Griffith fracture energy

To understand ductile-to-brittle transitions, the Rice criterion in which the ratio between the surface energy (Griffith fracture energy) and the unstable stacking fault energy is often... 

In the mechanics of composite materials, the interpretation of adhesion characteristics is based on the Griffith s theory concerning to the fracture process. The Griffith fracture energy, U, which determines the critical tension that starts crack propagation, with a length equal to is given by the relation ... 

Fig. 16 Graph of the strain energy W2, the fracture energy Wl and their difference, resulting in the Griffith length L. Cracks with sizes larger than will propagate in the fibre...

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... 

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. 

In such molecular dynamic simulations, one starts with an array of atoms or molecules , initially on a lattice, interacting with one another via an interatomic potential. These interacting potentials were taken by Paskin et al (1980, 1981) to be the Lennard-Jones potential (l> rij) = e[(l/rij) — 2(l/rij) ], where e denotes the depth of the potential energy and rij denotes the interatomic separation of the atoms. This potential is assumed to have a sharp cut-off at an arbitrarily chosen value 1.6 (lattice constant) of the interatomic separation. The external stress or force is applied only at the boundary surface atoms. In order to investigate the Griffith fracture phenomena, one can consider for example a two-dimensional lattice of linear size L, remove a few I L) consecutive bonds along a horizontal row in the middle of the network, and apply tensile force on the upper and lower surface atoms in the vertical direction. 

Qearly, a crack can initiate udien G = and will be unstable if dG/da < 0 thereafter. This is the Griffith fracture condition on which all fracture mechanics is based, although Griffith used the surface energy of the crack 7 so that ... 

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],... 

The classic Griffith-Orowan theory describes the relationship between strength and toughness of brittle materials such as ceramics (Griffith, 1920 Orowan, 1949). In the simple basic equation of the theory, the stress to fracture <7f is related to Youngs elastic modulus E, the fracture energy y and the critical crack length c by... 

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

The presence of a crack also increases the surface area. Griffith called the energy associated with a unit area of the crack the surface energy. Here we will call it the fracture energy for reasons that should become clear later. The fracture energy, T, associated with the crack may be expressed as... 

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]. 

If we assume Griffith-type fracture behavior, the energy released as the crack grows (a increases) must go into the formation of new fracture surface. The fracture energy Gc (sometimes called energy release rate) is therefore... 

The starting point of the fracture theory is the Griffith-Irwin theory of cohesive fracture. It has been extended to the adhesive fracture According to this theory the fracture strength a of an adhesive bond is related to the fracture energy e and the critical crack length 1. It is... 

There are two principal theories, or models, that attempt to describe what happens during brittle fracture, the Griffith fracture theory and the Irwin model. Both assume that fracture takes place through the presence of preexisting cracks or flaws in the polymer and are concerned with what happens near such a crack when a load is applied. Each leads to the definition of a fracture-toughness parameter and the two parameters are closely related to each other. The Griffith theory is concerned with the elastically stored energy near the crack, whereas the Irwin model is concerned with the distribution of stresses near the crack. Both theories apply strictly only for materials that are perfectly elastic for small strains and are therefore said to describe linear fracture mechanics. 

In Griffith s original treatment, the surface free energy per unit area of fracture plane was employed in place of the generalized fracture energy, Gc/2. His results therefore carried the implication of thermodynamic reversibility. In contrast, Gc merely represents energy dissipated during fracture. Nevertheless, provided that it is dissipated in the immediate vicinity of the crack tip and is independent of the overall shape of the test piece and the way in which forces... 

Figure 16.12. Four tests of fracture energy (a) Griffith test for cohesive fracture energy, (b) T tear test, (cMap test for adhesive fracture energy, and (d) peel tost.

Many tests, for example Tensile tests and Shear tests, measure a critical stress rather than an energy of fracture. Good has pointed out that this critical stress will also depend on the fracture energy. He adapted the Griffith - Irwin theory of fracture for application in adhesive bonds. According to this theory, the fracture stress Of of material of modulus E will be given by... 

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