TTT and CCT diagrams

Why it matters

The iron–carbon diagram says what forms after very slow cooling, but real parts are quenched in water or oil, air-cooled or held in salt baths. TTT and CCT diagrams add the missing variable, time, and so tell you whether a gear will become martensite, bainite or pearlite, how fast it must be quenched, and why alloy steels harden in oil when plain carbon steels need water.

Key ideas

Transformation kinetics. Austenite cooled below A1 does not transform instantly: it needs nucleation and diffusion-controlled growth. Just below A1 the driving force is small, so nucleation is slow; at low temperature diffusion is slow. The fastest transformation is in between, which gives the C-shaped curves.

TTT (isothermal transformation) diagram. Built by austenitising small samples, quenching them rapidly to a fixed temperature, holding for various times and examining the structure. It plots temperature against log time and shows:

• the start curve (about 1 % transformed) and the finish curve (about 99 %), and often the 50 % curve;
• the nose: the temperature (about 540 °C for eutectoid plain carbon steel) at which transformation starts soonest (under a second for plain eutectoid steel);
• the horizontal Ms (martensite start, about 220 °C for eutectoid steel) and Mf (martensite finish) lines. For hypoeutectoid and hypereutectoid steels an extra curve shows proeutectoid ferrite or cementite forming first above the nose.

Products of austenite (eutectoid steel).

• Coarse pearlite (just below 727 °C down to about 650 °C): widely spaced lamellae, softer.
• Fine pearlite (about 650–540 °C): thinner lamellae, harder and stronger, because the interlamellar spacing is smaller.
• Upper bainite (about 540–350 °C): feathery; ferrite laths with cementite between them.
• Lower bainite (about 350 °C to Ms): acicular plates with fine carbides inside; strong and tough.
• Martensite (below Ms): forms only when austenite is cooled so fast that diffusion is suppressed. The transformation is diffusionless and athermal — the amount depends on how far below Ms the steel is cooled, not on time. Martensite is a supersaturated body-centred tetragonal (BCT) solution of carbon; its hardness rises steeply with carbon content up to about 0.6 % C. It is hard and brittle and must be tempered.
• Retained austenite: if Mf is below room temperature (high-carbon and alloy steels), some austenite survives quenching; sub-zero treatment converts it.

Reading a path on a TTT diagram. Only isothermal paths (quench to a temperature, hold, then cool) can be read strictly. Example: quench to 600 °C and hold until the finish line → fine pearlite. Quench to 300 °C, hold → lower bainite. Quench straight below Mf → martensite. Quench to 600 °C, hold for half the transformation time, then quench to room temperature → about 50 % fine pearlite and 50 % martensite.

CCT (continuous cooling transformation) diagram. Real parts cool continuously. On a CCT diagram the curves lie lower and further to the right than on the TTT diagram for the same steel (it takes longer to reach a given transformed fraction when temperature keeps dropping). In plain carbon eutectoid steel, bainite does not form during continuous cooling. Cooling curves are superimposed to read the product, and the final hardness is often printed at the end of each curve.

Critical cooling rate. The slowest cooling rate whose curve just misses the nose of the CCT start curve, producing 100 % martensite. A plain carbon steel needs roughly 100–200 °C/s (water quench); alloy steels need far less.

What shifts the curves.

• Alloying elements (except cobalt) — Cr, Mo, Mn, Ni — and higher carbon (up to eutectoid) shift the C-curves to the right, lowering the critical cooling rate and raising hardenability.
• A coarser austenite grain size also shifts them right (fewer nucleation sites), but at the cost of toughness.
• Carbon and most alloying elements lower Ms and Mf.

Avrami kinetics. The fraction transformed at a fixed temperature follows an S-shaped curve against time described by the Avrami equation. Because time is plotted logarithmically, the 50 % time is not the arithmetic mean of the start and finish times.

Formulas

y = 1 − exp(−k·tⁿ) Avrami equation: y = fraction transformed (0–1), t = time (s), k = rate constant (s⁻ⁿ), n = Avrami exponent (typically 1–4); both from experiment at the given temperature.

t_y = [ −ln(1 − y) / k ]^(1/n) Time to reach fraction y.

t₀.₅ = (ln 2 / k)^(1/n) and rate = 1 / t₀.₅ Half-transformation time and the usual definition of transformation rate.

CR_crit ≈ (T_γ − T_nose) / t_nose A rough estimate of the critical cooling rate from the austenitising temperature T_γ (°C) to the nose (T_nose in °C, t_nose in s). It overestimates slightly because it uses the TTT nose; use the CCT diagram when available.

Worked examples

Example 1 (standard): Avrami kinetics. Given: at 600 °C a steel transforms with n = 2.5 and is 50 % transformed after 20 s.

1. k = ln 2 / t₀.₅ⁿ = 0.6931 / 20^2.5 = 0.6931 / 1788.9 = 3.87 × 10⁻⁴ s^(−2.5).
2. Time to 95 %: t = [−ln 0.05 / k]^(1/2.5) = [2.996 / 3.87 × 10⁻⁴]^0.4 = 35.9 s.
3. Fraction after 30 s: y = 1 − exp(−3.87 × 10⁻⁴ × 30^2.5) = 1 − exp(−1.910) = 0.85.

Example 2 (GATE level): finding t₀.₅ and the critical cooling rate. (a) At one temperature transformation is 1 % complete at 10 s and 99 % complete at 100 s. Find n and the 50 % time.

1. ln[−ln(1 − y)] = ln k + n·ln t. For y = 0.01: ln(0.01005) = −4.600; for y = 0.99: ln(4.605) = 1.527.
2. n = (1.527 − (−4.600)) / (ln 100 − ln 10) = 6.127 / 2.303 = 2.66.
3. ln k = −4.600 − 2.66 × 2.303 = −10.73.
4. t₀.₅ = (ln 2 / k)^(1/n) = exp[(ln 0.6931 + 10.73) / 2.66] = 49 s — not the average 55 s. (b) A steel is austenitised at 850 °C; the nose of its transformation-start curve is at 550 °C and 1.5 s. Rough critical cooling rate = (850 − 550)/1.5 = 200 °C/s, which needs a vigorous water quench.

Common mistakes

• Reading a continuous cooling curve directly on a TTT diagram as if it were exact.
• Thinking martensite forms with time at a fixed temperature; its amount depends on temperature below Ms.
• Calling martensite a phase on the equilibrium diagram; it is metastable and does not appear there.
• Averaging start and finish times on a log-time diagram.
• Saying alloying moves the curves left; it moves them right (more hardenable).
• Expecting bainite from continuous cooling of plain carbon eutectoid steel; it is obtained by isothermal holding (austempering).

For GATE PI

Expect questions that trace a time–temperature path on a TTT diagram and ask for the final microstructure, define the nose, Ms and critical cooling rate, compare TTT and CCT, and ask how alloying or carbon shifts the curves. Numericals use the Avrami equation (time for a given fraction, n or k from two data points) or a simple critical-cooling-rate estimate.

Quick check

1. What does the nose of a TTT curve represent?
2. A eutectoid steel is quenched to 400 °C and held until transformation ends. What forms?
3. Does adding chromium raise or lower the critical cooling rate?
4. Why is martensite called an athermal transformation?
5. With n = 2 and t₀.₅ = 10 s, what fraction is transformed at 20 s?

Answers: 1. The temperature at which austenite starts transforming in the shortest time; 2. Upper bainite; 3. Lowers it; 4. The amount formed depends on how far below Ms the steel is cooled, not on holding time; 5. 1 − 2^(−4) = 0.9375.