A unidirectional composite has Vf = 0.6, Ef = 230 GPa, and Em = 3 GPa. Using the iso-strain rule, estimate E1.

A unidirectional composite has Vf = 0.6, Ef = 230 GPa, and Em = 3 GPa. Using the iso-strain rule, estimate E1.

• A. 132.0 GPa
• B. 154.0 GPa
• C. 120.0 GPa
• D. 139.2 GPa

Answer: (D)

Under iso-strain, the stiffness along the fiber direction is a volume-fraction-weighted average of the constituents’ moduli because the fiber and matrix experience the same strain when loaded along the fibers. So E1 = Vf Ef + Vm Em. With Vf = 0.6, Ef = 230 GPa, Vm = 0.4, and Em = 3 GPa, E1 = 0.6×230 + 0.4×3 = 138 + 1.2 = 139.2 GPa. This matches the given answer. The other numbers wouldn’t come from this iso-strain calculation; they would require different assumptions or arithmetic, but the correct approach yields 139.2 GPa.

Under iso-strain, the stiffness along the fiber direction is a volume-fraction-weighted average of the constituents’ moduli because the fiber and matrix experience the same strain when loaded along the fibers. So E1 = Vf Ef + Vm Em. With Vf = 0.6, Ef = 230 GPa, Vm = 0.4, and Em = 3 GPa, E1 = 0.6×230 + 0.4×3 = 138 + 1.2 = 139.2 GPa. This matches the given answer. The other numbers wouldn’t come from this iso-strain calculation; they would require different assumptions or arithmetic, but the correct approach yields 139.2 GPa.