A hybrid carbon-aramid/epoxy composite is made by randomly mixing continuous aligned fibers of the same diameter, so that there are two carbon fibers for each aramid fiber. The fibers are assumed to be arranged in a square array with the closest possible packing. The stress-strain curves for longitudinal tensile loading of fiber and matrix materials are shown in Figure 3.10. Determine the composite longitudinal modulus \(E_{1}\).

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Stress (GPa) 0.72 0.1 2.8 2.1 Carbon fiber Aramid fiber Epoxy matrix 0.0164 0.0054 0.021 0.033 Strain FIGURE 3.10 Stress-strain curves for fiber and matrix materials in a hybrid composite.