Heat treatment and surface hardening of steels

Why it matters

The same medium-carbon steel can be soft enough to machine or hard enough to resist wear, depending only on how it was heated and cooled. Gears, camshafts, crankshaft journals, axle shafts and springs all depend on heat treatment and surface hardening to combine a hard, wear-resistant surface with a tough core. Choosing the wrong temperature, quenchant or case depth is a common root cause of cracked or prematurely worn automotive parts.

Key ideas

Why steel can be heat treated. Steel above A₃ (or A₁ for hypereutectoid steel) is austenite (FCC), which dissolves much more carbon than ferrite. What austenite turns into on cooling depends on the cooling rate, which the equilibrium Fe–C diagram cannot show. That is the job of the TTT (isothermal) diagram and the CCT (continuous-cooling) diagram.

• Slow cooling → coarse pearlite (soft). Faster → fine pearlite, then bainite.
• Cooling faster than the critical cooling rate (missing the nose of the C-curve) → martensite: a supersaturated body-centred tetragonal phase formed by a diffusionless shear transformation between Ms and Mf. Martensite hardness depends mainly on carbon content; alloying does not make martensite harder, it makes it easier to obtain.

Bulk heat treatments.

• Full annealing – heat about 30–50 °C above A₃ (hypoeutectoid) or above A₁ (hypereutectoid), hold, furnace cool. Coarse pearlite, maximum softness, relieves stress, refines a coarse cast or forged structure.
• Process (sub-critical) annealing – below A₁, restores ductility of cold-worked low-carbon steel by recrystallisation between drawing passes.
• Spheroidising – long hold just below A₁; cementite becomes spheroids, best machinability for high-carbon steel.
• Stress-relief annealing – typically 500–650 °C, removes residual stresses from welding, machining or cold work without changing the microstructure much.
• Normalising – heat about 30–50 °C above A₃ (or above A_cm for hypereutectoid steel), cool in still air. Finer pearlite and finer grains: stronger and harder than annealed steel, with good toughness; also breaks up the cementite network in hypereutectoid steels.
• Hardening – austenitise, then quench in brine, water, oil or polymer to form martensite. Faster quenchants harden more but raise distortion and cracking risk.
• Tempering – reheat hardened steel below A₁. Low temperature (about 150–250 °C) relieves stress and keeps most hardness (tools, bearings); medium (about 350–500 °C) for springs; high (about 500–650 °C) gives tempered martensite with the best toughness (shafts, connecting rods). Hardening plus high tempering is called hardening and tempering (Q&T). Some alloy steels show temper embrittlement in certain ranges – check the steel's data sheet.
• Austempering – quench into a salt bath above Ms and hold until bainite forms; tough, low distortion.
• Martempering (marquenching) – quench to just above Ms, equalise, then air-cool through the martensite range; martensite with less distortion and cracking. It must still be tempered.

Hardenability vs hardness. Hardness is the maximum value a steel reaches (set mostly by carbon). Hardenability is the depth to which it can be hardened, measured with the Jominy end-quench test. Alloying elements (Cr, Mo, Mn, Ni, B) shift the C-curve to the right and raise hardenability, allowing oil quenching and thicker sections.

Surface (case) hardening. Goal: hard, wear- and fatigue-resistant surface, tough core.

• Changing surface chemistry:
  • Carburising (pack, gas or liquid) of low-carbon steel (about 0.1–0.25 % C) at about 900–950 °C in the austenite range, raising surface carbon to about 0.8–1.0 %, then quenching and low tempering. Deep cases (about 0.5–2 mm): gears, camshafts, gudgeon pins.
  • Nitriding at about 500–570 °C (below A₁, in ferrite) in ammonia or plasma; hard nitrides of Al, Cr, Mo, V. No quench, minimal distortion, thin very hard case; needs nitriding steels.
  • Carbonitriding / cyaniding – carbon and nitrogen together; thinner cases at lower temperatures than carburising.
• Without changing chemistry (steel must already have about 0.35–0.6 % C):
  • Flame hardening – oxy-fuel flame heats the surface, followed by a water spray.
  • Induction hardening – high-frequency current heats a surface layer whose depth falls as frequency rises; crankshaft journals, axle shafts.
  • Laser and electron-beam hardening – very localised, thin cases.

Formulas

Cooling rate = (T₁ − T₂) / t Average rate over an interval (°C/s); the rate that matters for martensite is the rate near the nose of the C-curve (about 500–600 °C), not the overall average.

(C_s − C_x) / (C_s − C₀) = erf[x / (2√(D·t))] Fick's second-law solution for carburising a semi-infinite bar: C_s = surface carbon (wt %), C₀ = initial carbon (wt %), C_x = carbon at depth x (m), D = diffusion coefficient (m²/s), t = time (s). Assumes constant C_s and D.

D = D₀·exp(−Q / (R·T)) D₀ = pre-exponential factor (m²/s), Q = activation energy (J/mol), R = 8.314 J/(mol·K), T in kelvin. Take D₀ and Q from your data book.

x = K·√t → x₂ / x₁ = √(t₂ / t₁) Case depth at fixed temperature and fixed C_s, C₀, C_x; K is an empirical constant (mm/√h) for given conditions.

δ = 503·√(ρ_e / (μ_r·f)) Induction heating depth: δ in m, ρ_e = electrical resistivity (Ω·m), μ_r = relative permeability (1 above the Curie point), f = frequency (Hz).

Worked examples

Example 1 (standard) – scaling case depth. A gas-carburising cycle gives an effective case depth of 0.5 mm in 4 h. How long for 1.2 mm at the same temperature?

1. x₂/x₁ = √(t₂/t₁) ⇒ t₂ = t₁·(x₂/x₁)².
2. t₂ = 4 h × (1.2/0.5)² = 4 × 5.76.
3. t₂ = 23.0 h. Doubling the case depth needs four times the time – which is why deep cases are expensive.

Example 2 (GATE level) – carburising time from Fick's law. A 0.20 % C steel is carburised with surface carbon held at 1.00 % C. D for carbon in austenite at the process temperature = 1.6 × 10⁻¹¹ m²/s. Find the time for the carbon content at 0.5 mm depth to reach 0.60 %.

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. erf(z) = 0.500 ⇒ z = 0.4769 (from an erf table).
3. z = x/(2√(D·t)) ⇒ D·t = (x/(2z))² = (0.5 × 10⁻³/0.9539)² = 2.748 × 10⁻⁷ m².
4. t = 2.748 × 10⁻⁷/1.6 × 10⁻¹¹ = 1.717 × 10⁴ s = 4.77 h.

Example 3 – induction heating depth. For steel above its Curie point, ρ_e = 1.1 × 10⁻⁶ Ω·m, μ_r = 1. At f = 10 kHz: δ = 503 × √(1.1 × 10⁻⁶/10⁴) = 503 × 1.049 × 10⁻⁵ = 5.28 × 10⁻³ m ≈ 5.3 mm. At 100 kHz δ falls by √10 to about 1.7 mm – higher frequency for thinner cases.

Common mistakes

• Thinking alloying elements make martensite harder. Carbon sets martensite hardness; alloys raise hardenability.
• Confusing annealing (furnace cool, softest) with normalising (air cool, finer and stronger).
• Forgetting to temper after hardening (or after carburising and quenching); untempered martensite is brittle and full of residual stress.
• Using °C instead of kelvin in the Arrhenius equation.
• Assuming case depth is proportional to time; it grows with √t.
• Specifying induction or flame hardening for a low-carbon steel – there is too little carbon to form hard martensite; it must be carburised instead.
• Expecting nitrided parts to need quenching – nitriding is done below A₁ and needs none.

For GATE ME

Expect matching questions (process ↔ temperature range ↔ cooling medium ↔ resulting microstructure), statements on TTT/CCT diagrams, martensite, hardenability and the Jominy test, and comparisons between carburising, nitriding, induction and flame hardening. Numericals include case-depth scaling with √t, the erf carburising solution, diffusion-coefficient changes with temperature, and simple cooling-rate calculations. Practise reading a TTT diagram: which cooling curve gives pearlite, bainite or martensite.

Quick check

1. Which treatment gives finer pearlite: annealing or normalising?
2. Is nitriding done above or below A₁?
3. A case of 0.4 mm takes 2 h. How long does 0.8 mm take at the same temperature?
4. What does the Jominy test measure?
5. Why is low-carbon steel carburised before quenching?

Answers: 1. Normalising; 2. Below A₁ (about 500–570 °C); 3. 8 h; 4. Hardenability (hardness versus distance from the quenched end); 5. To raise surface carbon enough to form hard martensite.