TYPICAL STRESS-STRAIN CURVES

Typical stress-strain curves are shown for the commonly used fiber-reinforced materials fiberglass-epoxy, boron-epoxy, and a representative graphite-epoxy. These curves are not accurate enough for design use  

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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. 

Eig. 1. Typical stress—strain curves for cotton and PET fibers. A, industrial B, high tenacity, staple C, regular tenacity, filament D, regular tenacity, staple ... 

Fig. 2. Typical stress—strain curves of nonwoven fabrics, where (—) is woven (-), thermally bonded nonwoven and (-), needle-punched...

Typical stress—strain curves are shown in Figure 3 (181). The stress— strain curve has three regions. At low strains, below about 10%, these materials are considered to be essentially elastic. At strains up to 300%, orientation occurs which degrades the crystalline regions causing substantial permanent set. 

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.

Fig. 18.8 Typical stress-strain curve of amorphous thermoplastics below their glass transition temperature. Area under the curve is small compared with many crystalline plastics and hence the impact strength is usually low...

Some typical stress-strain curves for a carboxy-terminated polybutadiene proplnt (CTPB) containing 86% solids are given in Figure 8, and for a PBAA propellant (see Table 13) containing 83% solids in Figure 9 (Ref 52). The authors concluded that the CTPB proplnts studied were highly susceptible to humidity degradation... 

Figure 7.13 Typical stress-strain curve for a filled elastomer...

Figure 18.1 is the typical stress-strain curves of the filled rubber (SBR filled with fine carbon black, HAF),

A typical stress-strain curve for a pure gum natural rubber vulcanizate (i.e., without carbon black or other fillers ) is shown in Fig. 83. The stress rises slowly up to an elongation of about 500 percent (length six times initial length), then rises rapidly to a value at break in the neighborhood of 3000 pounds per square inch based on the... 

A strength increase is also produced at ultimate strength (F ) for steels however, the ratio f dynamic to static strength is less than at yield. A typical stress-strain curve describing dynamic and static response of steel is shown in Figure 5.5. Elongation at failure is relatively unaffected by the dynamic response of the material. 

FIGURE 5,3 Typical Stress-Strain Curve for Concrete... 

Figure 7.1 Typical stress-strain curves for (a) a brittle plastic and (b) a tough plastic with yield point, showing the parameters used for the evaluation of degradation in tests...

Fig. 3,34. Edge delamination test (EDT) (a) specimen configuration (b) typical stress-strain curve (c) outward curvature along specimen edges. After Whitney and Knight (1985).

The ends are pulled apart at a certain speed and the distance pulled is plotted versus pounds per square inch of tension placed on the sample. A typical stress-strain curve for a thermoplastic is given in Fig. 15.3. 

FIGURE 14.8 Typical stress-strain curves for plastics where (right) A is the elongation at yield point, B is the yield stress, C is the elongation at break, and the area under the curve is the ultimate strength. 

Figure 9. Typical stress-strain curve for solid propellants at 0.77 in./min. and 80°F. E is the slope of the tangent to the initial portion of the curve. A variety of curve shapes are possible depending on specific formulations and test conditions...

Typical stress-strain curves for the pure CR gum and the composites containing irradiated and nonirradiated PTFE powder are shown in Fig. 46. The addition of PTFE particles increases the elastic modulus of the CR matrix. In the presence of irradiated PTFE particles, the modulus of the CR matrix increases relative to that of a matrix containing nonirradiated PTFE particles. 

Fig. 47 Typical stress-strain curves of PTFE-based chloroprene composites. The first six hysteresis cycles are shown with solid lines. The seventh curve (dotted line) was investigated using an optical method...

Fig. 2 Typical stress-strain curves for amorphous polymers, a Elastic, anelastic, strain softening, and plastic flow regions can be seen, b Plastic flow occurs at the same stress level as required for yielding so strain softening does not exist, c Strain hardening occurs very close to yielding, suppressing both strain softening and plastic flow behaviour...

Fig. 86 Typical stress-strain curves relative to the sample IT0.7I0.3. a Effect of temperature at a strain rate of 2 x 10-3 s-1. b Effect of strain rate at a temperature of -40°C (From [60])...

Figure 12.1 Typical stress-strain curves for thermosets at a temperature below Tg (a) uniaxial tensile test (b) uniaxial compression test. 

In practice, up to 90% of polyurethanes are used in compression, a few percent in torsion, and very little in tension. There is considerable data on the tensile stress against tensile strain (elongation) for polyurethanes. Most polyurethane specification sheets provide this data. Figure 7.3 and Figure 7.4 show typical stress-strain curves for both polyester and polyether polyurethanes. 

As noted in Fig. 14.1 (a), commercial fibers of semicrystallme polymers are always cold-drawn after spinning to achieve further structuring through further macromolecular orientation and crystalline morphological changes, many of which are retained because of the low temperature of the cold-drawing processes. A typical stress-strain curve for a polycrystalline polymer at a temperature Tg < T < Tm appears in Fig. 14.6. 

Figure 6.5. Typical stress-strain curve for tendon. The diagram illustrates the stress-strain curve for an isolated collagen fiber from tendon. Note that collagen fibers from tendon fail at UTS values above 50 MPa and at strains between 10 and 20%. The slope of the linear portion of the curves at high strains is 2GPa.

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%. 

Typical stress-strain curves are shown in Fig. 13.86. In addition Fig. 13.87 gives a survey of specific tenacity versus specific modulus for the modem high-performance filaments. The range of the specific modulus varies from 3 to 300 N/tex (i.e. modulus approximately from 3 to 500 GPa), that of tenacity from 0.2 to 3.5 N/tex (i.e. tenacity approximately from 0.2 to 5 GPa). Diagonal lines show the ratio average value is about 0.02. In comparison Fig. 13.88 shows the same parameters for the conventional man made fibres. Here the ranges are much smaller and the average value of [Pg.480]

FIG. 13.89 Typical stress-strain curves of PET, cellulose II and PpPTA fibres. From Northolt and Baltussen (2002). Courtesy John Wiley Sons, Inc. 

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 11.4. Typical stress-strain curve of a PVA/nanotube composite. The material is a fiber containing 25wt% of MWNTs in a PVA matrix (molecular weight 195 000,99% hydrolized).

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. 

Figure 6.1 shows a typical stress-strain curve for a unidirectional SiCf/CAS composite loaded in uniaxial tension parallel to the fibers. The features of this curve are represenative of many ceramic matrix composites. In order to distinguish between the various damage states that a composite undergoes, it is convenient to divide the stress-strain curve into several sequential parts. 

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