Griffith criterion

Griffith [4] has evolved a criterion for fracture based on the energy release rate. When a crack propagates, two new surfaces are created. The energy supplied by means of applied stress is utilized in creating these surfaces. The rate at which this energy is released exceeds the rate at which the energy is consumed that point, at which it exceeds, marks the critical condition for fracture. 

Because this energy is per unit volume, the total internal energy in the parallelepiped of volume Vq is given by  

Elastic stored energy as a result of applied stress. 

In this equation, y is the surface energy of the material. The 2 in the equation represents the two surfaces created. Now, the total internal energy of the parallelepiped has become the sum of Equations 15.50 and 15.51. This sum is given by Equation 15.52. 

Plot showing the critical crack size for higher applied stress. 

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Fig. 4. The Griffith criterion for the fixed grip condition, (a) cracked plate with fixed ends (b) schematic of elastic energy...

For equilibrium systems with no contact hysteresis G = W, which is the classical Griffith criterion in fracture mechanics. For such a system, Eqs. 12 and 37 are the same. That is, the strain energy release rate is given by... 

J. P. Berry, Some Kinetic Considerations of the Griffith Criterion for Fracture, Journal of Mechanics and Physics of Solids, 8, 194-216 (1960). 

The use of the generalized Griffith criterion not only allows cracks to extend under tensile loading, but also allows cracks to extend in shear, even under moderate normal compression. This means that closed shear cracks can extend under intense loading (as near an explosive charge), causing the material to be much weaker under subsequent tensile loading. The reduction in the elastic moduli is also important in that it leads to the correct directional response as the rock is fractured. Thus, phenomena such as spall are modeled in a realistic fashion. 

The probability of failure in a sample of specimens of volume Yj is equal to that in another sample containing specimens of volume V, if the stresses applied to the specimens are related according to eq. 9. Using the Griffith criterion we get [13] ... 

Because most materials are not ideally brittle, the Griffith criterion has to be modified to include the energy dissipated in plastic deformation around the crack tip. The energy criterion for crack formation then becomes... 

This article is based on Griffith criterion, considering the slurry pressure, the conditions for the formation of the slurry seepage channel is derived, which is primarily related to the earth stress, medium tensile strength as well as grouting pressure. 

Fracture Strength. The fracture strength, ac, of composites shows a range of results, but ac cannot exceed that of the matrix. The notch effects and residual stress concentration could lower it further. Whether or not the filler particles behave as precursors of cracks depends on the particle diameter, d. This can be qualitatively understood by the fact that the stored deformation energy, C/, is a function of whereas the fracture surface energy, y, is proportional to d. Applying the Griffith criterion of fracture initiation,... 

Griffith set up an energy balance equation, comparing the amount of elastic energy released by crack extension with the amount of surface energy needed to generate the newly exposed crack surface. The Griffith criterion for britde fracture is expressed as... 

Two important conclusions may be drawn from the Griffith criterion (14.1)... 

Vega-Boggio, J. and Vingsbo, O. (1976) Application of Griffith criterion to fracture of boron fibers. J. Mater. Sci., 11 2242-2246. 

This approach was later modified independently by Irwin (51,52) and Oro-wan and Weld (53) and Orowan (54) by including a strain energy release rate term to account for changes caused by small-seale plastic deformations at the crack tip and surfaces. Below, an expression is derived using the modified Griffith criterion for the occurrence of spontaneous fracture of a brittle material depicted in Fig. 6.1. 

Rearrangement of Eq. (6.3) finally gives an expression of the critical stress limit defined generally as the modified Griffith criterion ... 

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