Strain and elasticity

Most of the experimental results on CJTE can be explained on the basis of molecular field theory. This is because the interaction between the electron strain and elastic strain is fairly long-range. Employing simple molecular field theory, expressions have been derived for the order parameter, transverse susceptibility, vibronic states, specific heat, and elastic constants. A detailed discussion of the theory and its applications may be found in the excellent review by Gehring Gehring (1975). In Fig. 4.23 various possible situations of different degrees of complexity that can arise in JT systems are presented. 

Other Transducers. Ultrasound also has been used for the measurement of force, vibration, acceleration, interface location, position changes, differentiation between the composition of differing materials, grain size in metals, and evaluation of stress and strain and elasticity in materials. Sonic devices can used to detect gas leaks, and to count discrete parts by means of an interrupted sound beam. Frequently, an ultrasonic device can be applied where photoelectric derices are used. Particularly tn situations where light-sensitive materials are being processed (hence presence of light must be avoided), ultrasonic devices may be the detectors of choice. 

The basis for the above-mentioned model47) was provided by Maxwell s nonlinear model obtained in general form in Ref. 48). Flere the total strain was divided into irreversible strain and elastic strain X, Stress a and velocity of irreversible strain ep were determined from the elastic strain. In Ref. 48) a number of functions a (a.) and ep(X) were defined more specifically. Beside that, Maxwell s nonlinear models were connected in parallel. Note that in case of one Maxwell s element X = a23), but in case of several elements connected in parallel this is not true and a is determined from the solution of the respective problem. In case of the uniaxial extension the model of Ref.47) takes the following form ... 

While the elastic properties of JT crystals could be an example of possible applications of the CITE theory for microscopic description of the materials properties, these properties are analyzed in advance and separated from others. It is related to the fact that strain and elastic susceptibility are the principal characteristics of structural phase transitions. 

Strain and Elasticity at Strnctnral Phase Transitions in Minerals... 

Figure 3. Spontaneous strains and elastic properties at the 422 < i> 222 transition in Te02. (a) Spontaneous strain data extracted from the lattice-parameter data of Worlton and Beyerlein (1975). The linear pressure dependence of (e - (filled circles) is consistent with second-order character for the transition. Other data are for non-symmetiy-breaking strains (e + 62) (open circles), 63 (crosses), (b) Variation of the symmetry-adapted elastic constant (Cn - Cu) at room temperature (after Peercy et al. 1975). The ratio of slopes above and below Po is 3 1 and deviates from 2 1 due to the contribution of the non-symmetry-breaking strains. (After Carpenter and Salje 1998).

Equations of the form of Equation (4) form the basis of the analysis of strain and elasticity reviewed in this chapter. The issues to be addressed are (a) the geometry of strain, leading to standard equations for strain components in terms of lattice parameters, (b) the relationship between strain and the driving order parameter, and (c) the elastic anomalies which can be predicted on the basis of the resulting free energy functions. The overall approach is presented as a series of examples. For more details of Landau theory and an introduction to the wider literature, readers are referred to reviews by Bruce and Cowley (1981), Wadhawan (1982), Toledano et al. (1983), Bulou et al. (1992), Salje (1992a,b 1993), Redfern (1995), Carpenter et al. (1998a), Carpenter and Salje (1998). 

Strain and Elasticity at Structural Phase Transitions system are trivial to derive from Equations (6)-(l 1). 

Tables 2-4 show the effect of the dry/cold. moderate, and humid/hot environments on the tensile properties of the adhesive FM 300K tested at the 10 "/s. lO /s. and lO Vs strain rates, respectively. The values of the yield strength, the yield strain, and the offset obtained with the SED method and the corresponding values from the 0.2 % offset method are shown. The tensile strength, rupture strain, and elastic modulus are provided for information. On average, the time to rupture of the specimens tested at the lO /s, lO /s, and lO Vs strain rates were 4 seconds. 6 minutes, and 15 hours, respectively. The data are listed in ascending order of yield strength. The tensile properties listed in parentheses at the bottom of each cell are averages for replicate specimens. For ease of comparison, these averages are summarized in Table 5.

PVB composite has higher compressive strain and elastic modulus compared with lightweight concrete. And the failure model and stress-strain curve shows the PVB composite is more ductile. 

CNT-polymer composites at very low nanotube loadings exhibit substantial electrostrictive strains when exposed to an electric field that is dramatically lower than that required by neat polymers. Zhang et al. have shown that the crystallinity. Young s modulus, dielectric constant, electrostrictive strain, and elastic energy density of electrostrictive poly(vinylidene fluoride-trifluor-oethylene-chlorofluoroethylene) P(VDF-TrFE-CFE)] can be simultaneously improved by inclusion of only 0.5 wt% of MWNTs. At an applied electric field of 54 MV m the 0.5 wt% nanocomposite generates a strain of 2%, which nearly doubles that of pure P(VDF-TrFE-CFE) polymer. 

Symmetrized strains and elastic constants for crystals with zircon and scheelite structure... 

Expressing elastic constants using the Generalized Hooke s law,... 

In this section, the effect on substrate curvature of the variation of mismatch strain and material properties through the thickness of layered films is analyzed. The derivation of the Stoney formula (2.7) in Section 2.1 refers only to the resultant membrane force in the film any through-the-thickness variation of mismatch strain in the film is considered only peripherally. Film thickness was taken into account explicitly in Section 2.2, but it was assumed there that mismatch strain and elastic properties of the material were uniform throughout the film. However, there are situations of practical significance for which this is not the case. Two of the most common cases are compositionally graded films in which the mismatch strain and the elastic properties vary continuously through the thickness of the film, and multi-layered films for which the mismatch strain and the elastic properties are discontinuous, but piecewise constant, from layer to layer throughout the thickness of the film. In both cases, the mismatch strain and the material properties are assumed to be uniform in the plane of the interface. With reference to the cylindrical r, 6,. z—coordinate system introduced in Section 2.1, the mismatch strain and film properties are now assumed to vary with z for fixed r and 6, but both are invariant with respect to r and 9, for fixed z. 

Strain and elasticity A plastic where its elastieity permits recovery of its shape and size after being subjected to deformation exhibits a Hookean or ideal elasticity. 

Ghaffari M, Kinsman W, Zhou Y, Murali S, Burlingame Q, Lin M, Ruoff R, Zhang Q (2013) Aligned nano-porous microwave exfoliated graphite oxide ionic actuators with high strain and elastic energy density. Adv Mater 25(43) 6277-6283... 

In recent years it was decided to define CTE as a function of primary creep strain [37]. However, primary creep strain and elastic strain are similar in magnitude, i.e., approximately one elastic deflection. The experiments on virgin Gilsocarbon also... 

The symbol a denotes viscous coefficient E, elastic modulus , the Poisson ratio. If flow residual stress is neglected, the polymer part is assumed to be in undeformed stress-free state at the solidifying temperature, j and j represent viscous strain and elastic strain of the polymer respectively., is the shrinkage strains which include thermal strain and volume strain originated from crystallization. is horizontal strain under the action of packing pressure. 

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