Question 4 of 7: TTT-Curve Shape, the Effect of Alloying on Hardenability, and Double-Nosed Curves

Question IV: TTT-Curve Shape, the Effect of Alloying on Hardenability, and Double-Nosed Curves (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.

4.1 — (i) 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 $A_1$, undercooling is small, so the free-energy difference driving nucleation is small and the nucleation barrier $\Delta G^{*}$ is large — nucleation is intrinsically slow, so the start time is LONG near $A_1$. Further below $A_1$, undercooling grows, $\Delta G_v$ increases, and nucleation becomes progressively easier.
2. Atomic mobility (diffusivity), $D=D_0\exp(-Q/RT)$. Carbon diffusion, needed to partition carbon between growing ferrite and cementite, slows exponentially as temperature falls. At LOW temperatures, well below the nose, diffusivity has collapsed so severely that even a large driving force cannot produce fast transformation — the start time is again LONG.
3. The nose is the trade-off optimum. At an intermediate temperature, undercooling already gives a healthy driving force while diffusivity has not yet collapsed — both factors are simultaneously favourable, so the start time reaches its overall MINIMUM there. The result, plotted as time (log scale) vs. temperature, is a curve with long times at BOTH ends and a minimum in between: the characteristic "C" shape.

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

4.2 — (ii) Why Cr addition moves the TTT curve to the right

Chromium is a substitutional, carbide-forming alloying element, and it retards the START of the diffusional pearlite (and bainite) reaction at EVERY hold temperature through two compounding effects. First, being a large substitutional atom, Cr itself diffuses far more sluggishly than the small interstitial carbon atom that controls pearlite growth in a plain-carbon steel; any transformation step that requires Cr to redistribute (or even just to be "pushed" ahead of an advancing ferrite/cementite interface, a solute-drag effect) is correspondingly slowed. Second, Cr is a strong carbide former: it competes with iron for the available carbon, tying some of it up as stable alloy carbides and altering the local thermodynamics/kinetics of cementite nucleation, which further delays the reaction. Because both effects act to slow nucleation and growth at every temperature along the "C" curve (nose included), the ENTIRE curve — not just one point on it — is displaced to LONGER times, i.e. to the right on the log-time axis, when Cr is added to a base composition such as SAE1045. This widens the gap between the vertical (time-zero) axis, representing the instant the steel is quenched from its austenitizing temperature, and the pearlite/bainite nose. That widened gap is exactly what is meant by increased HARDENABILITY: a slower, gentler, more practical cooling rate is now sufficient to miss the (now more distant) nose and transform to martensite through a thicker section, rather than the very fast, section-limited quench a plain-carbon steel's close-in nose would otherwise demand.

4.3 — (iii) Why a large alloy addition splits one "C" curve into two

A single "C" curve, as derived in 4.1, assumes ONE diffusional reaction competing against ONE diffusivity-controlled rate. A steel can host TWO mechanistically distinct reactions from the same undercooled austenite: the pearlite reaction (fully diffusional — BOTH carbon and the substitutional alloying element must partition between ferrite and cementite) and the bainite reaction (only carbon needs to diffuse; the ferritic component forms by a largely diffusionless, shear-like mechanism similar to martensite). A carbide-forming substitutional element such as Cr, present in a large enough amount, diffuses far more sluggishly than carbon at any given temperature, so it retards the FULLY diffusional pearlite reaction — which needs Cr to partition — MUCH more severely than it retards the bainite reaction, which does not depend on substitutional-element partitioning on the same timescale. The pearlite nose is therefore pushed out to distinctly longer times than the bainite nose, and because the two reactions are governed by different rate-limiting diffusion species, their two "C" curves need not share one continuous minimum. A temperature region between the two noses (a "bay," where both reactions are comparatively slow) can then open up, splitting what was one continuous "C" into two separate, offset noses — a double-nosed TTT curve. A small alloy addition merely shifts one combined curve to the right (4.2); a LARGE addition is what is needed to separate the two reactions' rate maxima far enough to resolve them into two distinct noses.