E2 Materials

Therefore, whether or not materials removed by sputtering redeposit on the substrate (cathode) surface depends on the relationship between the gap distance and the CDST e2. If the gap distance is equal to or greater than the CDST e2, materials removed by sputtering will not be redeposited on the substrate surface. Otherwise,... 

A composite material consists of flat, thin metal plates of uniform thickness glued one to another with a thin, epoxy-resin layer (also of uniform thickness) to form a multi-decker-sandwich structure. Young s modulus of the metal is Ej, that of the epoxy resin is E2 (where E2 < Ej) and the volume fraction of metal is Vj. Find the ratio of the maximum composite modulus to the minimum composite modulus in terms of Ej, E2 and V. Which value of gives the largest ratio ... 

The preceding restrictions on engineering constants for orthotropic materials are used to examine experimental data to see if they are physically consistent within the framework of the mathematical elasticity model. For boron-epoxy composite materials, Dickerson and DiMartino [2-3] measured Poisson s ratios as high as 1.97 for the negative of the strain in the 2-direction over the strain in the 1-direction due to loading in the 1-direction (v 2)- The reported values of the Young s moduli for the two directions are E = 11.86 x 10 psi (81.77 GPa) and E2 = 1.33x10 psi (9.17 GPa). Thus,... 

The values in Figures 2-11 and 2-12 are not entirely typical of all composite materials. For example, follow the hints in Exercise 2.6.7 to demonstrate that E can actually exceed both E., and E2 for some orthotropic laminae. Similarly, E, can be shown to be smaller than both E. and E2 (note that for boron-epoxy in Figure 2-12 E, is slightly smaller than E2 in the neighborhood of 6 = 60°). These results were summarized by Jones [2-6] as a simple theorem the extremum (largest and smallest) material properties do not necessarily occur in principal material coordinates. The moduli Gxy xy xyx exhibit similar peculiarities within the scope of Equation (2.97). Nothing should, therefore, be taken for granted with a new composite material its moduli as a function of 6 must be examined to truly understand its character. 

The mechanics of materials approach to the micromechanics of material stiffnesses is discussed in Section 3.2. There, simple approximations to the engineering constants E., E2, arid orthotropic material are introduced. In Section 3.3, the elasticity approach to the micromechanics of material stiffnesses is addressed. Bounding techniques, exact solutions, the concept of contiguity, and the Halpin-Tsai approximate equations are all examined. Next, the various approaches to prediction of stiffness are compared in Section 3.4 with experimental data for both particulate composite materials and fiber-reinforced composite materials. Parallel to the study of the micromechanics of material stiffnesses is the micromechanics of material strengths which is introduced in Section 3.5. There, mechanics of materials predictions of tensile and compressive strengths are described. 

The apparent Young s modulus, E2, of the composite material in the direction transverse to the fibers is considered next. In the mechanics of materials approach, the same transverse stress, 02, is assumed to be applied to both the fiber and the matrix as in Figure 3-9. That is, equilibrium of adjacent elements in the composite material (fibers and matrix) must occur (certainly plausible). However, we cannot make any plausible approximation or assumption about the strains in the fiber and in the matrix in the 2-direction. 

Predicted results for E2 are plotted in Figure 3-10 for three values of the fiber-to-matrix-modulus ratio. Note that if Vj = 1, the modulus predicted is that of the fibers. However, recognize that a perfect bond between fibers is then implied if a tensile <32 is applied. No such bond is implied if a compressive 02 is applied. Observe also that more than 50% by volume of fibers is required to raise the transverse modulus E2 to twice the matrix modulus even if E, = 10 x E ,l That is, the fibers do not contribute much to the transverse modulus unless the percentage of fibers is impractically high. Thus, the composite material property E2 is matrix-dominated. 

The predictions for E2 from Equation (3.13) are shown along with measured values for E2 in Figure 3-12. There, obviously this approach is an underestimate of the contribution of the flexible matrix material to E2. As we will see in Section 3.4, better approaches are available for prediction of E2, but at the cost of far more complexity. 

Which is plotted in Figure 3-16 for several values of Gf/G. Only for a fiber volume of greater than 50% of the total volume does G.,2 rise above twice G even when Gf/Gn, = 101 As with E2, the composite material shear modulus G. 2 is matrix-dominated. Measured values of G.,2 have a relation to the predicted values similar to those for E2 in Figure 3-12 (see Section 3.4.2). 

The foregoing are but examples of the types of mechanics of materials approaches that can be used. Other assumptions of physical behavior lead to different expressions for the four elastic moduli for a unidirectionally reinforced lamina. For example, Ekvall [3-2] obtained a modification of the rule-of-mixtures expression for and of the expression for E2 in which the triaxial stress state in the matrix due to fiber restraint is accounted for ... 

Figure 3-20 Bounds on E2 for a Glass-Epoxy Composite Material...

Figure 3-37 E2 Calculations for a Boron-Epoxy Composite Material (After Halplrt and Tsai [3-17])...

For fiber-reinforced composite materials, Tsai gives expressions for E, E2, v 2> 12 9 ° agreement with experimental data... 

Determine the extensional, bending-extension coupling, and bending stiffnesses of an equal-thickness bimetallic strip as shown in Figure 1-3 (a beam made of two different isotropic materials with E, v, a, E2, V2, and 02). Use the middle surface of the beam as the reference surface. 

Base-promoted E2 eliminations involving 1,2-dibromo-1,2-diphenylethane have been used to learn about the stereochemical preferences of this reaction. The meso starting material gives one alkene and the dl starting material gives another. 

The rate of the alkylation reaction depends on the enolate concentration, since it proceeds by a SN2-mechanism. If the concentration of the enolate is low, various competitive side-reactions may take place. As expected, among those are E2-eliminations by reaction of the alkyl halide 2 with base. A second alkylation may take place with mono-alkylated product already formed, to yield a -alkylated malonic ester however such a reaction is generally slower than the alkylation of unsubstituted starting material by a factor of about 10. The monoalkylation is in most cases easy to control. Dialkylated malonic esters with different alkyl substituents—e.g. ethyl and isopropyl—can be prepared by a step by step reaction sequence ... 

This question covers NSCS El and E2. This question tests the material that was covered in the textbook on pages 92-93. 

E2 Extraction and subsequent Uquid/liquid partition Plant material and foodstuffs with a water content below 70g/100g and a fat content below 2.5 g/100 g Cereals and cereal products, spices, fruit powder... 

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