Composites elastic behavior

Fiber-reinforced composite materials such as boron-epoxy and graphite-epoxy are usually treated as linear elastic materials because the essentially linear elastic fibers provide the majority of the strength and stiffness. Refinement of that approximation requires consideration of some form of plasticity, viscoelasticity, or both (viscoplasticity). Very little work has been done to implement those models or idealizations of composite material behavior in structural applications. 

In Section 2.2, the stress-strain relations (generalized Hooke s law) for anisotropic and orthotropic as well as isotropic materials are discussed. These relations have two commonly accepted manners of expression compliances and stiffnesses as coefficients (elastic constants) of the stress-strain relations. The most attractive form of the stress-strain relations for orthotropic materials involves the engineering constants described in Section 2.3. The engineering constants are particularly helpful in describing composite material behavior because they are defined by the use of very obvious and simple physical measurements. Restrictions in the form of bounds are derived for the elastic constants in Section 2.4. These restrictions are useful in understanding the unusual behavior of composite materials relative to conventional isotropic materials. Attention is focused in Section 2.5 on stress-strain relations for an orthotropic material under plane stress conditions, the most common use of a composite lamina. These stress-strain relations are transformed in Section 2.6 to coordinate systems that are not aligned with the principal material... 

Hong T. Hahn and Stephen W. Tsai, Nonlinear Elastic Behavior of Unidirectional Composite Laminae. Journal of Composite Materials, January 1973, pp. 102-118. 

N. J. Pagano and Sharon J. Hatfield, Elastic Behavior of Multilayered Bidirectional Composites, AIAA Journal, July 1972, pp. 931-933. 

Composite 1 with the higher fiber/matrix bonding shows a linear-elastic behavior up to = 160 MPa, which is clearly higher than that of composite 2. The following nonlinear region is small, resulting in an elongation at fracture of 0.32 %. 

Ceramic-matrix fiber composites, 26 775 Ceramics mechanical properties, 5 613-638 cyclic fatigue, 5 633-634 elastic behavior, 5 613-615 fracture analysis, 5 634-635 fracture toughness, 5 619-623 hardness, 5 626-628 impact and erosion, 5 630 plasticity, 5 623-626 strength, 5 615-619 subcritical crack growth, 5 628—630 thermal stress and thermal shock, 5 632-633... 

The dispersion of SiC-coated MWCNTs increases the microhardness and fracture toughness of SiC. The SiC coating on MWCNTs at 1150°C is effective in improving the weak adhesion between MWCNTs and the SiC matrix. SiC-coated MWCNT/SiC composites show elastic behavior due to the crack-bridging effect of MWCNTs. 

Although analytical models are very effective tools for understanding how changes in the elastic and creep behavior of the constituents of a composite influence overall creep behavior, one must not blindly assume that accurate predictions of composite creep behavior can be obtained based upon creep experiments conducted on the individual constituents. For instance, even if a monolithic ceramic and a composite were processed under identical conditions, the fracture and creep behavior of the monolithic ceramic may be... 

Consider a specimen of length Ls containing a very large number of wholly intact fibers. A stress a is suddenly applied to the specimen parallel to the fibers. The temperature has already been raised to the creep level and is now held fixed. Upon first application of the load, some of the fibers will break. The sudden application of the load means that the initial response is elastic. This elastic behavior has been modeled by Curtin,16 among others, but details will not be given here. If the applied stress exceeds the ultimate strength of the composite in this elastic mode of response, then the composite will fail and long-term creep is obviously not an issue. However, it will be assumed that... 

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 elastic behavior of NiAl has been studied repeatedly and the elastic moduli have been determined experimentally for polycrystals and single crystals as a function of composition and temperature (Wasilewski, 1966 Rusovic and Warlimont, 1977, 1979 Harmouche and Wolfenden, 1985, 1987). The elastic behavior has also been studied theoretically by quantum-mechanical, ab initio calculations, and the resulting elastic moduli are in close agreement with the experimental values (Yoo et al. 1990 Fu and Yoo, 1992b Freeman etal., 1992 Yoo and Fu, 1993). 

The Young s modulus of polycrystalline NiAl with a stoichiometric composition is about 235 GPa at room temperature (Harmouche and Wolfenden, 1987). The elastic moduli are functions of the composition, and the Young s modulus reaches a maximum of slightly more than 235 GPa, not at the stoichiometric composition as is expected, but at about 48 at.% Al which may be related to the difference in the defect character on both sides of stoichiometry. The effect of excess vacancies, which are produced by quenching from high temperatures, on the elastic behavior was studied... 

The major or exclusive constituent of yellow brass is P brass which is the intermetallic CuZn phase. It exhibits an A2 structure at high temperatures and a B2 structure at low temperatures, i.e. there is an order-disorder transition at about 460°C (Flinn, 1986 Massalski et al., 1990). Its range of homogeneity - between about 40 and 50 at.% Zn at higher temperatures - depends sensitively on temperature and does not include the stoichiometric 50 at.% composition at intermediate temperatures. This order-disorder transition has been used to study the effect of ordering, e.g. on elastic behavior (Westbrook, 1960 a Quillet and Le Roux, 1967), diffusion (Qirifalco, 1964 Hagel, 1967 Wever et al., 1989 Wever, 1992), recrystallization (Cahn, 1991), and hardness (Westbrook, 1960 a). 

Thus far four composites listed in Table I have been studied. NbTi/Cu is discussed briefly here. From its microstructure and manufacture, a rectangular cross-section bar, it was assumed that this composite has orthorhombic (orthotropic) symmetry in its physical properties. Materials with this symmetry have nine independent elastic constants. While deviations from elastic behavior were small, nine independent elastic constants were verified. Four specimens were prepared (Fig. 16) and 18 ultrasonic wave velocities were determined by propagating differently polarized waves in six directions, (100) and (110). An example cooling run is shown in Fig. 17 for E33, Young s modulus along the filament axis. These data typify the composites studies a wavy, irregular modulus/temperature curve. 

Moving to a larger scale, let us now look at the influence of microstructure on elastic behavior. As indicated in the previous section, the elastic constants are a fundamental property of single crystals through the geometry and stiffness of the atomic bonds. Thus, one may expect elastic behavior to be controlled simply by the choice of material. By using composite materials, however, one can control the final set of elastic properties with some precision, i.e., by mixing phases with different elastic constants. Clearly, it is useful to be able to predict the elastic constants of a composite from those of its constituents. This has been accomplished for many types of composite microstructures. For this section, however, the emphasis will be on (elastically) isotropic composites, i.e., composites contain-... 

Figure 3.9 Composite sphere assemblage used by Hashin (1983) for exact solutions to the elastic behavior of statistically isotropic composites.

Many composites are elastically anisotropic and, thus, more than the two elastic constants are needed to describe their elastic behavior. This is a very large topic and, for this text, just some of the basic ideas that apply to unidirectional fiber composites will be discussed. Consider a two-phase material, with the two geometries shown in Fig. 3.15, being subjected to a uniaxial tensile stress. For the structure in Fig. 3.15(a), the two phases are subjected to equal strain whereas. 

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