Griffith theory

The importance of inherent flaws as sites of weakness for the nucleation of internal fracture seems almost intuitive. There is no need to dwell on theories of the strength of solids to recognize that material tensile strengths are orders of magnitude below theoretical limits. The Griffith theory of fracture in brittle material (Griflfith, 1920) is now a well-accepted part of linear-elastic fracture mechanics, and these concepts are readily extended to other material response laws. 

The elastic modulus and strength are related by a Griffith theory type relationship. 

An example of a theory is the Griffith theory. It expresses the strength of a material in terms of crack length and fracture surface energy. Brittle fracture is based on the idea that the presence of cracks determines the brittle... 

J.S. Griffith, Theory of Transition Metal Ions, Cambridge University Press, Cambridge, 1961. 

In providing an overall picture of the Griffith theory applied to the comminution process, it must be pointed out that the theory requires that a tensile stress should exist across a crack to open it further. While a uniform compressive force can close a crack, a nonuniform one can lead to the occurrence of localized tensile stresses. In a comminution process the particles are subjected to nonuniform loading, and therefore it can be surmised that they normally break in tension and not in compression. However, the tensile component of loading in comminution does not form the major loading component and this contributes towards a lowering of the overall energy efficiency of comminution. 

Single crystals of zinc were broken106 by two cleavage and one tensile method. The 7 was about 100,400, and 575 erg/cm2, respectively, for these three arrangements. Also this wide spread of results is easier to reconcile with the new than with the Griffith theory. 

R. A. Marcus, J. Chem. Phys. 93 679 (1965). The addition of the George and Griffith theory (vibrational activation) to electrostatics of electron transfer. 

For the 2 2g and 5T2g-terms of the Oh-reference the Griffith theory could be appropriate. In the case of the Cl-interacting terms 3Tig or 4 Tig, the Figgis isotropic Hamiltonian can be applied. These theories offer the magnetic susceptibility formulae in closed forms. However, these approaches... 

In principle, then, the surface work which determines the fracture stress of the body can be calculated from the physical properties of the material. In practice this is not easy, since the energy density distribution can only be calculated exactly for linear elastic solids, for which 1 and Eq. (5) reverts to the Griffith theory. 

Developed chiefly in Russia, the kinetic theory of fracture at first appears to represent an entirely different account of fracture phenomena to that discussed in Section 1.2. In fact some Russian authors have claimed that the kinetic theory contradicts the Griffith theory of fracture. As we shall see, however, this is not the case. 

The point to notice is that a threshold level of stored energy in the bond is necessary before AG -> 0 and thus before the forward reaction can proceed. This stored energy is, of course, equal to AG and thus (when normalised) to the surface energy of the material. Thus we see that the kinetic model of fracture requires a minimum energy supply equal to the surface energy, which is the fracture criterion employed by Griffith. No contradiction therefore exists between the kinetic and Griffith theories. 

With ship failures during and immediately following World War II, interest in the Griffith theory was revived. Orowan [6] and Irwin [7] both recognized that significant plastic deformation accompanied crack advance in metallic materials, and that the plastic work about the advancing crack contributed to the work required... 

Analysis of Failure Failure of "Flawless" Materials Fracture Mechanics Griffith Theory Stress Intensity Factors Fracture Energy Viscoelastic Effects Examples Fatigue Conclusion... 

Griffith Theory. Griffith provided the first analysis of the degradation in strength as a function of flaw size by considering the problem of a small through-the-thickness line crack in a thin sheet of brittle material as illustrated in Figure 2 (13). 

Stress Intensity Factors. A seemingly different approach to fracture on the basis of stress intensity factors, (, 1 6, 17) is frequently encountered in the fracture mechanics literature. It is, therefore, appropriate to briefly discuss this approach and its relation to the Griffith theory. 

From the Griffith theory for the, g-values of low-spin Pgiii 1265,1266 (jjg formulation of Taylor (see also... 

To see how the fracture energy may be used in the initiation of chemical reactions, the concepts of fracture mechanics are introduced, including the strain rate and temperature dependence of the ductile-brittle behavior. The starting point is the Griffith theory which in its simplest form applies to perfectly brittle materials and states that for a crack to form, the elastic strain energy available must be at least sufficient to provide the energy of the new surfaces formed [74]. 

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