Griffith fracture theory

Griffith considered that fracture produces a new surface area and postulated that for fracture to occur the increase in energy required to produce the new surface must be balanced by a decrease in elastically stored energy. 

Second, to explain the large discrepancy between the measured strength of materials and those based on theoretical considerations, he proposed that the elastically stored energy is not distributed uniformly throughout the specimen but 

The elastically stored energy decreases and so —(dU/dc) is essentially a positive quantity. 

Griffith calculated the change in elastically stored energy using a solution obtained by Inglis [2] for the problem of a plate, pierced by a small elliptical crack, that is stressed at right angles to the major axis of the crack. Equation (12.1) then allows the fracture stress of the material to be defined in terms of 

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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. 

To evaluate the influx solution experimentally for an A/B cantilever beam configuration as shown in Fig. 1, we apply Griffith s theory at the critical moment of fracture, such that the incremental change in stored elastic energy U. with change in crack length a, is Just sufficient to overcome the fracture surface energy S... 

The principle behind the phenomenon of fracture of materials can be described by having recourse to Griffith s theory. Alternatively, this can be done by introducing the concept of fracture toughness. 

Besides Griffith s theory, the fracture of materials can be described in terms of a property known as fracture toughness. The fracture toughness of a material refers to its resistance to fracture in the presence of cracks or discontinuities. Fracture toughness is represented by... 

Their analysis of experimental data shows that tensile strength was the only parameter that varied as a function of particle size. Model simulation indicate that larger lumps were stronger than smaller lumps which is contradictory to Waters et al. [8], Teo and Waters [9], and Griffith [10] theory of fracture, which implies that larger particle are more likely to contain larger cracks and hence be more susceptible to breakage. 

The generalized theory therefore restores the explicit link between a continuum mechanics approach to fracture, which is of such great value in engineering design and practice, and the atomistic view which concerns us most in this review. This link has been lost since Griffith s theory was found to be inadequate for most real... 

Irwin proposed the concept of quasi-elastic fracture, which allows us to extend the limits of applicability of Griffith s theory [11], Irwin s criterion is valid not only for brittle materials, but also for elastic-plastic materials with significant plastic deformation developing until the moment of actual destruction of a material. 

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... 

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... 

We may thus conclude that the fracture process is determined by crack formation and crack propagation. Griffith crack theory is essentially a static conception of critical crack formation. Crack growth, however, also depends on dissipative processes. Below the critical load, crack propagation may advance very slowly. In such a case there is a dissipation of energy due to creep processes. Therefore, fracture is a time-dependent process. This aspect is neglected in the Griffith-Irwin theory of fracture. 

This issue was addressed by A.A. Griffith, whose theory is used today by engineers and scientists to determine the strength of materials containing defects [3]. This theory established an energy criterion for fracture which states that crack growth occurs when ... 

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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