Question 3 of 8

Question 3 (10 marks)

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.

Part (a) — baseline curve. For a cold-worked alloy annealed for a fixed time at increasing temperature, room-temperature tensile strength stays essentially flat through the recovery range (dislocations rearrange and annihilate, relieving internal stress, but the dislocation density — and hence strength — barely drops), then falls steeply through the recrystallization range as strain-free grains nucleate and consume the cold-worked structure, and finally declines more gently through grain growth as the new grains coarsen (strength falls further via the Hall–Petch relation, $\sigma_y = \sigma_0 + k_y d^{-1/2}$, as mean grain size $d$ increases).

Part (b) — effect of greater cold work. A more heavily cold-worked specimen starts from a higher room-temperature strength (more stored dislocation density) and its recrystallization curve shifts to a lower annealing temperature. The driving force for recrystallization is the stored strain energy of the cold-worked dislocation network; more cold work means more stored energy, which lowers the thermal activation needed to nucleate strain-free grains and drive the recrystallization front — so, for the same fixed annealing time, the drop in strength happens sooner (at lower $T$).

Part (c) — effect of higher alloy content. At the same degree of cold work as (a) (same starting strength and stored dislocation density), a higher content of alloying elements shifts the recrystallization curve to a higher annealing temperature. Solute atoms (substitutional or interstitial) segregate to and pin dislocations and the newly forming grain boundaries (solute drag), retarding both the nucleation and the migration of strain-free grain boundaries. More solute means a higher recrystallization temperature is needed to overcome this pinning within the same fixed anneal time — the same effect that raises recrystallization temperature for essentially every commercial (impure) alloy relative to its high-purity base metal.