Theory of rupture

Griffith, A. A., The theory of rupture , Proc. Firstlnt. Congr. for Applied Mechanics, 1924 55-63. 

Such genera) treatment of instability including the formation of black spots can be employed as an additional tool to verify the theory of rupture [54],... 

Hole-nucleation rupture of foam bilayers was considered on the basis of formation of nucleus-holes from molecular vacancies existing in the film in Section 3.4.4. The experimentally determined parameters of film rupture along with the hole-nucleation theory of rupture of amphiphile bilayers of Kashchiev-Exerowa [300,301,354,402] made it possible to evaluate the coefficient of lateral diffusion of vacancies in foam bilayer. 

Griffith, A. A., The Phenomena of Rupture Flow in Solids, Fhil. Trans. Royal Society of London, Ser. A, 221, 163-198, 1921 and The Theory of Rupture, Froceedings of First International Congress—Applied Mechanics, p. 55, 1924. 

On the other hand, one can assume a plasticity theoretical perspective on structural elements. Within this view concrete is considered as a rigid-plastic material which means that no deformations occur for stresses up to a certain limit, the yield point. For stresses at the yield point arbitrary large deformations are possible without any change in stresses. Although concrete is far from being a rigid-plastic material it is possible within this framework to develop a general theory of rupture which fits experimental data reasonably well. 

Griffith AA. The Theory of Rupture. Proc. 1st Int. Con. Applied Mechanics, Delft, The... 

In 1936, de Boer formulated his theory of a stressed bond which, despite its simplicity, still constitutes the basis for most models of chemical reactivity under stress [92], In order to fracture an unstressed bond which, in the absence of any vibration, is approximated by the Morse potential of Fig. 18, an energy D must be supplied. If, however, the bond is under tension due to a constant force feitt pulling on either end, the bond rupture activation energy will be decreased by an amount equivalent to the work performed by the mechanical force over the stretching distance from the equilibrium position. The bond potential energy in the presence of stress is given by ... 

The most developed and widely used approach to electroporation and membrane rupture views pore formation as a result of large nonlinear fluctuations, rather than loss of stability for small (linear) fluctuations. This theory of electroporation has been intensively reviewed [68-70], and we will discuss it only briefly. The approach is similar to the theory of crystal defect formation or to the phenomenology of nucleation in first-order phase transitions. The idea of applying this approach to pore formation in bimolecular free films can be traced back to the work of Deryagin and Gutop [71]. 

An understanding of the mechanism of creep failure of polymer fibres is required for the prediction of lifetimes in technical applications. Coleman has formulated a model yielding a relationship similar to Eq. 104. It is based on the theory of absolute reaction rates as developed by Eyring, which has been applied to a rupture process of intermolecular bonds [54]. Zhurkov has formulated a different version of this theory, which is based on chain fracture [55]. In the preceding sections it has been shown that chain fracture is an unlikely cause for breakage of polymer fibres. 

Acid and base catalysis of a chemical reaction involves the assistance by acid or base of a particular proton-transfer step in the reaction. Many enzyme catalysed reactions involve proton transfer from an oxygen or nitrogen centre at some stage in the mechanism, and often the role of the enzyme is to facilitate a proton transfer by acid or base catalysis. Proton transfer at one site in the substrate assists formation and/or rupture of chemical bonds at another site in the substrate. To understand these complex processes, it is necessary to understand the individual proton-transfer steps. The fundamental theory of simple proton transfers between oxygen and nitrogen acids and... 

Mention should be made in this connection of the physics and chemistry involved in faulting as well as in jointing and minor movements of the solid rocks. These phenomena have often been treated under the principles of elastic theory as applied to homogeneous bodies, yet there can be no question that the elastic properties and conditions of rupture of aggregates must differ in many essential particulars from those of homogeneous bodies. Here is a considerable field for experimentation. 

Oxidative chain reactions of organic compounds are current targets of theoretical and experimental study. The kinetic theory of collisions has influenced research on liquid-phase oxidation. This has led to determining rate constants for chain initiation, branching, extension, and rupture and to establishing the influence of solvent, vessel wall, and other factors in the mechanism of individual reactions. Research on liquid-phase oxidation has led to studies on free radical mechanisms and the role of peroxides in their formation. 

When two emulsion drops or foam bubbles approach each other, they hydrodynamically interact which generally results in the formation of a dimple [10,11]. After the dimple moves out, a thick lamella with parallel interfaces forms. If the continuous phase (i.e., the film phase) contains only surface active components at relatively low concentrations (not more than a few times their critical micellar concentration), the thick lamella thins on continually (see Fig. 6, left side). During continuous thinning, the film generally reaches a critical thickness where it either ruptures or black spots appear in it and then, by the expansion of these black spots, it transforms into a very thin film, which is either a common black (10-30 nm) or a Newton black film (5-10 nm). The thickness of the common black film depends on the capillary pressure and salt concentration [8]. This film drainage mechanism has been studied by several researchers [8,10-12] and it has been found that the classical DLVO theory of dispersion stability [13,14] can be qualitatively applied to it by taking into account the electrostatic, van der Waals and steric interactions between the film interfaces [8]. 

The evidence for single-electron transfer (SET) in the reactions of lithium aluminium hydride (LAH) with hindered primary alkyl iodides is overwhelming. A study has now shown for the first time that SET may also be involved in reactions of LAH with unhindered, unsubstituted primary alkyl iodides, the particular substrate studied being 1-iodoctane.98 A theory of the rates of, S 2 reactions and their relation to those of outer-sphere bond-rupture electron transfers has been presented in detail.99 A unified approach is introduced in which there can be a flux density for crossing the transition state, which is either bimodal, one part leading to, S 2 and the other to ET products, or... 

Mechanical Methods Static or rotating breaker bars or slowly revolving paddles are sometimes successful. Their application in conjunction with other methods is frequently better. As indicated in the theory of foams, they will work better if installed at a level at which the foam has had some time to age and drain. A rotating breaker works by deforming the foam, which causes rupture of the lamella walls. Rapidly moving slingers will throw the foam against the vessel wall and may cause impact on other foam outside the envelope of the... 

The most common failure criterion for granular materials is the Mohr-Coulomb failure criterion. Mohr introduced his theory for rupture in materials in 1910. According to his theory, the material fails along a plane only when a critical combination of normal and shear stresses exists on the failure plane. This critical combination, known as the Mohr-Coulomb failure criterion, is given by... 

Above the threshold, deformation occurs as a consequence of direct particle interaction. Several mechanisms of interaction have been suggested solution-precipitation flow of fluid between particles and cavity formation at the particle matrix interface. These theories of creep suggest several rules to improve creep behavior (1) increase the viscosity of the matrix phase in multiphase materials (2) decrease the volume fraction of the intergranular phase (3) increase the grain size (4) use fiber or whisker reinforcement when possible. As the creep rupture life is inversely proportional to creep rate, lifetime can be improved by improving creep resistance. 

Once formed the unstable waves grow until one of them (the fastest) conforms with Eq. (3.65) and then the film ruptures. During this time the film thins additionally, depending on the conditions under which it is produced. This kinetic part of the theory of critical thicknesses has been formulated and partially solved by Vrij [83]. 

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