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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  eText Main Menu  Textbook Table of Contents pg600 [V] G2 727060 / 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 stressstrain 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 aluminummatrix 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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 Spring '10
 sowell
 Physics, The Crucible

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