Heat treatment and surface hardening of steels

Why it matters

The same bar of medium-carbon steel can be soft enough to machine, tough enough for a shaft, or hard enough to resist wear on a gear tooth, depending only on how it was heated and cooled. Mechatronic hardware such as gears, cams, lead screws, bearings and actuator shafts relies on hardened surfaces over tough cores. Choosing the right treatment, and avoiding distortion and cracking, is a routine design and production decision.

Key ideas

Austenitising. Almost every steel heat treatment starts by heating into the austenite (γ) field of the Fe–Fe₃C diagram: about 30–50 °C above A₃ for hypoeutectoid steels, and about 30–50 °C above A₁ for hypereutectoid steels (heating above A_cm would coarsen the grain and dissolve all the useful carbides). What happens on cooling decides the final structure.

TTT and CCT diagrams. An isothermal transformation (TTT) diagram plots, for one steel, the time to start and finish the transformation of austenite at each temperature, giving the familiar C-curves. Slow transformation at high temperature gives coarse pearlite; nearer the nose (about 550 °C for plain eutectoid steel) it gives fine pearlite; below the nose, bainite. A continuous-cooling (CCT) diagram is the practical version for real cooling paths. The critical cooling rate is the slowest cooling that just misses the nose; cooling faster than this gives martensite.

Martensite. When austenite is cooled fast enough, carbon cannot diffuse out, and the FCC lattice shears diffusionlessly into body-centred tetragonal (BCT) martensite, supersaturated with carbon. It starts at M_s and is complete near M_f; both fall as carbon rises, so high-carbon steels can keep retained austenite at room temperature. Martensite hardness depends mainly on carbon content (up to about 0.6 % C) and is very high but brittle, with large residual stresses.

Bulk treatments.

• Full annealing: austenitise, then furnace cool. Coarse pearlite, lowest hardness, best for machining and cold forming. Process (subcritical) annealing below A₁ restores ductility between cold-working passes; stress-relief annealing (roughly 550–650 °C) removes residual stress from welding or machining without changing the microstructure much.
• Spheroidising: long hold just below A₁ turns cementite into spheres; used for high-carbon steels before machining.
• Normalising: austenitise (A₃/A_cm + 30–50 °C) and cool in still air. Finer pearlite and finer grain than annealing; slightly harder and stronger, better toughness. Used to refine cast or forged structures.
• Hardening (quenching): austenitise and quench in brine, water, oil or polymer, faster than the critical cooling rate. Severity: brine > water > oil > air. More severe quenches harden deeper but risk distortion and quench cracks.
• Tempering: reheat quenched steel below A₁ (typically 150–650 °C). Carbon precipitates as fine carbides, stresses relax, toughness rises and hardness falls. Low-temperature tempering keeps hardness (tools); high-temperature tempering gives tempered sorbite, the tough structure of quenched-and-tempered shafts.
• Austempering: quench into a salt bath above M_s and hold until austenite becomes bainite. Good toughness with less distortion.
• Martempering (marquenching): quench to just above M_s, hold until the temperature equalises through the section, then cool slowly through the martensite range, then temper. Minimises distortion and cracking.

Hardenability is the ability to form martensite to a depth, not the maximum hardness. It is measured by the Jominy end-quench test (hardness versus distance from the water-quenched end). Alloying elements (Mn, Cr, Mo, Ni, B) shift the C-curve nose to the right and so raise hardenability; carbon content mainly raises the attainable hardness.

Surface hardening gives a hard, wear- and fatigue-resistant case on a tough core.

• Changing the surface chemistry (thermochemical):
  • Carburising of low-carbon steel (about 0.1–0.25 % C) in a carbon-rich gas, liquid or solid medium at about 900–950 °C, followed by quench and low temper. Case typically 0.5–2 mm. Gears, cam followers.
  • Nitriding at about 500–550 °C in ammonia or plasma; hard nitrides of Al, Cr, Mo form, so it needs nitriding steels. No quench, so distortion is minimal; case thin (about 0.1–0.6 mm) but very hard.
  • Carbonitriding (gas) and cyaniding (liquid salt) add both C and N at intermediate temperatures; thin cases on small parts.
• Heating only the surface (no change in chemistry):
  • Induction hardening: an alternating current in a coil induces eddy currents concentrated in a surface layer whose depth falls as frequency rises; the surface is austenitised in seconds and quenched by spray. Needs steel with enough carbon (about 0.35–0.6 % C). Fast, localised, easily automated: shafts, gear teeth, lead-screw journals.
  • Flame hardening: an oxy-fuel flame followed by a quench spray; suits large or one-off parts.
  • Laser and electron-beam hardening: very localised, little distortion.

Formulas

x ∝ √(D·t)

• x: case depth reached by a given carbon concentration (m); D: diffusion coefficient of carbon in austenite (m²/s); t: time (s). At a fixed temperature, doubling the depth needs four times the time.

(C_s − C_x) / (C_s − C₀) = erf( x / (2·√(D·t)) )

• C_s: surface carbon (wt%); C₀: initial carbon of the steel (wt%); C_x: carbon at depth x (wt%). Fick's second law for a semi-infinite solid with constant surface concentration and constant D.

D = D₀·exp(−Q / (R·T))

• D₀: frequency factor (m²/s); Q: activation energy (J/mol); R = 8.314 J/(mol·K); T: absolute temperature (K). Take D₀ and Q from your data book.

δ = 503·√( ρ / (μ_r·f) )

• δ: induction (electromagnetic) skin depth (m); ρ: electrical resistivity (Ω·m); μ_r: relative permeability (1 above the Curie point); f: frequency (Hz). The hardened depth is of the order of δ.

Worked examples

Example 1 (standard): carburising time. A gear steel reaches an effective case depth of 0.5 mm after 4 h at 925 °C. How long for a 1.0 mm case at the same temperature?

1. At constant temperature and concentrations, x ∝ √t, so t₂ = t₁·(x₂/x₁)².
2. t₂ = 4 h × (1.0/0.5)² = 4 × 4.
3. t₂ = 16 h. Doubling the case depth quadruples the furnace time, which is why deep cases are expensive.

Example 2 (GATE level): carbon profile. A 0.20 % C steel is gas carburised with the surface held at 1.00 % C. At the carburising temperature D = 1.5 × 10⁻¹¹ m²/s. Find the time for the carbon content at 0.5 mm depth to reach 0.60 %. Take erf(0.477) = 0.500.

1. Left side: (C_s − C_x)/(C_s − C₀) = (1.00 − 0.60)/(1.00 − 0.20) = 0.40/0.80 = 0.500.
2. So erf(z) = 0.500, giving z = x/(2√(Dt)) = 0.477.
3. √(Dt) = x/(2 × 0.477) = 0.5 × 10⁻³ m / 0.954 = 5.24 × 10⁻⁴ m.
4. Dt = (5.24 × 10⁻⁴)² = 2.748 × 10⁻⁷ m².
5. t = 2.748 × 10⁻⁷ / 1.5 × 10⁻¹¹ = 1.83 × 10⁴ s = 5.1 h.

Example 3 (induction frequency). Hot steel above its Curie point has μ_r = 1 and ρ ≈ 1.2 × 10⁻⁶ Ω·m (check your data book). At f = 10 kHz, δ = 503 × √(1.2 × 10⁻⁶ / 10⁴) = 503 × 1.095 × 10⁻⁵ m = 5.5 mm; at 100 kHz, δ = 1.7 mm. Higher frequency gives a shallower hardened layer.

Common mistakes

• Austenitising hypereutectoid steel above A_cm before hardening. It coarsens grains and raises retained austenite; go just above A₁.
• Confusing hardness with hardenability. A 0.8 % C plain steel gets very hard but only shallowly; a 0.4 % C Cr-Mo steel is less hard but hardens through a thick section.
• Saying annealing and normalising differ only in temperature. The key difference is the cooling medium (furnace versus still air) and therefore the fineness of pearlite.
• Skipping tempering after quenching. Untempered martensite is brittle and can crack from residual stress, sometimes days later.
• Induction or flame hardening a low-carbon steel. Without carbon there is no hard martensite; low-carbon parts must be carburised.
• Using °C instead of K in the Arrhenius equation for D.

For GATE ME

Expect conceptual one-mark questions matching a treatment to its cooling medium or purpose (annealing, normalising, hardening, tempering, austempering, martempering), identifying the microstructure produced by a cooling path on a TTT diagram, and choosing a surface-hardening process (carburising for low-carbon steel, nitriding for minimal distortion, induction for selective hardening). Numericals are less common but can use √(Dt) scaling of case depth or the error-function solution. Practise sketching a TTT diagram with cooling curves for full annealing, normalising, oil quench, water quench and austempering.

Quick check

1. Which treatment gives coarse pearlite: furnace cooling or air cooling?
2. What crystal structure does martensite have?
3. A case of 0.8 mm takes 9 h. How long for 0.4 mm at the same temperature?
4. Which surface-hardening process needs no quench and gives minimal distortion?
5. What test measures hardenability?

Answers: 1. Furnace cooling (full annealing). 2. Body-centred tetragonal (BCT). 3. 9 × (0.4/0.8)² = 2.25 h. 4. Nitriding. 5. The Jominy end-quench test.