In class today we discussed that in a linear elastic system, in a experiment carried out under constant

load. We considered two states, one with a crack length equal to $c,$ and State II where the crack has

grown to $c+c.$ The magnitude of the change in the potential energy is twice the change in the

mechanical stored energy. However potential and the stored energy have opposite signs, the first

lowers the energy of the system when the stored energy increases the energy of the system.

Now consider a specimen being pulled between two crossheads under displacement control. In this

instance the load is a measured quantity which increases with cross$-$head displacement:

Use graphical construction of the load$-$displacement curve to show that the above result obtained

under constant load is also valid for crack growth under constant displacement.

Then show that the total change in the energy of the system as a result of the growth of the crack can

be expressed either as one half of the change in the potential energy or equal to the change in the

stored energy.

Why is the quantity above a negative quantity, that is the energy of the system decreases when the

crack advances?