Poisson’s ratio determination

All the above observations seem to justify Porter s approach (Eq. 11.11)), according to which the Poisson s ratio should depend only on the cumulative loss tangent. It was found that the unrelaxed Poisson s ratio determined from ultrasound (5 MHz) propagation rate, for 12 of amine-crosslinked epoxy stoichiometric networks, displays only small variations (Av < 0.01), in spite of the relatively large variations of the cohesive energy density (0.59 < CED <0.66 GPa) and the crosslink density (2.0 5.9 mol kg 1)-... 

In addition to chemical analysis a number of physical and mechanical properties are employed to determine cemented carbide quaUty. Standard test methods employed by the iadustry for abrasive wear resistance, apparent grain size, apparent porosity, coercive force, compressive strength, density, fracture toughness, hardness, linear thermal expansion, magnetic permeabiUty, microstmcture, Poisson s ratio, transverse mpture strength, and Young s modulus are set forth by ASTM/ANSI and the ISO. 

This is an important relationship. It states that the modulus of a unidirectional fibre composite is proportional to the volume fractions of the materials in the composite. This is known as the Rule of Mixtures. It may also be used to determine the density of a composite as well as other properties such as the Poisson s Ratio, strength, thermal conductivity and electrical conductivity in the fibre direction. 

Fig. 2.15. Release wavespeeds at very high pressure can be determined by experiments in which the sample thickness is varied for fixed thickness of a high velocity impactor. Data on aluminum alloy 2024 are shown. As indicated in the figure, shear velocity (C ) and Poisson s ratio (cr) at pressure can be calculated from the elastic and bulk speeds if thermodynamic equilibrium is assumed (after McQueen et al. [84M02]).

Consider a dispersion-stiffened composite material. Determine the Influence on the upper bound for the apparent Young s modulus of different Poisson s ratios in the matrix and In the dispersed material. Consider the following three combinations of material properties of the constituent materials ... 

In general. Equation 2-174 can be used to approximate fracture pressure gradients. To obtain an adequate approximation for fracture pressure gradients, the pore pressure gradient must be determined from well log data. ALso, the overburden stress gradient and Poisson s ratio versus depth must be known for the region. 

The designer must be aware that as the degree of anisotropy increases, the number of constants or moduli required to describe the material increases with isotropic construction one could use the usual independent constants to describe the mechanical response of materials, namely, Young s modulus and Poisson s ratio (Chapter 2). With no prior experience or available data for a particular product design, uncertainty of material properties along with questionable applicability of the simple analysis techniques generally used require end use testing of molded products before final approval of its performance is determined. 

Equation (20) yields the elastic modulus, Ec, of the composite in terms of the moduli and Poisson s ratios of the phases. If the Ec-modulus and vc-value are accurately measured and the Ef- and Em-moduli and the Poisson rations vf and vm are known, the average modulus of the mesophase, Ef, may be determined. Poisson s ratio of the mesophase may be found from the simple relation ... 

Another effect o(f orientation shows up as changes in Poisson s ratio, which can be determined as a function of time by combining the results of tension and torsion creep tests. Poisson s ratio of rigid unoriented polymers remains nearly constant or slowly increases with time. Orientation can drastically change Poisson s ratio (254). Such anisotropic materials actually have more than one Poisson s ratio. The Poisson s ratio as determined when a load is applied parallel to the orientation direction is expected to... 

Values for V, and f/, for a number of metal oxide glass components are listed in Table 5.6. In a similar manner, the compressive modulus, K, and Poisson s ratio, v, can be determined using these parameters ... 

Compressive measurements provide a means to determine specimen stiffness, Young s modulus of elasticity, strength at failure, stress at yield, and strain at yield. These measurements can be performed on samples such as soy milk gels (Kampf and Nussi-novitch, 1997) and apples (Lurie and Nussi-novitch, 1996). In the case of convex bodies, where Poisson s ratio is known, the Hertz model should be applied to the data in order to determine Young s modulus of elasticity (Mohsenin, 1970). It should also be noted that for biological materials, Young s modulus or the apparent elastic modulus is dependent on the rate at which a specimen is deformed. 

For Agar gel, experimental study of these coefficients were performed [7], The coefficient E was determined by compressive tests. Ultrasonic measurements of the Poisson s ratio v showed that it is almost equal to 0.5. Compressibility K (fig. 3) is deduced from K = Ej(3(1 — 2//)). 

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 relationship between the structure of the disordered heterogeneous material (e.g., composite and porous media) and the effective physical properties (e.g., elastic moduli, thermal expansion coefficient, and failure characteristics) can also be addressed by the concept of the reconstructed porous/multiphase media (Torquato, 2000). For example, it is of great practical interest to understand how spatial variability in the microstructure of composites affects the failure characteristics of heterogeneous materials. The determination of the deformation under the stress of the porous material is important in porous packing of beds, mechanical properties of membranes (where the pressure applied in membrane separations is often large), mechanical properties of foams and gels, etc. Let us restrict our discussion to equilibrium mechanical properties in static deformations, e.g., effective Young s modulus and Poisson s ratio. The calculation of the impact resistance and other dynamic mechanical properties can be addressed by discrete element models (Thornton et al., 1999, 2004). 

Determine the magnitude of the load required to produce a -1.29 x 10 mm change in a 10 mm diameter isotropic polycrystalline tin rod, assuming the deformation is entirely elastic. The Young s modulus fortin is 50GPa and Poisson s ratio, V, is 0.36. 

A cylindrical specimen of brass (an alloy of copper and zinc) with a diameter of 20 mm and length of 200 mm is pulled in tension elastically with a force of 50,000 N. If the Young s modulus is 97 GPa and Poisson s ratio is 0.34, determine a) the amount of longitudinal extension (the elongation in the direction of the uniaxial stress) and b) the transverse contraction in diameter. 

Determining mechanical characteristics of fibrous materials is far from simple, mainly because of their small diameter. In particular, in the case of anisotropic fibers such as carbon or aramid, we need to determine five elastic constants, assuming isotropy in the cross-sectional plane. Figure 9.3 shows three of the five elastic constants the longitudinal Young s modulus of fiber, E or E, the transverse Young s modulus E22 or Ej, and the principal shear modulus, or Not shown are the two Poisson ratios the longitudinal Poisson s ratio of... 

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