subscript

The passage around this formula

The first half of the argument is purely elastic and predates Griffith. An elliptical hole in a stressed plate does not merely remove load-bearing material; it redistributes the stress that would have passed through that material into the region around the hole’s sharpest curvature. For an elliptical flaw of half-length a and tip radius of curvature $\rho$ in a plate under remote tension $\sigma_\infty$ , the peak stress at the tip is approximately $\sigma_{\max} = \sigma_\infty\left(1 + 2\sqrt{\frac{a}{\rho}}\right)$. Three things follow. First, the concentration depends on the flaw’s aspect ratio, not on its absolute size — a long shallow scratch and a short sharp one can concentrate stress equally. Second, as the tip sharpens toward an…

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