In order to determine the tensile Young's modulus and tensile strength of carbon fibers, a tensile test of a resin-impregnated carbon/epoxy yarn having a fiber volume fraction of 0.6 is conducted. A separate tensile test is conducted on the neat resin epoxy matrix material, and both stress-strain curves are shown in Figure 10.34. Using these two stress-strain curves and micromechanics models, determine the fiber tensile Young's modulus, \(E_{\mathrm{f} 1}\), and the fiber tensile strength,\(s_{f 1}^{(+)}\).

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FIGURE 10.34 Stress (GPa) 1.448 X 0.1 0.0362 X = failure Resin-impregnated carbon/epoxy yarn X 0.0105 0.029 Strain