Fibers stress-strain curves

Tensile properties that are related to fiber stiffness can be used to measure the T of almost all fibers. The elastic modulus, that is, the sl pe of the Hookean region of the fiber stress-strain curve, is a measure of the fiber stiffness and can be used for T determination since, by definition, a glass is stlffer than rubber (Figure 6). Since the transition from a glassy to a rubbery state Involves a reduction in stiffness, the temperature at which the modulus is abruptly lowered is taken as... 

Textile Fibers. PTT POY is spun using PET POY or SDY fiber spinning machines. Table 5 shows the tenacities and elongations of PTT fiber as a function of spinning speed (64). Tenacity increases while the elongation decreases with increasing speed. The PTT fiber stress-strain curve, unlike PET, has an inflexion point like a knee (45,65). A fully oriented PTT fiber has a modulus of 2.58 GPa (374,000 psi) compared to 9.15 GPa (1.33 x 10 psi) of PET (45). 

A schematic stress-strain curve of an uncrimped, ideal textile fiber is shown in Figure 4. It is from curves such as these that the basic factors that define fiber mechanical properties are obtained. 

Fig. 4. Idealized stress-strain curves of an uncrimped textile fiber point 1 is the proportional limit, point 2 is the yield point, and point 3 is the break or...

The elasticity of a fiber describes its abiUty to return to original dimensions upon release of a deforming stress, and is quantitatively described by the stress or tenacity at the yield point. The final fiber quaUty factor is its toughness, which describes its abiUty to absorb work. Toughness may be quantitatively designated by the work required to mpture the fiber, which may be evaluated from the area under the total stress-strain curve. The usual textile unit for this property is mass pet unit linear density. The toughness index, defined as one-half the product of the stress and strain at break also in units of mass pet unit linear density, is frequentiy used as an approximation of the work required to mpture a fiber. The stress-strain curves of some typical textile fibers ate shown in Figure 5. 

Fig. 5. Stress—strain curves of some textile fibers (17). To convert N/mm to psi, multiply by 145.

Another aspect of plasticity is the time dependent progressive deformation under constant load, known as creep. This process occurs when a fiber is loaded above the yield value and continues over several logarithmic decades of time. The extension under fixed load, or creep, is analogous to the relaxation of stress under fixed extension. Stress relaxation is the process whereby the stress that is generated as a result of a deformation is dissipated as a function of time. Both of these time dependent processes are reflections of plastic flow resulting from various molecular motions in the fiber. As a direct consequence of creep and stress relaxation, the shape of a stress—strain curve is in many cases strongly dependent on the rate of deformation, as is illustrated in Figure 6. 

Fig. 6. The effect of rate of extension on the stress—strain curves of rayon fibers at 65% rh and 20°C. The numbers on the curves give the constant rates of...

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. 

The ratio of stress to strain in the initial linear portion of the stress—strain curve indicates the abiUty of a material to resist deformation and return to its original form. This modulus of elasticity, or Young s modulus, is related to many of the mechanical performance characteristics of textile products. The modulus of elasticity can be affected by drawing, ie, elongating the fiber environment, ie, wet or dry, temperature or other procedures. Values for commercial acetate and triacetate fibers are generally in the 2.2—4.0 N/tex (25—45 gf/den) range. 

The abihty of a fiber to absorb energy during straining is measured by the area under the stress—strain curve. Within the proportional limit, ie, the linear region, this property is defined as toughness or work of mpture. For acetate and triacetate the work of mpture is essentially the same at 0.022 N/tex (0.25 gf/den). This is higher than for cotton (0.010 N/tex = 0.113 gf/den), similar to rayon and wool, but less than for nylon (0.076 N/tex = 0.86 gf/den) and silk (0.072 N/tex = 0.81 gf/den) (3). 

Fig. 1. Stress—strain curves A, hard fiber, eg, nylon B, biconstituent nylon—spandex fiber C, mechanical stretch nylon D, spandex fiber E, extruded latex...

Most extmded latex fibers are double covered with hard yams in order to overcome deficiencies of the bare threads such as abrasiveness, color, low power, and lack of dyeabiUty. During covering, the elastic thread is wrapped under stretch which prevents its return to original length when the stretch force is removed thus the fiber operates farther on the stress—strain curve to take advantage of its higher elastic power. Covered mbber fibers are commonly found in narrow fabrics, braids, surgical hosiery, and strip lace. 

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 ... 

Stress—Strain Curve. Other than the necessity for adequate tensile strength to allow processibiUty and adequate finished fabric strength, the performance characteristics of many textile items are governed by properties of fibers measured at relatively low strains (up to 5% extension) and by the change ia these properties as a function of varyiag environmental conditions (48). Thus, the whole stress—strain behavior of fibers from 2ero to ultimate extension should be studied, and various parameters should be selected to identify characteristics that can be related to performance. 

Fig. 4. The stress—strain curves of a wool fiber at different relative humidities.

For a fiber immersed in water, the ratio of the slopes of the stress—strain curve in these three regions is about 100 1 10. Whereas the apparent modulus of the fiber in the preyield region is both time- and water-dependent, the equiUbrium modulus (1.4 GPa) is independent of water content and corresponds to the modulus of the crystalline phase (32). The time-, temperature-, and water-dependence can be attributed to the viscoelastic properties of the matrix phase. 

Fig. 3. Tensile stress—strain curve for (-) reinforced ceramic and ( " ) fiber-reinforced ceramic composite. A represents the point where the matrix...

Figure 3-47 Schematic Stress-Strain Curves for Fibers and Matrix...

Shear-stress-shear-strain curves typical of fiber-reinforced epoxy resins are quite nonlinear, but all other stress-strain curves are essentially linear. Hahn and Tsai [6-48] analyzed lamina behavior with this nonlinear deformation behavior. Hahn [6-49] extended the analysis to laminate behavior. Inelastic effects in micromechanics analyses were examined by Adams [6-50]. Jones and Morgan [6-51] developed an approach to treat nonlinearities in all stress-strain curves for a lamina of a metal-matrix or carbon-carbon composite material. Morgan and Jones extended the lamina analysis to laminate deformation analysis [6-52] and then to buckling of laminated plates [6-53]. 

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 ... 

The curves for 3M XP251S fiberglass-epoxy are shown in Figures C-1 through C-5 [C-1]. Curves are given for both tensile and compressive behavior of the direct stresses. Note that the behavior in the fiber direction is essentially linear in both tension and compression. Transverse to the fiber direction, the behavior is nearly linear in tension, but very nonlinear in compression. The shear stress-strain curve is highly nonlinear. The Poisson s ratios (not shown) are essentially constant with values v.,2 =. 25 and V21 =. 09. 

Even plastics with fairly linear stress-strain curves to failure, for example short-fiber reinforced TSs (RPs), usually display moduli of rupture values that are higher than the tensile strength obtained in uniaxial tests wood behaves much the same. Qualitatively, this can be explained from statistically considering flaws and fractures and the fracture energy available in flexural samples under a constant rate of deflection as compared to tensile samples under the same load conditions. These differences become less as the... 

Crazing. This develops in such amorphous plastics as acrylics, PVCs, PS, and PCs as creep deformation enters the rupture phase. Crazes start sooner under high stress levels. Crazing occurs in crystalline plastics, but in those its onset is not readily visible. It also occurs in most fiber-reinforced plastics, at the time-dependent knee in the stress-strain curve. 

Fig. 6-13 Stress-strain curves of different fiber materials.

FIGURE 12.18 Stress-strain curves of rubber-fiber composites developed for solid rocket motor insulator A, ethylene-propylene-diene monomer (EPDM) rubber-carbon fiber composites B, EPDM mbber-melamine fiber composites C, EPDM mbber-aramid fiber composites and D, EPDM rubber-aramid pulp composites. 1 and 2 stands for unaged and aged composites respectively. Carbon fiber- and melamine fiber-reinforced composites contain resorcinol, hexamine, and silica in the concentrations 10, 6 and 15, respectively and aramid fiber- and aramid pulp-based composites contain resorcinol, hexamine, and silica in the concentrations 5, 3 and 15, respectively. (From Rajeev, R.S., Bhowmick, A.K., De, S.K., and John, B., Internal communication. Rubber Technology Center, Indian Institute of Technology, Kharagpur, India, 2002.)... 

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