In 1913, Inglis calculated what the stresses and strains were in an elastic plate containing an elliptical crack, with semi-axes b and c, and under an applied stress σ - applied vertically in this case.
He found that the stress at the crack tip, σt , was given by
For a sharp crack, i.e. c >> b, the stress would be much greater at the crack tip So failure could occur by cracking because it’s only at a crack tip that the stress required to break a bond, or simultaneously break a given number of bonds in a unit area of material, is reached.
So far, so good, but σt depends on the SHAPE of the crack, i.e. c / b – and we know that the length is important.
It's the idea that a critical stress to break a bond is needed that is wrong.
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