Dissemination of IT for the Promotion of Materials Science (DoITPoMS)

DoITPoMS Teaching & Learning Packages Brittle Fracture Inglis and the crack tip stress idea
Brittle Fracture AimsBefore you startIntroductionWhen do atomic bonds break?Why do cracks weaken a material?Inglis and the crack tip stress ideaCan we calculate the energy changes?What about tension?Another way of expressing the energiesAnother way of calculating the energiesWhy bother if they are the same?Coping with a scatter in strengthSimulation of Weibull modulus experimentWhen does the sample fail completely?Sub-critical crack growth and R-curvesSummaryQuestionsGoing further
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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.

Image of an elastic plate containing an elliptical crack

He found that the stress at the crack tip, σt , 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 σt 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.

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