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ID: past-exam-of-the-materials-science-course-of-the-university-of-cambridge/2017/paper-1/5/c/solution

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Past exam of the materials science course of the University of Cambridge / 2017 / Paper 1 / 5 / c / Solution by

Codex  0 2026-10-20

Let

V_{c}

be the carbon-fibre volume fraction of the whole composite. Then

V_{m} = 0.4

and

V_{g} = 0.6 - V_{c}

. Under the same longitudinal rule of mixtures,

E = 3 (0.4) + 75 (0.6 - V_{c}) + 220 V_{c} = 46.2 + 145 V_{c} GPa .

Setting

E = 71.94 GPa

gives

V_{c} = 0.1775, V_{g} = 0.4225, V_{m} = 0.4000.

Thus carbon occupies 17.8% of the complete composite, or about

29.6%

of its total fibre volume. The resulting

60%

total fibre fraction is much more plausible than the glass-only estimate. This remains an ideal stiffness calculation requiring aligned, effectively loaded fibres; strength and fatigue checks are separate.

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