21-Mat-B7 Structure and Properties of Polymers · May 2016
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format. National Exams, May 2016 — 10-Met-B7, Physical Metallurgy of Non-Ferrous Metals and Alloys. Three hours, closed book, approved Casio/Sharp calculator only. Eight questions of 20 marks each; the rubric states that any five questions constitute a complete paper (100 marks total) and that only the first five appearing in the answer book are marked. All eight are answered here, because this set is a study resource rather than an exam script. The rubric explicitly notes that most questions require an essay-format answer and that clarity and organization are marked, so the answers below are written as structured prose rather than as note form.
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.
Alpha stabilizers (e.g. Al, O, N, C) raise the $\beta$-transus temperature and expand the hexagonal $\alpha$ phase field to higher temperature. Beta stabilizers lower the $\beta$-transus and expand the body-centred-cubic $\beta$ field; they fall into two sub-types — beta-isomorphous elements (V, Mo, Nb, Ta) that are completely miscible with $\beta$-Ti and simply depress the transus, and beta-eutectoid elements (Fe, Cr, Ni, Cu, Mn, Si) that depress the transus but also form a eutectoid reaction, potentially precipitating an intermetallic compound on slow cooling or aging. Neutral elements (Zr, Sn, Hf) are essentially isomorphous in both $\alpha$ and $\beta$ and have little effect on the transus temperature, but are still used for solid-solution strengthening in both phases.
The $\alpha$ phase is hexagonal close-packed (HCP), which offers relatively few independent, easily activated slip systems at room temperature (basal and prismatic $\langle a\rangle$ slip; the additional $\langle c+a\rangle$ pyramidal slip needed to accommodate strain along the c-axis has a much higher critical resolved shear stress), so an all-$\alpha$ alloy has limited room-temperature ductility and formability and tends toward twinning to accommodate c-axis strain. The $\beta$ phase is body-centred cubic (BCC), which has a much larger number of available slip systems ({110}, {112}, {123} planes each with $\langle 111\rangle$ slip directions) that are far more easily activated at room temperature. A beta-stabilized (or metastable-beta) titanium alloy therefore has substantially more room-temperature ductility and is far more amenable to cold rolling, forming and deep drawing than an alpha or near-alpha alloy, which typically must be hot- or warm-worked.
Aluminum is a strong, effective $\alpha$-stabilizer and solid-solution strengthener, but above an aluminum-equivalent content of roughly 6–9 weight percent (the "aluminum equivalent" rule of thumb, Al⊂eq⊂ = %Al + %Sn/3 + %Zr/6 + 10×(%O + %C + 2%N), kept below about 9), the ordered DO⊂19⊂ intermetallic $Ti_3Al$ ($\alpha_2$) phase becomes thermodynamically stable and precipitates within the $\alpha$ matrix. Because $\alpha_2$ is an ordered, brittle phase, its precipitation severely degrades ductility and fracture toughness and increases susceptibility to sustained-load and hot-salt cracking, even though it does provide some ordered-phase (superlattice) hardening. The roughly 8 percent limit is therefore not a solubility limit in the usual sense but an embrittlement threshold: alloy designers stay below it specifically to avoid forming $\alpha_2$, which is why essentially every commercial $\alpha$/near-$\alpha$/$\alpha$-$\beta$ titanium alloy (including Ti–6Al–4V) keeps its aluminum content at or below this value.
An equiaxed $\alpha$ microstructure presents a crack with relatively open, unobstructed grains to propagate through, along paths that stay comparatively straight and short. A transformed (acicular, Widmanstätten or "basketweave") microstructure, produced by cooling from the $\beta$ field, consists instead of interlocking colonies of fine $\alpha$ laths in a matrix of retained/transformed $\beta$, oriented in a limited number of crystallographic variants that criss-cross one another. A propagating crack in this structure is repeatedly deflected and forced to change direction as it crosses colony and lath boundaries with different orientations, which both lengthens the true crack path relative to its projected length and dissipates additional energy at each deflection (crack-path tortuosity and local mixed-mode branching); the fine lath boundaries also interrupt slip-band/shear-localization transmission across the structure, further raising the resistance to crack advance. The net effect is a measurably higher fracture toughness for a transformed or partly transformed structure than for an equiaxed structure of the same alloy and similar strength level, at some cost in ductility and fatigue-crack-initiation resistance, which is why forging and heat-treatment practice is chosen deliberately (mill-annealed/equiaxed vs. beta-annealed/transformed) to suit whichever property — ductility or toughness — governs the application.
