Stress-strain dependence

Equilibrium stress-strain dependences were determined in extension using a stress relaxation arrangement described earlier (21). Dry non-extracted samples were measured at 150 C in nitrogen atmosphere and extracted samples swollen in dimethylformamide were measured at 25 C. The equilibrium value of stress 6 e was reached within 2-4 min except of a few dry samples with the lowest tig, for which the equilibrium stress was determined using an extrapolation procedure described earlier (21). 

Polyurethane networks were prepared from polyoxypropylene (POP) triols(Union Carbide Niax Polyols) after removal of water by azeotropic distillation with benzene. For Niax LHT 240, the number-average molecular weight determined by VPO was 710 and the number-average functionality fn, calculated from Mjj and the content of OH groupSj determined by using excess phenyl isocyanate and titration of unreacted phenyl isocyanate with dibutylamine, was 2.78 the content of residual water was 0.02 wt.-%. For the Niax LG-56, 1 =2630, fn=2.78, and the content of H2O was 0.02wt.-%. The triols were reacted with recrystallized 4,4"-diphenylmethane diisocyanate in the presence of 0.002 wt.-% dibutyltin dilaurate under exclusion of moisture at 80 C for 7 days. The molar ratio r0H = [OH]/ [NCO] varied between 1.0 and 1.8. For dry samples, the stress-strain dependences were measured at 60 C in nitrogen atmosphere. The relaxation was sufficiently fast and no extrapolation to infinite time was necessary. 

The above results, which were formulated in the early thirties (TVeloar 1958), explain the main features of the elastic behaviour of polymer networks. Nevertheless, there are notable discrepancies between empirical data and the cited results. Further investigations demonstrated that the values of shear modulus and stress-strain dependence are determined substantially by topological constraints due to the proximity of the chains. The theory was improved by taking into account the discussed issue (Edwards 1967a, 1967b, 1969 Flory 1977 Erman and Flory 1978 Priss 1957, 1980, 1981). More recent developments are summarised in the work of Panyukov and Rabin (1996), where many additional relevant references could be found. 

D 14. — Determination of structural parameters of crosdinked polystyrene from stress — strain dependences and swelling in solvents with variable activity. Collection Czech. Chem. Commun., im Druck,... 

The deformation dependence of the stress in the Edwards tube model is the same as in the classical models [Eqs (7.32) and (7.33)] because each entanglement effectively acts as another crosslink junction in the network. Therefore, the Edwards tube model is unable to explain the stress softening at intermediate deformations, demonstrated in Fig. 7.8. The reason for the classical functional form of the stress strain dependence is that the confining potential is assumed to be independent of deformation. 

The deformation dependence of the confining potential [Eq. (7.62)] results in a non-classical stress strain dependence of the non-affine tube model. The prediction of this model for the stress-elongation relation in tension is qualitatively similar to the Mooney-Rivlin equation [Eg. (7.59)]... 

Magnetic latexes Stress-strain dependence Temporary reinforcement ... 

The experimental data were analyzed on the basis of Eq. 7. It is seen that the slopes of the straight lines (elastic moduli, G) are direction-dependent. The elastic modulus is larger if the compression force and the direction of pearl chain structure are parallel. This finding indicates a strong mechanical anisotropy. It can be concluded that the spatial distribution of the solid particles has a decisive effect on the stress-strain dependence. 

When the stress and the strain are parallel (Fig. 21b), a coil is used to create the magnetic field. In this case, we were able to measure the stress-strain dependence at O-lOOmT. In the experiments, the magnetic field intensity was varied and the elastic modulus was measured as a function of magnetic induction, B. 

To gain a better understanding of the influence of fiber reinforcement on creep of RubCon, we investigated the relationship between values of compressive stresses and creep deformations that are damped out with time. The analysis of the result diagrams (Figures 2.54 and 2.55) shows linear stress-strain dependence of fiber-reinforced and plain RubCon samples at short-term compressive loading. However, creep deformations of these samples do not linearly depend on compressive stress value due to highly elastic deformation of the polybutadiene binder. 

Tensile behavior is of primary importance when considering the properties of a thermoplastic elastomer. The stress-strain dependencies for the 3-arm star PBA-PMMA block copolymers listed in Table 3 are shown in Figure 8. The data were recorded at room temperature and with drawing rate of 5 mm/min. 

Doraiswamy and Metzner noted that use of the LCF approach is permissible at concentrations above that which would correspond to the transition from isotropic to aligned morphology, ( ) > 8/p. The theory provided fair description of the stress-strain dependence for systems containing 10 wt% GF and excellent agreement for those with 40 wt% GF. Also, the approach gave good predictions of the diagonal terms of the second-order orientation tensor. 

Since the early 1980 s, Princen s work was continued by several other authors, e.g., by Reinelt [1993]. The latter author considered theoretical aspects of shearing three-dimensional, highly concentrated foams and emulsions. Initially, the structure is an assembly of interlocked tetrakaid-ecahedra (which have six square surfaces and eight hexagonal ones). An explicit relation for stress tensor up to the elastic limit was derived. When the elastic limit is exceeded, the stress-strain dependence is discontinuous, made of a series of increasing parts of the dependence, displaced with a period of y = 2. ... 

From the point of view of mechanical performance, four types of materials have been identified. They are best discussed in terms of the stress-strain dependence ... 

Ductile with flow. These materials show still greater deformability than the typical ductile materials. Initially, the stress-strain dependence resembles that described for ductile resin, but before the rupture there is a zone of deformation where the stress remains about constant. Within this zone there is flow of material that usually leads to molecular alignment and/or to changes to the crystalline structure (viz. deformation of polyolefins). 

The low-speed stress-strain dependence for PS and HIPS is shown in Figure 12.6. These data well illustrate the change induced by incorporation of elastomeric particles into PS matrix. As shown,... 

The low-speed mechanical properties of polymer blends have been frequently used to discriminate between different formulations or methods of preparation. These tests have been often described in the literature. Examples of the results can be found in the references listed in Table 12.9. Measurements of tensile stress-strain behavior of polymer blends is essential [Borders et al., 1946 Satake, 1970 Holden et al., 1969 Charrier and Ranchouse, 1971]. The mbber-modified polymer absorbs considerably more energy, thus higher extension to break can be achieved. By contrast, an addition of rigid resin to ductile polymer enhances the modulus and the heat deflection temperature. These effects are best determined measuring the stress-strain dependence. 

In order to predict the stress-strain dependence for a polymer filled with a non-adhering filler on the basis of known stress-strain curve for pure polymer we have to find the deformed sample effective load bearing cross-section. 

At the identical values of ( )2 and strain rate, the smaller influence of a non-polar plasticizer (transformer oil) on a physical network of PDUE in comparison with DOS and TBP corresponds to the smaller deviation of stress-strain dependence (Figures 10.63, 10.64, soUd lines). 

From the point of view of mechanical performance, four types of materials have been identified. They are best discussed in terms of the stress-strain dependence 1. Brittle, showing proportionality between stress and strain up to the point of rupture. Here, the modulus, E = ct/e, is constant, independent of strain, . 

Fig. 12. Stress-strain dependence for corona modified composites. Fiber volume fraction 28%. C/PE - no treatment, C/TPE - fiber only treated, TC/PE - PE only treated, TC/TPE - fiber and PE both treated. (After ref 65).

Fig. 6. Typical tensile strength curves of the SWNT LBL films. Stress-strain dependence for (a) ((PEI/PAAXPEFSWNTisis and (b) a similar free-standing multilayer film made solely from polyelectrolsrtes. The dependence of the mechanical properties of the cross-linked LBL composites on humidity was tested in the range of relative humidity of 30— 100%, T = 298°C, and was found to be negligible See Refs. 74,75.

Stress-strain dependences of PO at uniaxial strain in a static-mechanical field, i.e., a(s) and its dependence on a number of factors, i.e., a(s, Fj) where Fj is temperature (7), pressure (p), draw rate (Fsupermolecular structural parameters of PO systems, molecular weight (M), and... 

Fig. 1.8 Stress-strain dependencies for brittle and semibrittle material...

PAE reveals a stress-strain dependence typical of thermoplastic elastomers, as shown in Figure 12 [57]. 

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