Crack growing and fracture criterion

Dear iMechanicians,

First I'd like to thank the ones sharing their lecture notes, it's
very helpful for someone who is learning fracture mechanics by himself like I
do. 

Nevertheless, I would have some questions regarding the
energetic aspect of the crack propagation. Please do not hesitate to correct me
if I am wrong. Questions are related to this lecture note, from Professor Suo: node/7507

Written as a conclusion in the lecture note, a crack is
supposed to grow when the energy release rate is equal to the fracture energy
(Fracture criterion paragraph, bottom of page 3) 

But as I've understood, the energy release rate is the
amount of energy required for the crack to grow. So it's a kind of threshold
value and it varies according to the crack length and is independent of the
load. 

Concerning the fracture energy, it is the part of the energy
given by the load that is not stored as potential elastic energy in the body.
It provokes inelastic processes such as plastic deformation around the crack
tip and crack growing. It is dependant of the load. 

So should we say the crack grows when the fracture energy
becomes great enough and equals the energy release rate? That is to say the
fracture energy can be lower than the critical value of G, if the load is
insufficient for instance. In this case, there would be only elastic
deformation and perhaps plastic deformation too.

This leads to another question. How is the energy shared
between elastic and inelastic processes? The lecture talked about the "small fraction
going to inelastic processes" (fracture energy paragraph, page 3). 

I've tried to understand the process but I'm not sure about it.
I would say the body tends to reduce its potential energy as much as possible,
spending it in inelastic processes. On the other hand, the crack growth
provides some new potential energy, a surface energy. Finally, there is equilibrium
(growth's stop) when a new creation of surface would provide more potential
surface energy than the loss of potential elastic energy.

I would very much appreciate if someone could help me. 

Thanks in advance!

Kind regards, 

Paul

PS: how to delete the ugly part of code at the begeinning of the post ? I've used the copy paste from word but it doesn't work.