# Inglis and the crack tip stress idea

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, σ_{t} , was given by

$${\sigma _{\rm{t}}} = \sigma {\rm{ }}\left( {1 + 2{c \over b}} \right)$$

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 σ_{t} depends on the SHAPE of the crack, i.e. c / b – and we know that the length is important.

By looking at crack tip stress fields using photoelasticity, we can see that stresses are indeed concentrated at crack tips**. **Inglis was correct about this.

It's the idea that a critical stress to break a bond is needed that is wrong.