Typical Stress-Strain Properties

Typical stress-strain diagrams for brittle and ductile materials are shown in Fig, 2.7. For brittle materials such as cast iron, glass, some epoxy resins, etc., the stress strain diagram is linear from initial loading (point 0) nearly to rupture (point B) when average strains are measured. As will be discussed subsequently, stress and strain are point quantities if the correct mathematical definition of each is used. As a result, if the strain were actu- 

An approximate sketch of the stress-strain diagram for mild steel is shown in Fig. 2.8(a). The numbers given for proportional limit, upper and lower yield points and maximum stress are taken from the literature, but are only approximations. Notice that the stress is nearly hnear with strain until it reaches the upper yield point stress which is also known as the elastic-plastic tensile instability point. At this point the load (or stress) decreases as the deformation continues to increase. That is, less load is necessary to sustain continued deformation. The region between the lower yield point and the maximum stress is a region of strain hardening, a concept that is discussed in the next section. Note that if true stress and strain are used, the maximum or ultimate stress is at the rupture point. 

The elastic-plastic tensile instability point in mild steel has received much attention and many explanations. Some polymers, such as polycarbonate, exhibit a similar phenomenon. Both steel and polycarbonate not only show an upper and lower yield point but visible striations of yielding, plastic flow or slip lines (Luder s bands) at an approximate angle of 54.7° to the load axis also occur in each for stresses equivalent to the upper yield point stress. (For a description and an example of Luder s band formation in polycarbonate, see Fig. 3.7(c)). It has been argued that this instability point (and the appearance of an upper and lower yield point) in metals is a result of the testing procedure and is related to the evolution of internal damage. That this is the case for polycarbonate will be shown in Chapter 3. For a discussion of these factors for metals, see Drucker (1962) and Kachanov (1986). 

If the strain scale of Fig. 2.8(a) is expanded as illustrated in Fig. 2.8(b), the stress-strain diagram of mild steel is approximated by two straight lines one for the linear elastic portion and one which is horizontal at a 

Lower yield point, OLyp Proportional limit, OpL 

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Fig. 2. Typical stress—strain properties of staple fibers at 65% rh and 21°C. Rate of elongation is 50%/min. To convert N/tex to gf/den, multiply by 11.3.

The mechanical properties of acryUc and modacryUc fibers are retained very well under wet conditions. This makes these fibers well suited to the stresses of textile processing. Shape retention and maintenance of original bulk in home laundering cycles are also good. Typical stress—strain curves for acryhc and modacryUc fibers are compared with wool, cotton, and the other synthetic fibers in Figure 2. 

A typical stress—strain curve generated by a tensile tester is shown in Eigure 41. Creep and stress—relaxation results are essentially the same as those described above. Regarding stress—strain diagrams and from the standpoint of measuring viscoelastic properties, the early part of the curve, ie, the region... 

Fig. 41. Typical stress—strain curve. Points is the yield point of the material the sample breaks at point B. Mechanical properties are identified as follows a = Aa/Ae, modulus b = tensile strength c = yield strength d = elongation at break. The toughness or work to break is the area under the curve.

The influence of the annealing process at a higher temperature was also studied, and important changes in the properties of a sample annealed at 55°C during 5 days (PTEB-CR sample) were observed [33]. The PTEB-CR specimens were stretched at 1 and 10 cm/min, but the behavior was similar in both cases. Typical stress-strain plots are shown in Fig. 14 for samples stretched at 23°C... 

FE simulations of the stress-strain properties of fiUer-reinforced elastomers are an important tool for predicting the service live performance of mbber goods. Typical examples are the evaluation of rolling resistance of tires due to hysteresis energy losses, mainly in the tire tread or the adjustment of engine mounts in automotive applications. 

For both EPDM-LDH and XNBR-LDH nanocomposites, the various tensile properties are summarized in Table 13 and their typical stress-strain plots are shown in Fig. 58 [104]. In Fig. 58a, the gum vulcanizates of both rubber systems showed typical NR-like stress-strain behavior with a sharp upturn in the stress-strain plot after an apparent plateau region, indicating strain-induced crystallization. With the addition of LDH-C10 in the XNBR matrix, the stress value at all strains increased significantly, indicating that the matrix undergoes further curing (Fig. 58b). 

In an attempt to simplify the discussion, we ignore the fact that the modulus and properties of bone are dependent on the testing direction and mineral content. A typical stress-strain curve for cortical bone is illustrated in Figure 6.7. Mineralized ECMs show a much higher modulus and UTS, and the strain at failure is markedly decreased. In the same manner that increased crosslinking increases the UTS of unmineralized tissue, mineral deposition acts as a crosslink and improves the UTS and the modulus of bone. The UTS for cortical bone varies from 100 to 300 MPa, the modulus varies from several to more than 20GPa, and the strain at failure falls to only 1 to 2%. 

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. 

It is necessary to state more precisely and to clarify the use of the term nonlinear dynamical behavior of filled rubbers. This property should not be confused with the fact that rubbers are highly non-linear elastic materials under static conditions as seen in the typical stress-strain curves. The use of linear viscoelastic parameters, G and G", to describe the behavior of dynamic amplitude dependent rubbers maybe considered paradoxical in itself, because storage and loss modulus are defined only in terms of linear behavior. 

The mechanical properties were evaluated by two sets of tensile measurements. Typical stress-strain curves are shown in Figure 4. The modulus and stress decrease with increasing aging time. Similar results are observed for all aging samples at all three temperatures. Both testing methods provided essentially the same tensile data at 400% extension. The scatter of the tensile data is due to the experimental error associated with the measurement. 

Figure 6. Example of the relationship between a typical stress-strain diagram and some mechanical properties. Key A, proportional limit B, ultimate strength a, MOR cr., FSPL Acr/Ae (from origin to A), MOE ...

The mechanical strength of a hair is determined by measuring its tensile properties using a Diastron or Instron tensile tester. The slope of the post-yield and the breaking force obtained from a typical stress-strain curve have been found to relate to the loss of mechanical strength of the hair and to the percent f reduction of disulfide bonds [79,82,196],... 

The effect of the size of EPDM domains in the PP dominant matrix has been investigated since the initial study of TPV (15-19). It is well known that the size of the rubber domain affects the mechanical properties of both TPE and TPV. Wu (29) suggested that the critical mbber domain size and the critical distance between rubber domains are very important for toughness in rubber-filled nylon. This also appears to be the case of TPV. The typical stress-strain curve for TPV is shown in Fig. 8.17. 

If the materials are anisotropic, they will present different properties in the different directions. Examples of these polymeric materials are polymer fibers, such as polyethylene terephthalate, PET, nylon fibers, injection-molded polymers, fiber-reinforced composites with a polymeric matrix, and crystalline polymers where the crystalline phase is not randomly oriented. A typical method for measuring the modulus in tension is the stress-strain test, in which the modulus corresponds to the initial slope of the stress-strain curve. Figure 21.4 shows typical stress-strain curves for different types of polymeric materials. 

Very recently the first synthesis of a main chain LCE has been described [46]. It turns out, as was to be expected due to the completely different location of the mesogenic units, that the stress strain properties of these novel materials are rather different from what is known from side chain LCEs. For example, the main chain LCEs require a stretching by a factor of about 5 to get macroscopic alignment of the director. Such an extension is not even an option for side chain LCEs, which typically rupture when elongated by a factor between about 2 and 3. Thus in many ways the main chain LCEs might resemble more closely a classical rubber than the sidechain LCEs. 

Physical Properties The usual values of tensile strength, tensile modulus, and ultimate elongation at various temperatures can be obtained from the typical stress-strain curves shown in Figs. 22-01 and 22-02. Such properties as tensile strength and modulus are inversely proportional to temperature, whereas elongation reaches a maximum value at about 300°C. Other factors, such as humidity, film thickness, and tensile elongation rates, were found... 

In the study of swollen networks, two problems are of major importance The dependence of the stress-strain properties on the solvent or polymer fraction and the mking contributions to the free energy of the network or the elastic contribution to the chemical potential. Latest research seems to provide an improved insight into some special effects which are typical for swollen and completely crosslinked networks, and for unswollen (and swollen) incompletely crosslinked networks. The relaxation on the deformation dependence of topological constraints, which leads to a constraint release, is one of them. 

A typical stress-strain curve of 1, 2-EHD contpared with LDPE and rubber indicates that the 1, 2-EBD has intermediate properties between plastics suid rubber (Fig. 6). The relationship between "dynamic elastic modulus"(E) and temperature of 1, 2-PBD having 25 crystallinity is shown Fig. 7. The E of 1, 2-PBD is similar to that of EVA and smaller than that of LDPE above 40°C. The E of 1, 2-PBD is the smallest than those of EVA and LDPE below 20°C. 

The mechanical behaviour of polymeric materials is often characterised by their stress/strain properties. A tension stress is applied at a very slow rate to a piece of material, which usually has a standardised dumbbell shape, as illustrated in Figure 2.15. Elongation, i.e. strain, is measured until the sample breaks. The results are usually displayed as a plot of stress versus strain. The stress reported to the smallest section of the sample is expressed in newtons per square centimetre (N/cm ). The strain is usually expressed as the percentage of the original length of the sample (AL/L x 100). Some typical stress/ strain plots are shown in Figure 2.16. 

To determine the actual effects of normal weathering, specimens are exposed outdoors in different locations and different climates. Changes in color, cracking, crazing, chalking, and stress-strain properties are recorded at various time intervals. (Mildew might also be observed.) Typical check periods are 1, 2, 5, 10, and 20 years exposure. Test specimens are... 

Fig. 6.1 Typical stress-strain relationship of the ACL and the definition of material properties (modulus, strength, and strain at failure) with schematic drawings of the microstructure of collagen fibers. Numerical data of the strength, modulus, and strain at failure are referred from the original work [5]...

The two techniques employed involved separating the chains prior to cross linking by either dissolution or stretching. After cross linking, the solvent is removed or the stretching force is relaxed, and the network is studied (unswollen) with regard to its stress-strain properties, typically in elongation. - ... 

The test results are summarized in Table 14.2 and some typical test curves are shown in Fig. 14.3. Several improvements in the stress-strain properties of the soil can be seen from the results. The peak sbess (actual peak sttess or the sttess at 20% axial strain where a peak was not evident) increased as the fiber content increased. The increase was very significant, by 204% with 3% carpet fibers at 34.5 kPa confinement, and by 157% with 3% carpet fibers at 34.5 kPa confinement. 

The mechanical properties of acrylic fiber are deficient under hot-wet conditions. This is primarily due to the fact that the wet Tg of acrylonitrile copolymers is lower than the boiling point of water. Textile wet-processing must be carried out in such a way as to minimize yarn or fabric distortion. Shape retention and maintenance of original bulk under the lower temperatures in home laimdering cycles are acceptable. Typical stress-strain curves for acrylic fiber in air and in wet conditions are shown in Figure 3. 

The physical characteristics of current commercial mbber and spandex fibers are summarized in Table 1. Typical stress—strain curves for elastomeric fibers, hard fibers, and hard fibers with mechanical stretch properties are compared in Figure 2. 

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