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

For the aluminium alloy, write $K_{IC,\mathrm{Al}}$ and ${\sigma }_{y,\mathrm{Al}}$ for the appropriate data-book properties at the relevant material state and temperature. The yield-limited screening bounds from part(c), with $r\simeq 0.70\mathrm{m}$, areFor $K$ in $\mathrm{MPa}\sqrt{\mathrm{m}}$ and ${\sigma }_y$ in $\mathrm{MPa}$, the numerical substitutions are $t_{\max }(\mathrm{mm})=318.31[K/(Y{\sigma }_y){]}^2$ and $t_{\mathrm{yield}}(\mathrm{mm})=7000/{\sigma }_y$.

A high-strength alloy's large yield stress can require a small allowable leak-before-break thickness even when its minimum pressure thickness is modest. FCC structure generally favors low-temperature plasticity, but does not by itself establish the alloy's fracture toughness, weld performance, corrosion behavior or fatigue resistance.

TODO: exact numerical thickness pending the identified 2018 NST Data Book values and alloy condition. The accessible Engineering2011/revised2019 book is not confirmed as the supplied edition; generic aluminium property ranges are not substituted as if they were the exam's values.

For Ti–6Al–4V, use its own fracture toughness and yield stress inThe same unit-conversion formulas from part(i) apply. A feasible yield-limited screening interval requires $t_{\mathrm{yield}}<t_{\max }$, using consistent crack geometry and low-temperature properties.

High specific strength and corrosion resistance can be attractive, but cost, fabrication, joining and toughness must also be assessed. The label HCP is not a sufficient rule that every titanium alloy has the same sharp ductile-to-brittle transition as ferritic steel; actual low-temperature alloy and microstructural data are needed.

TODO: exact numerical thickness pending the 2018 NST Data Book's Ti–6Al–4V property pair. No historical value or material-specific Arctic toughness is invented.

For mild steel, the corresponding bounds areA relatively low yield stress increases the thickness needed to carry pressure, but a favorable toughness-to-yield-strength ratio can give a much larger leak-before-break upper bound. This tradeoff often makes a tough structural steel more attractive than choosing the highest strength alone.

For Arctic service, the ductile-to-brittle transition is crucial. A room-temperature toughness cannot be assumed to persist below the transition, and welding, constraint and loading rate affect the comparison. A suitably qualified low-temperature steel can be practical; the word mild alone does not establish that qualification.

TODO: exact numerical thickness pending the 2018 NST Data Book values. The temperature and state of the tabulated toughness must also be identified before making a numerical service claim.

For high-strength steel, useAt fixed toughness, raising yield stress reduces $t_{\max }$ 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 $K_{IC}^2/{\sigma }_y$, since simultaneous satisfaction requiresUse 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.