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
i.e. the energy is at a maximum, or
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
i.e. the energy is at a minimum, or
That is, as the crack grows, the resistance to cracking, R, increases faster than the driving force, G.
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