Stress-strain curves composites

The mechanical piopeities of stmctuial foams and thek variation with polymer composition and density has been reviewed (103). The variation of stmctural foam mechanical properties with density as a function of polymer properties is extracted from stress—strain curves and, owkig to possible anisotropy of the foam, must be considered apparent data. These relations can provide valuable guidance toward arriving at an optimum stmctural foam, however. 

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

Fig. 25.2. The stress-strain curve of o continuous fibre composite (heavy line), showing how it relates to those of the fibres and the matrix (thin lines). At the peak the fibres are on the point of failing.

Many fibrous composites are made of strong, brittle fibres in a more ductile polymeric matrix. Then the stress-strain curve looks like the heavy line in Fig. 25.2. The figure largely explains itself. The stress-strain curve is linear, with slope E (eqn. 25.1) until the matrix yields. From there on, most of the extra load is carried by the fibres which continue to stretch elastically until they fracture. When they do, the stress drops to the yield strength of the matrix (though not as sharply as the figure shows because the fibres do not all break at once). When the matrix fractures, the composite fails completely. 

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]. 

Let s address the issue of nonlinear material behavior, i.e., nonlinear stress-strain behavior. Where does this nonlinear material behavior come from Generally, any of the matrix-dominated properties will exhibit some degree of material nonlinearity because a matrix material is generally a plastic material, such as a resin or even a metal in a metal-matrix composite. For example, in a boron-aluminum composite material, recognize that the aluminum matrix is a metal with an inherently nonlinear stress-strain curve. Thus, the matrix-dominated properties, 3 and Gj2i generally have some level of nonlinear stress-strain curve. 

However, not all properties are improved by filler. One notable feature of the mechanical behaviour of filled elastomers is the phenomenon of stresssoftening. This manifests itself as a loss of stiffness when the composite material is stretched and then unloaded. In a regime of repeated loading and unloading, it is found that part of the second stress-strain curve falls below the original curve (see Figure 7.13). This is the direct opposite of what happens to metals, and the underlying reasons for it are not yet fully understood. 

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.)... 

FIGURE 22.8 Payne effect (left) and stress-strain curves right) of solution-based styrene-butadiene rubber (S-SBR) composites with fixed amounts of carbon black N220 and graphitized black N220g, as indicated. (From Kluppel, M. and Heinrich, G., Kautschuk, Gummi, Kunststoffe, 58, 217, 2005. With permission.)... 

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

Fig. 2 The typical tensile-stress/strain curves of the [0/90] plain weave C/SiC composites up to high temperatures... 

Typical tension stress-strain curves of baseline and irradiated unidirectional T300/934 composites tested in [0] and [90] orientations at three different temperatures (121 are shown in Figures 11 and 12. Irradiation had essentially no effect on the fiber-dominated tensile modulus of the [0] specimen and caused only a small (10-15%) reduction in strength at the low and elevated temperatures. For the matrix-dominated [90] laminates, irradiation caused a very substantial decrease in strength at three test temperatures (-38% at -157°C, -26% R.T., -13% 121°C). Irradiation increased the modulus at -157°C and R.T. (10 - 15%), but lowered it at 121°C (-15%). These results are consistent with results obtained on the neat resin specimens discussed above. 

Figure 11. Temperature-dependent stress—strain curves for [0] composite laminates. (Reproduced from reference 12.)...

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 5.112 Idealized stress-strain curve for a tough ceramic-matrix composite. Reprinted, by permission, from R. W. Davidge and 1. J. R. Davies, in Mechanical Testing of Engineering Ceramics at High Temperatures, B. F. Dyson, R. D. Lohr, and R. Morrell, eds., p. 251. Copyright 1989 by Elsevier Science Publishers, Ltd.

In cross-ply laminates, the stress-strain behavior is slightly nonlinear, as illustrated in Figure 5.123. The stress-strain behavior of a unidirectional lamina along the fiber axis is shown in the top curve, while the stress-strain behavior for transverse loading is illustrated in the bottom curve. The stress-strain curve of the cross-ply composite, in the middle, exhibits a knee, indicated by strength ajc, which corresponds to the rupture of the fibers in the 90° ply. The 0° ply then bears the load, until it too ruptures at a composite fracture strength of ct/. 

The stress-strain curves for cortical bones at various strain rates are shown in Figure 5.130. The mechanical behavior is as expected from a composite of linear elastic ceramic reinforcement (HA) and a compliant, ductile polymer matrix (collagen). In fact, the tensile modulus values for bone can be modeled to within a factor of two by a rule-of-mixtures calculation on the basis of a 0.5 volume fraction HA-reinforced... 

Figure 9 is a schematic of a uniaxial stress-strain curve. The gradually decreasing slope and plateau region followed by diminishing stress just before rupture are typical features of the composite propellant stress-strain curve. This behavior is readily understood when one considers the... 

A combination of an energy criterion and the failure envelope has been proposed by Darwell, Parker, and Leeming (22) for various doublebase propellants. Total work to failure was taken from the area beneath the stress-strain curve, but the biaxial failure envelope deviated from uniaxial behavior depending on the particular propellant formulation. Jones and Knauss (46) have similarly shown the dependence of failure properties on the stress state of composite rubber-based propellants. 

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. 46 Stress-strain curves for the pure chloroprene rubber (CR gum) and PTFE-based chloro-prene composites...

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...

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