21-Mat-A6 Materials Selection and Design for Materials Processing · December 2016
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 an SAE/AISI 1040 steel (0.40 wt%C), a hypoeutectoid composition lying between the eutectoid (0.77 wt%C) and pure iron on the Fe–Fe3C diagram. Its equilibrium (slow-cool) room-temperature microstructure is proeutectoid ferrite ($\alpha$) plus pearlite ($\alpha$+Fe3C lamellae), with the proeutectoid fraction set by the lever rule at 727 °C: $W_\alpha=(0.77-0.40)/(0.77-0.022)\approx0.49$. All three treatments below start from austenitizing above the upper critical (A3) line and differ only in cooling rate and holding practice.
(i) Normalizing. The steel is heated to about 55 °C above the A3 line (fully austenitic, fine prior-austenite grain from the recrystallization that accompanies austenitizing) and then cooled in still air. Air cooling is faster than a furnace cool but far slower than a liquid quench, so the austenite transforms diffusionally to ferrite + pearlite while crossing the TTT/CCT curve closer to the nose — giving finer ferrite grains and a finer interlamellar pearlite spacing than a full anneal of the same steel. The purpose is to refine and homogenize a coarse or non-uniform as-cast/as-forged grain structure and relieve the internal stresses of prior working, at a lower cost than annealing (no controlled furnace cool) and with somewhat higher strength/hardness than the annealed condition.
(ii) Spheroidizing. The steel is held for a prolonged time at a temperature just below A1 (727 °C), or cycled repeatedly just above and below A1, starting from an already-pearlitic or cold-worked structure. Because the cementite lamellae in pearlite have a high surface-to-volume ratio (hence high interfacial energy), prolonged sub-critical annealing drives Fe3C to spheroidize — the lamellae break up and coalesce into discrete, roughly spherical carbide particles dispersed in a continuous ferrite matrix — because a sphere minimizes total interfacial area for a given carbide volume (the same capillarity-driven coarsening logic as Ostwald ripening). The resulting spheroidite microstructure is the softest, most ductile state a given steel can be put in, which is precisely why it is the preferred condition for cold forming or machining operations that would otherwise be limited by a hard, lamellar pearlitic structure.
(iii) Full annealing. The steel is austenitized above A3 (as for normalizing) and then furnace-cooled at a very slow, controlled rate (the furnace is typically shut off and the steel cools with it, sometimes over many hours). The very slow cool keeps the transformation close to the top of the TTT/CCT diagram, near equilibrium, producing coarse proeutectoid ferrite and coarse pearlite with wide interlamellar spacing. This is the softest, most stress-free, most machinable condition obtainable by full austenitizing (softer than a normalized structure, though generally less soft than spheroidite), and is used to remove the effects of prior cold work or non-equilibrium casting/welding structures and to prepare the steel for further cold forming.
Martensite forms by a diffusionless, athermal, shear (military) transformation: on quenching fast enough to miss the pearlite/bainite nose entirely, carbon has no time to partition by diffusion, so the FCC austenite lattice shears directly into a body-centred TETRAGONAL (not cubic) ferrite-like structure with all of the parent austenite's carbon trapped in interstitial solid solution. The resulting supersaturation of carbon distorts the lattice (the tetragonality $c/a$ increases with %C) and, together with a very high dislocation/twin density inherited from the shear, makes martensite the hardest and most brittle of the transformation products. Its amount depends only on how far the temperature has fallen below $M_s$ (athermal), not on holding time.
Bainite forms by a mixed mechanism: an initial diffusionless, shear transformation of small platelets/laths of ferrite (like martensite, supersaturated in carbon at the instant of formation), followed immediately by diffusion-controlled rejection of that excess carbon as fine, discrete carbide particles — either within the ferrite laths (lower bainite, carbides at roughly 55–60° to the lath axis, formed at lower temperature where carbon diffusion is sluggish enough that it cannot escape the lath before precipitating inside it) or between the laths (upper bainite, carbides precipitated from the residual, carbon-enriched austenite between laths, formed at higher temperature where carbon can diffuse fully out before precipitating). Because it requires TIME for that carbon partitioning step, bainite formation is isothermal/diffusion-limited above $M_s$, not athermal, and its amount at a given temperature increases with holding time (following a C-curve kinetics on the TTT diagram) rather than depending only on undercooling.
Neither phase appears on the EQUILIBRIUM Fe–Fe3C diagram because that diagram is, by construction, a map of phases in true thermodynamic equilibrium — it assumes infinitely slow cooling, giving full diffusional partitioning of carbon between $\alpha$ (0.022 wt%C max) and Fe3C (6.70 wt%C) at every temperature. Martensite and bainite are both METASTABLE, non-equilibrium products that exist only because cooling is too fast for the equilibrium (pearlitic) reaction to go to completion: martensite is the limiting case of zero diffusion, bainite an intermediate case of partial (carbon-only, not iron-lattice) diffusion. A TTT or CCT diagram, not the equilibrium phase diagram, is the correct tool for locating them, because only the TTT/CCT map shows transformation as a function of the KINETIC variables (time and cooling rate) that the equilibrium diagram deliberately suppresses.
