21-Mat-A6 Materials Selection and Design for Materials Processing · December 2017
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
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.
Take a 2xxx-series (Al–Cu, e.g. 2024) or 6xxx-series (Al–Mg–Si) alloy as the working example. All hardenable (precipitation-strengthenable) aluminum alloys are heat-treated by the same three-stage sequence:
Stage 1 — Solution heat treatment. The alloy is heated into the single-phase $\alpha$ (Al solid solution) field, above the solvus for its composition (e.g. ∼495–505 °C for 2024), and held long enough for the equilibrium second-phase constituent (e.g. Al2Cu, $\theta$) to fully dissolve into solid solution. Resulting microstructure: a single-phase, homogeneous $\alpha$ solid solution, with the alloying element(s) fully dissolved and the as-cast/as-worked second-phase particles gone.
Stage 2 — Quenching. The solution-treated alloy is rapidly cooled (typically a cold water quench) to room temperature. The quench is fast enough that diffusion cannot keep pace, so the alloy crosses the solvus without precipitating the equilibrium phase. Resulting microstructure: a supersaturated solid solution (SSSS) — still single-phase $\alpha$, but now thermodynamically unstable, carrying far more solute in solution at room temperature than the equilibrium diagram allows, together with a large excess of quenched-in vacancies.
Stage 3 — Aging (precipitation heat treatment). The SSSS is held either at room temperature (natural aging, e.g. the T4 temper) or at an elevated temperature typically in the 120–190 °C range (artificial aging, e.g. the T6 temper). Resulting microstructure: the excess vacancies enable solute clustering into GP zones, which with further aging (or higher aging temperature) evolve toward metastable, then equilibrium, precipitates (e.g. for Al–Cu: GP zones $\to\theta''\to\theta'\to\theta$); peak strength (peak aging) occurs at an intermediate, semi-coherent precipitate size that best resists dislocation motion, with overaging (coarser, incoherent, widely spaced equilibrium precipitates) softening the alloy again.
Factor 1 — annealing temperature and time. Once primary recrystallization of the deformed aluminum sheet is complete, continued annealing drives normal grain growth, a thermally activated, curvature-driven boundary migration process whose rate follows an Arrhenius-type mobility, giving a parabolic growth law $D^n - D_0^n = kt\exp(-Q/RT)$ (n typically ≈ 2–3 for a clean metal). Both a higher annealing temperature and a longer hold time increase the final grain size $D$; controlling the temperature–time schedule (e.g. stopping the anneal once the target size is reached, or annealing continuously at a lower temperature for a controlled dwell in a continuous coil-anneal line) is therefore the primary lever over the ultimate grain size once nucleation of new grains is complete.
Factor 2 — second-phase particle (Zener) pinning. Aluminum sheet alloys are rarely single-phase: dispersoid particles (e.g. Al3Zr, Al6Mn, or Al–Fe–Si constituents, depending on alloy series) exert a retarding (Zener pinning) pressure on migrating grain boundaries that opposes the boundary's own curvature-driven driving pressure. Growth stalls when the two balance, giving the Zener limiting grain size derived in Question 3(c):
$$D_{\max} = \frac{4r}{3f}$$for dispersoid particles of radius $r$ and volume fraction $f$. A finer, more closely spaced dispersoid distribution (smaller $r$, larger $f$) caps the ultimate grain size at a smaller value and, importantly, suppresses ABNORMAL (discontinuous) grain growth — the runaway growth of a few grains at the expense of their neighbours — which is otherwise a risk once normal growth stagnates near $D_{\max}$ and any locally under-pinned boundary can break away. In practice, alloy designers deliberately add dispersoid-forming elements (Zr, Mn) at levels chosen to fix $D_{\max}$ for a target sheet grain size, rather than leaving grain size to temperature/time control alone.
