Understanding failure criteria

In conclusion, classical lamination theory enables us to calculate forces and moments if we know the strains and curvatures of the middle surface (or vice versa). Then, we can calculate the laminae stresses in laminate coordinates. Next, we can transform the laminae stresses from laminate coordinates to lamina principal material directions. Finally, we would expect to apply a failure criterion to each lamina in its own principal material directions. This process seems straightfonward in principle, but the force-strain-curvature and moment-strain-curvature relations in Equations (4.22) and (4.23) are difficult to completely understand. Thus, we attempt some simplifications in the next section in order to enhance our understanding of classical lamination theory. 

So far, we understand that the flowability of powders depends on their failure stresses from the Mohr-Coulomb failure criterion. Therefore, analyses of powder flows... 

In order to understand the behavior of composite propellants during motor ignition, we conducted a study of the mechanical and ultimate properties of a propellant filled with hydroxy-terminated polybutadiene under imposed hydrostatic pressure. The mechanical response of the propellant was examined by uniaxial tensile and simple shear tests at various temperatures, strain rates, and superimposed pressures from atmospheric pressure to 15 MPa. The experimentally observed ultimate properties were strongly pressure-sensitive. The data were formalized in a specific stress-failure criterion. 

The above understanding forms the basis for the development of thermophysical and thermomechanical property sub-models for composite materials at elevated and high temperatures, and also for the description of the post-fire status of the material. By incorporating these thermophysical property sub-models into heat transfer theory, thermal responses can be calculated using finite difference method. By integrating the thermomechanical property sub-models within structural theory, the mechanical responses can be described using finite element method and the time-to-failure can also be predicted if a failure criterion is defined. 

Kinloch(4) observed that the selection of appropriate failure criteria for the prediction of joint strength by conventional analysis is fraught with difficulty. The problem is in understanding the mechanisms of failure of bonded joints, and in assigning the relevant adhesive mechanical properties. Current practice is to use the maximum shear-strain or maximum shear-strain energy as the appropriate failure criterion. However, the failure of practical joints occurs by modes including, or other than, shear failure of the adhesive. This difficulty has led to the application of fracture mechanics to joint failure. 

It should be noted that for an adhesive which is behaving primarily as an elastic solid, the detachment failure criterion used by Derail et al. is equivalent to a stored elastic energy density criterion but under conditions where the deformation is primarily viscous, the two criteria are quite different. None of these authors has been able to successfully link the values of these failure criteria to fundamental interfacial properties or the thermodynamic work of adhesion. Clearly, much remains to be done to complete our understanding of the relationships among surface properties, adhesive rheology, and peel force. 

To understand the failure in this model, an approximate criterion for the brittle or ductile fracture was proposed. One considers the sequence of the weakest bonds and asks for the average failure voltage for the nth weakest bond. It is given by... 

One criterion for a bona fide membrane-fusion protein is that membrane fusion can be reconstituted by transfection of the candidate fusion protein into nonfusing cells or by reconstitution into lipid vesicles (White, 1990 White, 1992 White and Blobel, 1989). Transfection of meltrin a into fibroblasts did not lead to an increase in cell fusion (Yagami-Hiromasa et al., 1995). Clearly, failure to reconstitute fusion does not rule out a role in fusion because the cellular fusion machinery may be more complex than viral fusion proteins. Muscle cells might contain other proteins that are required for meltrin a to promote membrane fusion but that are not expressed or active in fibroblasts. Ultimately, the identity of a bona fide cell-cell fusion protein or protein machine will only be determined by reconstituting membrane fusion with defined components. In the interim, it will be important to more accurately understand the roles of meltrin a and fertilin in the cascade of steps that result in membrane fusion and thereby perhaps distinguish between a direct and indirect role in fusion. 

In order to understand the confusion, it has to be remembered that all designers and engineers over the past 400 years have been educated in Galileo s principle that failure depends on the stress, i.e. the negative pressure, in the material. This stress criterion of failure states that rupture occurs when the stress reaches a critical value. In mathematical terms this is Equation (15.2) which gives ultimate force proportional to area. 

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