Question 2 of 7: Constructing a CCT Curve, and the Physical Origin of the TTT "C" Shape

Question II: Constructing a CCT Curve, and the Physical Origin of the TTT "C" Shape (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.

2.1 — (i) Experimental construction of a CCT curve

A CCT (continuous-cooling-transformation) curve is built from a batch of identically austenitized specimens of the SAME steel, each then cooled continuously (never held isothermally) at its own fixed rate:

1. Austenitize every specimen identically — same temperature above $A_3$, same soak time — to start from an identical, homogeneous austenite grain structure in each.
2. Cool one specimen continuously at a chosen, constant rate from the austenitizing temperature to room temperature, using a dilatometer (for precise, programmable rates) or a practical quench medium (furnace, still air, oil, water) for coarser rate control.
3. Record a transformation-sensitive property continuously through the cooling run — dilatometric length/volume change is standard, since austenite, ferrite, pearlite, bainite and martensite each have a distinct specific volume, so the dilation-vs-temperature (equivalently, vs. time, since the rate is fixed and known) trace departs measurably from the pure-thermal-contraction baseline exactly where a transformation starts, and returns to a new baseline slope where it ends.
4. Confirm the transformation product metallographically and/or by hardness testing on the fully cooled specimen (pearlite, bainite and martensite are readily distinguished this way), cross-checking the dilatometric inference.
5. Repeat steps 2–4 with fresh, identically austenitized specimens across a SERIES of cooling rates, spanning very slow (furnace cool) to very fast (severe water/brine quench).
6. Plot each individual cooling curve on temperature (vertical) vs. log(time) (horizontal) axes, marking the transformation-start and transformation-finish points directly on each curve from its own dilatometric data.
7. Join the start points across all cooling curves into one locus, and the finish points into a second locus — together with $M_s$/$M_f$ (read from the fastest-cooled curves, which pass straight down into the martensite range), these two joined loci define the CCT diagram, and the steepest curve that just grazes the pearlite-start "nose" identifies the critical cooling rate.

2.2 — (ii) Why a TTT curve is "C"-shaped

The time needed for a diffusional transformation (pearlite or bainite) to start at a given isothermal hold temperature is controlled by the PRODUCT of two rate factors that trend in opposite directions as temperature falls below $A_1$:

1. Thermodynamic driving force (undercooling), $\Delta G_v$. Just below $A_1$, the undercooling is small, so the free-energy difference driving nucleation is small and the critical nucleus size/activation barrier $\Delta G^{*}$ is large — nucleation is intrinsically slow, so the transformation-start time is LONG near $A_1$. As temperature falls further below $A_1$, undercooling increases, $\Delta G_v$ grows, $\Delta G^{*}$ shrinks, and nucleation becomes progressively easier and faster.
2. Atomic mobility (diffusivity), $D=D_0\exp(-Q/RT)$. Diffusion of carbon (needed to partition it between the growing ferrite and cementite lamellae) slows exponentially as temperature falls. Near $A_1$ diffusion is still fast, but at LOW temperatures (well below the nose) diffusivity has collapsed so severely that even though the thermodynamic driving force is now large, atoms simply cannot rearrange fast enough — nucleation and growth are again slow, so the transformation-start time is LONG at low temperature too.
3. The nose is where the two effects trade off. At an intermediate temperature, undercooling is already large enough to give a healthy driving force, while diffusivity has not yet collapsed — both rate factors are simultaneously favourable, so the transformation-start time reaches its overall MINIMUM there. Above the nose, the driving-force term dominates the increase in transformation time; below the nose, the diffusivity term dominates. The result, plotted as time (log scale) vs. temperature, is necessarily a curve with long times at BOTH ends and a minimum in between — the characteristic "C" shape.

$M_s$ marks a separate, purely athermal boundary below which martensite forms instantaneously by shear (no diffusion involved at all), which is why the "C" curve is truncated by a horizontal $M_s$ line rather than continuing to curve downward.