3: Fracture Toughness

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:

  • The crack length, a, that will result in fast fracture for a given applied stress.
  • The applied stress, σ, that will result in fast fracture for a given crack length.