Theories of fracture toughness parameters

There are two principal theories, or models, that attempt to describe what happens during brittle fracture, the Griffith fracture theory and the Irwin model. Both assume that fracture takes place through the presence of preexisting cracks or flaws in the polymer and are concerned with what happens near such a crack when a load is applied. Each leads to the definition of a fracture-toughness parameter and the two parameters are closely related to each other. The Griffith theory is concerned with the elastically stored energy near the crack, whereas the Irwin model is concerned with the distribution of stresses near the crack. Both theories apply strictly only for materials that are perfectly elastic for small strains and are therefore said to describe linear fracture mechanics. 

A long strip of pol5mier 1 cm wide and 1 mm thick, which contains no cracks, is subjected to a tensile force of 100 N along its length. This produces a strain of 0.3%. Another strip of the same polymer is identical except that it has a crack of length 1 mm perpendicular to its long axis at its centre. If the value of y for the polymer is 1500 J m , estimate the tensile load necessary to break the second strip. 

Young s modulus E is given by the equation a = Ee, where r is the applied stress and e the corresponding strain. Thus E = F/ Ae), where F is the applied force and A is the cross-sectional area over which it is applied. Substituting the data given leads to 

Assuming that plane-stress conditions apply, equation (8.19) shows that F = Aag = A 4yEf(nl), where Fb is the breaking force and / the length of the crack. Substitution leads to 

Equation (8.22) is often written in a slightly different way, making use of the strain-energy release rate, G, which is the energy available per unit increase in crack area. Using the notation introduced for relation (8.18) it follows that 

---