Tensile stress difference

In practice, since we are only interested in an estimate of the effect, we resort to an approximate analysis in which the relevant chemical potentials and mass flux, and attendant strain rate are all evaluated heuristically. The argument begins with reference to fig. 11.6 with the claim that the vacancy formation energy for the faces subjected to tensile stresses differs from that on the faces subjected to compressive stresses. Again, a rigorous analysis of this effect would require a detailed calculation either of the elastic state of the crystal or an appeal to atomistic considerations. We circumvent such an analysis by asserting that the vacancy concentrations are given by... 

The elastic effects in polymer melts are associated with the molecular coil deformation shown in Fig. 3.9. The effects include die swell, a diameter increase when the melt exits from a die and flow instabilities such as melt fracture (causing a rough surface). One measure of the elastic effects is the tensile stress difference — a-yy that occurs in shear flow in the xy axes. There can be a tensile stress in the direction of flow, or a compressive stress (Tyy on the channel walls, or a combination of the two. Figure 5.7 shows that, as the shear rate increases, the value of m... 

The flow curve of a broad MWD polyethylene is more non-Newtonian than that of a narrow MWD polyethylene (Fig. 5.7). These polymers have the same Mw, so, by Eq. (3.8), have the same zero-shear rate viscosity. The elastic stresses at low shear rates are influenced by the high molecular weight tail of the MWD. When the tensile stress difference is small, it can be described by... 

During start-up, the tensile stress difference in the test fluid will be a balance of inertial, interfacial, and drag forces... 

Fig. 2. Etependence of Wirotest (a) indications as a function of tensile stress, when applying different lengths between the probe and the tested surface.

Whereas in the scope of plastic deformations differences are observed Arc welding of pipes <6 32 mm, wall thickness 6,5 mm has caused own tensile stress of 260 MPa in the jont, relief at 720°C during 4 hours, has caused a lowering of stress to 60 MPa. 

Under compression or shear most polymers show qualitatively similar behaviour. However, under the application of tensile stress, two different defonnation processes after the yield point are known. Ductile polymers elongate in an irreversible process similar to flow, while brittle systems whiten due the fonnation of microvoids. These voids rapidly grow and lead to sample failure [50, 51]- The reason for these conspicuously different defonnation mechanisms are thought to be related to the local dynamics of the polymer chains and to the entanglement network density. 

It has been shown quantitatively (21) that the difference in shrinkage rates between the inside and outside of a drying body indeed results in a tensile drying stress. O. This tensile stress is a function of thickness, F ... 

Both Watts and sulfamate baths are used for engineering appHcation. The principal difference in the deposits is in the much lower internal stress obtained, without additives, from the sulfamate solution. Tensile stress can be reduced through zero to a high compressive stress with the addition of proprietary sulfur-bearing organic chemicals which may also contain saccharin or the sodium salt of naphthalene-1,3,6-trisulfonic acid. These materials can be very effective in small amounts, and difficult to remove if overadded, eg, about 100 mg/L of saccharin reduced stress of a Watts bath from 240 MPa (34,800 psi) tensile to about 10 MPa (1450 psi) compressive. Internal stress value vary with many factors (22,71) and numbers should only be compared when derived under the same conditions. 

Consider the design of a glass window for a vacuum chamber (Fig. 18.6). It is a circular glass disc of radius R and thickness f, freely supported in a rubber seal around its periphery and subjected to a uniform pressure difference Ap = 0.1 MPa (1 atmosphere). The pressure bends the disc. We shall simply quote the result of the stress analysis of such a disc it is that the peak tensile stress is on the low-pressure face of... 

Fig. 18.6. A flat-faced pressure window. The pressure difference generates tensile stresses in the low-pressure face.

That is, although we required equal x-direction displacements of the two layers (the proportion of N in each layer was adjusted to create that equal-displacement condition), the lateral displacfiments arfi guitfijjjffer-ent. Those different displacements are a violation of the requireddeToT- mation compatibility of laminae in a laminatir Tolemedy this violation, the top layer must get wider by application of a lateral tensile stress aj, and the bottom layer must get narrower by application of a compressive stress Oy. The two deformations must result in equal-width laminae to satisfy deformation compatibility. Moreover, the lateral stresses in each layer must satisfy force equilibrium in the y-direction, i.e.,... 

Whereas ductile materials, such as iron and mild steel, are often considered not to crack when charged with hydrogen and subjected to a tensile stress below the yield stress, the position is different with high-strength ferrous alloys where, depending on the strength of the steel and the hydrogen content, failure may occur well below the yield stress. However, the fracture process is not instantaneous and there is a time delay before cracks are... 

There are a number of different modes of stress-strain that can be taken into account by the designer. They include tensile stress-strain, flexural stress-strain, compression stress-strain, and shear stress-strain. 

Brittleness Brittle materials exhibit tensile stress-strain behavior different from that illustrated in Fig. 2-13. Specimens of such materials fracture without appreciable material yielding. Thus, the tensile stress-strain curves of brittle materials often show relatively little deviation from the initial linearity, relatively low strain at failure, and no point of zero slope. Different materials may exhibit significantly different tensile stress-strain behavior when exposed to different factors such as the same temperature and strain rate or at different temperatures. Tensile stress-strain data obtained per ASTM for several plastics at room temperature are shown in Table 2-3. 

Test rate and property The test rate or cross-head rate is the speed at which the movable cross-member of a testing machine moves in relation to the fixed cross-member. The speed of such tests is typically reported in cm/min. (in./min.). An increase in strain rate typically results in an increase yield point and ultimate strength. Figure 2-14 provides examples of the different test rates and temperatures on basic tensile stress-strain behaviors of plastics where (a) is at different testing rates per ASTM D 638 for a polycarbonate, (b) is the effects of tensile test-... 

Fig. 7-7 Tensile stress-strain curves of three different moisture contents at 23°C (73°F) and different areas under the curves.

Also common is the occurrence of transitions between different crystalline forms under tensile stresses. We recall here, for instance, the solid-to-solid transitions under stress of nylon 6 [76], PVDF [77, 78], and polybutylene terephtalate (PBT) [79-83]. 

In the identification of different polymorphs in polymers the FTIR technique presents, with respect to the diffraction techniques, the advantage of easier and more rapid measurements. In particular, the high speed of the measurements allows to study the polymorphic behavior under dynamic conditions. As an example let us recall the study of the transition from the a toward the P form of PBT induced by tensile stresses, evaluated by quantitative analysis of the infrared spectra [83],... 

FIGURE 3.6 Tensile stress-strain plots of acrylic mbber (ACM)-silica hybrid nanocomposites using different tetraethoxysilane (TEOS) concentrations. The number in the legends indicates wt% TEOS concentrations. (From Bandyopadhyay, A., Bhowmick, A.K., and De Sarkar, M., J. Appl. Polym. Sci., 93, 2579, 2004. Courtesy of Wiley InterScience.)... 

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