Thickness direction

A piezo-composite consists of a piezoelectric active phase and a passive plastic phase [2]. In the 1-3-configuration adopted in our case, piezoelectric rods parallely aligned in thickness direction are imbedded in a three-dimensional plastic matrix (Fig. 1). The distance between the rods has to be chosen inferior to the half wave length of the shear wave in the matrix material ensuring that the whole compound is vibrating as a quasi-homogeneous material. 

Because the fibers generally are anisotropic, they tend to be deposited on the wire in layers under shear. There is Htde tendency for fibers to be oriented in an out-of-plane direction, except for small undulations where one fiber crosses or passes beneath another. The layered stmcture results in the different properties measured in the thickness direction as compared to those measured in the in-plane direction. The orthotropic behavior of paper is observed in most paper properties and especially in the electrical and mechanical properties. 

Density and Ink Film Thickness. Because ink film thickness directly impacts color, it is important to control film thickness on press. The amount of ink transferred to paper, along with a related factor, dot gain, which refers to how the halftone dots spread under the pressure of the printing process, is the tool by which a press operator monitors color on press. 

Plastic Stra.ln Ra.tlo. The plastic strain ratio is the ratio of strains measured in the width over the thickness directions in tensile tests. This ratio characterizes the abhity of materials to resist thinning during forming operations (13). In particular, it is a measure of the abhity of a sheet material to resist the thinning and failure at the base of a deep drawn cup. The plastic strain ratio is measured at 0°, 45°, and 90° relative to the rolling direction. These three plastic strain ratios Rq, R, and R q, are combined to obtain the average strain ratio, cahed the R or the R value, and its variation in strain ratio, cahed... 

A blow moulding die which has an outside diameter of 40 mm and a die gap of 2 mm is used to produce a plastic bottle with a diameter of 70 mm. If the swelling ratio of the melt in the thickness direction is 1.8 estimate... 

By similar analysis it may be shown that for a short rectangular slit the swelling ratios in the width (T) and thickness (//) directions are given by... 

For control or calibration purposes, film thickness can be determined by mounting a sectioned specimen and measuring the oxide film thickness directly on the screen of a projection microscope at a known magnification. Alternatively, the loss in weight of an anodised sample of known area may be found after the film has been stripped in a boiling solution made up as follows ... 

Due to the relatively weak forces between the layers of MMT, water and other polar molecules can enter between the unit layers, causing the lattice to expand in the thickness direction. The charge deficiency on the sheet surface is typically balanced by exchangeable cations adsorbed between the unit layers and around their edges because of the substitution of ions of different valence. 

TEM is still the most powerful technique to elucidate the dispersion of nano-filler in rubbery matrix. However, the conventional TEM projects three-dimensional (3D) body onto two-dimensional (2D) (x, y) plane, hence the structural information on the thickness direction (z-axis) is only obtained as an accumulated one. This lack of z-axis structure poses tricky problems in estimating 3D structure in the sample to result in more or less misleading interpretations of the structure. How to elucidate the dispersion of nano-fillers in 3D space from 2D images has not been solved until the advent of 3D-TEM technique, which combines TEM and computerized tomography technique to afford 3D structural images, incidentally called electrontomography . 

In order to compare the finite element model with the one-dimensional Chiao model, an extremely simple mesh of only five elements extending in a column from the laminate centerline to the outer surface was used to model the gradients in the laminate through-thickness direction. Figure 7 shows the reaction history (fractional concentration of reactive species, C, versus time) obtained from this run, selected at the location nearest the heated surface. This figure also shows the comparison with the quasi-isothermal and Chiao models. 

Fitting the data in Figure 54 using the relationship p / = c, with c a constant that could represent. shows that several combinations of the powers a and b can be used, as long as the exponents a and b are related as 6 % 0.45a. These fit results are inconsistent with the mentioned values for a and b hence the sheath thickness probably is not constant. This was also deduced from direct measurement of the lEDs [161, 235,486, 487]. In contrast, a recently developed method to determine the sheath thickness directly from deposition experiments [ 150,151, 488] revealed that the value of is constant for the conditions where pco - is constant [487]. 

Figure 6 Chain orientation along the hoop, length, and thickness directions measured at different positions along the length of a standard PET bottle. Polarized ATR spectra were recorded for (a) the outer and (b) the inner surfaces of the bottle, respectively. Reproduced with permission from Smith et al. [35]. Copyright Elsevier 2006.

Figure 4.6 The machine direction (MD), cross machine direction (CD) and thickness direction (z) of a sheet of paper.

For the thickness direction, the modulus of the reinforcement being very much higher (20 times, for example) than that of the matrix, the matrix between the reinforcement layers is subjected to significant deformation that is sometimes qualified as amplified strain . 

For essentially all of the data sets found in Tadmor and Klein [8] the melting results resemble the data shown in Figs. 6.9 and 6.10. The data analysis is of course difficult near the end of melting since the bed often breaks into segments. In essentially ail cases, however, the fraction of the bed remaining in the cross-channel direction (width) is much greater than in the thickness direction. Also, in general the last third of the v-direction material appears to melt in the last turn of the... 

In the classical literature analysis the system equations were manipulated to eliminate V y, the velocity of the solid bed consumption in the thickness direction (y direction), from the analysis by using the assumption that the solid bed reorganizes. This allowed a straightforward differential analysis and a closed form solution in the cross-channel x direction for solids melting. In this analysis, the y-direction velocity V y is retained as a variable because this facilitates the calculation of the change in bed thickness, which was found to be very important in the reevaluation of the literature data, as shown in Figs. 6.9 and 6.10. 

Enhanced stiffness and strength in the thickness direction due to the presence of out-of-plane orientation of some fibers. 

For the ILD process, it is less feasible to continue measuring over field oxide, because multiple oxide layers are present (also see Fig. 6). The true thickness and thickness uniformity of the particular level of an ILD proeess can be confounded by the presence of the underlying previous layers. Thus, after the first metal process, it is preferable to measure the oxide thickness directly on a metal line. 

As with tensile properties, both compressive strength and modulus depend on the fiber content and hber orientation (see Table 5.8). The interlaminar shear strength reported in Table 5.8 is a measure of the shear strength in the thickness direction of the SMC sheet. It is determined by three-point flexural testing of beams with short span-to-depth ratios and is considered to be a quality-control test for molded composites. 

To solve the preceding set of equations, Equation 5.62 is plugged into Equation 5.60. By separately determining the compaction properties of the fiber bed [32] an evolution equation for the pressure can be obtained. Because this is a moving boundary problem the derivative in the thickness direction can be rewritten [32] in terms of an instantaneous thickness. The pressure field can then be solved for by finite difference or finite element techniques. Once the pressure is obtained and the velocity computed, the energy and cured species conservation equations can be solved using the methodology outlined in Section 5.4.1. 

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