Free-edge analysis

In this section, an analytical solution to calculate residual stresses in an FGM disk is discussed, based on simple linear elastic plate theories of classical mechanics, and used for the calculation of residual stresses in a plane stress state. An equi-biaxial stress analysis differs from a plane stress state by simply replacing the Young s modulus A by the corresponding biaxial modulus E = E/( 1 - v). In this way, the residual thermal stress can be calculated in the centre of the FGM disk, far enough away from the free edges where a complex stress state is present. 

To employ this approach in the considered example, the membrane was described in a continuum limit through a surface, h(y,z), identified as the position of the bilayer midplane. The results of such an analysis for the cases of a tensionless and a 10% stretched membrane are shown in the main panel of Fig. 11 with red and black solid symbols, respectively. The solid lines are fits of the power spectrum It2 with (21). It can be seen that, indeed, Aa = 0.066/f2 g) (predicted by the free edge simulations) corresponds to the membrane tensionless state. The bending rigidity of the bilayer is 4.5kBT and seems to decrease with tension, presumably due to membrane thinning. 

At the substrate-adhesive interface both the shear and tensile stresses reach a maximum at the free edge of the adhesive bond. Harrison and Harrison used a finite element analysis to determine the effect of varying Poisson s ratios on interfacial shear strengths.Rubbery materials can distribute the stress over larger areas while materials with lower Poisson s ratios produce greater interfacial shear stresses. 

It was noted in Section 2.3.2 that most of the current interfacial fracture mechanics methodologies describe steady-state crack propagation, but not the initiation of interfacial cracks. A recent approach to the prediction of initiation is based on the calculation of the singular stress field at the free edge of a bimaterial system loaded on the top layer [59,60]. Because the crack is assumed not to exist initially in this analysis, a very different singular field is predicted, and the results can be used to predict initiation of cracks in residually stressed coatings. Because the predictions of this theory sometimes contradict the predictions of the Suo and Hutchinson approach, we shall briefly review it as a final note. 

FAILURE ANALYSIS OF COMPOSITE LAMINATES WITH FREE EDGE... 

In this study, the problem to be analyzed was a laminate under in-plane uniaxial tension. For stress analysis, the region of interest was subdivided into a number of elements with a very dense, and uniform mesh used near the free edge. 

Stress distribution in the neighborhood of the free edge was calculated using the pseudo 3-D finite element program. In-plane stresses were Gn, G22, cji2 interlaminar stresses were Gzy, and Gzx- For ease of comparison, a tensile in-plane load (Nx) of 1000 Ib/in was used in the analysis. 

Accompanying the free-edge interlaminar stress analysis was the use of reduced lamina moduli to account for the lamina matrix cracking predicted by the Tsai-Hill criterion. Caution must be exercised in this reduction of elastic constants. When a certain elastic constant is reduced, in order to satisfy constraint conditions on the elastic constants, the remaining constants should also be adjusted. For example, due to transverse matrix failure, E2 was reduced to a small value (e.g. 100 psi). In order to meet the constraint condition like V23 < E2/E3, V23 should also be reduced. 

When a load is applied, if the product is to remain in equilibrium there must be equal force acting in the opposite direction. These balancing forces, as an example, are the reactions at the supports. For purposes of structural analysis there are several supports conditions that have been defined. The free (unsupported), simply supported, and fixed supports are the most frequently encountered. The free (unsupported) condition occurs where the edge of a body is totally free to translate or rotate in any direction. The fixed (clamped or built-in) support condition at the end of a beam or plate prevents transverse displacement and rotation. The condition can... 

Quantitative data on local structure can be obtained via an analysis of the decaying slope next to the absorption edge. The absorption of an X-ray photon boosts a core electron up into an unoccupied band of the material which, in a metal, is the conduction band above the Fermi level. Electrons in such a band behave as if nearly free and no fine structure would be expected on the absorption tail . However, fine structure is observed up to 500 to 1000eV above the edge (see Figure 2.73(b)). The ripples are known as the Kronig fine structure or extended X-ray absorption fine structure (EX AFS). 

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