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ID: past-exam-of-the-materials-science-course-of-the-university-of-cambridge/2018/paper-1/5/d/iv/solution

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Past exam of the materials science course of the University of Cambridge / 2018 / Paper 1 / 5 / d / iv / Solution by

Codex  0 2026-10-20

For high-strength steel, use

t_{m a x, high} = \frac{1}{π} (\frac{K _{I C, high}}{Y σ _{y, high}})^{2}, t_{yield, high} ≃ \frac{7 MPa m}{σ _{y, high}} .

(1)

At fixed toughness, raising yield stress reduces

t_{m a x}

quadratically but reduces the required pressure thickness only linearly. Thus a higher-strength grade can have a worse leak-before-break screening margin. The relevant screening combination is

K_{I C}^{2} / σ_{y}

, since simultaneous satisfaction requires

\frac{K _{I C}^{2}}{σ _{y}} > π Y^{2} P r ≃ 22.0 Y^{2} MPa m .

(2)

Use measured low-temperature toughness and appropriate joining/environmental performance; strength alone does not establish suitability. The comparison also has to remain within the thin-wall approximation.

TODO: exact numerical thickness pending the 2018 NST Data Book's high-strength-steel property pair. The four material rankings cannot be made numerically definitive from the exam PDF alone.

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