ABSTRACT
If a crack has developed in a structure, the crack may propagate catastrophically when the stress intensity and the crack length combine to reach a critical situation. The basic formulation of the continuum theory of initiation of crack propagation will now be reviewed.*
Let us first consider an elastic sheet of thickness t with a plane crack of length L = 2a through the sheet (Figure 11.1). The sheet is loaded in uniaxial tension S. After applying the load, there is a strain energy U stored in the body that depends on the magnitude of the load, the material properties, and the geometry of the body. In particular, U depends on the crack length L. If, at some load, the crack extends by amount dL, there is a release of the stored strain energy:
d dU =
∂ ∂ U L
L. (11.1)
At the same time, energy of amount dE is expended to fracture the material and create a new free surface dA = 2tdL:
dE = GdA, (11.2)
where G is the energy of crack growth per unit area. The fundamental assumption is that G is a material constant that has to be determined by materials testing. This is known as the Griffith hypothesis.
