Polymer stress-strain diagram

Figure 15.4 Stress-strain diagrams for typical polymers. (Source Wittcoff and Reuben, Industrial Organic Chemicals, John Wiley Sons, 1996. Reprinted by permission of John Wiley Sons, Inc.)...

Figure 15.4 gives the stress-strain diagrams for a typical fiber, plastic, and elastomer and the average properties for each. The approximate relative area under the curve is fiber, 1 elastomers, 15 thermoplastics, 150. Coatings and adhesives, the two other types of end-uses for polymers, will vary considerably in their tensile properties, but many have moduli generally between elastomers and plastics. They must have some elongation and are usually of low crystallinity. 

Fig.2.21. Stress-strain diagram for various types of polymers (for explanation, see text) Og = yield strength Og = tensile strength at break...

Finally, the modulus of elasticity E (Young s modulus), which is a measure of the stiffness of the polymer, can be calculated from the stress-strain diagram. According to Hooke s law there is a linear relation between the stress o and the strain e ... 

In terms of the mechanical behavior that has already been described in Sections 5.1 and Section 5.2, stress-strain diagrams for polymers can exhibit many of the same characteristics as brittle materials (Figure 5.58, curve A) and ductile materials (Figure 5.58, curve B). In general, highly crystalline polymers (curve A) behave in a brittle manner, whereas amorphous polymers can exhibit plastic deformation, as in... 

Figure 5.77 Comparison of idealized stress-strain diagrams for metals, amorphous polymers, and elastomers.

Figure 1.9. Deformation of typical elastoplastic materials (hardened metal and polymer) in the stress-strain diagram (after Guy, 1976).

Comparing the calculated and experimental stress-strain diagrams for real plastic foams, we will take Eo in Eq. (77) as the elasticity modulus of the polymer base Y and y are foam and polymer base densities (volumetric weights), respectively ... 

Young s Modulus. Young s moduli, E, for several resins are plotted vs. temperature in Fig. 7. Young s moduli were determined from stress-strain diagrams. At 4K, their values are within 10%. Therefore, the low-temperature values of E do not depend markedly on the detailed chemical structure. It must be emphasized that epoxy resins are energy-elastic and have a nearly linear stress-strain behavior to fracture at low temperatures. No rate dependence was found over several decades. This is not true for many high polymers, such as polyethylene (PE), which are not cross-linked. PE behaves viscoelastically, even at 4 K [%... 

Still further differences are observed for stress/strain diagrams of what are known as hard elastic or springy polymers. These polymeric states should exhibit a large energy-elastic component which is attributed to a special network structure (see Figure 38-10). However, electron microscopic studies do not provide any evidence for the proposed network structure. 

The stress / strain diagrams of stretched polymers differ significantly from those of unstretched polymers (Figure 11-18). The absence of an upper flow limit, that is, the absence of cold flow, is especially noticeable. Of course, orientation of chain segments and crystallites hinders viscoelastic and viscous flow. 

Quasi-static tensile test - tensile properties without yield point - data Polymer Solids and Polymer Melts C. Bierdgel, W. Grellmann The following Table 4.2 shows a summary of available tensile properties of thermoplastics according to stress-strain diagrams of type a and d ( Fig. 4.3). Table 4.2 Tensile properties of thermoplastics without yield point. ... 

Stress-strain diagrams are commonly used to represent the mechanical properties of polymers. Stress is defined as the average force per unit of cross section. Strain is defined as the length over unstrained (original) length. Figure 2 shows a few examples of such curves, and the polymers associated with them. 

In the isogel state, deformation is so easy that, when stresses are applied in one direction to a linear polymer, the molecules are oriented. This leads to anisotropy, which can be controlled mechanically, and optically by X-rays. The stress-strain diagrams for the direction of orientation and that at right angles to it are different,... 

The production of crystals in a polymer by the action of stress, usually in the form of an elongation. It occurs in fiber spinning, or during rubber elongation, and is responsible for enhanced mechanical properties. Simultaneous readings of load and deformation, converted to stress and strain, plotted as ordinates and abscissas, respectively, to obtain a stress-strain diagram. 

Average stiffness The ratio of change in stress to change in strain between two points on a stress-strain diagram, particularly the points of zero stress and breaking stress. Brown R (1999) Handbook of physical polymer testing, vol 50. Marcel Dekker, New York. 

Figure 5.2 Stress-strain diagrams for modified epoxy networks containing varying concentrations of CTPEGA. Reprinted with permission from D. Ratna, A.B. Samui and B.C. Chakraborty, Polymer International, 2004, 3,1882. 2004, John Wiley...

The Vc and Me values for crosslinked polymer networks can also be evaluated from stress-strain diagrams on the basis of theories for the rubber elasticity of polymeric networks. In the relaxed state the polymer chains of an elastomer form random coils. On extension, the chains are stretched out, and their conformational entropy is reduced. When the stress is released, this reduced entropy makes the long polymer chains snap back into their original positions entropy elasticity). Classical statistical models of entropy elasticity affine or phantom network model [39]) derive the following simple relation for the experimentally measured stress cr ... 

In different experiments film specimens were stretched in the machine direction at constant rate of elongation (85 % strain per minute) at 300 K and 343 K and 10-scan spectra (resolution 4 cm ) were taken in about 11 %-strain intervals with radiation polarized alternately parallel and perpendicular to the direction of stretch and unpolarized radiation. In Fig. 13 the FTIR spectra recorded during elongation at 300 K in the 690-750 cm wavenumber region are shown separately for the parallel and perpendicular polarization directions alongside the corresponding stress-strain diagrams for 300 K and 343 K. The reduction of intermolecular forces in the polymer at elevated temperature is readily reflected by the considerably lower stress level of the 343 K experiment. 

The close relation between the composition and the mechanical properties of these polymers is reflected in the stress-strain diagrams measured at 300 K and 348 K (Figs. 47 and 48). Hence, at ambient temperature for the spedfied experimental conditions a distinct increase of initial modulus (11. 45 and 1 MNm ), stress-hysteresis (ratio of area bounded by a strain cycle to the total area underneath the elongation curve 60,80 and 90 %) and extension set (30,65 and 100 %) can be obsened with increasing hard segment content of polyester urethane (a) to (c). 

The stress-strain diagrams of the deuterated specimens taken at 300 K did not deviate significantly from the mechanical data of the undeuterated polymers and are not shown separately. 

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