Question 5 of 8: Heat Treatments Read from the Fe–Fe 3 C Phase Diagram

Question 5: Heat Treatments Read from the Fe–Fe₃C Phase Diagram (20 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.

Given. The paper's own partial Fe–Fe₃C diagram (reproduced below) fixes: eutectic at 1148 °C / 4.30 wt.%C; eutectoid at 727 °C / 0.77 wt.%C; maximum solubility of C in α-ferrite 0.022 wt.%C (at 727 °C); the pure-iron α/γ transus at 912 °C; and cementite fixed at 6.70 wt.%C. AISI/SAE numbers give the carbon content directly: 1090 = 0.90 wt.%C (hypereutectoid), 1040 = 0.40 wt.%C and 1020 = 0.20 wt.%C (both hypoeutectoid).

Find. For each target microstructure, the composition/temperature the diagram supports and the processing route (heating, holding, cooling) that produces it.

Approach. Part (a) uses the room-temperature lever rule across the α/Fe₃C tie line to bound the alloy composition; parts (c) and (d) use a linear interpolation of the GS (upper-critical, A₃) phase boundary between the two points the diagram actually supplies — (0 wt.%C, 912 °C) and (0.77 wt.%C, 727 °C) — to locate the austenitizing/intercritical temperatures, then the lever rule again for the intercritical austenite fraction in (d); part (b) is a subcritical-anneal kinetics argument, not a lever-rule calculation.

1. Part (a) — hypoeutectoid composition with < 10 wt.% total cementite. At room temperature a steel below the eutectoid composition is, to a very good approximation, a mixture of proeutectoid α-ferrite and pearlite, and the OVERALL cementite content is fixed by the same α/Fe₃C tie line the diagram supplies regardless of how the carbon is split between the two microconstituents: $$W_{\text{Fe}_3\text{C}} = \frac{C_0 - 0.022}{6.70 - 0.022}$$ Setting $W_{\text{Fe}_3\text{C}} = 0.10$ and solving for $C_0$: $$\boxed{C_0 = 0.022 + 0.10\,(6.70 - 0.022) = 0.6898 \approx 0.69\ \text{wt.\%C}}$$ Any hypoeutectoid steel at or below about 0.69 wt.%C (e.g. a 1060 or leaner grade) therefore satisfies the <10% cementite target — obtained simply by a full anneal (austenitize above A₃, then furnace-cool) so the alloy reaches this room-temperature equilibrium mixture. As a check, a fully pearlitic (eutectoid, 0.77 wt.%C) steel itself carries $W_{\text{Fe}_3\text{C}}=11.20\%$ — i.e. every hypoeutectoid alloy already clears 10% automatically, and the practical content of part (a) is choosing a composition comfortably below the eutectoid and slow-cooling it to equilibrium.
2. Part (b) — spheroidite in a 1090 steel. A 1090 steel (0.90 wt.%C) is hypereutectoid, so its as-transformed room-temperature structure is pearlite plus a proeutectoid cementite network at the prior-austenite grain boundaries — both hard and, for the network, brittle. Spheroidite is obtained by a prolonged subcritical (spheroidizing) anneal: hold the steel just below A₁ (727 °C), typically around 690–700 °C, for many hours (often 15–25 h industrially). No new phase forms — the composition and phase amounts (α + Fe₃C, in the same 0.90 wt.%C proportions) are unchanged from the diagram — but the cementite lamellae and grain-boundary film are thermodynamically unstable against their own curvature: sharp, high-curvature cementite edges have a higher local solubility in the surrounding ferrite (Gibbs–Thomson effect) than the flatter regions, so carbon diffuses away from the sharp edges and re-deposits on the low-curvature regions, coarsening the lamellae into isolated spheres that minimize the total α/Fe₃C interfacial area. The result is the softest, most machinable, most cold-formable structure a 1090 steel can have.
3. Part (c) — a normalized 1040 steel. Normalizing austenitizes above the upper-critical (A₃) temperature and then air-cools (faster than a furnace anneal, slower than a liquid quench). For a hypoeutectoid steel the A₃ temperature is read from the GS boundary; using the diagram's own two end-points (912 °C at 0 wt.%C, 727 °C at the 0.77 wt.%C eutectoid) as a linear approximation, $$T_{A_3}(C_0) = 912 - \frac{912-727}{0.77}\,C_0 = 912 - 240.26\,C_0\ (^{\circ}\text{C})$$ For the 1040 steel, $C_0=0.40$: $$\boxed{T_{A_3}(0.40) = 912 - 240.26(0.40) = 815.9\,{}^{\circ}\text{C}}$$ Normalizing practice austenitizes roughly 50 °C above A₃ to ensure full, uniform austenitization, i.e. about $815.9+50\approx 865.9\,{}^{\circ}\text{C}$, followed by still-air cooling to room temperature. The faster air cool (versus a furnace cool) undercools the alloy further below A₁ before pearlite nucleates, giving a finer pearlite interlamellar spacing, a finer prior-austenite/proeutectoid-ferrite grain size, and correspondingly higher strength and hardness than the same steel fully annealed.
4. Part (d) — a 1020 steel with an equiaxed MA (martensite/retained austenite) dispersion in ferrite. This is the classic intercritical anneal + quench route used to make dual-phase (DP) steel. Using the same linear A₃ relation, the 1020 steel's ($C_0=0.20$) upper-critical temperature is $$T_{A_3}(0.20) = 912 - 240.26(0.20) = 864.0\,{}^{\circ}\text{C}$$ so the intercritical (α+γ) window for this steel runs from A₁ = 727 °C up to about 864 °C. Choosing an intercritical hold at, say, $T=800\,{}^{\circ}\text{C}$ (comfortably inside that window), the austenite-boundary composition at that temperature follows from inverting the same A₃ relation, $$C_\gamma(800) = \frac{912-800}{240.26} = 0.466\ \text{wt.\%C}$$ and, taking the α-solvus composition as essentially fixed at $C_\alpha\approx0.022\ \text{wt.\%C}$ (the diagram gives no separate curve for it inside the intercritical range), the lever rule gives the austenite fraction formed at 800 °C: $$\boxed{f_\gamma = \frac{0.20-0.022}{0.466-0.022} = 0.401\ (\approx 40\ \text{vol.\%})}$$ Holding at 800 °C nucleates this γ as small, roughly equiaxed islands at the ferrite grain boundaries and triple points (heterogeneous nucleation sites), each island carbon-enriched to 0.466 wt.%C by the lever-rule partitioning above. A subsequent rapid (e.g. water) quench then transforms those carbon-enriched islands to martensite — with some retained austenite where the local $M_s$ has been depressed enough by the enrichment — while the remaining $1-f_\gamma\approx0.60$ (60 vol.%) stays untransformed intercritical ferrite. The product is exactly the requested equiaxed MA-constituent dispersion in a ferrite matrix.