspection Interval
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the modulus e and surface energy. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
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subscript
subscript
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Applied directly to metals, the criterion underpredicts fracture stress badly, because accounts only for the two new surfaces. In a metal, the overwhelming majority of the energy consumed goes into plastic work in a zone ahead of the tip — dislocation motion, void nucleation, blunting. The repair is to replace the surface energy with an effective work-of-fracture term that absorbs plastic dissipation. That substitution is conceptually cheap and physically enormous: it can raise the energy cost of crack extension by three or four orders of magnitude, and it is the reason a ductile alloy tolerates flaws that would destroy a glass of the same nominal strength.
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