Griffith equation

When rubbers eventually fracture, they do so by tearing. Fracture surface energies, using the Griffith equation, have been found to be of the order of 10 J m , whereas the true surface energies are only 0.1-1.0 J Hence, more energy is involved in fracture than is required to form new surfaces, and, as with other polymers, this extra energy is assumed to be used up in viscoelastic and flow processes that occur between the molecules immediately before the rubber breaks. 

The mean critical defect size (c), calculated from the Griffith equation,107108 increases markedly with increasing spinel content (Fig. 14.7). For 0.5 pm in situ spinel composites, the defect size increases up to -20%, and then decreases slightly with further additions of spinel. However, for the preformed spinel composites there is a gradual increase in defect size up to 30% spinel additions. The increase in defect size is in general much more marked at 20%, in... 

Eq. (13.145) is called the Griffith equation for thin sheets, i.e. in plane stress, where Gic, known as the fracture energy, has replaced 2y. A frequently used parameter in plane stress is the critical stress energy factor Kq, which in the case of a wide sheet (plane stress) is defined as... 

Fracture Surface Energy Calculation Berry s Method (8). The dimensions of double cantilever test specimen and techniques are illustrated in Ref. 3. We determined the surface work by substituting the measured quantities from the cleavage tests into Griffiths equation. Three cantilever bars were used. 

Generally, for any dimension therefore, if a crack of length I already exists in an infinite elastic continuum, subject to uniform tensile stress a perpendicular to the length of the crack, then for the onset of brittle fracture, Griffith equates (the differentials of) the elastic energy E with the surface energy E ... 

The tensile strength is, theoretically, related to the modulus by the — simplified — Griffith equation for brittle fracture ... 

Changes in modulus also affect fracture behaviour. The relaticmship between the two is most clearly seen in the case of brittle fracture. For a wide, thick plate containing an edge crack of length a, the critical applied stress at fracture Oc is related to the Young s modulus , the Poisson s ratio v, and the fracture surface energy Gjc of the material by the Griffith equation ... 

Mechanical Behavior. At present, it is not possible to reconcile all the diverse dependences on stoichiometry. However, clearly there is no a priori reason for trends in all properties to be related. By a modification of the Griffith equation (45)... 

Fracture mechanics, essential work of fracture 884, 885 Fracture mechanics, Griffith equation 878, 882, 885 Fracture mechanics, J-integral 881-885 Fracture mechanics, hnear elastic (LEFM) 878, 881, 893... 

This approach indicates that the fracture stress depends on the material parameters, E and yand on the crack size c. Equation (8.10) is commonly termed the Griffith equation. In order to confirm this equation, Griffith introduced cracks of known size into glass bodies and measured their effect on the strength of the glasa The data obtained by Griffith are shown in Fig. 8.6, plotted to show that fracture stress is inversely proportional to Vc, as predicted by Eq. (8.10). 

For cases where V(ir/o/8fracture stress from this equation is less than that obtained from the Griffith equation. Fracture is not, however, predicted to occur under these conditions because the energy approach is a more global approach. Equation (8.11) will, however, be useful for cases when V(7rp/8 1. 

Equation 18.12 is often called the Griffith equation and shows that fracture stress depends on the following ... 

When dealing with brittle fractures, the Griffith equation correlates the length of the crack (, with the critical stress at break, due to crack propagation as follows ... 

Ceramics are brittle materials at moderate temperatures, which means that a ceramic material is prone to catastrophic failure when the fracture stress is exceeded. The strength of a ceramic material can be described by the Griffith equation (1), as follows ... 

With G, replaced by 2y, this is known as the Griffith equation, see S.N.5. 

An equation similar to eqn 5.21 was first derived by Griffith. The Griffith equation for a wide thin sheet is... 

A second paradox is the use of the word shear to describe the fracture. It is evident from the calculation used to obtain Equation (15.5) that shear is not mentioned. The joint peels but does not slide or shear (Fig. 15.11). Only tension forces and displacements are needed to explain the failure of the joint. In fact, it would be far more logical to describe this failure as a tension failure, just as the Griffith equation describes tension failure. Of course, shear stresses exist around the crack tip, as in every crack geometry known, but the energy associated with these stresses remains constant as the crack moves and therefore cannot drive the crack. 

The validity of the Griffith equation is not restricted to the fixed-grip situation considered here. If the grips are not held fixed then at constant load, an increase in 2a will generate an increase in specimen length nevertheless, an extension of the theory shows eqn (5.21) still to be valid. 

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