Brittle fracture theory, Griffith

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. 

This equation for lap joint failure is surprising in a number of ways. It is equivalent to Griffith s brittle fracture theory for glass [4], Moreover, it fits the puzzling historic results for lap joint failure which showed that the overlap length was not important for long joints, and the strength increased with sheet thickness d and stiffness E. Additionally, it is now clear why chemical environment can weaken the Joint because the failure depends on work of adhesion W, which decreases markedly with surface contamination. 

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... 

The Griffith theory of brittle fracture postulates that the fracture is due to ... 

British thermal unit (Btu) A British thermal unit is the energy needed to raise the temperature of 1 lb of water ]°F (0.6°C) at sea level. As an example, one lb of solid waste usually contains 4,500 to 5,000 Btu. Plastic waste contains greater Btu than other materials of waste. See calorie energy consumption heat, brittle Easily broken, damaged, disrupted, cracked, snapped. See design-failure theory, Griffith metal fracture. 

One general comment is that defects are not as strong a controlling feature of breakage in these extensible textile fibres as in many other materials. Rupture forces cannot be calculated from modulus and crack depth as in Griffiths brittle fracture, or even from the later theories of fracture mechanics. As described below, Moseley (1963) showed that severe damage could be imposed on nylon and polyester fibres with no effect on strength at room temperature. 

Fracture mechanics for brittle materials is basically derived from the theory presented by Griffith (1920). Initially it was proposed for an elliptical crack in an infinite elastic and homogeneous medium subjected to distant tensile forces and the conditions for crack propagation were formulated for that case. Later, the brittle fracture mechanics were developed for various situations in real structural elements, with non-negligible plastic deformations and with several complications necessary to account for heterogeneity of materials, time effects, etc. In that approach the crack s appearance and propagation is considered as a basic effect of loading and as phenomena directly related to final failure. 

The analysis was first carried out by Griffith in a treatment of the brittle fracture of metals. Actually, the considerations are of general nature and can also be applied to polymers, after introducing some physically important but formally simple modifications. Griffith s approach is based on linear elasticity theory and its utility for polymers may look questionable at first, as those are neither elastic nor linear under the conditions near to failure. However, as we will see, the theory is indeed applicable and provides also here a satisfactory description of crack growth. 

What remains to be established is a criterion that will differentiate between the tendency of the solid to respond to external loading by brittle fracture or ductile deformation. This is not an easy task, because it implies a connection between very complex processes at the atomistic level and the macroscopic response of the solid in fact, this issue remains one of active research at present. Nevertheless, phenomenological theories do exist which capture the essence of this issue to a remarkable extent. In an early work, Griffith developed a criterion for the conditions under which brittle fracture will occur [140]. He showed that the critical rate of energy per unit area Gi, required to open an existing crack by an infinitesimal amount in mode I loading is given by... 

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