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.
Recrystallization is a nucleation-and-growth process driven by the stored strain energy of the deformed structure, and its onset temperature for a fixed anneal time is not a fixed material constant — it can be moved by changing either the driving force or the resistance to boundary migration.
Method 1 — increase the prior cold work. The driving pressure for recrystallization is the stored energy of the dislocation substructure left by deformation, which increases with the amount of prior strain. A more heavily cold-worked can body carries a higher dislocation density and a finer, more misoriented cell/subgrain structure, both of which raise the driving force and increase the density of potential nucleation sites (at grain boundaries, shear bands and second-phase particles). Because the process is thermally activated, a larger driving force lets recrystallization go to completion at a lower temperature for the same soak time — roughly, $T_{rex}$ falls as the percent cold work rises, with the effect saturating above about 60–80 percent reduction. Redesigning the draw-and-wall-ironing schedule to take more reduction per pass before the anneal step is therefore a direct lever on the required furnace temperature.
Method 2 — reduce the solute (impurity) content. Even small amounts of dissolved solute (Fe, Si, Mn, Cu at the tens-to-hundreds of ppm level typical of can-body alloy 3104) segregate to and drag on migrating grain boundaries, raising the activation energy for boundary motion and pushing $T_{rex}$ up (solute or Zener-Lucke drag). Specifying a higher-purity ingot, or an alloy with fewer/lower minor alloying additions, removes solute atoms from the boundary and lets it move at a lower temperature. In practice the two methods are combined: the can stock is taken to a high total cold-work fraction before the final in-line anneal, using an alloy composition chosen to minimise unnecessary solute drag, which together allow the anneal to run at a lower furnace set-point (and hence lower energy input) while still recrystallizing fully within the line speed available.
Factor 1 — second-phase particle (Zener) pinning. Dispersoid particles left in the microstructure — Al-Mn/Al-Fe-Mn constituents and dispersoids in can-stock and structural sheet alloys — exert a retarding (Zener drag) pressure on a migrating grain boundary because detaching the boundary from a particle it intersects costs interfacial energy. Growth stops once the driving pressure from boundary curvature falls to the pinning pressure, giving a limiting grain size $D_{max}=4r/3f$, where $r$ is the mean particle radius and $f$ the volume fraction. A finer, more closely spaced dispersoid population (achieved by the homogenization/pre-heat practice before hot rolling) therefore locks in a finer ultimate grain size.
Factor 2 — annealing temperature and time (thermal schedule). For a fixed particle population, the anneal soak temperature and duration set both how many new grains nucleate during recrystallization (a higher temperature and faster heat-up favour a higher nucleation rate relative to growth rate, giving a finer initial recrystallized grain size) and how far normal grain growth is allowed to proceed afterward, since boundary mobility is itself thermally activated. A schedule held just long enough to complete recrystallization, then cooled promptly, yields a finer ultimate grain size than one that overshoots into the grain-growth regime; this is the second lever (alongside particle pinning) that a mill uses to hit a target grain size for a structural sheet's formability and surface (orange-peel) requirements.
