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A composite material consists of parallel fibers of Young’s modulus E_{f} in a matrix of Young’s modulus E_{m}. The volume fraction of fibers is V_{f}. Derive an expression for E_{c}, Young’s modulus of the composite along the direction of the fibers, in terms of E_{f}, E_{m} and V_{f}. Obtain an analogous expression for the density of the composite, r_{c}. Using material parameters given in the next table, find r_{c} and E_{c} for the following composites: (a) carbon fiber–epoxy resin (V_{f }= 0.5), (b) glass fiber–polyester resin (V_{f} = 0.5), (c) steel–concrete (V_{f} = 0.02).
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