Poisson s ratio and

Fig. 7. Relations between elastic constants and ultrasonic wave velocities, (a) Young s modulus (b) shear modulus (c) Poisson s ratio and (d) bulk...

Contact mechanics deals with the deformation of solids in contact. Consider two elastic bodies, shown schematically in Fig. 3, of radii of curvature R[ and Rt, Young s moduli E and E2, and Poisson s ratios and V2. Define... 

Furthermore, u, and , refer to the Poisson s ratio and Young s modulus of each of the contacting materials. Finally, iua represents work of adhesion. It is related to the surface energies y and yi of the two materials and their interfacial energy Fiiby... 

As is true for macroscopic adhesion and mechanical testing experiments, nanoscale measurements do not a priori sense the intrinsic properties of surfaces or adhesive junctions. Instead, the measurements reflect a combination of interfacial chemistry (surface energy, covalent bonding), mechanics (elastic modulus, Poisson s ratio), and contact geometry (probe shape, radius). Furthermore, the probe/sample interaction may not only consist of elastic deformations, but may also include energy dissipation at the surface and/or in the bulk of the sample (or even within the measurement apparatus). Study of rate-dependent adhesion and mechanical properties is possible with both nanoindentation and... 

The convention normally used is that direct stresses and strains have one suffix to indicate the direction of the stress or strain. Shear stresses and strains have two suffices. The first suffix indicates the direction of the normal to the plane on which the stress acts and the second suffix indicates the direction of the stress (or strain). Poisson s Ratio has two suffices. Thus, vi2 is the negative ratio of the strain in the 2-direction to the strain in the 1-direction for a stress applied in the 1-direction (V 2 = — il for an applied a ). v 2 is sometimes referred to as the major Poisson s Ratio and U2i is the minor Poisson s Ratio. In an isotropic material where V21 = i 2i. then the suffices are not needed and normally are not used. 

Example 3.9 For the 2 mm thick unidirectional carbon fibre/PEEK composite described in Example 3.6, calculate the values of the moduli, Poisson s Ratio and strains in the global direction when a stress of = 50 MN/m is applied. You should use... 

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... 

Thus, three reciprocal relations must be satisfied for an orthotropic material. Moreover, only 2, V13, and V23 need be further considered because V21, V31, and V32 can be expressed in terms of the first-mentioned group of Poisson s ratios and the Young s moduli. The latter group of Poisson s ratios should not be forgotten, however, because for some tests they are what is actually measured. 

Hondras, G. (1959). The evaluation of Poisson s ratio and the modulus of materials of a low tensile resistance by the Brazilian (indirect tensile) test with particular reference to concrete. Australian Journal of Applied Science, 10, 245-68. 

Elastomers are solids, even if they are soft. Their atoms have distinct mean positions, which enables one to use the well-established theory of solids to make some statements about their properties in the linear portion of the stress-strain relation. For example, in the theory of solids the Debye or macroscopic theory is made compatible with lattice dynamics by equating the spectral density of states calculated from either theory in the long wavelength limit. The relation between the two macroscopic parameters, Young s modulus and Poisson s ratio, and the microscopic parameters, atomic mass and force constant, is established by this procedure. The only differences between this theory and the one which may be applied to elastomers is that (i) the elastomer does not have crystallographic symmetry, and (ii) dissipation terms must be included in the equations of motion. 

In Table 1 are listed conversions between Lame coefficients, Young s modulus, Poisson s ratio, /, and C,/k/ for an isotropic elastic homogeneous medium. 

Similar arguments can be applied to Poisson s ratio, and the free contraction parallel to axis 2 when a tensile stress is applied parallel to axis 1, V12, is found to obey the rule of mixtures... 

Delaminations can occur during cure as a result of high internal stresses. These stresses develop due to resin shrinkage and thermal volume changes. The level of stresses depend on several material properties, such as the Young s modulus, Poisson s ratio, and thermal expansion coefficients of both resin and fibers. In addition, the level of stresses also depends on several conditions, such as fiber orientation, fiber volume fraction, and part geometry. 

Here we have conducted experiments to develop an understanding of how the commercial size interacts with the matrix in the glass fiber-matrix interphase. Careful characterization of the mechanical response of the fiber-matrix interphase (interfacial shear strength and failure mode) with measurements of the relevant materials properties (tensile modulus, tensile strength, Poisson s ratio, and toughness) of size/matrix compositions typical of expected interphases has been used to develop a materials perspective of the fiber-sizing-matrix interphase which can be used to explain composite mechanical behavior and which can aid in the formulation of new sizing systems. 

For lower symmetries there is more than one Young Modulus and shear modulus and Poisson s ratio, and their interrelation is not so simple. 

Typical materials for the electrolyte are YSZ, samaria doped ceria (SDC), and LaGaC>3. The intrinsic property of the thermal expansion behavior of an electrolyte depends only on the material species. However, the other mechanical properties (Young s modulus, Poisson s ratio, and strength) depend on the morphology through the manufacturing processes. Accordingly, the reported mechanical properties are not unique. The reported thermal expansion coefficient (TEC) and other mechanical properties for the electrolyte materials are listed in Table 10.1. 

Where P is the applied normal load, a is the contact radius, v is the Poisson s ratio and /z is the coefficient of friction. For the above-described experiments,... 

The relationship between the shear modulus, Poisson s ratio and the tensile modulus is given by Equation 13-10 ... 

Note E is Young s modulus, is the thermal expansion coefficient, v is Poisson s ratio, and a is the thermal diffusivity for the ceramic material T, is the surface temperature, is the average temperature of the ceramic body, and is the initial temperature. 

Stress-Strain Relations as Equations of State. Simple theory of elasticity assumes that the material is isotropic and that induced stresses and strains are linearly related to each other as long as they are small. The theory further assumes that the stress and the strain tensors always have the same axes. Poisson s ratio and... 

Thus CMP pads play an important role in dishing of patterned wafers. The model presented here parameterizes CMP pads using Young s modulus, Poisson s ratio, and pad thickness plus an unusual fcstretch term. Control of these parameters could lead to improvements in dishing and erosion outcomes during polishing. 

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