Equation 31 · Why Materials Fail: Fracture, Flaws and the Inspection Interval
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The practically important consequence is size scaling. Because a larger stressed volume samples more of the flaw population, mean strength falls as the specimen grows, and the ratio of strengths of two specimen geometries goes as the ratio of their effective volumes raised to the power 1/m [ 12 ] . Small-coupon test data therefore systematically overstate the strength of a full-size component, and the overstatement is worse for materials with low Weibull modulus — that is, for exactly the materials whose scatter already makes them hard to design with.
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