Stress-strain curve for fibers

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

The numerical simulation method of Termonia [67-72] was reviewed in Section 20.C.1 since it can be used in calculating the elastic moduli of composites. As described in that discussion, this method actually allows the calculation of complete stress-strain curves for fiber-reinforced composites. It must be emphasized that the ability of this method to simulate the mechanical properties of composites under large deformation by using a reasonable physical model is of far greater importance and uniqueness than its ability to model the elastic behavior. 

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

Fig. 9. Stress-strain curves for 2D-C/SiC composites with different fiber/matrix bonding... 

Figure 13.6 (a) Elongation as a function of wind-up speed for partially oriented yarn, (b-d) Stress-strain curves of fibers of PET blends with 3% copolyester of 1,4-phenyleneterephthalate and p-oxybenzoate (CLOTH) and 3% copolymer of 6-oxy-2-naphthalene and p-oxybenzoate (CO), spun at 3500, 4000 and 4500 m/min (1) PET control (2) 3 % CLOTH (3) 3 % CO the loci of the theoretical extensions of the PET control are shown as dashed curves [17]. From Orientation suppression in fibers spun from melt blends, Brody, H., J. Appl. Polym. Sci., 31, 2753 (1986), copyright (1986 John Wiley Sons, Inc.). Reprinted by permission of John Wiley Sons, Inc. 

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.

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 6.1. Stress-strain curve for aorta. Tensile stress-strain curve for human thoracic aorta in the circumferential direction obtained at a strain rate of 50% per minute. At strains less than 0.2, the elastic fibers dominate the behavior, whereas above 0.2, alignment of collagen fibers occurs. (Adapted from Silver, 1987.)...

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.

Figure 6.6. Stress-strain curve for skin. Stress-strain curves for wet back skin from rat at strain rates of 10 and 50% per minute. The low modulus region involves the alignment of collagen fibers along the stress direction that are directly stretched in the linear region. Disintegration of fibrils and failure occurs at the end of the linear region. (Adapted from Silver, 1987.)...

Figure 7.4. Total, elastic, and viscous stress-strain curves for collagen fibers from rat tail tendon. The total stress-strain curve (open boxes) was obtained by collecting all the initial, instantaneous, force measurements at increasing time intervals and then dividing by the initial cross-sectional area. The elastic stress-strain curve (closed diamonds) was obtained by collecting all the force measurements at equilibrium and then dividing by the initial cross-sectional area. The viscous component curve (closed squares) was obtained as the difference between the total and the elastic stresses. Error bars represent one standard deviation of the mean.

Determination of the Elastic and Viscous Stress-Strain Curves for Model Collagen Fiber Systems... 

Figure 7.6. Effective mechanical fibril length versus fibril segment length. Plot of effective fibril length in pm determined from viscous stress-strain curves for rat tail tendon and self-assembled collagen fibers versus fibril segment length. The correlation coefficient (R2) for the line shown is 0.944 (see Silver et al., 2003).

Figure 7.7. Total, elastic, and viscous stress-strain curves for uncrosslinked self-assembled type I collagen fibers.Total (open squares), elastic (filled diamonds), and viscous (filled squares) stress-strain curves for self-assembled uncrosslinked collagen fibers obtained from incremental stress-strain measurements at a strain rate of 10%/min. The fibers were tested immediately after manufacture and were not aged at room temperature. Error bars represent one standard deviation of the mean value for total and viscous stress components. Standard deviations for the elastic stress components are similar to those shown for the total stress but are omitted to present a clearer plot. The straight line for the elastic stress-strain curve closely overlaps the line for the viscous stress-strain curve. Note that the viscous stress-strain curve is above the elastic curve suggesting that viscous sliding is the predominant energy absorbing mechanism for uncrosslinked collagen fibers.

Fig. 7. Comparison of stress-strain curves for carbon-fiber-reinforced epoxy composites of different thermal histories. Error rectangles were drawn to indicate a 95% confidence level for both stress and strain...

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. 

Given Eqn. (57), the elastic stress-strain curve for a fiber bundle is... 

---