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I teach Materials Science to undergraduate engineering students. We devote 2 or 3 lectures on Fracture where we mainly introduce Griffith's formula and the stress intensity formula. I face a difficulty in reconciling the two which I would lke to present here.
The Griffiths equation gives the fracture stress s for a given crack size c:
s=sqrt[2 E g/ (p c)] (1)
The stress concentration formula gives the max stress at the crack tip as
s=s0 [1+2 sqrt (c/r)] (2)
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