21-Mat-A4 Deformation Behaviour and Properties of Materials · May 2014
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format. National Exams, May 2014 — 10-Met-A4, Structure of Materials. Three hours, closed book, one approved calculator (Casio or Sharp). Eight questions of 20 marks each; the rubric asks for any five, and only the first five in the answer book are marked. All eight are solved here, because this set is a study resource rather than an exam script. All necessary equations, constants and the error-function table are provided in the exam's own appendix and are used directly below.
Note on the exam title. The printed exam header reads 10-Met-A4, Structure of Materials. Only two of the eight questions (VI and VIII) are substantially deformation/mechanical-properties content; the paper as a whole is a broad introductory materials-science survey — bonding, crystallography, polymers, diffusion, XRD, phase diagrams, dislocations — and is answered as such below.
Check — figure-read values. Question VI.3's stress-strain curve and Question VII's Cu–Ag solvus/liquidus positions are read from the printed figures rather than given numerically. Graphically-read values carry a few percent uncertainty that closed-form calculations do not — this is flagged again at the point of use.
Reference texts. The answers below are keyed to the works normally recommended for this syllabus code:
Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.
Given. $\sigma = \sigma_0\exp(-t/\tau)$; test data $\sigma_0^{test}=7$ MPa $\to$ $6.8$ MPa after $6$ weeks ($42$ days); band must stay $\ge 10$ MPa for a full year ($365$ days).
Find. The initial stress $\sigma_0$ that must be applied when the band is slipped over the rods.
Approach. Use the test data to back out the relaxation time $\tau$, then require $\sigma(365\ \text{days}) = 10$ MPa exactly (the minimum-holding condition) and solve for $\sigma_0$.
Check: $12.9\exp(-365/1449) = 12.9\times0.775=10.0$ MPa — the band is exactly at its 10 MPa floor after one year, so any initial stress at or above 12.9 MPa keeps it tight throughout.
Thermoplastics consist of linear or branched chains held together only by secondary (van der Waals/hydrogen) bonds between chains; heating provides enough thermal energy for chains to slide past one another, so the material softens and can be repeatedly re-melted, reshaped and recycled — the transition is physical and reversible. Thermosets, by contrast, form a covalently cross-linked three-dimensional network during an initial cure (heat or catalyst); once cured, the cross-links are permanent covalent bonds, so the material cannot re-melt — heating beyond the cure temperature degrades (chars/decomposes) the network rather than softening it. Consequently thermosets are generally harder, more dimensionally stable at elevated temperature, and more brittle than thermoplastics, but are not recyclable by remelting the way thermoplastics are.
Given. Orthorhombic PE unit cell $a=0.741$ nm, $b=0.494$ nm, $c=0.255$ nm, containing 2 ethylene ($\text{C}_2\text{H}_4$) repeat units; $A_C=12.01$, $A_H=1.008$ g/mol. Branched-PE sample density $\rho_s=0.925\ \text{g/cm}^3$; totally amorphous density $\rho_a=0.870\ \text{g/cm}^3$.
Find. (a) theoretical (100% crystalline) density $\rho_c$; (b) %crystallinity of the branched sample.
Approach. (a) $\rho_c = nM_{repeat}/(V_cN_A)$ with $n=2$ repeat units/cell. (b) Apply the given crystallinity formula with $\rho_c$ from (a).
| Quantity | Value |
|---|---|
| Relaxation time, $\tau$ | $1449$ days |
| Required initial stress, $\sigma_0$ | $12.9$ MPa |
| PE theoretical density, $\rho_c$ | $0.998$ g/cm$^3$ |
| Branched PE %crystallinity | $46.4\%$ |
