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

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

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.