Stress-strain curves of polymers

Typical stress-strain curves at different temperatures relative to Tg are shown for an amorphous polymeric material in Fig. 8.4(a) and for the partially crystalline condition in Fig. 8.4(b). 

For both types of material, the graph of axial stress o against linear strain e is a straight line for temperatures well below Tg and the material is brittle. 

At temperatures up to amorphous polymers deform elastically in tension until the so-called yield stress Oy is reached, when the stress falls to a lower value a j, known as the draw stress. 

Data for some common polymeric materials are given in Table 8.1. 

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On the basis of what has been discussed, we are in the position to provide a unified understanding and approach to the composite elastic modulus, yield stress, and stress-strain curve of polymers dispersed with particles in uniaxial compression. The interaction between filler particles is treated by a mean field analysis, and the system as a whole is macroscopically homogeneous. Effective Young s modulus (JE0) of the composite is given by [44]... 

The stress-strain curves of ductile thermoplastics (including both glassy amorphous polymers such as bisphenol-A polycarbonate and semicrystalline polymers such as polyethylene at room temperature) have the general shapes shown in Figure 11.16(a), which can be compared with the shape of the stress-strain curve of a very brittle material shown in Figure 11.16(b). The stress-strain curves of polymers which are neither very ductile nor very brittle under the testing conditions being utilized have appearances which are intermediate between these. two extremes. 

Fig. 6.18 Illustration of five conventional stress-strain curves of polymer materials under constant strain rates. 1 hard and brittle, 2 hard and tough, 3 hard and strong, 4 soft and tough, and 5 soft and weak...

Haward, R. N. (1987). The Apphcation of a Simphfied Model for the Stress-Strain Curves of Polymers. Polymer, 28(8), 1485-1488. 

Figure 15.34 compares the typical tensile and bending stress-strain curves of polymer fibers. In most cases, the bending stress-strain curve lay below the tensile curve. This is because the compressive side of the fiber yields more easily than the tensile side. The bending rigidity (or flexural rigidity) of a circular fiber is... 

FIGURE 38.2 Stress-strain curves of polyvinyl chloride-ground rubber tire (PVC-GRT) and PVC-Cl-GRT blends. (Reprinted from Naskar, A.K., Bhowmick, A.K., and De, S.K., J. Appl. Polym. ScL, 84, 622, 2002. With permission from Wiley InterScience.)... 

Indeed, it has been observed that the onset of yielding of isotropic polymers is approximately constant, 0.02< [<0.025, which implies that 0.04shear yield strain, the plastic shear deformation of the domain satisfies a plastic shear law. For temperatures below the glass transition temperature, the continuous chain model enables the calculation of the tensile curve of a polymer fibre up to about 10% strain [6]. Figure 7 shows the observed stress-strain curves of PpPTA fibres with different moduli compared to the calculated curves. 

Figure 11.11 Stress-strain curves of PET, PTT and PBT fibers [69]. From Jake-ways, R., Ward, I. M., Wilding, M. A., Desborough, I. J. and Pass, M. G., J. Polym. Sci., Polym. Phys. Ed., 13, 799-813 (1975), Copyright (1975 John Wiley Sons, Inc.). This material is used by permission of Wiley-Liss, Inc., a subsidiary of John Wiley Sons, Ltd...

Figure 13.6 (a) Elongation as a function of wind-up speed for partially oriented yarn, (b-d) Stress-strain curves of fibers of PET blends with 3% copolyester of 1,4-phenyleneterephthalate and p-oxybenzoate (CLOTH) and 3% copolymer of 6-oxy-2-naphthalene and p-oxybenzoate (CO), spun at 3500, 4000 and 4500 m/min (1) PET control (2) 3 % CLOTH (3) 3 % CO the loci of the theoretical extensions of the PET control are shown as dashed curves [17]. From Orientation suppression in fibers spun from melt blends, Brody, H., J. Appl. Polym. Sci., 31, 2753 (1986), copyright (1986 John Wiley Sons, Inc.). Reprinted by permission of John Wiley Sons, Inc. 

The effect of gas compression on the uniaxial compression stress-strain curve of closed-cell polymer foams was analysed. The elastic contribution of cell faces to the compressive stress-strain curve is predicted quantitatively, and the effect on the initial Young s modulus is said to be large. The polymer contribution was analysed using a tetrakaidecahedral cell model. It is demonstrated that the cell faces contribute linearly to the Young s modulus, but compressive yielding involves non-linear viscoelastic deformation. 3 refs. 

Figure 3. Stress-strain curves of three gradient polymers and one interpenetrating network of poly(methyl methacrylate) with 2-chloroethyl acrylate at comparable strain rates of 2-3% /sec and same temperature of 80° C. The numerals in parentheses indicate concentrations (mole percent) of chloroethyl acrylate in poly(methyl methacrylate).

Notwithstanding this great variety of mechanical properties the deformation curves of fibres of linear polymers in the glassy state show a great similarity. Typical stress-strain curves of poly(ethylene terephthalate) (PET), cellulose II and poly(p-phenylene terephtha-lamide (PpPTA) are shown in Fig. 13.89. All curves consist of a nearly straight section up to the yield strain between 0.5 and 2.5%, a short yield range characterised by a decrease of the slope, followed by a more or less concave section almost up to fracture. Also the sonic modulus versus strain curves of these fibres are very similar (see Fig. 13.90). Apart from a small shoulder below the yield point for the medium- or low-oriented fibres, the sonic modulus is an increasing, almost linear function of the strain. 

Figure 10. Effect of hot-stretching on subsequent room temperature Instron stress strain curves of one BPFC-DMS block polymer. 27% silicone of DPn = 36.

The influence of temperature on the stress-strain behavior of polymers is generally opposite to that of straining rates. This is not surprising in view of the correspondence of time and temperature in the linear viscoelastic region (Section I l.5.2.iii). The curves in Fig. 11-23 are representative of the behavior of a partially crystalline plastic. 

The mechanical properties of a craze were first investigated by Kambour who measured the stress-strain curves of crazes in polycarbonate (Lexan, M = 35000) which had first been grown across the whole cross-section of the specimen in a liquid environment and subsequently dried. Figure 25 gives examples of the stress-strain curves of the craze determined after the 1st and 5th tensile loading cycle and in comparison the tensile behavior of the normal polymer. The craze becomes more and more elastic in character with increasing load cycles and its behavior has been characterized as similar to that of an opencell polymer foam. When completely elastic behavior is observed the apparent craze modulus is 25 % that of the normal poly-... 

Fig. 1. Typical stress-strain curve of a polymer exhibiting (dilatational) craze plasticity...

As could be expected, the mechanical properties of a crazed polymer differ from those of the bulk polymer. A craze containing even 50% microcavities can still withstand loads because fibrils, which are oriented in the direction of the load, can bear stress. Some experiments with crazed polymers such as polycarbonate were carried out to get the stress-strain curves of the craze matter. To achieve this aim, the polymer samples were previously exposed to ethanol. The results are shown in Figure 14.24 where the cyclic stress-strain behavior of bulk polycarbonate is also illustrated (32). It can be seen that the modulus of the crazed polymer is similar to that of the bulk polymer, but yielding of the craze occurs at a relatively low stress and is followed by strain hardening. From the loading and unloading curves, larger hysteresis loops are obtained for the crazed polymer than for the bulk polymer. 

The first case, Ef < e, is typical of polymer matrix composites schematic stress-strain curves are given in Figure 15.10. When e < 8, two different modes of failure can take place depending on y. Figure 15.11 gives a schematic representation on the stress-strain curves of the components multiplied by their respective volume fractions as well as the stress-... 

When the tubes were opened the gasses above the polymers were analyzed for O2, N2, and CO2. The analyses were not significantly different from that of laboratory air. The stress-strain curves of the polymer samples were run to 300% elongation at 25 C and 60 C (on different specimens). Gage marks were initially 2.5 cm apart, jaws were 7.5 cm apart, and crosshead speed was 5 cm/min, unless specified. Sol fractions of insoluble polymers were determined by extraction with tetrahydrofuran at 25 C. Intrinsic viscosities [n]> of soluble polymers were determined, also in tetrahydrofuran at 25 C. A differential scanning calorimeter was used to measure the heat of fusion,... 

Figure 11.16. (a) General shapes of the stress-strain curves of ductile thermoplastics. Some such polymers manifest a very distinct post-yield stress drop, while many others do not. (b) For comparison, the general shape of the stress-strain curve is shown for a very brittle material. 

Figure 11.17. Schematic representation [150] of the structural changes that occur in the crystalline domains, in different regions of the stress-strain curve of a semicrystalline polymer.

Figure 1. The effect of relative humidity (RH) on mechanical properties [stress-strain curves] of at thermoplastic starch polymer.

That crystallization increases the elastic stress has already been demonstrated in Figure 6-8, in which the Mooney-Rivlin plot shows a rise at high extension ratios. However, it should be remembered that part of this increase is due to finite extensibility of network chains. In Figure 6-13 we show the stress-strain curves of natural rubber at two temperatures. At 0 °C there is considerable strain-induced crystallization, and we observe a dramatic rise in the elastic stress above X = 3.0. Wide-angle X-ray measurements show the appearance of crystallinity above this strain. At 60 °C there is little or no crystallization, and the stress-strain curve shows a much smaller upturn at high strains. The latter is presumably due only to the finite extensibility of the polymer chains in the network. 

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