Tension, uniaxial

Force per unit area along the axis of the deformation is called the uniaxial tension or stress. We shall use the symbol a as a shorthand replacement for F/A and attach the subscript t to signify tension. The elongation, expressed as a fraction of the original length AL/Lq is called the strain. We shall use 7j as the symbol for the resulting strain (subscript t for tension). Both o... 

Another commonly used elastic constant is the Poisson s ratio V, which relates the lateral contraction to longitudinal extension in uniaxial tension. Typical Poisson s ratios are also given in Table 1. Other less commonly used elastic moduH include the shear modulus G, which describes the amount of strain induced by a shear stress, and the bulk modulus K, which is a proportionaHty constant between hydrostatic pressure and the negative of the volume... 

For duetile materials in uniaxial tension, the reliability is the probabilistie requirement to avoid yield ... 

Engineering constants (sometimes known as technical constants) are generalized Young s moduli, Poisson s ratios, and shear moduli as well as some other behavioral constants that will be discussed in Section 2.6. These constants are measured in simple tests such as uniaxial tension or pure shear tests. Thus, these constants with their obvious physical interpretation have more direct meaning than the components... 

First, consider uniaxial tension loading in the 1-direction on a flat piece of unidirectionally reinforced lamina where only the gage section is shown in Figure 2-20. The specimen thickness is not just one lamina, but several laminae all of which are at the same orientation (a single lamina would be too fragile to handle). The strains and E2 are measured so, by definition,... 

As the third major measurement to try to determine the remaining properties G 2 S, consider uniaxial tension loading at 45° to the 1-direction on a flat piece of iamina, i.e., a 45° off-axis test, as shown in Figure 2-26. By measurement of alone, obviously... 

In a uniaxial tension test to determine the elastic modulus of the composite material, E, the stress and strain states will be assumed to be macroscopically uniform in consonance with the basic presumption that the composite material is macroscopically Isotropic and homogene-ous. However, on a microscopic scSeTBotFTfhe sfre and strain states will be nonuniform. In the uniaxial tension test,... 

The stress-intensity factors are quite different from stress concentration factors. For the same circular hole, the stress concentration factor is 3 under uniaxial tension, 2 under biaxiai tension, and 4 under pure shear. Thus, the stress concentration factor, which is a single scalar parameter, cannot characterize the stress state, a second-order tensor. However, the stress-intensity factor exists in all stress components, so is a useful concept in stress-type fracture processes. For example. 

Although nearly all creep and stress-relaxation tests are made in uniaxial tension, it is possible to make biaxial tests in which two stresses are applied at 90° to one another, as discussed in Section VI. In a uniaxial test there is a contraction in the transverse direction, but in a biaxial test the transverse contraction is reduced or even prevented. As a result, biaxial creep is less than uniaxial creep--in cquihiaxial loading it is roughly hall as much for equivalent loading conditions. In the linear region the biaxial strain 2 in each direction is (255.256)... 

Fond et al. [84] developed a numerical procedure to simulate a random distribution of voids in a definite volume. These simulations are limited with respect to a minimum distance between the pores equal to their radius. The detailed mathematical procedure to realize this simulation and to calculate the stress distribution by superposition of mechanical fields is described in [173] for rubber toughened systems and in [84] for macroporous epoxies. A typical result for the simulation of a three-dimensional void distribution is shown in Fig. 40, where a cube is subjected to uniaxial tension. The presence of voids induces stress concentrations which interact and it becomes possible to calculate the appearance of plasticity based on a von Mises stress criterion. 

The fiber fragmentation test is at present one of the most popular methods to evaluate the interface properties of fiber-matrix composites. Although the loading geometry employed in the test method closely resembles composite components that have been subjected to uniaxial tension, the mechanics required to determine the interface properties are the least understood. 

In the [ 45]j tensile test (ASTM D 3518,1991) shown in Fig 3.22, a uniaxial tension is applied to a ( 45°) laminate symmetric about the mid-plane to measure the strains in the longitudinal and transverse directions, and Ey. This can be accomplished by instrumenting the specimen with longitudinal and transverse element strain gauges. Therefore, the shear stress-strain relationships can be calculated from the tabulated values of and Ey, corresponding to particular values of longitudinal load, (or stress relations derived from laminated plate theory (Petit, 1969 Rosen, 1972) ... 

The [10°] off axis tension specimen shown in Fig 3.23 is another simple specimen similar in geometry to that of the [ 45 ]s tensile test. This test uses a unidirectional laminate with fibers oriented at 10° to the loading direction and the biaxial stress state (i.e. longitudinal, transverse and in-plane shear stresses on the 10° plane) occurs when it is subjected to a uniaxial tension. When this specimen fails under tension, the in-plane shear stress, which is almost uniform through the thickness, is near its critical value and gives the shear strength of the unidirectional fiber composites based on a procedure (Chamis and Sinclair, 1977) similar to the [ 45°]s tensile test. 

Cox (1952) first considered a shear-lag model where an elastic fiber is embedded in an elastic matrix which is subjected to uniaxial tension. Perfect bonding is assumed... 

Effect of laminate layup and stacking sequence on stress concentration and strength of boron fiber-epoxy matrix composites containing circular holes under uniaxial tension . 

Quotient of the length (/) of a sample under uniaxial tension or compression and its original length (/o)... 

Again, the stress in each component is approximated as being pure uniaxial tension that is, there is no stress in the 1-3 plane, and ct/i = ct/3 = = (7 3 = 0. Once... 

In bulk material, the resistivity is independent of crystal orientation because silicon is cubic. However, if the carriers are constrained to travel in a very thin sheet, eg, in an inversion layer, the mobility, and thus the resistivity, become anisotropic (18). Mobility is also sensitive to both hydrostatic pressure and uniaxial tension and compression, which gives rise to a substantial piezoresistive effect. Because of crystal symmetry, however, there is no piezoelectric effect. The resistivity gradually decreases as hydrostatic pressure is increased, and then abrupdy drops several orders of magnitude at ca 11 GPa (160,000 psi), where a phase transformation occurs and silicon becomes a metal (35). The longitudinal piezoresistive coefficient varies with the direction of stress, the impurity concentration, and the temperature. At about 25°C, given stress in a (100) direction and resistivities of a few hundredths of an O-cm, the coefficient values are 500—600 m2/N (50—60 cm2/dyn). 

Uniaxial tension testing with superposed hydrostatic pressure has been described by Vernon (111) and Surland et al. (103). Such tests provide response and failure measurements in the triaxial compression or tension-compression-compression octants. 

Forced sinusoidal shear strain imposed by vibrating outer ring of annular plate of propellant on an electrodynamic shaker Forced sinusoidal uniaxial tension and compression imposed by vibrating weighted rectangular column of propellant on electrodynamic shaker... 

Forced sinusoidal uniaxial tension and shear imposed by mechanical drive to tensile bar or double-lap shear specimen... 

Sharma (90) has examined the fracture behavior of aluminum-filled elastomers using the biaxial hollow cylinder test mentioned earlier (Figure 26). Biaxial tension and tension-compression tests showed considerable stress-induced anisotropy, and comparison of fracture data with various failure theories showed no generally applicable criterion at the strain rates and stress ratios studied. Sharma and Lim (91) conducted fracture studies of an unfilled binder material for five uniaxial and biaxial stress fields at four values of stress rate. Fracture behavior was characterized by a failure envelope obtained by plotting the octahedral shear stress against octahedral shear strain at fracture. This material exhibited neo-Hookean behavior in uniaxial tension, but it is highly unlikely that such behavior would carry over into filled systems. 

Segmental orientation in model networks of PDMS in uniaxial tension is measured by infrared dlchroism, Measurements are made for four tetrafunctlonal end-linked networks. Results of experiments are compared with predictions of calculations based in (i) the widely used Kuhn expression and (ii) the RIS formalism. The Kuhn expression is found to considerably overestimate the segmental orientation. The RIS approach leads to values of segmental orientation that fall between predictions of the affine and phantom network models. This indicates that the nematic-like Intermolecular contributions to orientation are not significant. 

Hirotsu applied a constant uniaxial tension J to a cylindrical NIPA gel immersed in water and observed considerable dependence of the first-order... 

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