Polystyrenes stress-strain curve

Proportion of Hard Segments. As expected, the modulus of styrenic block copolymers increases with the proportion of the hard polystyrene segments. The tensile behavior of otherwise similar block copolymers with a wide range of polystyrene contents shows a family of stress—strain curves (4,7,8). As the styrene content is increased, the products change from very weak, soft, mbbedike materials to strong elastomers, then to leathery materials, and finally to hard glassy thermoplastics. The latter have been commercialized as clear, high impact polystyrenes under the trade name K-Resin (39) (Phillips Petroleum Co.). Other types of thermoplastic elastomers show similar behavior that is, as the ratio of the hard to soft phase is increased, the product in turn becomes harder. 

Figure 5.84 Stress-strain curves for polystyrene (PS) and high-impact polystyrene (HIPS). Reprinted, by permission, from N. G. McCrum, C. P. Buckley, and C. B. Bucknall, Principles of Polymer Engineering, 2nd ed., p. 200. Copyright 1997 by Oxford University Press.

Figure 3.3 shows representative stress-strain curves for a variety of polymeric materials. At normal use temperatures, such as room temperature, rigid polymers such as polystyrene (PS) exhibit a rapid increase in stress with increasing strain until sample failure. This behavior is typical of brittle polymers with weak interchain secondary bonding. As shown in the top curve in Figure 3.3, the initial stress-strain relation in such polymers is approximately linear and can be described in terms of Hooke s law, i.e., S = Ee, where E is Young s modulus, typically defined as the slope of the stress-strain plot. At higher stresses, the plot becomes nonlinear. The point at which this occurs is called the proportional limit. 

Fig. 3 Percentage of gauche conformations along the stress-strain curve of atactic polystyrene. The dashed curve is the stress-strain curve (From [11])...

Some plastic materials have different tensile and compressive characteristics. For example, polystyrene is tough under compressive load but very brittle in tension. However, for most elastoplastic materials, the stress-strain curves in compression are the same as in tension. Hence, the deformation properties of these materials in tension may also be applied to those in compression, which is of great interest to gas-solid flows. 

The mechanical properties of a macrolattice of SBS has been investigated (65). The sample consists of a hexagonal array of polystyrene cylinders embedded in the polybutadiene matrix. The stress-strain curves... 

Fig. 1-2. Stress-strain curves, (a) Synthetic fiber, like nylon 66. (b) Rigid, britile plastic, like polystyrene, (c) Tough plastic, like nylon 66. (d) Elastomer, like vulcanized natural rubber.

Fig. 29, Representative stress-strain curves of polystyrene containing increasing weight fraction of PB-2.76 K...

Similar stress-strain curves have been obtained for polystyrene crazes. However, these results do not necessarily reveal the real mechanical behavior of the craze. The removal of the solvent from samples will cause shrinkage and have a significant plasticizing effect on the craze fibrils. This has to... 

Figure 14.38 Stress-strain curves for polystyrene and high impact polystyrene. (From Ref. 48.)...

Figures 13.16 and 13.17 are plots of the compressive stress-strain data for two amorphous and two crystalline polymers, respectively, while Figure 13.18 shows tensile and compressive stress-strain behavior of a normally brittle polymer (polystyrene). The stress-strain curves for the amorphous polymers are characteristic of the yield behavior of polymers. On the other hand, there are no clearly defined yield points for the crystalline polymers. In tension, polystyrene exhibited brittle failure, whereas in compression it behaved as a ductile polymer. The behavior of polystyrene typifies the general behavior of polymers. Tensile and compressive tests do not, as would normally be expected, give the same results. Strength and yield stress are generally higher in compression than in tension.

Socrate et al. (2000) considered an axially symmetric problem, with a rubber sphere in the centre of a short cylinder of matrix the spheres are in a row, aligned with the tensile stress axis. The potential positions of crazes were predetermined, initially running radially from the material interface, then becoming normal to the tensile stress along the cylinder. The initial stress concentration is greatest in the polymer near the equator of the sphere (Fig. 4.11a). The model, for a 20% volume fraction of rubber, predicts a yield point in the tensile stress-strain curve at an average strain of 1%, and 24 MPa stress, when the first craze propagates across the section. However, this relieves the stress in the polystyrene, and a tensile stress concentration... 

There is experimental evidence, for many rubber-toughened polymers, that the rubber particles cavitate early in the deformation. The degree of cross-linking is kept relatively low in the polybutadiene phase of ABS to aid cavitation, and sometimes silicone oil is added for the same reason. Figure 4.12 shows both the conventional stress-strain curve and the volumetric strain versus tensile strain for rubber-modified polystyrene. When the polystyrene yields, the volume strain increases at a higher rate. Majority of the dilatational strain is due to cavitation in the rubber phase. 

Polymers such as polystyrene and poly(methyl methacrylate) with a high E at ambient temperatures fall into the category of hard brittle materials which break before point Y is reached. Hard tough polymers can be typified by cellulose acetate and several curves measured at different temperatures are shown in Figure 13.16(a). Stress-strain curves for poly(methyl methacrylate) are also shown for comparison [Figure 13.16(b)]. 

There remains the question of whether the drop in load observed at yielding arises from the purely geometrical strain softening associated with a true-stress-strain curve of the form shown in fig. 8.4(c), where there is no drop in the true stress but merely a reduction in slope of the stress train curve, or whether there is actually a maximum in the true-stress strain curve as shown in fig. 8.4(d). Experiments on polystyrene and PMMA in compression, under which the geometrical effect cannot take place, show that a drop in load is still observed. Results from extensive studies of PET under a variety of loading conditions also support the idea that a maximum in the true-stress train curve may occur in a number of polymers. 

Typical stress-strain curves for plastics are shown in Fig. 1.2. The figure shows qualitatively (a) the steep, but non-linear curve associated with amorphous, brittle thermoplastics such as unmodified polystyrene, (b) the equivalent graph for a similar brittle thermoplastics material to which rubber has been added to produce a high impact grade and (c) an intrinsically tough thermoplastics material, such as a nylon (polyamide). 

Figure 8.1 shows stress-strain curves of atactic polystyrene (PS) in compression at 295 K for two structures with different initial states well annealed, i.e., furnace cooled from Tg + 20 K to room temperature, and rapidly quenched into ice water (Hasan and Boyce 1993). In both cases there is a gradual transition to fully developed plasticity that is reached at the peak of a yield phenomenon which is more prominent in the annealed material. Both curves show several unloading histories, starting with one close to the upper yield peak. All unloading paths show prominent Bauschinger effects of plastic strain recovery that is independent of the pre-strain. These indicate the presence of strain-induced back stresses and some recoverable stored elastic strain energy. In both cases the flow stress moves toward a unique flow state attained at a strain of around 0.3. 

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