Phase Transformations & Heat Treatment of Steels and Alloys

Changing properties with heat. Learn transformation kinetics (nucleation and growth, the Avrami/JMAK equation), TTT and CCT diagrams, pearlite, bainite and martensite, hardening by quenching (quench media, severity, distortion and cracking), hardenability and the Jominy test, tempering and the Hollomon–Jaffe parameter, annealing, normalising, spheroidising, stress relieving, surface hardening (carburising, nitriding, induction), and precipitation (age) hardening of aluminium alloys — with Python for Avrami kinetics and equivalent tempering treatments.

The same steel can be as soft as 150 HB or as hard as 60 HRC depending only on heat treatment. By controlling heating temperature, time and cooling rate, engineers choose between strength, hardness, toughness and machinability.

Heat treatment is how gears, bearings, springs, tools and aircraft aluminium get their properties.

An analogy

Quenching steel is like freezing a crowd mid-movement: atoms that would normally rearrange into relaxed ferrite and cementite are trapped in a strained, hard arrangement (martensite). Tempering then lets them relax just enough to become tough without losing too much hardness.

Common heat treatments

Treatment and purpose:

TTT and CCT diagrams

Isothermal (TTT) diagrams show pearlite forming at high temperature (coarse to fine), bainite at intermediate temperature (tough, used in austempering), and martensite below M_s by a diffusionless shear transformation (hard, brittle BCT structure). Continuous cooling (CCT) diagrams apply to real quenches; the critical cooling rate is the slowest that avoids the pearlite nose and gives full martensite.

Hardenability

Hardenability is the ability to form martensite deep inside a part — different from maximum hardness (set by carbon). Alloying elements (Mn, Cr, Mo, Ni, B) shift CCT curves to longer times, allowing oil quenching of thick sections with less distortion. Measured with the Jominy end-quench test (hardness vs distance from the quenched end). Quench severity, part size and geometry, and retained austenite control final properties; distortion and quench cracking are major risks.

Surface and precipitation hardening

Surface hardening: carburising and carbonitriding (then quench and temper), gas or plasma nitriding (no quench, low distortion), induction and laser hardening (local heating of medium-carbon steel). Precipitation hardening of Al–Cu (2xxx), Al–Mg–Si (6xxx) and Al–Zn–Mg (7xxx) alloys: solution treat → quench → age (natural T4 or artificial T6) — fine coherent precipitates (GP zones, θ″) block dislocations; over-ageing coarsens them and softens. Also used for maraging steels, 17-4PH stainless and nickel superalloys.

Formulas

Worked example: Martensite start

Given: 0.4% C, 0.8% Mn, 1% Cr steel

Find: M_s.

Answer: ≈ 333 °C

Worked example: Avrami t₅₀

Given: k = 2 × 10⁻⁴, n = 2.5

Find: t₅₀.

Answer: 26.1 s

Worked example: Tempering equivalence

Given: P = 16 708, T = 500 °C

Find: Time.

Answer: ≈ 41 h

Transformation kinetics and tempering equivalence

import math
# Avrami (JMAK) transformation kinetics and Hollomon-Jaffe tempering parameter
k_av, n = 2.0e-4, 2.5                          # 1/s^n, Avrami exponent
for t in (10, 20, 30, 40, 60):
    X = 1 - math.exp(-k_av * t ** n)
    print(f"t = {t:2d} s: fraction transformed {X:.3f}")
t50 = (math.log(2) / k_av) ** (1 / n)
print(f"time to 50% transformation {t50:.1f} s")
# Tempering: equivalent treatments via P = T (C + log10 t), T in K, t in h, C = 20
C = 20.0
P = (550 + 273) * (C + math.log10(2))
T2 = 600 + 273
t2 = 10 ** (P / T2 - C)
print(f"P = {P:.0f}; 2 h at 550 C is equivalent to {t2*60:.0f} min at 600 C")
# t = 10 s: fraction transformed 0.061
# t = 20 s: fraction transformed 0.301
# t = 30 s: fraction transformed 0.627
# t = 40 s: fraction transformed 0.868
# t = 60 s: fraction transformed 0.996
# time to 50% transformation 26.1 s
# P = 16708; 2 h at 550 C is equivalent to 8 min at 600 C

Isothermal transformations follow an S-curve: a slow start (nucleation), rapid growth, then saturation — the TTT diagram plots the start and finish times at each temperature. The Hollomon–Jaffe parameter trades temperature for time: tempering 50 °C hotter reaches the same hardness in minutes instead of hours, useful for induction tempering lines.

Common mistakes

Applications

Key takeaways

Going further