Stress-strain behavior networks

Other interesting features of elastomeric networks can be revealed using the plots of the reduced stress, crred = /( — -2) against inverse extension ratio 1. This can be analyzed from the stress-strain behavior described by a phenomenological expression suggested by Mooney [78] and Rivlin and Saunders [79] ... 

We have presented information on the elastic and viscous stress-strain behaviors for a variety of different ECMs in preparation for relating changes in external loading and mechanochemical transduction processes. In order to determine the exact external loading in each tissue that stimulates mechanochemical transduction processes we must take into account the balance between passive loading incorporated into the collagen network in the tissue and active loading applied externally. Inasmuch as the passive load is different for each tissue and is also a function of age (the tension in tissues decreases with age), the net load experienced at the cellular level is difficult to calculate. 

Quested et al. [16] have conducted an extensive experimental program on the stress-strain behavior of the elastomer solithane while subjected to an ambient at high pressure. Some of their experimental results are reproduced in Fig. 13. (Note that the reported stress is the deviatoric, not the total, stress as observed from the fact that the reported stress is zero for X = 1 for the various imposed ambient pressures). For the classic ideal affine network model (all stress caused by ideal Nc Gaussian chains in a volume v with no nonbonded interactions)... 

Thermosets are polymeric materials which when heated form permanent network structures via the formation of intermolecular crosslinks. Whether the final product has a glass transition temperature, Tg, above or below room temperature, and therefore normally exists as an elastomer or a glass, it is, strictly speaking, a thermo-set. In practice, however, thermosets are identified as highly crosslinked polymers that are glassy and brittle at room temperature. These materials typically exhibit high moduli, near linear elastic stress-strain behavior, and poor resistance to fracture. 

It appears that the following peculiarities of the network structure in the elastomer matrix outside the adsorption layer are of importance for a molecular understanding of stress-strain behavior for these materials ... 

Figure 5. Stress-strain behavior of Boltorn H40/HDI networks.

Fig. 9. Eqiulibrium stress-strain behavior of entangled networks in uniaxial extensicm and compression. The solid lines (p = 0.5, 0.75,1.00) were calculated for the primitive segment model (. 62 and II-5). The short-dash line is the Doi-Edwards model (Eq. 40 and 11-11). The long-dash line is the affine Gaussian network model (Eq. 41 and n-12) adjusted to have the same initial modulus...

R.J. Farris, "The Stress-Strain Behavior of Mechanically Degradable Polymers," In POLYMER NETWORKS STRUCTURAL AND MECHANICAL PROPERTIES, ed. A.J. Chompff and S. Newman, pp. 341-394, Plenum, New York, 1971. 

Figure 11.13. Comparison of the predictions of two models for the stress-strain behavior of elastomeric networks. There are 100 Kuhn segments between adjacent network junctions in this particular example. Stress is denoted by a, shear modulus by G, and draw ratio by X.

The stress-strain behavior of thermosets (glassy polymers crosslinked beyond the gel point) is not as well-understood as that of elastomers. Much data were analyzed, in preparing the previous edition of this book, for properties such as the density, coefficient of thermal expansion, and elastic moduli of thermosets [20,21,153-162]. However, most trends which may exist in these data were obscured by the manner in which the effects of crosslinking and of compositional variation were superimposed during network formation in different studies, by... 

The equilibrium small-strain elastic behavior of an "incompressible" rubbery network polymer can be specified by a single number—either the shear modulus or the Young s modulus (which for an incompressible elastomer is equal to 3. This modulus being known, the stress-strain behavior in uniaxial tension, biaxial tension, shear, or compression can be calculated in a simple manner. (If compressibility is taken into account, two moduli are required and the bulk modulus. ) The relation between elastic properties and molecular architecture becomes a simple relation between two numbers the shear modulus and the cross-link density (or the... 

The potential of the mesogenic units for alignment has a marked effect on the stress-strain behavior [85, 111, 112]. Consider a uniaxial stress applied to a liquid-crystalline network synthesized in an isotropic state this means without any macroscopic orientation. 

A large amount of experimental work has been reported on the stress-strain behavior of swollen polymeric networks. Fitting of stress-strain data measured at different degrees of dilution to Eqs. (29.43)-(29.45) enables one to determine, k, and... 

Kim, C. S. Y. Ahmad, J. Bottaro, J. Farzan, M., Improvements in the Stress-Strain Behavior of Urethane Rubbers by Bimodal Network Formation. J. Appl. Polym. Set 1986, 32, 3027-3038. 

K. C. Frisch, Topologically Interpenetrating Polymer Networks, Pure Appl. Chem. 43, 229 (1975). Topological Interpenetration. Stress/strain behavior, tensile strength, Tg. Polyurethane SINs. 

Stress-Strain Behavior In Chapter 9 the theory of rubber elasticity was developed. Young s modulus was given as = 3nRT. Indeed, the modulus, a direct measure of the stiffness, increases with cross-link density. Ordinary cross-linked networks have a distribution of active chain lengths. Assuming a random cross-linking process, then (Mc)J(Mc) should be about 2. 

Figure 11.12 Stress-strain behavior of bimodal poly(dimethyl siloxane) networks. Each curve is labeled with the mol% of the short chains. The area under each curve represents the energy required for rupture (22).

The modifications of Eq(8) leading to Eq(16), taken together with Eq (6) (with Ro replacing Rc) generates a partition function appropriate for networks crosslinked in a deformed state. Using this formalism, one can show that the network remains partially oriented in the absence of an external force, and that stress-strain behavior is characteristic of that foxmd for materials prepared in this way. Further details are given elsewhere (20). 

The first five mechanical properties of the set mentioned before are related to the stress-strain behavior of the yarns. In Fig. 2b, the first derivative of the stress-strain curve (i.e., the modulus-strain curve) was given. Clearly, two maxima are seen that can be attributed to two different mechanisms. According to unpublished work [9], the first maximum can be related to straining of an entanglement network in the sense of Ball et al. [10] (see Fig. 16). After breaking up the entanglements, the tie molecules proper, connecting... 

Fedors and Landel [103] point out that stress-strain behavior of swollen elastomers can be determined experimentally more conveniently by measurements in uniaxial compression than uniaxial extension. In extension, strains of the order of a few hundred percent are required whereas, in compression, strains of the order of only a few percent provide sufficient data for analysis. SBR-glass bead composites cured by means of dicumyl peroxide were used for stress-strain measurements to estimate the concentration of the eftective network chains per unit volume of ttie whole rubber. It was found that with decreasing volume fraction of the composite, tire effective network density decreased linearly at first and then rather rapidly in an unexpected and inexplicable manner. 

Very little work has been done on elastomers subjected to torsion. There are, however, some results on stress-strain behavior and network thermoelasticity [2]. More results are presumably forthcoming, particularly on the unusual bimodal networks and on networks containing some of the unusual fillers described in Section 1.11. 

Twardowski TE, Gaylord RJ (1989) The localization model of rubber elasticity and the stress-strain behavior of a network formed by cross-linking a deformed melt. Polym Bull 21(4) 393-400... 

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