Rupture criteria

From the stress fields, the estimate of the damage of the interim storage structure is canied out by using a rupture criterion as post-processing. Two criteria were taken into account to study the influence of the three-dimensional form of the pattern a parabolic 2-PS criterion based on only major and minor principal stresses, and a 3-PS one taking also account of the intermediate principal stress (where 0c and 0, are the uniaxial compressive and tensile strengths of the material) ... 

Orowan (1949) first proposed a rupture criterion in terms of elastic strength, surface energy (two new surfaces being generated upon fracture) and atomic structure. Fracture was expected to happen under a tensile stress u,h determined as (Appendix E)... 

Another important parameter by modeling of liquid bridge is a rupture criterion, i.e., the critical distance between particles h pt when the rupture of the bridge occurs. To detect rupture of the liquid bridge the criteria... 

If some other criterion such as creep-rupture strength is of primary importance, the alloy choice may be restricted. Here it would be necessary to have thennal fatigue comparisons only for the alloys that pass the primary screening. When alloy selection reaches this stage some further cautions are in order. 

AB cements tend to be essentially brittle materials. This means that when subjected to mechanical loading, they tend to rupture suddenly with minimal deformation. There are a number of different types of strength which have been identified and have been determined for AB cements. These include compressive, tensile and flexural strengths. Which one is determined depends on the direction in which the fracturing force is applied. For full characterization, it is necessary to evaluate all of these parameters for a given material no one of them can be regarded as the sole criterion of strength. 

Agglomerates in a sheared fluid rupture when the hydrodynamic stress exceeds a critical value in dimensionless form the criterion for rupture is Fa > Facrjt. Rupture occurs within a short time of application of the critical stress, and thus can be distinguished from erosion, which occurs over much longer time scales. 

In discussing the reaction pathways, we believe that the general evidence leads to the conclusion that hydrogenolysis proceeds via adsorbed hydrocarbon species formed by the loss of more than one hydrogen atom from from the parent molecule, and that in these adsorbed species more than one carbon atom is, in some way, involved in bonding to the catalyst surface. In the case of ethane, this adsorption criterion is met via a 1-2 mode or a v-olefin mode. Mechanistically it is difficult to see how the latter could be involved in C—C bond rupture in ethane. With molecules larger than ethane, other reaction paths are possible One is via adsorption into the 1-3 mode, and another involves adsorption as a ir-allylic species. 

As shown in Sect. 2, the fracture envelope of polymer fibres can be explained not only by assuming a critical shear stress as a failure criterion, but also by a critical shear strain. In this section, a simple model for the creep failure is presented that is based on the logarithmic creep curve and on a critical shear strain as the failure criterion. In order to investigate the temperature dependence of the strength, a kinetic model for the formation and rupture of secondary bonds during the extension of the fibre is proposed. This so-called Eyring reduced time (ERT) model yields a relationship between the strength and the load rate as well as an improved lifetime equation. 

One of the simplest criteria specific to the internal port cracking failure mode is based on the uniaxial strain capability in simple tension. Since the material properties are known to be strain rate- and temperature-dependent, tests are conducted under various conditions, and a failure strain boundary is generated. Strain at rupture is plotted against a variable such as reduced time, and any strain requirement which falls outside of the boundary will lead to rupture, and any condition inside will be considered safe. Ad hoc criteria have been proposed, such as that of Landel (55) in which the failure strain eL is defined as the ratio of the maximum true stress to the initial modulus, where the true stress is defined as the product of the extension ratio and the engineering stress —i.e., breaks down at low strain rates and higher temperatures. Milloway and Wiegand (68) suggested that motor strain should be less than half of the uniaxial tensile strain at failure at 0.74 min.-1. This criterion was based on 41 small motor tests. 

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. 

Elastic Properties. The ability of a fiber to deform under below-rupture loads and to return to its original configuration or dimension upon load removal is an important performance criterion. Permanent deformation may be as detrimental as actual breakage, rendering a product inadequate for further use. Thus, the repeated stress or strain characteristics are of significance in predicting or evaluating functional properties. 

It has also been shown54 that T50 test pieces can be successfully used with complete fracture as the criterion of failure. This obviously results in a longer test but the means of assessment is much easier and not subjective. Although rupture is not widely used as a measure of ozone attack it is used in fatigue tests (Chapter 12) and could possibly be used for static ozone tests. 

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... 

The problem in question is really very complicated. Here we have many potential possibilities formation of quasi-liquid hydrogen in cavities of nanomaterials, physical adsorption of hydrogen molecules, absorption of H-atoms, formation-rupture of covalent C-H bonds with possible eluation of carbon in the form of gaseous hydrocarbons. But the complicity of the problem cannot create obstacles to the true science. As every new field, chemistry of hydrogen in carbon nano-materials requires serious and all-round experimental investigations. Only such investigations can precede to theoretical treating of the phenomenon and be the criterion of the accuracy of different theoretical constructions. 

As shown in Table V, 2,3-dimethylbutane is the major reaction product in every case except for the cis isomer on platinum. Since both mechanisms A and B (nonselective and selective) compete on platinum films (86, 87), and probably as well on nickel and rhodium films, the excess of 2,3-dimethylbutane over the amounts expected by Mechanism A may be assigned to Mechanism B, involving the selective rupture of —CHj—CHj— bonds. a,a,, -Tetraadsorbed species were suggested to be associated with Mechanism B (89), whose contribution increases with different metals in the same order, Pt < Ni < Rh, as that for multiple exchange of methane (90). Since multiple exchange of methane is usually taken as a criterion for the ability of a metal to form adsorbed methylene, this result is in fair agreement with the proposed a,a,J ,)S-tetraadsorbed precursors (Scheme 34). The latter were... 

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