The energy balance of crack propagation

The propagation of a crack can be understood by calculating an energy balance. As the stress state of the material changes when the crack propagates, 

As before, we study the case of a infinite plate of thickness t that contains an internal crack of length 2a and is loaded with a homogeneous stress a (see figure 5.3). In the following, we will only consider one half of the crack xi 0, see figure 5.6) the other half is identical due to symmetry. All energy contributions for the whole crack are thus twice the values given here. 

Depending on the load case, the loading points of a load F may shift by distance 6 when the crack propagates, so an external work of 

During crack propagation, changes in the stress and strain fields cause a 

When the crack propagates by an amount da, new surfaces are formed on both sides of the crack with an area of tda. To create new surface in a 

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