Brittle polymers, stress-strain curve

Figure 9.3. Stress-strain curves for (a) rigid amorphous plastics material showing brittle fracture and (b) rubbery polymer. The area under the curve gives a measure of the energy required to break the...

Figure 5.89 Schematic illustration of stress-strain curves for continuous, unidirectional fiber-reinforced composites containing brittle fibers in a ductile matrix. Contributions from fibers and matrix are shown as dashed lines at (a) low fiber volume fractions and (b) high fiber volume fractions. Adapted from N. G. McCrum, C. P. Buckley, and C. B. Bucknall, Principles of Polymer Engineering, 2nd ed., p. 267. 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. 

Mechanical Properties. The room temperature modulus and tensile strength are similar to those of other amorphous thermoplastics, but the impact strength and ductility are unusually high. Whereas most amorphous polymers arc glass-like and brittle below their glass-transition temperatures, polycarbonate remains ductile to about — 10°C. The stress-strain curve for polycarbonate typical of ductile materials, places it in an ideal position for use as a metal replacement. Weight savings as a metal replacement are substantial, because polycarbonate is only 44% as dense as aluminum and one-sixth as dense as steel. 

Figure 7 shows the stress-strain curves for the three polymers (23, 24). As seen from the initial slopes of the curves, the Young s moduli of these polymers are similar ( 500 MPa). In contrast, their elongations at break point are significantly different. Thus, poly(3) is rather hard and brittle, whereas poly(4a) is fairly ductile. 

The most common type of stress-strain tests is that in which the response (strain) of a sample subjected to a force that increases with time, at constant rate, is measured. The shape of the stress-strain curves is used to define ductile and brittle behavior. Since the mechanical properties of polymers depend on both temperature and observation time, the shape of the stress-strain curves changes with the strain rate and temperature. Figure 14.1 illustrates different types of stress-strain curves. The curves for hard and brittle polymers (Fig. 14.1a) show that the stress increases more or less linearly with the strain. This behavior is characteristic of amorphous poly-... 

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. 

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. 

Stress-strain curves developed during tensile, flexural and compression tests may be quite different from each other. The moduli determined in compression are generally higher than those determined in tension. Flaws and sub-microscopic cracks significantly influence the tensile properties of brittle polymeric materials. However, they do not play such an important role in compression tests as the stresses tend to close the cracks rather than open them. Thus, while tension tests are more characteristic of the defects in the material, compression tests are characteristic of the polymeric material as it is. The ratio of compressive strength to tensile strength in the case of polymers is in the range 1.5 to 4.0 [Dukes, 1966]. 

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.

FIGURE 41.8 Representative stress-strain curve for a cellular solid. The plateau region for compression in the case of elastomeric foam (a rubbery polymer) represents elastic buckling for an elastic-plastic foam (such as metallic foam), it represents plastic yield, and for an elastic-brittle foam (such as ceramic) it represents crushing. On the tension side, point A represents the transition between cell wall bending and cell wall alignment In elastomeric foam, the alignment occurs elastically, in elastic plastic foam it occurs plastically, and an elastic-brittle foam fractures at A. 

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)]. 

Figure 1.2 Typical schematic tensile stress-strain curves for polymers (a) brittle, amorphous thermoplastic, (b) same polymer with toughening additive, (c) intrinsically tough, semi-crystalline thermoplastic. The curves should be taken only to convey trends and not relative breaking stresses, which vary with the precise materials...

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