Longitudinal strain

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... 

The importance of combining longitudinal strain analyses is that it often provides the designer with a minimum wall thickness on which to base the ultimate choice of pipe configuration. For instance, assume that the combined longitudinal analysis indicates a... 

A second equation relating the radial and tangential stresses can be written if the longitudinal strain eL and stress oL are taken to be constant across the wall that is, that there is no distortion of plane sections, which will be true for sections away from the ends. The longitudinal strain is given by ... 

In this equation e is the longitudinal strain and er is the strain in the width (transverse) direction or the direction perpendicular to the applied force It can be shown that when Poisson s ratio is 0.50, the volume of the specimen remains constant while being stretched. This condition of constant volume holds for liquids and ideal rubbers. In general, there is an increase in volume, which is given by... 

It is not necessary to know the bulk modulus to convert E to G. If the transverse strain, , of a specimen is determined during a uniaxial tensile test in addition to the extensional or longitudinal strain e their ratio, called F oisson s ratio, v can be used ... 

Poisson s ratios. One Poisson s ratio, vin gives the transverse strain r caused by an imposed strain e,. in the longitudinal direction. The second Poisson s ratio, vTi,. gives the longitudinal strain caused by a strain in the transverse direction. Thus... 

Ctjki is a fourth order tensor that linearly relates a and e. It is sometimes called the elastic rigidity tensor and contains 81 elements that completely describe the elastic characteristics of the medium. Because of the symmetry of a and e, only 36 elements of Cyu are independent in general cases. Moreover only 2 independent rigidity constants are present in Cyti for linear homogeneous isotropic purely elastic medium Lame coefficient A and /r have a stress dimension, A is related to longitudinal strain and n to shear strain. For the purpose of clarity, a condensed notation is often used... 

A dimensionless quantity, symbolized by either s or e, for the change in length (/) due to some force or interaction per unit length thus, s = A///. Linear strain is also known as longitudinal strain. Relative elongation is also measured by A///. 

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... 

The value of irreversible longitudinal strain in experimental measurements is taken 1112) as ... 

In this case the velocity of irreversible longitudinal strain can be determined in the following way ... 

Beside the molecular-weight distribution, the behavior of melts under longitudinal strain is affected by the ramification of macromolecules which can be seen from comparison of dependencies 2 and 4. The difference in the behavior of samples stems, apparently, from the fact that sample 2 contains 0.1 CH3 groups per 100 atoms of carbon and sample 4 contains 0.24 CH3 groups. 

As discussed above, series of experiments and even a limited number of tests in longitudinal strain under constant-force conditions are representative and very informative in terms of behavior of thermoplastics in processing. However, unfortu-... 

Elasticity of solids determines their strain response to stress. Small elastic changes produce proportional, recoverable strains. The coefficient of proportionality is the modulus of elasticity, which varies with the mode of deformation. In axial tension, E is Young s modulus for changes in shape, G is the shear modulus for changes in volume, B is the bulk modulus. For isotropic solids, the three moduli are interrelated by Poisson s ratio, the ratio of traverse to longitudinal strain under axial load. 

The exact laws, based on continuum analysis of the fibers and the matrix, would be very complicated. The analysis would involve equilibrium of stresses around, and in, the fibers and compatibility of matrix deformation with the fiber strains. Furthermore, end and edge effects near the free surfaces of the composite material would introduce complications. However, a simplified model can be developed for the interior of the composite material based on the notion that the fibers and the matrix interact only by having to experience the same longitudinal strain. Otherwise, the phases behave as two uniaxially stressed materials. McLean5 introduced such a model for materials with elastic fibers and he notes that McDanels et al.6 developed the model for the case where both the fibrous phase and the matrix phase are creeping. In both cases, the longitudinal parameters are the same, namely... 

The same techniques were used in the present work to study the effects of orientation and rubber content upon the creep behavior of rubber-toughened SAN polymers at room temperature. As in previous work, the tests were conducted at low strain rates and were terminated at longitudinal strains between 5 and 6%. 

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 ... 

Earlier work (4,6) demonstrated that a high gradient in the volume strain-longitudinal strain curve is associated with a large drop in the modulus of the material. This is to be expected, as the crazes have much lower moduli than the material from which they were formed (7). As a result of the creep tests described above, the 100 sec tensile modulus of Luran S 757R at a strain of 0.5% fell from 1.99 to 1.30 GN/m2, and the modulus of Luran S 776S at a similar strain fell from 1.65 to 0.98 GN/m2. 

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