Formation of a crack in an clastic solid initially subjected to uniform uniaxial tension disrupts the trajectories of the maximum principal stress in the manner depicted in Fig. 2.1.1a. This indicates that stress concentrations must arise near the crack tip. They were calculated by Inglis (1913) as the limit case of his solution for an elliptical hole.
From Inglis’s solution, Griffith (1921, 1924) noted that the strength criterion cannot be applied because the stress at the tip of a sharp crack is infinite no matter how small the load is (Fig. 2.1.1b). He further concluded that the formation of a crack necessitates a certain energy per unit area of the crack plane.
Figure 2.1.2 Crack growth in a cracked specimen: (a) initial situation; (b) со-planar crack growth upon further loading.
which is a material property, provided the structure is so large that the crack tip region in which the fracture process takes place is negligible. However, more general approaches accept that the specific energy required for crack growth may depend on the cracking history instead of being a constant. In such cases, the energy required for a unit advance of the crack is called the crack growth resistance, Ті.
The basic problem in fracture mechanics is to find the amount of energy available for crack growth and to compare it to the energy required to extend the crack. Although conceptually simple, the problem is far from trivial and deserves a detailed analysis.