Tempering of Steel — Four Stages, Secondary Hardening, Temper Embrittlement, and Hollomon-Jaffe Calculator

Tempering is the heat treatment applied to quench-hardened martensite to reduce brittleness, relieve quench stresses, and achieve a target balance of hardness, strength, and toughness. As-quenched martensite — a supersaturated, heavily dislocated body-centred tetragonal (BCT) solid solution of carbon in iron — is too brittle for almost every engineering application: it is susceptible to quench cracking, hydrogen-assisted fracture, and catastrophic brittle failure under any impact or cyclic load. Tempering transforms this microstructure progressively through four overlapping stages, each driven by thermally activated diffusion of carbon and substitutional alloying elements, each producing a different microstructural product, and each shifting the hardness-toughness balance by a predictable amount governed by the Hollomon-Jaffe tempering parameter. This article provides a graduate-engineer-level treatment of every aspect of tempering: the four stages and their microstructural products, the Hollomon-Jaffe parameter and its derivation, secondary hardening in alloy and tool steels, temper embrittlement mechanisms and avoidance, double and triple tempering practice, and tempering specifications for common engineering steels.

Why Martensite Must Be Tempered

As-quenched martensite is the hardest microstructure achievable in steel — up to 900+ HV in high-carbon grades — but it is also the most brittle. Three factors combine to make as-quenched martensite dangerously brittle:

1. Carbon supersaturation of the BCT lattice: The tetragonality (c/a > 1) proportional to carbon content creates enormous lattice strains that resist dislocation motion, raising yield strength dramatically but eliminating the ductile flow that normally redistributes stress concentrations.
2. Extremely high dislocation density: The martensitic transformation generates dislocation densities of 10¹⁴–10¹⁶ m⁻² — comparable to heavily cold-worked metal. These tangles block further dislocation motion and promote brittle fracture initiation at stress concentrations.
3. Residual quench stresses: Uneven cooling during quenching generates large tensile residual stresses at the surface or within the component that add to service loads and can initiate cracking without any external load (quench cracking).

Tempering addresses all three by thermally activating diffusion of carbon out of the BCT solid solution (reducing tetragonality), promoting dislocation recovery and rearrangement (reducing density), and relieving quench stresses through stress relaxation. The price is a reduction in hardness; the challenge of tempering practice is choosing the conditions that achieve the required hardness reduction while maximising toughness and avoiding the embrittlement zones.

The Four Stages of Tempering

The Hollomon-Jaffe Tempering Parameter

The Hollomon-Jaffe (H-J) parameter is the most widely used empirical tool for quantifying the combined effect of tempering temperature and time on hardness. It originates from the observation that the hardness after tempering at temperature T for time t is the same as after tempering at a different temperature T′ for a time t′, provided a specific combination of T and log(t) is equal for both conditions.

Derivation

Hollomon-Jaffe parameter derivation:
  Tempering softening rate follows an Arrhenius-type kinetics:
    d(HRC)/dt = A · exp(−Q_t / RT)

  where Q_t = apparent activation energy for tempering (~125–200 kJ/mol)
        R = 8.314 J/mol·K;  T in Kelvin

  Integrating for constant temperature:
    ΔHRC = f(t · exp(−Q_t / RT))

  Taking logarithms and re-arranging:
    log(t) = Q_t / (2.303·R·T) + constant
    2.303·R·T·log(t) = Q_t + constant · T

  Hollomon-Jaffe showed empirically that a single parameter P captures this:
    P = T · (C + log₁₀(t)) × 10⁻³    [T in Kelvin, t in hours]

  where C is a material-dependent constant:
    C = 14–15: low-carbon plain carbon steels
    C = 18–20: medium-carbon Cr-Mo-V alloy steels (most common default: 20)
    C = 20–22: high-alloy tool steels

  Key property:
    If P₁ = T₁(C + log t₁) × 10⁻³ = P₂ = T₂(C + log t₂) × 10⁻³
    → same hardness results from both conditions (equivalence principle)

  Equivalent time at T₂ for the same tempering effect as T₁,t₁:
    log t₂ = (T₁/T₂) · (C + log t₁) − C
    t₂ = 10^[(T₁/T₂)(C + log t₁) − C]

  Temperature sensitivity of P (practical rule):
    P increases by ~0.5 × 10³ per 30°C increase at constant t
    → 10°C error in furnace temperature changes P by ~0.17 × 10³
    → Equivalent to ~3 hours time error at 600°C
    → Temperature accuracy is far more important than time accuracy in tempering!

Worked Example — Section Thickness Compensation

Problem: A 25 mm diameter bar of 4140 (EN 19) is specified to be tempered at 600°C × 1 h.
A 75 mm diameter bar of the same grade needs the same tempering effect
(same H-J parameter → same hardness). What temperature or time is required?

Step 1 — Calculate P for 25 mm bar:
  T₁ = 600 + 273 = 873 K;  t₁ = 1 h;  C = 20
  P₁ = 873 × (20 + log₁₀(1)) × 10⁻³ = 873 × (20 + 0) × 10⁻³ = 17.46 × 10³

Step 2 — The 75 mm bar heats more slowly; effective centre temperature lags by ~15°C.
  Actual centre temper for 75 mm bar at 600°C furnace:  T_eff ≈ 585°C = 858 K
  Target P₁ = 17.46 × 10³
  Required time at 858 K:
    log t₂ = (17.46 × 10³ / 858) − 20 = 20.35 − 20 = 0.35
    t₂ = 10^0.35 = 2.24 h  → Round to 2.5 hours for safety

Alternatively — increase temperature to 610°C for the 75mm bar (centre at 595°C = 868 K):
    log t₂ = (17.46 × 10³ / 868) − 20 = 20.12 − 20 = 0.12
    t₂ = 10^0.12 = 1.32 h → approximately 1.5 hours same effect

Practical recommendation: for section thickness >50 mm, add 15 min per additional 25 mm
of section thickness beyond 25 mm (SAE J406 rule of thumb).

Secondary Hardening

Secondary hardening is the phenomenon in which the hardness of an alloy steel increases during tempering at 450–600 °C after an initial softening at lower tempering temperatures. It occurs only in steels containing significant concentrations of strong carbide-forming elements and is the physical basis for the cutting performance of high-speed steels and the elevated-temperature strength of Cr-Mo pressure vessel steels.

Thermodynamics — Why Alloy Carbides Replace Cementite

Carbide stability sequence (decreasing stability at ~500°C):
  TiC > NbC > V₄C₃ > Mo₂C > W₂C > Cr₇C₃ > Cr₂₃C₆ > Fe₃C (cementite, least stable)

Driving force for alloy carbide precipitation:
  Fe₃C + [Mo]  →  Mo₂C + Fe(matrix)   at T > ~450°C
  ΔG < 0 at these temperatures because Mo₂C is thermodynamically more stable than Fe₃C
  when Mo is present in the matrix above its equilibrium solubility in ferrite at 500°C

Alloy carbide precipitate properties:
  Mo₂C:  hexagonal; lattice parameter near-coherent with BCC Fe; precipitate size 1–5 nm
  V₄C₃:  NaCl structure; very fine; excellent strengthening contribution
  Cr₇C₃: orthorhombic; coarser; less strengthening per unit volume fraction
  W₂C:   hexagonal; similar to Mo₂C; primarily in high-speed steels

Orowan strengthening from secondary carbides:
  Δσ = M · G · b / λ   (simplified Orowan bypassing)
  λ = inter-particle spacing (nm) — very small for 1–5 nm carbides on {110} planes
  → Secondary hardness increment: 5–15 HRC above plain carbon steel at same temperature

  M2 high-speed steel (6W2Mo5Cr4V, ~1%C) triple tempered at 560°C:
  Peak secondary hardness: 64–66 HRC — same or higher than as-quenched hardness (64 HRC)
  Red hardness maintained to 600°C: HRC remains ~60 after 30 min at 600°C
  → enables dry cutting of hardened steels and cast iron at high cutting speeds

Double and Triple Tempering in High-Speed Steels

The standard procedure for M2 high-speed steel after austenitising at 1220–1230 °C and oil or gas quenching:

1. Cryogenic treatment (optional, −80 °C): Transforms a significant fraction of retained austenite (typically 20–30% after quench) to martensite before any tempering, increasing the secondary hardness response. Specified in some tooling standards but adds process complexity.
2. First temper at 560 °C × 1 h: Decomposes most retained austenite; precipitates initial Mo₂C and V₄C₃ secondary carbides; produces some fresh (untempered) martensite from RA decomposition on cooling. Secondary hardness not fully developed yet.
3. Cool to room temperature. Verify Ms (martensite start) of residual austenite is above room temperature — if not, the fresh martensite formed has been quenched again and needs tempering.
4. Second temper at 560 °C × 1 h: Tempers fresh martensite from first cycle; additional secondary carbide precipitation; retained austenite fraction drops to <5%.
5. Third temper at 560 °C × 1 h: Final temper; any remaining fresh martensite is tempered; maximum hardness and toughness combination achieved. Most tool manufacturers specify three tempers minimum.

Temper Embrittlement — Two Distinct Phenomena

Two separate embrittlement phenomena share the name “temper embrittlement” but have completely different causes, temperature ranges, reversibility, and mitigation strategies. Confusing the two leads to incorrect process design and potential service failures.

Tempered Martensite Embrittlement (TME) — 250–350 °C, Irreversible

TME (also called 300 °C embrittlement) occurs in high-carbon steels (>0.4%C) tempered in the Stage III temperature range. The mechanism is the precipitation of thin cementite films on prior austenite grain boundaries during Stage III carbide formation. These continuous or semi-continuous films provide easy transgranular-to-intergranular crack propagation paths: a crack nucleating at a stress concentration propagates along the low-energy cementite-ferrite interface rather than through the tougher ferrite matrix.

TME characteristics:
  Temperature range: 250–350°C (Stage III cementite film formation)
  Steel types affected: high-carbon steels (C > 0.4%), especially those with
    coarse prior austenite grain size (ASTM grain number < 7)
  Fracture mode: mixed intergranular + quasi-cleavage on {100} planes
  Toughness reduction: Charpy energy at 20°C can drop 50–70% vs. lower or higher temper
  Reversible? NO — cementite films once formed require full re-austenitisation to remove

Avoidance:
  · Temper at T < 200°C (Stage I only; retain hardness, accept reduced toughness)
  · OR temper at T > 400°C (Stage IV; cementite spheroidises; films fragment)
  · NEVER hold in the 250–350°C range for extended times in high-carbon steels
  · Fine prior austenite grain size (ASTM 9–12) reduces grain boundary area available
    for continuous film formation → reduces TME severity

Most critical application: safety-critical springs, bolts, and shafts in
  spring steels (60SiCr7, SAE 9260), where temper temperature must be verified
  to be above 400°C to avoid TME while maintaining required hardness (44–50 HRC).

Reversible Temper Embrittlement (RTE) — 375–575 °C

RTE (also called 500 °C embrittlement, Krupp embrittlement, or Grange-Bain embrittlement) occurs when susceptible low-alloy steels are slowly cooled through or held at 375–575 °C. The embrittlement is produced by diffusion of tramp impurity elements — phosphorus (P), antimony (Sb), tin (Sn), and arsenic (As) — from the bulk grain matrix to prior austenite grain boundaries, where they reduce grain boundary cohesion energy by approximately 30–50% per monolayer coverage. This weakening raises the ductile-to-brittle transition temperature (DBTT) by 50–150 °C without any measurable change in room-temperature hardness or tensile strength — making it undetectable by routine hardness testing but dangerous in low-temperature or impact service.

Reversible temper embrittlement kinetics:
  The Bruscato X factor (composite impurity parameter) predicts susceptibility:
    X = (10P + Sb + 4Sn + As) / 100   [elements in wt ppm]
    X < 15: low susceptibility (modern clean-steel practice target)
    X > 25: high susceptibility (old steel practices; recycled scrap input)

  Bruscato J factor (alternative, considers Mn and Si interaction):
    J = (Si + Mn) × (P + Sn) × 10⁴   [Si, Mn in wt%; P, Sn in wt%]
    J < 100: acceptable for Charpy-tested applications
    J > 200: high risk of significant DBTT shift

Effect of Molybdenum:
  Mo (0.3–0.5 wt%) is the most effective mitigation alloying element.
  Mo reduces RTE by two mechanisms:
  1. Mo segregates to grain boundaries preferentially over P, Sb, Sn, As
     (higher binding energy to boundary) → physically displaces harmful elements
  2. Mo forms Mo₂P, Mo₃P compounds that remove P from solid solution in grain interior
     → reduces the driving force for P boundary segregation
  Typical Mo addition for RTE resistance: 0.20–0.50 wt% (EN 24 / 4340 range)

PWHT vulnerability:
  Cr-Mo pressure vessel steels (1.25Cr-0.5Mo, 2.25Cr-1Mo) used in refinery vessels
  are most vulnerable: PWHT at 620–650°C required by ASME, but subsequent service
  at 300–400°C or slow cool to ambient can induce RTE over years.
  API 934 monitors DBTT shift by Charpy surveillance specimens in vessels.

Tempering Specifications for Common Engineering Steels

Tempering Practice — Process Control and Quality Assurance

Furnace Atmosphere and Oxidation

Tempering is typically performed in air furnaces for most engineering steels — the low oxygen partial pressure at tempering temperatures (below 700 °C) produces only a thin, removable oxide layer on the steel surface. However, for precision components with tight dimensional tolerances or high-quality surface finish requirements, tempering in protective atmosphere (nitrogen, endothermic gas, or vacuum) prevents surface oxidation and decarburisation. Precision gear teeth, aerospace bearing races, and tool steel cutting edges are typically tempered under protective atmosphere or in neutral salt baths to preserve surface integrity.

Temperature Measurement and Calibration

Because the H-J parameter shows that a 10 °C error in tempering temperature produces the equivalent of approximately 1.7 hours of time error (at 600 °C), temperature measurement accuracy is critical. The following control hierarchy applies:

• Thermocouple types: Type K (chromel-alumel) adequate for 100–700 °C; Type N preferred for precision work and extended life above 500 °C; minimum 2–point calibration per ASTM E230
• Survey thermocouples: NADCAP-accredited heat treatment shops perform Temperature Uniformity Surveys (TUS) per AMS 2750 (Grade 3 minimum for tempering: ±8 °C throughout working zone)
• Load thermocouples: For critical aerospace components, thermocouples are attached to representative parts to verify actual part temperature, not just furnace chamber temperature
• Soak time: Timing starts only after all thermocouples confirm the part has reached within 8 °C of the set temperature (not when the furnace thermocouple reaches set point)

Quench-to-Temper Interval

The time between quenching and tempering must be controlled to prevent cracking of as-quenched martensite. Hydrogen dissolved during quenching (from water or oil vapour decomposition) diffuses through the BCT lattice and accumulates at stress concentrations; delayed tempering allows hydrogen embrittlement cracking to develop in susceptible medium-carbon alloy steels. General practice: temper within 4 hours of quenching for plain and low-alloy steels; within 1 hour for high-alloy and tool steels containing >1%C or significant retained austenite. Some standards (AMS 2759) specify “temper within 2 hours of quench or cool to 65 °C minimum within 15 minutes” as a compromise for thick sections that may crack if tempered while still hot at the core.

Frequently Asked Questions

Recommended References

Further Reading