Tensile force

For a component subjected to a uniaxial force, the engineering stress, a, in the material is the applied force (tensile or compressive) divided by the original cross-sectional area. The engineering strain, e, in the material is the extension (or reduction in length) divided by the original length. In a perfectly elastic (Hookean) material the stress, a, is directly proportional to be strain, e, and the relationship may be written, for uniaxial stress and strain, as... 

PRESSURE. If a body of fluid is at rest, the forces are in equilibrium or the fluid is in static equilibrium. The types of force that may aci on a body are shear or tangential force, tensile force, and compressive force. Fluids move continuously under the action of shear or tangential forces. Thus, a fluid at rest is free in each part from shear forces one fluid layer does not slide relative to an adjacent layer. Fluids can be subjected to a compressive stress, which is commonly called pressure. The term may be defined as force per unit area. The pressure units may be dynes per square centimeter, pounds per square foot, torr. mega-Pascals, etc. Atmospheric pressure is the force acting upon a unit area due to the weight of the atmosphere. Gage pressure is the difference between the pressure of the fluid measured (at some point) and atmospheric pressure. Absolute pressure, which can be measured by a mercury barometer, is the sum of gage pressure plus atmospheric pressure. 

Force = tensile force exerted on fiber — at mechanical equilibrium fiber exerts an equal and opposite inward force... 

Mechanical failures occur when the part is exposed to some t5q)e of force that exceeds its capability. A part may be exposed to three different t5q)es of forces tensile, compression, and vacuum-generated stresses. Many processes require super- or subatmo-spheric pressure. In a fluoropol5mier-Iined vessel or a stand-alone vessel at elevated pressure, the walls are subjected to tensile stress. Compression stress develops in parts such as seals and gaskets where force is applied to the part, for instance, by placing it between bolted flanges. Vacuum can be a permanent or transient feature of a process and subjects a part to complex forces which could be a combination of tensile and compression. 

At a high hold-down force, tensile stresses in the radial direction in the wall hinder the formation of wrinkles, and fracture at the punch or die radius becomes the limiting factor. The maximum cup height takes place at the junction of wall wrinkle and fracture, as illustrated in Fig. 27 [68]. 

Pullout force Tensile stress at yield Shear strength... 

A polymer responds to a pulling force (tensile stress) by being stretched (tensile strain). The mechanical properties of a polymer can be described partly by the values derived from the tensile stress-strain curve (Figure 2.10). Polymers are viscoelastic materials - that is, they can behave simultaneously as liquids with viscous flow and as elastic solids. When a polymer is stretched, the sample goes throngh varions stages. The first part of the curve describes the elastic properties of the polymer, when the sample can be stretched without permanent distortion. 

Figure 6. 2D SAXS patterns of PET and PBT bristles, cold drawn, A = 3.5 (A = 2.3) and annealed with fixed ends for 6 h at 240°C (180°C), recorded at room temperature at a forced tensile deformation e or tensile set (residual elongation) in percent (a) PET, e = 0, (b) PET, = 8, (c) PET, = 0(5.5), (d) PET, , = 4.7(8), (e) PBT, e = 0, and (f) PBT, ,.= 6.7(16.7). The value in brackets is the forced elongation in percent during the previous measurement under stress. Each square covers the range -0.15 nm < 3 2, 3 < 0.15 nm with the modulus of the scattering vector defined by s = (sj2 + % ) = (2/A)sin 9. Vertical straining direction [22]...

The paper discusses the application of dynamic indentation method and apparatus for the evaluation of viscoelastic properties of polymeric materials. The three-element model of viscoelastic material has been used to calculate the rigidity and the viscosity. Using a measurements of the indentation as a function of a current velocity change on impact with the material under test, the contact force and the displacement diagrams as a function of time are plotted. Experimental results of the testing of polyvinyl chloride cable coating by dynamic indentation method and data of the static tensile test are presented. 

The separation of two surfaces in contact is resisted by adhesive forces. As the nonnal force is decreased, the contact regions pass from conditions of compressive to tensile stress. As revealed by JKR theory, surface tension alone is sufficient to ensure that there is a finite contact area between the two at zero nonnal force. One contribution to adhesion is the work that must be done to increase surface area during separation. If the surfaces have undergone plastic defonnation, the contact area will be even greater at zero nonnal force than predicted by JKR theory. In reality, continued plastic defonnation can occur during separation and also contributes to adhesive work. 

A different approach is followed by Kadlec and Dubinin who calculate the theoretical tensile strength from a 6-12 relation for molecular forces (cf. Section 1.3) as... 

There is another aspect of tensile deformation to be considered. The application of a distorting force not only stretches a sample, but it also causes the sample to contract at right angles to the stretch. If w and h represent the width and height of area A in Fig. 3.1, both contract by the same fraction, a fraction which is related in the following way to the strain ... 

It is necessary to establish some conventions concerning signs before proceeding further. When the applied force is a tensile force and the distortion is one of stretching, F, dL, and dw are all defined to be positive quantities. Thus dw is positive when elastic work is done on the system. The work done by the sample when the elastomer snaps back to its original size is a negative quantity. 

Until now we have restricted ourselves to consideration of simple tensile deformation of the elastomer sample. This deformation is easy to visualize and leads to a manageable mathematical description. This is by no means the only deformation of interest, however. We shall consider only one additional mode of deformation, namely, shear deformation. Figure 3.6 represents an elastomer sample subject to shearing forces. Deformation in the shear mode is the basis... 

By analogy with Eq. (3.1), we seek a description for the relationship between stress and strain. The former is the shearing force per unit area, which we symbolize as as in Chap. 2. For shear strain we use the symbol y it is the rate of change of 7 that is involved in the definition of viscosity in Eq. (2.2). As in the analysis of tensile deformation, we write the strain AL/L, but this time AL is in the direction of the force, while L is at right angles to it. These quantities are shown in Fig. 3.6. It is convenient to describe the sample deformation in terms of the angle 6, also shown in Fig. 3.6. For distortion which is independent of time we continue to consider only the equilibrium behavior-stress and strain are proportional with proportionality constant G ... 

As long as the moduli are constants, it makes no difference in either a tensile or shear experiment which variable, stress or strain, is independent and which is dependent that is, we could apply a constant force and measure the strain or induce a constant strain and measure the force responsible. The modulus is the ratio of the stress to the strain. If the ratio were calculated as the ratio of the strain to the stress, the reciprocal of the modulus would result. The latter is called the compliance and is given the symbols D and J for tensile and shear conditions, respectively. When they are independent of time, the moduli and compliances for a particular deformation are simply reciprocals. 

Returning to the Maxwell element, suppose we rapidly deform the system to some state of strain and secure it in such a way that it retains the initial deformation. Because the material possesses the capability to flow, some internal relaxation will occur such that less force will be required with the passage of time to sustain the deformation. Our goal with the Maxwell model is to calculate how the stress varies with time, or, expressing the stress relative to the constant strain, to describe the time-dependent modulus. Such an experiment can readily be performed on a polymer sample, the results yielding a time-dependent stress relaxation modulus. In principle, the experiment could be conducted in either a tensile or shear mode measuring E(t) or G(t), respectively. We shall discuss the Maxwell model in terms of shear. 

An important application of Eq. (3.39) is the evaluation of M, . Flory et al.t measured the tensile force required for 100% elongation of synthetic rubber with variable crosslinking at 25°C. The molecular weight of the un-cross-linked polymer was 225,000, its density was 0.92 g cm , and the average molecular weight of a repeat unit was 68. Use Eq. (3.39) to estimate M. for each of the following samples and compare the calculated value with that obtained from the known fraction of repeat units cross-linked ... 

Fig. 2. Illustrations of forces to which adhesive bonds are subjected, (a) A standard lap shear specimen where the black area shows the adhesive. The adherends are usually 25 mm wide and the lap area is 312.5 mm. The arrows show the direction of the normal apphcation of load, (b) A peel test where the loading configuration, shown by the arrows, is for a 180° peel test, (c) A double cantilever beam test specimen used in the evaluation of the resistance to crack propagation of an adhesive. The normal application of load is shown by the arrows. This load is appHed by a tensile testing machine or other...

The principal type of shear test specimen used in the industry, the lap shear specimen, is 2.54 cm wide and has a 3.23-cm overlap bonded by the adhesive. Adherends are chosen according to the industry aluminum for aerospace, steel for automotive, and wood for constmction appHcations. Adhesive joints made in this fashion are tested to failure in a tensile testing machine. The temperature of test, as weU as the rate of extension, are specified. Results are presented in units of pressure, where the area of the adhesive bond is considered to be the area over which the force is appHed. Although the 3.23-cm ... 

Peel tests are accompHshed using many different geometries. In the simplest peel test, the T-peel test, the adherends are identical in size, shape, and thickness. Adherends are attached at thek ends to a tensile testing machine and then separated in a "T" fashion. The temperature of the test, as well as the rate of adherend separation, is specified. The force requked to open the adhesive bond is measured and the results are reported in terms of newtons per meter (pounds per inch, ppi). There are many other peel test configurations, each dependent upon the adhesive appHcation. Such tests are well described in the ASTM hterature. 

Normalised fiber mechanical properties are expressed in terms of unit linear density. For example, in describing the action of a load on a fiber in a tensile test, units of N/tex or gram force per denier (gpd) are generally used. If this is done, the term tenacity should be used in place of stress. The tme units of stress are force per unit cross-sectional area, and the term stress should be reserved for those instances where the proper units are used. 

Other elastomeric-type fibers iaclude the biconstituents, which usually combine a polyamide or polyester with a segmented polyurethane-based fiber. These two constituents ate melt-extmded simultaneously through the same spinneret hole and may be arranged either side by side or ia an eccentric sheath—cote configuration. As these fibers ate drawn, a differential shrinkage of the two components develops to produce a hehcal fiber configuration with elastic properties. An appHed tensile force pulls out the helix and is resisted by the elastomeric component. Kanebo Ltd. has iatroduced a nylon—spandex sheath—cote biconstituent fiber for hosiery with the trade name Sidetia (6). 

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