Griffith’s energy criterion

Using fracture mechanics and the Griffith s energy criterion, Chow et al. have derived an analytical relation to determine the interfacial fracture energy between a brittle film and a polymeric substrate. 

It is assumed that the limit equilibrium state is reached if cracks develop and increase on the surface of the body volume under action of external loadings. In linear fracture mechanics, Irwin s force criterion and an equivalent Griffith s energy criterion completely determine the equilibrium condition of a continuum elastic body with a crack [9],... 

Alternatively to the Griffith s energy criterion, In the 1950s Irwin calculated the stresses in the vicinity of a crack tip based on linear elasticity theory. He introduced a constant, K, the stress intensity factor, to characterize the magnitude of the stress field. If K (Kj in mode I) reaches a critical value Kc (Kjc), then the crack will propagate in the material Kjc is generally expressed in MPam. ... 

The transition between cohesive and adhesive failure in a simple bi-material joint has been studied by Kendall (1975). Based on Griffith s energy approach, a criterion is derived for deflection along the interface for a short crack for an isotropic material... 

From Griffith s energy failure criterion, the termais constant, which implies that strength... 

Equation (8.50) is known as Griffith s fracture criterion. It includes a critical value of the strain energy release rate, denoted Gjc, and the latter is determined by the surface parameter w. The subscript T is used in the literature to indicate reference to the opening mode V of Fig. 8.30 and to discriminate it from other possible modes of loading. From Eqs. (8.49) and (8.50) follows the critical value of the tensile stress, as... 

Majerus (61, 62) has approached the failure behavior of highly filled polymers by a thermodynamic treatment in which the ability to resist rupture is related to the propellant s ability to absorb and dissipate energy at a certain rate. An energy criterion which requires failure to be a function of both stress and strain was originally stated by Griffith (36) for brittle materials and later adapted to polymers by Rivlin and Thomas (80). Williams (115) has applied an energy criterion to viscoelastic materials such as solid propellants where appropriate terms are included for viscous energy dissipation. 

The eneigy criterion arising from Griffith s work implies that fracture occurs when sufficient energy is released by the growth of the crack to supply the requirements of new fracture surface. The eneigy released comes from the stored elastic or potential... 

The concept of quasi-brittle fracture implies that some materials that exhibit the characteristics of plastic materials at standard test, collapse in tests of the sample with a crack due to the quasi-brittle mechanism, that is, plastic deformation is concentrated in a narrow layer near the tip of a crack. For such materials, Griffith s criterion is relevant instead of the value of the surface energy to introduce the work of plastic deformation at the crack tip. 

Griffith s criterion for brittle fracture involves a remarkably simple expression. It is straightforward to relate the energy release rate to the stress intensity factors introduced above to describe the stresses and displacements in the neighborhood of the crack. In particular, for mode / loading in plane strain, the energy release rate Gi and the stress intensity factor A / are related by... 

The energy criterion for fracture is simply an extension of Griffith s hypothesis which describes quasi-static crack propagation as the conversion of the work done, Wd, by the external force and the available elastic energy stored in the bulk of the specimen, U, into surface free energy, y. It may be written ... 

The energetic criterion, according to which the crack development into a mechanically solicited composite releases a certain amount of elastic energy that is stocked in material and can be evaluated. When its level attains a critical value, G, the cracks will propagate until the material s fracture. The critical energy of propagation represents an intricate characteristic of material, and in the case of brittle fracture, the Griffith criterion can be ex-... 

The similarity between elastic and extending viscoelastic cracks carries over to the criteria for crack extension. In Sect. 4.6, the implications of an energy balance criterion for the growth of a crack in a viscoelastic body are explored. The condition obtained depends only on the initial values of the relaxation functions and takes the same form as that derived by Griffith for an elastic body. There follows, in Sect. 4.7, a demonstration valid in viscoelasticity, that the above condition may be expressed in terms of critical values of the stress intensity factors, which in turn are expressed in terms of distributions of cohesive forces at the crack ends. In this way, Barenblatt s elastic fracture criterion has been extended to viscoelasticity. 

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