Griffith crack propagation

Griffith derived a similar equation using an energy balance approach, equating stored energy with the energy required for crack propagation ... 

If Vt 1240 meters/sec in the matrix and branching will occur in the rubber at 29 meters/sec, we calculate A/Co = 0.047. Thus, branching can occur after a matrix crack acceleration distance of only 2 to 5/x (assuming a Griffith crack length of 50-100fi) hence, ample room for the development of fast cracks or fast crazes exists in the ABS structure. Note that the expressions for craze instability, acceleration, and speed (Equations 1, 6, 7) show that the macro strain rate of the specimen is irrelevant— fast cracks and crazes propagate in specimens strained even at slow creep rates. 

Griffith used an energy balance approach to predict the crack propagation conditions (see Williams, 1984). The driving force is the elastically stored energy in the notched samples, which can be used to create new surfaces. A parameter Gc, the critical elastic strain energy release rate [GIc in mode I], can be determined and expressed in J m-2. 

It is possible to write down approximate conditions for crack propagation in a very simple way. Consider the Griffith crack, as it is called, a disk-shaped crack with a length l (Fig. 12.82). 

Using Griffith analysis [28, pp. 797, 819] for the crack propagation in the green body, the green strength, o-, is given by... 

At room temperature, PP is close to its Tg(0-25°C) and well above its normal brittle-ductile transition temperature ( -30°C). However the presence of surface cracks in the photo-oxidized film is apparently sufficient to promote brittle failure at room temperature. According to the Griffith crack theory, once a critical crack length has been exceeded, a critical crack velocity is required to propagate the crack. If this velocity is not exceeded, cold drawing of the amorphous zones ensues. 

We may thus conclude that the fracture process is determined by crack formation and crack propagation. Griffith crack theory is essentially a static conception of critical crack formation. Crack growth, however, also depends on dissipative processes. Below the critical load, crack propagation may advance very slowly. In such a case there is a dissipation of energy due to creep processes. Therefore, fracture is a time-dependent process. This aspect is neglected in the Griffith-Irwin theory of fracture. 

Starting from the energy balance of the process Griffith proposed the following so-called crack propagation criterion. This criterion corresponds to the value of stress causing further crack propagation ... 

This critical point marks the onset of crack propagation. Griffith calculated the critical stress far from the crack location for a plate of unit width, and showed that for a homogeneous, isotropic material, a relationship exists between the critical stress, i7c half the crack length, a ... 

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