Stretch ratio

Table 7. Effect of Stretch Ratio on Tensile Strength and Elongation of a VDC—VC Copolymer ...

A plausible assumption would be to suppose that the molecular coil starts to deform only if the fluid strain rate (s) is higher than the critical strain rate for the coil-to-stretch transition (ecs). From the strain rate distribution function (Fig. 59), it is possible to calculate the maximum strain (kmax) accumulated by the polymer coil in case of an affine deformation with the fluid element (efl = vsc/vcs v0/vcs). The values obtained at the onset of degradation at v0 35 m - s-1, actually go in a direction opposite to expectation. With the abrupt contraction configuration, kmax decreases from 19 with r0 = 0.0175 cm to 8.7 with r0 = 0.050 cm. Values of kmax are even lower with the conical nozzles (r0 = 0.025 cm), varying from 3.3 with the 14° inlet to a mere 1.6 with the 5° inlet. In any case, the values obtained are lower than the maximum stretch ratio for the 106 PS which is 40. It is then physically impossible for the chains to become fully stretched in this type of flow. 

Of course, the network strands cannot be stretched completely. Stretching ratios of 1.4 for PC [31, 90] and of 1.3 for epoxy polymers [37] have been reported. The chain contour length of the strands is an appropriate measure for a simple estimation of the number of strands that are stretched across the deformation zone. The chain contour length of the strands is assumed to be proportional to... 

Fig. 71 Lifetime curves as a function of the creep load for nylon 66 yarns with different draw ratios (d.r.). The yarn with a stretch ratio of 5.6 is from a different polymer batch [54]. The drawn lines represent the regression lines of the observed data...

Again, as for films, careful consideration of the optimal stretch ratios with or without heat setting of the naphthalate composition is essential to ensure cost effectiveness in a specific container. In the absence of this optimization, performance may be inferior to properly designed containers from the much less costly PET resin. 

A general problem when comparing experimental, simulation and analytical results among each other is that the different parameters have to be matched in a meaningful way. One such way is based on the relative stretching of chains in a brush. In Fig. 8 we plot in (a) simulation results for the stretching ratio... 

Stretching denotes a monoaxial or biaxial mechanical stress of a molded article close to the glass transition temperature. This leads to a controlled orientation of the molecular chains in the direction of stretching and thus to a substantial change in some physical properties. Fibers and foils made of synthetic polymers gain their optimal properties only by this mechanical post-treatment. Stability, stiffness, and dimensional stability of fibers, for example, increase nearly proportionally with the stretch ratio, whereas stretchability decreases. In practice, the stretch ratio is between 1 2 and 1 6, depending on the polymer material and the desired properties. 

As shown in Fig. 1, a cubic body of material under consideration is deformed in the directions of orthogonal axes Xt. If this mode of deformation, the coordinate axes coincide with the principal strain axes. In the principal stresses af corresponding to the principal strains are measured as functions of stretch ratios X, in the directions of Xh W can be calculated from... 

In principle, W can be determined from Eq. (2) if principal stresses at are measured as functions of applied principal stretch ratios X,-. However, since bW/bJ/ rather than W itself are more directly connected with the stress-strain relations [see Eq. (11)], their determination from the measurements of at and X,- is more feasible than that of W. 

Blatz and Ko19) also devised an apparatus which allows strip-biaxial extension testing to be performed (Fig. 6). Here one of the stretch ratios, say X2, is held at unity while the sample sheet is extended in the direction of the stretch ratio Xj. 

Measurements of stresses ot and stretch ratios X,- must be made with extreme care and precision, for small errors in them lead to a gross uncertainty in the calculation of dW/dlf. Naturally, the specimen must be deformed as homogeneously as possible. 

For example, the volume change of an acrylonitrile-butadiene rubber (NBR)40 sample at X = 2 relative to the volume of its undeformed state was about 5 x 10 4, and the values for the other vulcanizates were less than this. We therefore assumed that the use of Eqs. (34) and (35) is warranted for the computation of dW/dlt for our rubber samples, except at very small deformations for which// < 3.02. In most cases, stress relaxation was allowed to proceed at given stretch ratios and 1- and 10-min isochronal stress values were taken for the calculations. 

There is no reason to anticipate that, in general, linear Mooney-Rivlin plots are obtained at least over a certain range of relatively small stretch ratios. Though not illustrated here, our data on the carbon-filled SBR gave the Mooney-Rivlin plots of markedly upward curvature, and again this curvature was found to be due mainly to the dependence of BW/bli on Xj. 

For the analysis of experimental force-deformation data, it is necessary to use a suitable constitutive equation for the material under test. The constitutive equation relates the stresses and strains that are generated in the wall during compression, and therefore relates the tensions and stretch ratios. For example, Liu et al. (1996) used a Mooney-Rivlin constitutive equation to investigate the compression of polyurethane microcapsules and the functions f, /2 and fa are produced in... 

Numerical simulations produce force-deformation data whose shape and magnitude is dependent on the initial parameters defined within the model, including the elastic modulus (E), the uninflated cell radius (rQ) and the initial stretch ratio (ls). Experimental data are fitted to these numerical simulations allowing intrinsic material properties to be derived. 

Fig. 3.12 (a) A pom-pom with three arms at each branch point (q = 3). At short times the polymer chains are confined to the Doi-Edwards tuhe. Sc is the dimensionless length of branch point retraction into the tube X is the stretch ratio where L is the curvilinear length of the crossbar and Lq is the curvilinear equilibrium length, (b) Relaxation process of a long-chain-branched molecule such as LDPE. At a given flow rate e the molecule contains an unrelaxed core of relaxation times t > g 1 connected to an outer fuzz of relaxed material of relaxation t < g 1, behaving as solvent. [Reprinted by permission from N. J. Inkson et al., J. Rheol., 43(4), 873 (1999).]... 

Poly(vinyl chloride) may be calendered in plasticized or unplasticized form and thin film can be produced by calendering followed by stretching (with stretch ratios of up to 8 1). Such products have a very wide range of uses. 

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