1: Toughness and Crack Growth
Another important material property is toughness. Toughness is a measure of how much energy a material can absorb to fracture. Fracture is based on crack growth within a material. The ease with which a crack can be generated determines the energy required for fracture.
A good example of this is a balloon. If we place a pin prick in an uninflated balloon, and begin blowing it up, a critical amount of air (or pressure) will be required in the balloon before it will burst. You can try this yourself.
We need to add energy to make the crack grow, i.e. to increase the size of the crack surface. By blowing up the balloon we are adding gas pressure and elastic tension (energy) to the system.
To make this flaw unstable (i.e. grow) we have to increase the energy in the balloon just enough, by blowing it up, such that if the crack advances, more energy is released (in relieving pressure and elastic tension) than is absorbed (by the creation of a new crack surface). This then is the critical pressure for fast fracture of a pressure vessel (in this case the balloon) containing a flaw (in this case the pinprick) of a given size.