Griffith crack

Ernsberger, F.M. (1963) Current status of the Griffith crack theory of glass strength, in Progress in Ceramic Science, vol. 3, ed. Burke, J.E. (Pergamon, Oxford) p. 58. 

Fig. 18. Adhesive contact of elastic spheres. pH(r) and pa(r) are the Hertz pressure and adhesive tension distributions, (a) JKR model uses a Griffith crack with a stress singularity at the edge of contact (r = a) (b) Maugis model uses a Dugdale crack with a constant tension aa in a < r < c [1111.

The Griffith crack equation has been shown to apply, albeit with some scatter of results, to the brittle polymeric materials poly(methyl methacrylate) and poly(styrene) when cracks of controlled size have been introduced deliberately into the specimens. Such experiments give values of surface energy that are very large, typically 10 - 10 J m , which is about 100 times greater than the theoretical value calculated from the energy of the chemical bonds involved. This value of y thus seems to be made up of two terms, Le. 

Griffith stress and Tf = observed fracture stress. We note that V = 0 when C = Co, and Tg = Tf (Tg = Tf for unnotched specimens—t.e., those containing only the intrinsic Griffith cracks). However, V — V[Pg.110]

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. 

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). 

Fig. 12.82. The Griffith crack is a disk-shaped crack. When it is in equilibrium, the strain energy expanding it is equal to the surface energy contracting it. For a quantitative argument, it can be represented by a flat disk of small thickness, 8, and relatively considerable radius 112.

The second method of developing surface cracks is to expose the surface to hot sodium vapour.1 With various kinds of glass, this treatment produces visible markings (Fig. 45). It is interesting that neither the metallic films nor the sodium vapour show scratches or drawing marks etching with hydrofluoric acid, on the other hand, shows scratches, but does not show the Griffith cracks,2 as Andrade has called them. 

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. 

Figure 2. Schematic of a through crack in an infinite plate, that is, a "Griffith Crack."...

Extrapolation of the line in Figure 9 to 48 MN/m (i.e., 80% of 60 MN/m ) indicates that the square root of the reciprocal of the filler size should be 0.31, corresponding to a filler size of 10 pm. Then, on the basis of the hypothesis that the filler acts as a Griffith crack having an effective length proportional to the filler size, a strength of 48 MN/m should result from the use of a filler of 10 pm. 

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. 

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