Strain lateral

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. 

When a bar is elongated axially, as in Figure 2-25, it will contract laterally. The negative ratio of the lateral strain to the axial strain is called Poisson s ratio v. For isotropic materials, materials that have the same elastic properties in all directions, Poisson s ratio has a value of about 0.3. 

Poison s ratio It is the proportion of lateral strain to longitudinal strain under conditions of uniform longitudinal stress within the proportional or elastic limit. When the material s deformation is within the elastic range it results in a lateral to longitudinal strain that will always be constant. In mathematical terms, Poisson s ratio is the diameter of the test specimen before and after elongation divided by the length of the specimen before and after elongation. Poisson s ratio will have more than one value if the material is not isotropic... 

Kibler LA, El-Aziz AM, Hoyer R, Kolb DM. 2005. Tuning reaction rates by lateral strain in a palladium monolayer. Angew Chem Int. Ed 44 2080-2084. 

E. Konofagou and J. Ophir, A new elastographic method for estimation and imaging of lateral displacements, lateral strains, corrected axial strains and Poisson s ratios in tissues, Ultrasound Med. Biol., 1998, 24, 1183-1199. 

In a sample under small uniaxial deformation, the negative quotient of the lateral strain (flat) and the longitudinal strain (fiong) in the direction of the uniaxial force... 

Note 1 Lateral strain f lat is the strain normal to the uniaxial deformation. 

Figure 5.5 Schematic illustration of tensile strain and corresponding lateral strain. From Z. Jastrzebski, The Nature and Properties of Engineering Materials, 2nd ed. Copyright 1976 by John Wiley Sons, Inc. This material is used by permission of John Wiley Sons, Inc.

One approach which does not utilize a confining fluid has been developed by Saylak (83). This technique involves an optical system which continuously monitors the lateral strain in a uniaxial specimen. The specimen must be circular in cross section, and the volume change computation requires uniform dewetting throughout the sample. This method is not rate and temperature limited since no mechanical attachments or fluids are in contact with the sample. A schematic of the lateral strain device is shown in Figure 13. Surland and Givan (104) also describe an... 

Poisson s ratio-ratio of lateral strain to axial strain in an axial loaded specimen. It is a constant that relates the modulus of rigidity to Young s modulus. 

The first quantitative study of deformation mechanisms in ABS polymers was made by Bucknall and Drinkwater, who used accurate exten-someters to make simultaneous measurements of longitudinal and lateral strains during tensile creep tests (4). Volume strains calculated from these data were used to determine the extent of craze formation, and lateral strains were used to follow shear processes. Thus the tensile deformation was analyzed in terms of the two mechanisms, and the kinetics of each mechanism were studied separately. Bucknall and Drinkwater showed that both crazing and shear processes contribute significantly to the creep of Cycolac T—an ABS emulsion polymer—at room temperature and at relatively low stresses and strain rates. 

Longitudinal strain es was measured in the central 20 mm of the specimen, and lateral strain e1 was measured simultaneously at the center of the gage portion is usually negative in a tensile test. The lateral strain e2 was not measured. In the calculations all specimens, including those cut from a drawn sheet, were assumed to be transversely isotropic— i.e., ei = e2. On the basis of this assumption the volume strain AV/V was calculated from the expression ... 

In discussing shear deformation, it is convenient to distinguish between the initial elastic and viscoelastic response of the polymer to the applied load and the subsequent time-dependent response. However, the distinction is somewhat arbitrary and is not as fundamental as that between elastic volume response and crazing. Viscoelastic shear deformation continues throughout the period under load. The observed time-dependence of lateral strain reflects both generalized viscoelastic relaxation and shear band formation. Since crazing consists simply of displacement in the tensile stress direction, it makes no contribution to lateral strain therefore —e specifically measures deformation by shear processes. 

A similar graph can be plotted for the maximum lateral strain rate d/dt (—ei) (see Figure 5) this gives an apparent activation volume of ca. 3000 A3 for the shear processes in both ASA polymers. 

Volume Strain Vs. Longitudinal Strain. Volume strains (AV/V0) were calculated from longitudinal strain ci and lateral strain c2 by use of the following expression ... 

The simplest way to test the compressibility of a bed of solids (whether it is dry or wet) is by the one-dimensional compression test. A cylindrical plug of the powder is compressed axially in a cylinder which confines the sample and prevents lateral strains -... 

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