Lateral contraction ratio

If the spring is subjected to a 50% overload for 1 day, estimate the percentage increase in the extension over the normal 1 day extension. The shear stress in the material is given by 16 WR/d. Use the creep curves supplied and assume a value of 0.4 for the lateral contraction ratio. 

Note 5 Poisson s ratio is also sometimes called the lateral contraction ratio and is sometimes used in cases of non-linear deformation. The present definition will not apply in such cases. 

Creep lateral contraction ratio The ratio of lateral strain to longitudinal strain measured simultaneously in a creep experiment (also known as Poisson s ratio). 

Figure 8.6 Photograph of the extensometry system of Clayton, Darlington and Hall (1) upper arm of tensile extensometer (2) specimen (3) brass contact pieces on lateral extensometer arms (4) lower arm of tensile extensometer and (5) glass plates with shoulders resting on ends of lateral extensometer arms. (Redrawn from Clayton, D., Darlington, M.W. and Hall, M.M. (1973) Tensile creep modulus, creep lateral contraction ratio, and torsional creep measurements on small nonrigid specimens. J. Phys. E., 6, 218. Copyright (1973).)...

Clayton, D., Darlington, M.W. and Hall, M.M. (1973) Tensile creep modulus, creep lateral contraction ratio, and torsional creep measurements on small nonrigid specimens. J. Phys. E., 6,218. 

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... 

The modulus term in this equation can be obtained in the same way as in the previous example. However, the difference in this case is the term V. For elastic materials this is called Poissons Ratio and is the ratio of the transverse strain to the axial strain (See Appendix C). For any particular metal this is a constant, generally in the range 0.28 to 0.35. For plastics V is not a constant. It is dependent on time, temperature, stress, etc and so it is often given the alternative names of Creep Contraction Ratio or Lateral Strain Ratio. There is very little published information on the creep contraction ratio for plastics but generally it varies from about 0.33 for hard plastics (such as acrylic) to almost 0.5 for elastomers. Some typical values are given in Table 2.1 but do remember that these may change in specific loading situations. 

Stress is equal to the force per unit area, and strain or elongation is the extension per unit length. For an isotopic solid, i.e., one having the same properties regardless of direction, the strain is defined by Poisson s ratio, V = y /j which is the change in thickness (lateral contraction) to the change in length. 

Figure 16 illustrates several test specimens which have been used (46) in the multiaxial characterization of solid propellants. The arrows indicate the direction of load application. The strip tension or strip biaxial test has been used extensively in failure studies. It can be seen that the propellant is constrained by the long bonded edge so that lateral contraction is prevented and tension is produced in two axes simultaneously. The sample is free to contract normal to these axes. The ratio of the two principal tensile stresses may be varied from 0 to 0.5 by varying the bonded length of incompressible materials. 

When a material is stretched there is also contraction in the direction perpendicular to the direction of stretching. The ratio of the lateral contraction to the longitudinal extension is Poisson s ratio. For incompressible materials, Poisson s ratio is 0.5 and as rubbers are very nearly incompressible they have values close to this. 

Any Poisson ratio V Change in width per unit width lateral contraction (13.7)... 

The concept of stress-induced dilatation affecting the relaxation time or rate has been suggested by others (5, 6, 7, 8). The density of most solids decreases under uniaxial stress because the lateral contraction of the solid body does not quite compensate for the longitudinal extension in the direction of the stress, and the body expands. The Poisson ratio, the ratio of such contraction to the extension, is about 0.35 for many polymeric solids it would be 0.5 if no change in density occurred, as in an ideal rubber. The volume increase, AV, accompanying the tensile strain of c, can be described by the following equation ... 

In Eq. 10.18, v is the Poisson s ratio, named after French mathematician Simeon-Denis Poisson (1781-1840). Poisson s ratio is the dimensionless ratio of relative diameter change (lateral contraction per unit breadth) to relative length change (longitudinal... 

An experiment such as that in Fig. 11 -12a can produce changes in the volume as well as the shape of the test specimen. The elastic moduli listed in this figure are related by Poisson s ratio p, which is a measure of the lateral contraction accompanying a longitudinal extension ... 

The Poisson ratio, like the bulk, tensile, and shear creep compliance, is an increasing function of time because the lateral contraction cannot develop instantaneously in uniaxial tension but takes an infinite time to reach its ultimate value. In response to a sinusoidal uniaxial stretch, the complete Poison ratio is obtained ... 

Crazing is an important source of toughness in mbber-modified thermoplastics. A craze can be described as a layer of polymer a nanometer to a few micrometers thick, which has undergone plastic deformation approximately in the direction normal to the craze plane as a response to tension applied in this direction [Kambour, 1986]. Crazing occurs without lateral contraction. As a result, the polymer volume fraction in the craze is proportional to 1/, where is the draw ratio in the craze. The reduction in density occurs on such a small scale that the refractive index is markedly reduced, which accounts for the reflectivity of the craze [Kramer, 1983]. 

Answer This fluid flow description is consistent with elongational flow in the x direction, and simultaneous lateral contraction in the y and z directions, transverse to the primary flow. The process occurs at constant volume and constant density such that Poisson s ratio is... 

Poison s ratio, is, describes the lateral contractions — c and —Sy, due to a tensile stress that also... 

If a tensile load is applied to a material, the material will elongate on the axis of the load (perpendicular to the tensile stress plane), as illustrated in Figure 2(a). Conversely, if the load is compressive, the axial dimension will decrease, as illustrated in Figure 2(b). If volume is constant, a corresponding lateral contraction or expansion must occur. This lateral change will bear a fixed relationship to the axial strain. The relationship, or ratio, of lateral to axial strain is called Poisson s ratio after the name of its discoverer. It is usually symbolized by v. 

The moduli are related to each other by the Poisson number, or Poisson ratio, which is the ratio of the relative lateral contraction to the axial extension or axial strain ... 

With orientation, the thickness is reduced and the surface enlarged. If film is longitudinally stretched in the elastic state, the thickness and the width are reduced in the same ratio. If lateral contraction is prevented, stretching reduces the thickness only. 

The bulk modulus 1/p and Young s modulus E are related through the equation at the bottom of Fig. 4.144. The symbol a represents Poisson s ratio, the linear, lateral contraction divided by the linear extension in a tensile experiment. One can compute that a value of 0.5 for Poisson s ratio leads to a constant volume on extension, a situation often achieved in rubbery materials. Most crystals and glasses have a Poisson s ratio between 0.2 and 0.35. Note that a value of o close to 0.5 makes Young s modulus much smaller than the bulk modulus, a case realized by rubbery macromolecules which can change their shape on extension at constant volume (see Sect. 4.6.5). The bulk modulus of small-molecule liquids and solids decreases normally with increasing temperature, while increasing pressure causes an increase. 

The Poisson ratio // is a measure of the relative lateral contraction induced by a tensile stress in an isotropic material ... 

Protrusion of CNTs lateral contraction of rubber on 106 stretching, due to mismatch in Poisson s ratio between rubber and network of rigid fibres. 

When, for example, a load is acting on an elastic body in x direction, it elongates not only in the direction of the acting load, but contracts laterally, as well. Thus, contraction must occur in the transverse y and z directions. Empirically, it was observed that transverse strains are constant fractions of longitudinal extension. The ratio of the lateral contractive strain to the axial strain is called Poisson s ratio , denoted by v and expressed as ... 

This ratio denotes a reduction in cross-section elongation. In brittle materials, there is a small change in the cross-section with elongation, so v is low. Thus, when a sample of material is stretched on one axis, it tends to get thinner also on the other two axes. If, during the uniaxial tension, no lateral contraction occurs, then v = 0. 

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