Question

A unidirectional composite of a resin is prepared with continuous fibers, wherein the volume fraction of the fiber in the composite is 0.7. Assume that the resin has a modulus of 9 GPa and the fiber has a modulus of 90 GPa. A sample of this composite, possessing a breadth of 4 mm and a thickness of 1 mm, is subjected to a uniaxial tensile test along the direction of the fiber.
Corresponding to a strain of 0.5%, the force applied on the sample is ............ N. {(Round off to the nearest integer)}

Hint:

In unidirectional fiber composites under axial load, the Voigt model (rule of mixtures) gives accurate estimates: \( E_c = V_f E_f + V_m E_m \).

Answer 1

Correct Answer: 1300

First, compute the modulus of the composite (Voigt model, for longitudinal direction): \[ E_c = V_f E_f + (1 - V_f) E_m = 0.7 \cdot 90 + 0.3 \cdot 9 = 63 + 2.7 = 65.7 \, {GPa} \] Convert strain to decimal: \( \varepsilon = 0.5% = 0.005 \) Stress: \[ \sigma = E_c \cdot \varepsilon = 65.7 \cdot 10^3 \cdot 0.005 = 328.5 \, {MPa} \] Area = breadth × thickness = \(4 \times 1 = 4 \, {mm}^2 = 4 \times 10^{-6} \, {m}^2\) Force: \[ F = \sigma \cdot A = 328.5 \times 10^6 \cdot 4 \times 10^{-6} = 1314 \, {N} \]