It can be shown that the energy required for fracture, Gc, is a function of the stress, σ, the crack length, a, and the modulus, E, such that:
This equation can be rearranged to give:
From this equation a stress intensity factor, K, can be defined:
We can therefore say that fast fracture occurs when a critical stress intensity factor, Kc, is reached, ie. K= Kc. Kc is referred to as the fracture toughness of the material.
If Kc is known the following can be derived from the equation: