Uniaxial deformation ratio

Note 3 For elastomers, which are assumed incompressible, the modulus is often evaluated in uniaxial tensile or compressive deformation using X - as the strain function (where X is the uniaxial deformation ratio). In the limit of zero deformation the shear modulus is evaluated as... 

On the contrary, are(j u/0red clearly shows some dependence on the structure of the crosslinks, changing from around 0.27 to 0.10 as the branching density z increases from 0.01 to 0.5. The different time scale of the experiments can not have effected the results, because is was proved that G is independent of frequency. The deformation ratio X is 1.00005 in case of torsional vibrations and 1.02-1.04 in case of uniaxial extension. Hence it ap-... 

The variation of the elastic free energy between the elastically deformed state and the initial undeformed state is the work accomplished by the force F applied to the sample. For a uniaxial deformation along the x axis yielding a macroscopic deformation ratio Ax ... 

Figure 15.4 2H NMR spectra in a uniaxially compressed PDMS network (M = 10500 g.mol"1, deformation ratio X = 0.5), for different values of the angle Q between the applied uniaxial force and the magnetic field B0...

Figure 15.5 Spectra simulated with a phantom network, in which each chain is elongated, and thus oriented, along its end-to-end vector. A gaussian distribution of the end-to-end vectors is assumed, a relaxed (isotropic) state b uniaxially elongated state (deformation ratio A, = 2.5). Affine displacement of junctions is assumed. No...

In section 3.1.3. we proposed a simple model to calculate the anisotropic form factor of the chains in a uniaxially deformed polymer melt. The only parameters are the deformation ratio X of the entanglement network (which was assumed to be identical to the macroscopic recoverable strain) and the number n, of entanglements per chain. For a chain with dangling end submolecules the mean square dimension in a principal direction of orientation is then given by Eq. 19. As seen in section 3.1.3. for low stress levels n can be estimated from the plateau modulus and the molecular weight of the chain (n 5 por polymer SI). 

For uniaxial deformations, two distinct principal extension ratios Ax and Ap, along and perpendicular to the director respectively, satisfy the relation Xz Xp = 1 because of the incompressibility of rubbers. 

Fig. 2 Scanning confocal microscopy images of blend films of ultra-high-molecular-weight polyethylene and 10 wt% EHO-OPPE (see Fig. 1). (a) As prepared film, (b) Uniaxially deformed sample drawn to a draw ratio of 80. Both images were acquired by detecting the polarization direction oriented parallel to the (eventual) deformation direction. Inset shows images acquired by detecting the orthogonal polarization direction. Adapted with permission from [35]. Copyright 2000 American Chemical Society...

Fig. 10 (a) Molecular stmcture of N,iV -bis-(2 -ethylhexyl)perylene-3,4,9,10-tetracarbox-yldiimide (EE-PTCDI). (b) Fluorescence spectra of a LLDPE/EE-PTCDI blend film containing 0.1 wt% EE-PTCDI before and after uniaxial deformation to different draw ratios (Dr), (c) Picture of the same material in which the center portion has been uniaxially deformed to a draw-ratio of 4. The image was taken under excitation with ultraviolet light, (b, c) adapted with permission from [52]. Copyright 2008 American Chemical Society... 

The molecular orientation of the epoxy networks was investigated using rheooptical FTIR spectroscopy and uniaxial deformation was carried out above and below the Tg. The effects of diol chain length and molar ratio on the mechanical properties and orientation parameter were discussed (79). 

Special specimen preparation as with tensile testing. However, the extraction of intrinsic mechanical parameters from creep indentation data is analytically complex [3, 4]. Confined compression or unconfined compression tests require preparation of cylindrical cored specimens of tissue and underlying bone. With unconfined compression, the free draining tissue edges and low aspect ratio, layered nature of the test specimen may introduce error. Compression of a laterally confined specimen by a porous plunger produces uniaxial deformation and fluid flow. Confined compression creep data has been analyzed to yield an aggregate equilibrium compressive modulus and permeability coefficient [5] and uniaxial creep compliance [6]. 

Both the affine and the phantom network models predict that the reduced stress, [/ ], measured in uniaxial deformation is independent of the deformation ratio. However, it... 

Dubrovic et al. have studied the NR films crosslinked by y-irradiation under both relaxed and uniaxial deformation state by ESR. Figure 25.11 shows the ESR spectra of the spin probe dilfused non-irradiated and irradiated NR matrix at relaxed state. The intensity of the broad component is more pronounced and the narrow component is strongly reduced in case of the 200 kGy irradiation dose applied crosslinked NR films in comparison with the non-crosslinked NR films at unstretched condition. The ratio of intensity for narrow (7n) to broad (4) spectral lines reduces with application of irradiation, which is due to the decrease in sol components by irradiation induced cross-linking process. The amount of broad component is not pronounced at higher irradiation doses, which may be attributed to the heterogeneous distribution of... 

To simplify the discussion of rubber elasticity, only uniaxial deformation will be considered in this chapter. More complicated strain functions will be considered in the chapter on gels. Consider a uniaxial deformation in the x-direction. It is convenient to define a deformation ratio ... 

A stress-strain isotherm for the uniaxial deformation of natural rubber, at ambient temperature, that was cross-linked in the liquid state is shown in Fig. 8.1.(5) Here f is the nominal stress defined as the tensile force,/, in the stretching direction divided by the initial cross-section, and a is the extension ratio. Using the most rudimentary form of molecular rubber elasticity theory f can be expressed as (6-9)... 

Figure 3. Segmental orientation in a uniaxially deformed network. denotes the ratio of the orientation function for a real network to that of a phantom network. Values of the ratio are expressed in terms of the reciprocal extension ratio o( Calculations are made for a network with and J =0.1 for various values of e, where e represents the strength of coupling of a segment to its environment.

The general Landau theory, which was developed by de Gennes to describe critical phenomena in MFCs, has been appUed to elastic networks comprised of PLCs [66]. The Landau formalism also allows one to make contact with the theory used to describe conventional orientation phenomena in nonmesogenic polymer networks. In particular, a mechanical deformation via its associated stress field a influences g (and therefore Tc and 5c) analogously to external magnetic or electric fields. For a small (uniaxial) extension ratio X = e —, where e is the strain, the form of g in Eq. (5.16) is modified by the additional terms as follows ... 

At solid body deformation the heat flow is formed, which is due to deformation. The thermodynamics first law establishes that the internal eneigy change in sample dU is equal to the sum of woik dW, carried out on a sample, and the heat flow dQ into sample (see the Eq. (4.31)). This relation is valid for any deformation, reversible or irreversible. There are two thermo-d5mamically irreversible cases, for which dQ = -dW, uniaxial deformation of Newtonian liquid and ideal elastoplastic deformation. For solid-phase polymers deformation has an essentially different character the ratio QIW is not equal to one and varies within the limits of 0.35 0.75, depending on testing conditions [37]. In other words, for these materials thermodynamically ideal plasticity is not realized. The cause of such effect is thermodynamically nonequilibrium nature or fractality of solid-phase polymers structure. Within the frameworks of fractal analysis it has been shown that this results to polymers yielding process realization not in the entire sample volume, but in its part only. 

The uniaxial compressive modulus Yc describes the passive counter pressure acting against the electrical field and can be derived using the actuator s geometry. The ratio of actuation pressure pei and coxmteracting modulus determines the resulting deformation ratio ... 

It is possible to predict whether an already stretched network swells more or less than an undeformed network at equilibrium. The threshold is obtained by comparing equations (158) and (171), (160) and (172), with p 2 = P2m- The solution is A =P2m - The physical explanation was given by Treloar. If the dry sample is uniaxially deformed, with an extension ratio A lower than the isotropic deformation then when swelling occurs, the clamps act as restrictions to swelling deformation and the net result is a compression. Thus a deformed network swells more than an isotropic network if If A sample is stretched when immersed completely in excess solvent, a new swelling... 

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