Young s modulus fiber

The mechanical properties of particulate-filled composites are generally isotropic that is, they are invariant with direction provided there is a good dispersion of the fillers. On the other hand, fiber-filled composites are typically anisotropic. In general, fibers are usually oriented either uniaxially or randomly in a plane. In this case, the composite has maximum modulus and strength values in the direction of fiber orientation. For uniaxially oriented fibers. Young s modulus, measured in the orientation direction (longitudinal modulus, El) is given by Equation 9.1 ... 

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. 

Eor reinforcement, room temperature tensile strength and Young s modulus (stress—strain ratio) are both important. Typical values for refractory fibers are shown in Table 2. 

Fig. 1. Specific strength and Young s modulus of various engineering materials where CF = carbon fiber HM/UHM = high modulus/ultrahigh modulus ...

Fig. 2. Young s modulus corrected for porosity as a function of preferred orientation curve is based on theoretical model where = rayon-based fibers Q — PAN-based fibers and A = pitch-based fibers (2). To convert GPa to psi, multiply by 145,000.

Sihcon carbide fibers exhibit high temperature stabiUty and, therefore, find use as reinforcements in certain metal matrix composites (24). SiUcon fibers have also been considered for use with high temperature polymeric matrices, such as phenoHc resins, capable of operating at temperatures up to 300°C. Sihcon carbide fibers can be made in a number of ways, for example, by vapor deposition on carbon fibers. The fibers manufactured in this way have large diameters (up to 150 P-m), and relatively high Young s modulus and tensile strength, typically as much as 430 GPa (6.2 x 10 psi) and 3.5 GPa (507,500 psi), respectively (24,34) (see Refractory fibers). 

E, = Young s modulus for an isotropic fiber v, = Poisson s ratio for an isotropic fiber... 

The apparent Young s modulus, E2, of the composite material in the direction transverse to the fibers is considered next. In the mechanics of materials approach, the same transverse stress, 02, is assumed to be applied to both the fiber and the matrix as in Figure 3-9. That is, equilibrium of adjacent elements in the composite material (fibers and matrix) must occur (certainly plausible). However, we cannot make any plausible approximation or assumption about the strains in the fiber and in the matrix in the 2-direction. 

Obviously, the assumptions involved in the foregoing derivation are not entirely consistent. A transverse strain mismatch exists at the boundary between the fiber and the matrix by virtue of Equation (3.8). Moreover, the transverse stresses in the fiber and in the matrix are not likely to be the same because v, is not equal to Instead, a complete match of displacements across the boundary between the fiber and the matrix would constitute a rigorous solution for the apparent transverse Young s modulus. Such a solution can be found only by use of the theory of elasticity. The seriousness of such inconsistencies can be determined only by comparison with experimental results. 

Tsai conducted experiments to measure the various moduli of glass-fiber-epoxy-resin composite materials [3-1]. The glass fibers and epoxy resin had a Young s modulus and Poisson s ratio of 10.6 x 10 psi (73 GPa) and. 22 and. 5 x 10 psi (3.5 GPa) and. 35, respectively. 

Dow and Rosen s results are plotted in another form, composite material strain at buckling versus fiber-volume fraction, in Figure 3-62. These results are Equation (3.137) for two values of the ratio of fiber Young s moduius to matrix shear modulus (Ef/Gm) at a matrix Poisson s ratio of. 25. As in the previous form of Dow and Rosen s results, the shear mode governs the composite material behavior for a wide range of fiber-volume fractions. Moreover, note that a factor of 2 change in the ratio Ef/G causes a factor of 2 change in the maximum composite material compressive strain. Thus, the importance of the matrix shear modulus reduction due to inelastic deformation is quite evident. 

Composite materials typically have a low matrix Young s modulus in comparison to the fiber modulus and even in comparison to the overall laminae moduli. Because the matrix material is the bonding agent between laminae, the shearing effect on the entire laminate is built up by summation of the contributions of each interlaminar zone of matrix material. This summation effect cannot be ignored because laminates can have 100 or more layersi The point is that the composite material shear moduli and G are much lower relative to the direct modulus than for isotropic materials. Thus, the effect of transverse shearing stresses. 

This model was applied by Mukherjee et al. [20] for various natural fibers. By considering diverse mechanisms of deformation they arrived at different calculation possibilities for the stiffness of the fiber. According to Eq. (1), the calculation of Young s modulus of the fibers is based on an isochoric deformation. This equation sufficiently describes the behavior for small angles of fibrils (<45°) [19]. 

A springlike deformation of the fibrils overweighs at angles >45°. That means the length of the fibrils remains constant and Young s modulus of the fibers can be given by ... 

Table 12 Tensile Strength and Young s Modulus of Sisal, Flax, and Glass Fiber MTs with a Fiber Content of 40% (weight) [60]...

Sisal, flax, and glass fiber MTs can be classified by their mechanical properties, tensile strength, and Young s modulus (Table 12). 

Tests by Roe et al. [63] with unidirectional jute fiber-reinforced UP resins show a linear relationship (analogous to the linear mixing rule) between the volume content of fiber and Young s modulus and tensile strength of the composite over a range of fiber content of 0-60%. Similar results are attained for the work of fracture and for the interlaminate shear strength (Fig. 20). Chawla et al. [64] found similar results for the flexural properties of jute fiber-UP composites. 

Fiber content (wt%) Tensile strength (MPa) Young s modulus (MPa) Elongation at break (%) Tear strength Hardness (shore-D) (kN/m) Tension set (%) Density (g/cm )... 

Since a core is required, it is not possible to produce fibers with a small diameter and present production diameters are in the range of 100-150 pm, compared to an average of 10-20 pm for solgel derived fibers. Being very stiff with a high Young s modulus... 

The decrease in the fiber diameter of fabric resulted in a decrease in porosity and pore size, but an increase in fiber density and mechanical strength. The microfiber fabric made of PCLA (1 1 mole ratio) was elastomeric with a low Young s modulus and an almost linear stress-strain relationship under the maximal stain (500%) in this measurement. 

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