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

DoITPoMS Teaching & Learning Packages Brittle Fracture When does the sample fail completely?
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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When does the sample fail completely?

It is incorrect to say that failure must occur when

G = R

There will be some cracking but complete failure (as in tension) also requires that

$${{{{\rm{d}}^2}U(c)} \over {{\rm{d}}{c^2}}} < 0$$

 i.e. the energy is at a maximum, or

$${{{\rm{d}}G} \over {{\rm{d}}c}} > {{{\rm{d}}R} \over {{\rm{d}}c}}$$

In other words failure will be catastrophic when the rate of increase of the driving force with crack growth is greater than the change in R with crack growth, which we have taken as a constant.

Alternatively cracking will be stable when

$${{{{\rm{d}}^2}U(c)} \over {{\rm{d}}{c^2}}} > 0$$

i.e. the energy is at a minimum, or

$${{{\rm{d}}G} \over {{\rm{d}}c}} < {{{\rm{d}}R} \over {{\rm{d}}c}}$$

That is, as the crack grows, the resistance to cracking, R, increases faster than the driving force, G.

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