Question 1 of 7: Multiple-Choice and True/False — Iron, Steel and Martensite Fundamentals

Question I: Multiple-Choice and True/False — Iron, Steel and Martensite Fundamentals (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.

1.1 — Why γ-Fe dissolves so much more carbon than α-Fe

Interstitial carbon solubility is governed by the size of the INDIVIDUAL hole a carbon atom must occupy, not by the total free volume summed over the whole structure. FCC γ-iron is the more densely packed structure (atomic packing factor 0.74 versus 0.68 for BCC α-iron), so its total interstitial "empty space" is actually smaller — but the octahedral interstitial site in FCC has a radius ratio $r_{hole}/r_{atom}=0.414$, appreciably larger than BCC's own octahedral site ($r_{hole}/r_{atom}=0.155$, and even BCC's larger tetrahedral site is only 0.291). A carbon atom (covalent radius ≈0.077 nm) sitting in the small, geometrically distorted BCC octahedral site strains the surrounding lattice severely, which caps solubility at only about 0.022 wt% C at 727 °C; the same atom in FCC's larger, more symmetric hole strains the lattice far less, allowing solubility up to 2.14 wt% C at 1148 °C. Answer: (c) — γ-iron's total empty space is smaller, but its individual interstitial sites are bigger.

1.2 — Purpose of the Jominy end-quench test

The Jominy end-quench test water-quenches only one end of a standard cylindrical bar and then measures hardness at fixed intervals along its length, generating a hardness-versus-distance-from-quenched-end curve. Because cooling rate falls off continuously and reproducibly with distance from the quenched end, this single test maps out how deeply a given steel composition can be hardened for a whole range of cooling rates in one specimen — that is exactly the definition of hardenability: the capacity of a steel to form martensite to a given depth, not the maximum hardness it can reach (which is set almost entirely by carbon content, independent of alloying). Answer: (b) hardenability.

1.3 — Mechanism that does not strengthen martensite

Martensite is strengthened by three mechanisms that all act simultaneously and diffusionlessly the instant the shear transformation occurs: (i) interstitial solid-solution strengthening from carbon trapped in the body-centred-tetragonal lattice (by far the dominant term, since carbon that was soluble in FCC austenite is now forced into the much smaller BCT octahedral sites, causing severe local strain); (ii) dislocation/substructure strengthening, since the shear transformation itself generates an extremely high density of dislocations (or internal twins in high-carbon martensite); and (iii), to a lesser extent, grain-size (Hall–Petch) strengthening from the fine martensite lath/plate packet size inherited from the prior austenite grain size. Dispersion hardening requires a fine, deliberately precipitated second-phase particle distribution, which needs time and thermally activated diffusion to nucleate and grow — the martensitic shear transformation is far too fast (essentially athermal, occurring at the speed of sound in the lattice) for any such precipitate to form; carbide precipitation only becomes possible afterward, during tempering. Answer: (d) Dispersion hardening.

1.4 — Martensite transformation vs. deformation twinning

Both processes are diffusionless, homogeneous shear mechanisms with a well-defined crystallographic habit plane and shear direction, and both can occur athermally at very high rates. Their essential difference is what the shear accomplishes: martensitic transformation reorganizes the parent lattice into a genuinely new crystal structure/phase (FCC austenite → BCT martensite in steel), whereas deformation twinning merely reorients a region of the SAME lattice into its mirror-image orientation across the twin plane — no new phase is created, only a change in crystallographic orientation of the existing phase. Twinning is also, in most engineering metals, a secondary deformation mode activated when slip is difficult (not the primary strengthening mechanism metals rely on); it can occur in cubic metals too (twinning is not restricted to HCP structures, ruling out option (b)), and it is not itself strengthening in the way a phase change is. Answer: (c).

1.5 — Conditions promoting deformation twinning in low-carbon steel

Deformation twinning is favoured whenever ordinary dislocation slip cannot supply the imposed strain rate fast enough, or is otherwise suppressed — classically at low temperature and/or very high strain rate (impact/shock loading), where the critical resolved shear stress for slip rises faster than that for twinning, so twinning becomes the kinetically favoured relief mechanism. Low-carbon (ferritic, BCC) steel does twin under these conditions (e.g., ballistic impact, explosive forming, or fracture at very low temperature) — it is not twinning-immune. Answer: (a) The strain rate is very high.

1.6–1.10 — True/False items

I.6 — False. White cast iron and the white-solidified chill zone of any cast iron form carbon as cementite (Fe₃C), not graphite; only gray, ductile and malleable irons are processed (via Si content and/or heat treatment) to favour graphite precipitation instead.

I.7 — True. Every steel composition has its own $M_s$/$M_f$ temperatures and its own critical cooling rate (set by its own TTT "nose" position); provided the actual cooling rate exceeds that steel's OWN critical rate — achievable for any steel given a severe enough quench and small enough section — austenite is diffusionlessly sheared to martensite. Very low-hardenability compositions simply require a more severe quench (e.g., thin foil plus iced brine) than a highly alloyed steel does.

I.8 — True. Interstitial-free (IF) steel is deliberately micro-alloyed with Ti and/or Nb to tie up essentially all residual interstitial C and N as stable carbonitrides, removing the mobile interstitial solute needed to form Cottrell atmospheres that pin dislocations. Without pinned dislocations there is no discontinuous yielding, hence no yield-point elongation and no Lüder's bands — IF steel yields smoothly, which is exactly why it is prized for stamped automotive panels (no stretcher-strain surface marking).

I.9 — True. Pearlite is the classic lamellar mixture of ferrite and cementite formed by diffusional, cooperative growth just below $A_1$. Bainite, though formed at lower temperature by a more complex (partly displacive, partly diffusional) mechanism and with a much finer, non-lamellar (feathery/acicular) carbide morphology, is likewise fundamentally a two-phase mixture of ferrite and cementite (or, in some bainite variants, ferrite plus a transition carbide) — never a single homogeneous phase.

I.10 — False. The hardness of freshly quenched (untempered) martensite is overwhelmingly controlled by its interstitial carbon content (through BCT lattice distortion and dislocation density), essentially independent of which substitutional alloying elements are present. Alloying elements instead control hardenability — how deep/how slowly a section can be cooled and still form martensite — not the hardness of the martensite once formed.