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55 a schematic illustration of the stress strain

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Unformatted text preview: on, and loading direction at an angle to the x axis. 50 FIGURE 14.5–4 The variation of elastic modulus as a function of orientation with respect to the fiber axis for epoxyglass composite (Vf 0.6). Ecl = 43.2 GPa Composite elastic modulus (GPa) 40 30 20 10 Ect = 7.05 GPa 0 0 30 60 90 θ The achievable tensile strength of composites loaded under isostrain conditions can be estimated using a variation of equation 14.5–6 as follows: cu fu Vf m Vm (14.5–14) where cu is the ultimate strength of the composite, f u is the ultimate strength of the fiber, and m is the flow stress of the matrix at a strain corresponding to the failure strain of the fiber. It is assumed that once widespread failure occurs in the fibers, the matrix will be unable to withstand the increased stress and the composite will fail. This requires that the volume fraction of fiber be larger than the following critical value Vcrit : mu m fu Vcrit m (14.5–15) | v v where mu is the ultimate strength of the matrix. We can see from this equation that Vcrit is higher if the strain hardening capability of the matrix material is high and the strain to fracture in the fiber is low. The important quantities are shown graphically in Figure 14.5–5. Equation 14.5–14 yields composite strength values that are often not as accurate as predictions of the modulus. A number of factors are responsible for this behavior. As | e-Text Main Menu | Textbook Table of Contents pg600 [V] G2 7-27060 / IRWIN / Schaffer Part III 13.01.98 plm QC2 rps MP Properties σ σ fu σ mu σ'm ε fu ε mu ε FIGURE 14.5–5 A schematic illustration of the stress-strain curves for a typical fiber and matrix showing the ultimate strength of the fiber ( fu ), the ultimate strength of the matrix ( mu ), and the strength of the matrix at the strain corresponding to the failure strain of the fibers ( m). discussed in Chapter 9, the microstructure of the matrix has a strong influence on its tensile properties. The presence of fibers can modify the microstructure of the surrounding matrix because of residual stresses and interdiffusion between the matrix and fiber materials. Microstructure is also affected by processing temperatures and conditions of the composite. Thus, the tensile properties of the matrix in a composite can be substantially different from the tensile properties of the matrix material by itself. In contrast, the elastic modulus is related to atomic bonding energies that are not significantly affected by microstructural changes. Therefore, the elastic modulus remains unaffected by processing. ....................................................................................................................................... EXAMPLE 14.5–2 An aluminum-matrix composite is to be designed with SiC fibers. Estimate the critical fiber volume fraction needed for strengthening. Assume that the fiber fractures at the strain at which the matrix begins to yield. The following data are provided: the yield strength of the matrix is 400 MPa, the ultimate strength of the matrix is 482 MPa, and the ...
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