Jominy Hardenability Calculator — Steel Composition to Hardness Profile
The Jominy end-quench test (ISO 642 / ASTM A255) is the universal method for measuring steel hardenability — the capacity to harden throughout a cross-section when quenched. A 25 mm diameter bar is austenitised, end-quenched with a controlled water jet, and Rockwell C hardness measured at 1.5 mm intervals from the quenched face. This calculator predicts the full Jominy hardness profile and ideal critical diameter DI from steel composition using the Grossmann multiplying factor method, and converts Jominy position to equivalent cooling rate and bar section diameter for oil and water quenching.
Key Takeaways
- Hardenability is the depth of hardening, not the maximum hardness — the latter is controlled almost exclusively by carbon content.
- The Grossmann ideal critical diameter DI is a single-number characterisation of hardenability, independent of quench severity; practical bar diameters achieved depend on the quench severity H-factor.
- Manganese, chromium, molybdenum, and boron are the most potent hardenability-increasing alloying elements in engineering steels.
- Coarser prior austenite grain size (lower ASTM number) increases hardenability by reducing grain boundary nucleation sites for pearlite and bainite.
- The maximum as-quenched hardness of a fully martensitic steel is given by HRCmax ≈ 20 + 60 × %C (simplified Koistinen–Marburger approximation for %C 0.20–0.60).
- H-band steels (e.g., 4140H, 8620H) are specified by guaranteed minimum and maximum Jominy hardness values at each distance, which is the most reliable basis for heat treatment process design.
Jominy Hardenability and Section Size Calculator
Enter steel composition (wt%) and prior austenite grain size. Use preset buttons for common grades. Results include DI, Jominy profile chart, and key-position hardness values.
Method: Grossmann DI multiplying factor approach (ASM Handbook Vol. 4, SAE J406). Jominy hardness profile modelled from DI using piece-wise correlation calibrated against published Jominy band data for wrought carbon and alloy steels. Maximum hardness from Koistinen approximation: HRCmax ≈ 20 + 60×%C. Results are screening estimates; validate against measured Jominy data per ASTM A255 / ISO 642 for production heat treatment design.
Hardenability: Definition and Engineering Significance
Hardenability is the property of a steel that determines the depth and distribution of hardness produced by quenching from the austenitising temperature. It is emphatically not the same as hardness: the maximum surface hardness after quenching is controlled almost entirely by carbon content, whereas hardenability — how deeply that hardness penetrates — is controlled by alloy composition, austenite grain size, and the quench severity. A medium-carbon plain steel (1040) and a medium-carbon chromium-molybdenum alloy steel (4140) of identical carbon content will achieve the same surface hardness after an ideal quench, but the 4140 will remain hard to a far greater depth because its higher hardenability suppresses the formation of softer transformation products (ferrite, pearlite, bainite) in the interior.
The engineering importance of hardenability is greatest wherever mechanical components must develop high strength and toughness through the full cross-section after heat treatment: quenching and tempering of structural shafts, gears, crankshafts, and pressure vessel forgings. A steel with insufficient hardenability for the section size will develop a soft, coarse pearlitic or bainitic core beneath the hardened surface case — acceptable for some surface-wear applications but catastrophic where fatigue or impact loading requires high core toughness.
The Jominy End-Quench Test Standard Procedure
The Jominy test is standardised in ISO 642:1999 and ASTM A255-20. The key procedural requirements are:
- Specimen: 25 mm diameter × 100 mm long bar, machined to tolerance ±0.1 mm on diameter.
- Austenitising: Temperature specified as 50°C above Ac3 (typically 830–870°C for most engineering steels), held for 30 minutes after the specimen reaches temperature. Temperature uniformity within ±5°C.
- Transfer time: Maximum 5 seconds from furnace to quench fixture to avoid pre-transformation in transit.
- Water jet: 12.5 mm diameter orifice, free-jet velocity 2.5 ± 0.1 m/s, water temperature 24 ± 3°C, jet impinging on bottom face of vertical bar.
- Hardness measurement: Two parallel flats ground 0.38 mm deep on opposite sides of the bar. Rockwell C or Vickers hardness measured at J1.5, J3, J5, J7, J10, J13, J15, J20, J25, J32, J40 positions.
The Grossmann Ideal Critical Diameter Method
The Grossmann DI (ideal critical diameter) approach, developed by Grossmann at the Illinois Institute of Technology and systematised in ASM Handbook Vol. 4, calculates a single number representing hardenability independently of quench severity. DI is defined as the diameter of a bar that would achieve 50% martensite at its geometric centre when quenched in a theoretically ideal quenchant of infinite severity (Grossmann H = ∞).
D_I Calculation: Multiplying Factor Method
D_I (mm) = D_I,C × f_Mn × f_Si × f_Cr × f_Mo × f_Ni × f_V × f_GS Where D_I,C is the base factor from carbon content and grain size, and each f_X is the multiplying factor for element X. ── Carbon base factor D_I,C (ASTM grain size 7) ───────────────── %C D_I,C (mm) 0.10 3.3 0.20 5.6 0.30 7.9 0.40 10.9 0.50 14.0 0.60 16.5 ── Multiplying factors (Grossmann, SAE J406) ──────────────────── f_Mn = 1 + 3.33 × %Mn (range 0.20–1.80%) f_Si = 1 + 0.70 × %Si (range 0.10–0.40%) f_Cr = 1 + 2.16 × %Cr (range 0–2.00%) f_Mo = 1 + 3.00 × %Mo (range 0–0.50%) f_Ni = 1 + 0.36 × %Ni (range 0–3.50%) f_V = 1 + 1.73 × %V (range 0–0.20%) ── Grain size correction ──────────────────────────────────────── ASTM 5 → f_GS = 1.17 ASTM 6 → f_GS = 1.08 ASTM 7 → f_GS = 1.00 (reference) ASTM 8 → f_GS = 0.91
The resulting DI is then used to determine the actual critical diameter DC achieved under a real quench of severity H (Grossmann quench severity factor) through the relationship:
D_C = D_I / (1 + 0.5 × D_I / (H × D_C)) [iterative solution]
Approximate simplified form:
D_C ≈ D_I × (H / (1 + 0.5 × H)) for H values 0.2–5.0
Quench severity H-values (Grossmann):
Still oil H ≈ 0.3–0.4
Agitated oil H ≈ 0.5–0.8
Still water H ≈ 1.0
Agitated water H ≈ 1.0–1.5
Brine (sat. NaCl) H ≈ 1.5–2.0
Maximum As-Quenched Hardness and Martensite Fraction
The maximum hardness achievable on the quenched surface of a Jominy bar — corresponding to 100% martensite at J1.5 — is governed almost exclusively by the carbon content of the steel. The relationship is described by the Koistinen–Marburger approach combined with empirical carbon-hardness data from ASM:
Maximum HRC (100% martensite) ≈ 20 + 60 × %C
(simplified, valid for %C 0.20–0.60)
More accurate (Maynier, 1978):
HRC_max = 42.4 × %C + 14.4 [for %C ≤ 0.55]
HRC_max = 57.0 × %C + 3.4 [for %C > 0.55]
Martensite start temperature (Ms, Andrews 1965):
Ms (°C) = 539 − 423×%C − 30.4×%Mn − 17.7×%Ni
− 12.1×%Cr − 7.5×%Mo
Koistinen-Marburger martensite fraction:
f_M = 1 − exp(−0.011 × (Ms − T_q))
where T_q = quench temperature (room temperature for full quench)
The hardness at positions beyond J1.5 decreases as the local cooling rate slows, allowing increasing fractions of ferrite, pearlite, and bainite to form alongside martensite. The gradient of the Jominy curve — steep for plain carbon steels, gradual for highly alloyed steels — directly reflects this transition from martensitic to mixed to fully diffusional microstructures. For the relationship between microstructural constituents and their transformation kinetics, the TTT diagram and CCT diagram for the specific steel should be consulted alongside Jominy data.
Jominy Position to Cooling Rate and Section Size
Each Jominy distance corresponds to a defined cooling rate at 700°C, measured during the standard end-quench test by thermocouple instrumentation. These cooling rates are in turn correlated to equivalent positions in oil-quenched and water-quenched bars of standard diameters, enabling a Jominy curve to be directly mapped onto the expected hardness distribution across a real component cross-section. This is the core of the engineering application of Jominy data. For the relationship between cooling rate and microstructural outcome, consult the CCT diagram for the specific steel grade.
| Jominy J (mm) | Cooling rate at 700°C (°C/s) | Bar surface — oil quench | Bar centre — oil quench | Bar centre — water quench |
|---|---|---|---|---|
| J 1.5 | 315 | Surface (any diameter, any quench) | — | Centre of 5 mm bar |
| J 3 | 130 | Surface of 12 mm bar | — | Centre of 10 mm bar |
| J 5 | 56 | Surface of 25 mm bar | Centre of 10 mm bar | Centre of 20 mm bar |
| J 7 | 32 | Surface of 37 mm bar | Centre of 14 mm bar | Centre of 28 mm bar |
| J 10 | 14 | Surface of 50 mm bar | Centre of 25 mm bar | Centre of 50 mm bar |
| J 15 | 5.6 | Surface of 75 mm bar | Centre of 50 mm bar | Centre of 90 mm bar |
| J 20 | 3.3 | Surface of 100 mm bar | Centre of 75 mm bar | Centre of 130 mm bar |
| J 25 | 2.2 | Surface of 125 mm bar | Centre of 100 mm bar | Centre of 170 mm bar |
| J 32 | 1.3 | Surface of 175 mm bar | Centre of 150 mm bar | Core of 250 mm bar |
| J 40 | 0.7 | Core of 150 mm bar (oil) | Centre of 250 mm bar | — |
Common Steel Hardenability Grades
| Steel Grade | Nominal Composition | DI typical (mm) | HRC at J10 | Max through-hardened dia (oil) | Application |
|---|---|---|---|---|---|
| 1040 | 0.40C–0.75Mn | 20–30 | 32–42 | ~20–25 mm | Plain carbon, light section, small shafts |
| 1060 | 0.60C–0.75Mn | 25–35 | 45–52 | ~25–30 mm | Rails, springs (low alloy) |
| 4130 | 0.30C–1.0Cr–0.20Mo | 50–70 | 42–48 | ~50 mm | Aerospace structures, thin-wall tube |
| 4140 | 0.40C–1.05Cr–0.20Mo | 75–100 | 48–54 | ~75 mm | Shafts, gears, bolting, general machinery |
| 4340 | 0.40C–0.80Cr–0.25Mo–1.80Ni | 150–200 | 54–58 | ~150 mm | Heavy section, high-strength aircraft and defence |
| 8620 | 0.20C–0.55Cr–0.20Mo–0.55Ni | 50–75 | 30–38 | Case hardening grade | Gears, camshafts (carburised) |
| 52100 | 1.00C–1.50Cr | 50–80 | 60–64 | ~50 mm | Bearing races, balls, rollers |
| H13 | 0.40C–5.0Cr–1.35Mo–1.0V | >250 | 52–56 | Air-hardening | Hot work tooling, die casting dies |
Alloying Elements and Their Effect on Hardenability
Carbon
Carbon increases both the maximum as-quenched hardness and the base hardenability factor DI,C. However, high carbon also raises the martensite start temperature Ms, increases the volume change during transformation (quench cracking risk), and reduces the toughness of the as-quenched martensite. Most structural engineering steels are limited to 0.25–0.45%C as a balance between strength and toughness after quenching and tempering.
Manganese
Manganese is the most cost-effective hardenability additive in low- and medium-alloy steels, with a multiplying factor of approximately 3.33 per wt%. It acts by retarding the pearlite reaction through partitioning to austenite and carbides. Manganese levels are typically limited to 1.6–1.8% to avoid excessive retained austenite and centre segregation in large ingots.
Chromium and Molybdenum
Chromium (f = 1 + 2.16 × %Cr) strongly suppresses both the pearlite and bainite reactions, making it the alloying element of choice in 4000- and 5000-series steels. Molybdenum (f = 1 + 3.00 × %Mo) is particularly effective at suppressing bainite and also reduces temper embrittlement susceptibility when added at 0.15–0.50%. The synergistic effect of Cr and Mo together is why 4140 (Cr-Mo) and 4340 (Ni-Cr-Mo) steels achieve deep hardenability from relatively modest alloy additions. Molybdenum also improves elevated-temperature strength — see the annealing and normalising guide for thermal stability considerations.
Nickel
Nickel increases hardenability (f = 1 + 0.36 × %Ni) while simultaneously improving toughness of the tempered martensite at low temperatures — a unique combination not achievable with Mn, Cr, or Mo additions alone. In 4340 steel (1.80%Ni), nickel provides both deep hardenability and superior notch toughness, making 4340 the standard for aircraft landing gear, pressure vessel nozzles, and large section forgings requiring high Charpy impact values. For Charpy impact testing methodology, see the Charpy impact test guide.
Vanadium and Grain Size Effects
Vanadium provides a modest hardenability multiplying factor (f = 1 + 1.73 × %V) but its primary metallurgical role in medium-alloy steels is to refine the prior austenite grain size through the pinning of austenite grain boundaries by vanadium carbides or nitrides. This grain refinement reduces hardenability slightly (lower ASTM grain size number = higher fGS) but substantially improves the toughness of the resulting tempered martensite. For the relationship between grain boundaries and mechanical properties, see the grain boundaries guide.
H-Band Hardenability Specification
H-band steels are specified under ASTM A304 and ISO 683-2 with guaranteed minimum and maximum Jominy hardness values at each distance from the quenched end, replacing (or supplementing) the conventional chemical composition specification. The hardenability band is established by testing heats at the extreme composition limits within the allowed range and plotting the envelope of Jominy curves. Specifying steel by hardenability band rather than composition is the most reliable approach for heat treatment process design, particularly for:
- High-volume automotive production where quench uniformity may vary
- Large cross-section forgings where core hardness is a design requirement
- Induction hardening applications where the depth of hardening is a functional specification
- Applications requiring a minimum case depth after carburising or nitriding
FAQ
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Recommended References
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