Hardness validation
How Phases predicts Vickers hardness, which published correlations it uses, and the 25-case literature comparison including the cases it misses.
Every simulator in Phases can report a hardness number, and a hardness number is the result most engineers act on. Before you act on one, you should know that it is an empirical correlation evaluated on predicted phase fractions — not a measurement, and not a first-principles calculation. This page states exactly which correlations are used, what they were compared against, and where they are known to be wrong.
One routine, all four simulators#
Hardness is computed by a single Fortran routine, hardness(cc, crate, x, hv). The file is byte-identical in all four solver packages, so heat treatment, CCT, RSW and V-Gleeble all report hardness on the same basis.
The routine takes three inputs: the composition array (it reads C, Mn, Si, Ni, Cr, Mo, Cu and V), the cooling rate, and the phase fractions at that point in the run. It does not know anything else about the process. Two runs that arrive at the same phase fractions, composition and instantaneous cooling rate get the same hardness, whatever route they took.
The correlations#
The model is a hybrid: different published equations are used for different constituents, and two of them branch at 0.12 wt% carbon.
| Constituent | Condition | Equation (HV) | Source |
|---|---|---|---|
| Martensite | C < 0.12% | 200 + 930·C | Krauss 2005, lath martensite |
| Martensite | C ≥ 0.12% | 884·C·(1 − 0.3·C²) + 294 | Kasuya–Yurioka 1993, stated valid 0.12–0.50% C |
| Martensite | both branches | plus 27·Si + 11·Mn + 8·Ni + 16·Cr | Maynier 1978 alloying correction |
| Bainite | C < 0.12% | 145 + 202·C + 44·Si + 30·Mn + 19·Cu + 24·Cr + 15·Ni + 11·Mo + 300·V | Kasuya–Yurioka non-martensite, noted valid 0.02–0.30% C |
| Bainite | C ≥ 0.12% | −111 + 1180·C + 55·Si + 47·Mn + 23·Ni + 67·Cr + 103·Mo + 21·log₁₀(Vr) | Maynier 1978, noted valid 0.10–0.50% C |
| Ferrite + pearlite | all | 42 + 223·C + 53·Si + 30·Mn + 12.6·Ni + 7·Cr + 19·Mo + (10 − 19·Si + 4·Ni + 8·Cr + 130·V)·log₁₀(Vr) | Maynier 1978 |
Vr is the cooling rate converted to °C per hour and clamped to a minimum of 1 °C/h before the logarithm is taken. Composition terms are in wt%.
The constituents are then combined by a rule of mixtures:
HV = (x_ferrite + x_pearlite)·HV_FP + x_bainite·HV_B + x_martensite·HV_M
Austenite contributes nothing to this sum. Three floors are enforced: 60 HV for ferrite+pearlite, 150 HV for bainite, and 50 HV for the total.
Two consequences follow directly from that formula. The number is a bulk mixture hardness, so it must not be read as the hardness of one phase — the product enforces this in its own reporting rules. And because hardness is evaluated on predicted phase fractions, its accuracy is bounded by the accuracy of the phase-transformation model described in known limits.
The validation record#
The model was compared against published hardness data for 25 cases spanning 14 grades, at two cooling rates: 0.01 °C/s (slow, expected ferrite+pearlite) and 100 °C/s (fast, expected martensite). Most grades were run at both rates; three appear at only one. A case passes if the predicted HV falls inside the published range, and is recorded as a near-miss (~OK) if it falls within 15% of that range.
The recorded outcome is 25 of 25 passing: 19 inside range, 6 near-miss, 0 failures.
| Grade | Rate (°C/s) | Model HV | Literature range | Status |
|---|---|---|---|---|
| DC01 | 0.01 | 103 | 85–120 | OK |
| DC03 | 0.01 | 94 | 80–105 | OK |
| DC05 | 0.01 | 82 | 70–95 | OK |
| DC06 | 0.01 | 70 | 65–95 | OK |
| DC01 | 100 | 406 | 280–380 | ~OK |
| DC03 | 100 | 298 | 250–340 | OK |
| DC05 | 100 | 260 | 200–280 | OK |
| DC06 | 100 | 222 | 180–240 | OK |
| HC260LA | 0.01 | 97 | 85–115 | OK |
| HC300LA | 0.01 | 103 | 100–130 | OK |
| HC380LA | 0.01 | 120 | 120–155 | ~OK |
| HC420LA | 0.01 | 129 | 135–170 | ~OK |
| HC260LA | 100 | 285 | 230–310 | OK |
| HC420LA | 100 | 418 | 340–430 | OK |
| DP450 | 0.01 | 104 | 100–170 | OK |
| DP600 | 0.01 | 138 | 120–220 | OK |
| DP450 | 100 | 281 | 270–360 | OK |
| DP600 | 100 | 316 | 340–430 | ~OK |
| DP780 | 100 | 451 | 420–550 | OK |
| 20MnB5 | 0.01 | 165 | 170–230 | ~OK |
| 20MnB5 | 100 | 494 | 430–520 | OK |
| 22MnB5 | 0.01 | 179 | 150–240 | OK |
| 22MnB5 | 100 | 515 | 440–530 | OK |
| EN13261 | 0.01 | 221 | 250–400 | ~OK |
| EN13261 | 100 | 664 | 620–720 | OK |
Read the pass rate for what it is. Two cooling rates is a coarse grid, the comparison ranges are published ranges rather than coupons cut from your material, and this is the record for the 14 grades listed. It says nothing about DC04, HC340LA, DP500, 20MnB8, 25MnB5 or 29MnB7, which appear in the catalog but not in this table.
Where it is weakest#
Each of the six near-misses has a recorded explanation (HC380LA and HC420LA share one):
- DC01 at 100 °C/s (406 vs 280–380) — the Kasuya–Yurioka branch overestimates right at the 0.12% C boundary where the two martensite equations meet.
- HC380LA and HC420LA at 0.01 °C/s — slightly below range; the predicted pearlite fraction is small so ferrite dominates the mixture.
- DP600 at 100 °C/s (316 vs 340–430) — the model retains some ferrite at this rate. Real spot-weld nuggets cool faster than 100 °C/s.
- 20MnB5 at 0.01 °C/s (165 vs 170–230) — the model produces significant ferrite, which pulls the mixture down.
- EN13261 at 0.01 °C/s (221 vs 250–400) — the model forms more ferrite than expected and should be forming more bainite at moderate rates.
A separate verification run across 17 grades and 7 simulation modes found two further systematic problems that show up as hardness error:
- Low-carbon grades in weld-HAZ cooling. At a peak of 1350 °C and Δt8/5 = 15 s, DC04 is predicted at 275 HV with 97.4% martensite and HC260LA at 277 HV with 95.3% martensite, against an expected 150–200 HV and a mixed ferrite+bainite structure. At 0.08% C these steels have low hardenability, and the current kinetics parameters over-predict martensite for them.
- EN13261 at high hardness. 662 HV in the HAZ mode and 649 HV in hot stamping, against expected 450–550 HV.
That same review records that the hardness coefficients are phase-only and fixed, and lists composition-dependent hardness coefficients as recommended future work.
There is also a structural point worth knowing: when the correlations were re-examined, the conclusion was that the equations themselves were already well calibrated across roughly 0.02–0.40% C, and that the mismatches then visible came from the phase-transformation model returning the wrong phase fractions. If a hardness number looks wrong to you, check the phase fractions first.
What it was compared against#
Maynier et al., Hardenability Concepts with Applications to Steel, AIME 1978, pp518–545; Kasuya, T. & Yurioka, N., Welding Journal 72(6), 1993, pp263s–268s; Krauss, G., Steels: Processing, Structure, Performance, ASM International 2005; Li et al., A Computational Model for the Prediction of Steel Hardenability, Met Trans B 29B, 1998, pp661–672; EN 10130:2006, EN 10268:2006 and EN 13261:2009; and product datasheets from ArcelorMittal, ThyssenKrupp, Voestalpine and SSAB.
Using this in practice#
Ask for hardness the same way you ask for anything else:
Load DC06 and run a heat treatment simulation, then tell me the predicted hardness
Treat the answer as a simulation result that depends on input assumptions and material-data quality, and have it reviewed before it becomes an engineering decision. For weld-specific hardness, including why nugget hardness is a theoretical maximum, see RSW validation. For the general approach, see how we validate; for what each simulator resolves per material, see the capability matrix.
Related: heat treatment · CCT and TTT · virtual Gleeble · glossary