What is the effect of austenite grain size on martensite start temperature?

Austenite grain size has a modest but measurable effect on Ms temperature. Finer austenite grains (ASTM grain size 8–10) generally produce slightly lower Ms compared with coarse-grain austenite (ASTM 3–5) of the same composition, because finer grains have more grain boundary area that provides nucleation sites for martensite embryos but also more grain boundary constraint. Experimental data shows the Ms shift with grain size is typically 5–15°C across the range ASTM 3–10 — small compared with the compositional effects (42°C per 0.1%C). More significant is the effect of prior austenite grain size on martensite morphology: coarse grains (>100 µm) produce plate martensite with a midrib and twin substructure in high-carbon steels; fine grains tend to produce lath martensite at the same carbon content. This morphological change affects toughness substantially but Ms itself only modestly. The empirical Ms equations discussed above do not include grain size as a variable.

Calculator & Guide 📅 March 25, 2026 ⏳ 14 min read 👤 MetallurgyZone

Martensite Start Temperature Calculator — Ms, Mf, Retained Austenite, and Hardness from Steel Composition

Q: What is the Andrews (1965) equation for martensite start temperature?

The Andrews (1965) empirical equation for Ms temperature is: Ms (°C) = 539 − 423×%C − 30.4×%Mn − 17.7×%Ni − 12.1×%Cr − 7.5×%Mo + 10×%Co − 7.5×%Si. It was derived by multiple linear regression on 66 steels with compositions in the ranges 0.03–0.64%C, 0.17–1.96%Mn, 0–4.89%Ni, 0–9.41%Cr, 0–4.27%Mo, 0–9.0%Co. Andrews reported a standard deviation of ±17°C for this dataset. The equation remains the most widely cited and used Ms prediction formula in the literature and in industrial heat treatment practice, though it underestimates Ms for high-carbon (>0.6%C) steels and does not include terms for V, Nb, W, or B additions.

Q: What is the Koistinen-Marburger equation and how is it used to predict retained austenite?

The Koistinen-Marburger (1959) equation describes the fraction of martensite formed as a function of temperature below Ms: f_M = 1 − exp[−0.011 × (Ms − T)], where f_M is the martensite volume fraction (0 to 1) and T is the temperature in °C. The residual austenite fraction is therefore f_γ = 1 − f_M = exp[−0.011 × (Ms − T)]. This athermal kinetics model shows that martensite transformation is not complete at Ms − 200°C for most steels — typically 2–10% retained austenite remains even after quenching to room temperature. For steel quenched to room temperature (T_q = 25°C), the retained austenite fraction is approximately: f_γ = exp[−0.011 × (Ms − 25)]. For M2 high-speed steel with Ms ≈ 200°C: f_γ = exp[−0.011 × 175] = exp(−1.925) ≈ 0.15 (15% RA). The constant 0.011 was empirically determined by Koistinen and Marburger for plain-carbon and low-alloy steels; some alloy steels require a different constant (typically 0.008–0.015 depending on composition).

Q: How does carbon content affect the martensite start temperature?

Carbon is the most powerful suppressor of Ms in steel. In the Andrews equation, each 0.1% increase in carbon reduces Ms by approximately 42°C (−423°C per 1%C). In the Barbier equation, the carbon effect is non-linear due to the exponential term: Ms = 565 − 600×(1 − exp(−0.96×%C)) − ..., which more accurately captures the diminishing effect of carbon at high concentrations (above ~0.5%C). The physical basis is that dissolved carbon atoms create a tetragonal distortion of the BCC (BCT) martensite lattice, requiring more undercooling to supply the free energy necessary for the diffusionless shear transformation. In high-carbon steels (>0.6%C), Ms can fall below 200°C, meaning the Mf temperature drops below ambient temperature and significant retained austenite is unavoidable without sub-zero treatment. At 1.0%C (tool steel range), Ms ≈ 115°C using Andrews and Mf ≈ −100°C — so approximately 25–35% retained austenite forms in as-quenched tool steels.

Q: How is the martensite start temperature used to design preheat for welding?

Ms temperature is a critical input for welding preheat calculation because the HAZ martensite transformation occurs at Ms (typically 350–450°C for low-alloy structural steels). Cold cracking (hydrogen-assisted cracking) occurs when three conditions coincide: susceptible (martensitic) microstructure, sufficient hydrogen, and sufficient tensile stress. Preheat slows the cooling rate through the martensite transformation range, allowing hydrogen to diffuse away from the HAZ before the brittle martensite forms. Preheat temperature is typically set at or above the minimum temperature needed to reduce cooling rate such that the time above Ms is extended (allowing hydrogen diffusion). Several codes (BS EN ISO 17663, Uwer-Höhe method, CEN TR 10347) use Pcm or CE as a proxy for Ms to derive minimum preheat temperatures. The Pcm formula (Ito-Bessyo cold cracking parameter) is directly related to hardenability and implicitly to Ms: Pcm = %C + %Si/30 + (%Mn + %Cu + %Cr)/20 + %Ni/60 + %Mo/15 + %V/10 + 5×%B.

Q: What is the Mf temperature and why is it important for heat treatment design?

Mf (martensite finish temperature) is the temperature at which martensite transformation is nominally complete — defined as the temperature where approximately 95–99% of austenite has transformed to martensite. It is approximately Mf ≈ Ms − 150°C to Ms − 215°C depending on composition, though the Koistinen-Marburger equation shows that transformation is asymptotic and never truly reaches 100% for most alloy steels. If Mf lies above room temperature (e.g., plain carbon steels with Ms ≈ 250°C → Mf ≈ 50°C), the as-quenched part contains very little retained austenite and minimal dimensional instability. If Mf falls below ambient (high-alloy steels, high-carbon steels), significant retained austenite remains, requiring sub-zero treatment at −60 to −80°C (or cryogenic at −196°C) to convert additional austenite. For tool steels and bearing steels, Mf well below ambient is unavoidable — triple tempering cycles are used to convert retained austenite progressively rather than completing the transformation before the first temper.

Q: How is as-quenched hardness related to Ms temperature and carbon content?

As-quenched martensite hardness is primarily a function of carbon content dissolved in the austenite before quenching, not of the alloy additions that influence Ms. The empirical relationship by Krauss and others is approximately: HRC ≈ 64 − 264×(Ms/1000) for fully martensitic steels, or more directly: HRC_max ≈ 20 + 60×√(%C) (Vickers: HV ≈ 127 + 949×%C for plain martensite). At 0.20%C (carburised case, D2/H13 base): HRC ≈ 47; at 0.40%C: HRC ≈ 57; at 0.60%C: HRC ≈ 63; at 0.80%C: HRC ≈ 65; above 0.60%C, hardness plateaus because additional retained austenite (from the depressed Ms) offsets the carbon strengthening. The alloy additions (Cr, Ni, Mo, Mn) that reduce Ms improve hardenability (depth of hardening) by suppressing pearlite/bainite formation, but do not materially increase the maximum as-quenched hardness of fully martensitic samples at a given carbon content.

Q: Which Ms equation is most accurate for high-alloy and stainless steels?

For conventional low-alloy steels (C < 0.5%, alloy < 5% total), the Andrews (1965) and Steven-Haynes (1956) equations are adequate (±20–30°C). For high-alloy steels (9–12% Cr, HSLA steels, tool steels), the Barbier (2012) equation provides significantly better accuracy by using a non-linear carbon term: Ms = 565 − 600×(1 − exp(−0.96×%C)) − 31×%Mn − 13×%Cr − 9×%Mo − 18×%Ni + 10×%Co + 15×%Al. Barbier validated this against a dataset of 780 steels with wide composition ranges. For martensitic stainless steels (AISI 410, 420, 440C), none of the above equations is accurate without specific calibration — 440C (1%C, 17%Cr) gives Ms ≈ 250°C experimentally but Andrews predicts ~90°C. The Calculation of Phase Diagrams (CALPHAD) approach using thermodynamic software (Thermo-Calc with TCFE steel database) provides the most accurate Ms prediction for complex alloys, though at the cost of requiring specialist software.

The martensite start temperature (Ms) is the temperature at which the diffusionless shear transformation from austenite to martensite begins on cooling of steel from the austenitising temperature. It is the single most important transformation temperature in steel heat treatment: it governs quench severity requirements, retained austenite content, as-quenched hardness, dimensional change, cold-cracking risk in welding, and the minimum preheat needed for hardenable steels. This calculator implements four validated empirical equations — Andrews (1965), Steven–Haynes (1956), Barbier (2012), and Kung (1992) — plus the Koistinen–Marburger kinetics equation for retained austenite fraction, Vickers hardness estimation, and a live plot of the martensite transformation curve.

Key Takeaways

Carbon is the most powerful Ms depressant: each 0.1 wt%C reduces Ms by approximately 42 °C (Andrews) — the non-linear Barbier equation is more accurate above 0.5 wt%C.
Koistinen–Marburger equation: f_M = 1 − exp[−0.011 × (Ms − T)] describes martensite fraction as a function of quench temperature below Ms.
Retained austenite (RA) at room temperature is given by: f_γ = exp[−0.011 × (Ms − 25)]. For Ms = 200 °C, RA ≈ 15%.
Mf (martensite finish) ≈ Ms − 150 to Ms − 215 °C. If Mf < 25 °C, sub-zero treatment is needed to reduce RA.
As-quenched Vickers hardness is primarily a function of carbon content: HV ≈ 127 + 949 × %C + 27 × %Si + 11 × %Mn + 8 × %Ni + 16 × %Cr + 21 × %Mo (Seyffarth, for fully martensitic microstructure).
All four equations have ±15–30 °C accuracy for conventional low–alloy steels; accuracy degrades for compositions outside each equation’s calibration range.

Martensite Start Temperature Calculator

Andrews (1965) · Steven–Haynes (1956) · Barbier (2012) · Kung (1992)
+ Koistinen–Marburger retained austenite · Mf estimation · As-quenched HV · Live transformation curve

Steel Grade Presets

Steel Composition (wt %)

Carbon (C) 0–2.5% Enter 0–2.5%

Manganese (Mn) 0–10%

Silicon (Si) 0–3%

Chromium (Cr) 0–20%

Nickel (Ni) 0–30%

Molybdenum (Mo) 0–10%

Cobalt (Co) 0–20% (raises Ms)

Aluminium (Al) 0–3% (raises Ms)

Tungsten (W) 0–20%

Vanadium (V) 0–5%

Copper (Cu) 0–5%

Quench Stop Temperature T_q (°C) 25 = ambient; −196 = LN₂ cryo

Ms Temperature — Four Empirical Equations

—

°C

Andrews
(1965)

—

°C

Steven–Haynes
(1956)

—

°C

Barbier
(2012)

—

°C

Kung
(1992)

Derived Properties (using mean Ms)

—

°C

Mean Ms

—

°C

Mf estimate
(Ms − 215)

—

Retained γ at T_q
(Koistinen–Marburger)

—

As-quenched HV
(Seyffarth, fully mart.)

Martensite Transformation Curve (Koistinen–Marburger)

Martensite fraction Retained austenite T_q quench stop Ms Mf

Step-by-Step Calculation

—

_q) Ms Mf 25°C ~30% M₊ ~90% M₊ Ms Mf Koistinen–Marburger Transformation Curve f_M T (°C) 0 .2 .4 .6 .8 1.0 Ms Mf 25°C RA≈3% fᴠ = 1−exp[−0.011×(Ms−T)] Koistinen–Marburger (1959) © metallurgyzone.com — Example: Ms = 350 °C (0.40%C, 0.75%Mn, 1.05%Cr steel). Mf ≈ 135 °C. RA at 25 °C ≈ 3%.

Fig. 1 — Left: Schematic continuous cooling curve showing the three temperature zones relative to Ms and Mf: austenite stable (above Ms), martensite transformation zone (Ms to Mf), and below-Mf zone where transformation approaches completion. Right: Koistinen–Marburger transformation curve for an example steel (Ms = 350 °C), showing martensite fraction f_M as a function of quench temperature. At 25 °C (ambient quench), retained austenite is approximately 3% for this composition. A steel with lower Ms (e.g. 200 °C) would show ~15% RA at the same quench stop temperature. © metallurgyzone.com

The Four Empirical Ms Equations: Derivation and Accuracy

All empirical Ms equations are derived by multiple linear (or non-linear) regression of measured Ms temperatures against steel composition from a calibration dataset. Each equation is therefore only as reliable as the composition range covered by its training data. The calculator above presents four equations to give a range of predictions and highlight disagreement — large spread (> 50 °C between equations) signals that the composition is outside the calibration range of at least one equation and that experimental measurement is advisable.

Andrews (1965) — The Standard Reference

Andrews (1965) — Journal of the Iron and Steel Institute, 203, 721–727:

  Ms (°C) = 539 − 423×%C − 30.4×%Mn − 17.7×%Ni − 12.1×%Cr
              − 7.5×%Mo + 10×%Co − 7.5×%Si

  Calibration range:
    C:  0.03–0.64%  |  Mn: 0.17–1.96%  |  Ni:  0–4.89%
    Cr: 0–9.41%     |  Mo: 0–4.27%     |  Co: 0–9.0%
    Si: 0–1.99%

  Dataset: 66 steels (includes plain-carbon, Mn, Cr-Mo, Ni-Cr-Mo, Co steels)
  Standard deviation: ±17°C on training data

  Reported coefficient effects (per 1 wt%):
    C:  −423°C  (dominant depressant)
    Mn: −30.4°C
    Ni: −17.7°C
    Cr: −12.1°C
    Mo: −7.5°C
    Co: +10.0°C  (only common element that RAISES Ms)
    Si: −7.5°C

  LIMITATION: Linear in carbon — overestimates Ms above 0.6%C where
  the non-linear carbon effect becomes significant.

Steven and Haynes (1956)

Steven & Haynes (1956) — JISI, 183, 349–359:

  Ms (°C) = 561 − 474×%C − 33×%Mn − 17×%Ni − 17×%Cr − 21×%Mo

  Calibration range:
    C: 0.1–0.55%  |  Mn: 0.2–1.7%  |  Ni: 0–5%
    Cr: 0–3.5%    |  Mo: 0–1%

  Dataset: Low-alloy steels for structural and engineering applications
  No Si, Co, Al, W terms

  Note: Higher carbon coefficient (474 vs 423 in Andrews) often gives
  lower Ms predictions for medium-carbon steels. No Co term — not
  applicable for tool steels with significant Co content.

Barbier (2012) — Non-Linear Carbon Treatment

Barbier (2012) — Advanced Engineering Materials, 14(8):

  Ms (°C) = 565 − 600×(1 − exp(−0.96×%C))
              − 31×%Mn − 13×%Cr − 9×%Mo − 18×%Ni
              + 10×%Co + 15×%Al

  Calibration range:
    C: 0–1.5%    |  Mn: 0–3.5%  |  Cr: 0–16%
    Mo: 0–5%     |  Ni: 0–12%   |  Co: 0–10%
    Al: 0–1.5%

  Dataset: 780 steels — much broader than Andrews or Steven–Haynes
  Includes high-Cr (martensitic stainless) and high-C steels

  Key advantage: Non-linear carbon term captures the diminishing
  effect of C on Ms at high concentrations (>0.5%C).

  At low C: 600×(1−exp(−0.96C)) ≈ 600×0.96×C = 576C (similar to linear)
  At C=0.5: term = 600×(1−exp(−0.48)) = 600×0.381 = 229°C
  At C=1.0: term = 600×(1−exp(−0.96)) = 600×0.617 = 370°C
  vs Andrews linear: 423×1.0 = 423°C (overestimates Ms suppression)

  RECOMMENDED for compositions with C > 0.5% or Cr > 5%.

Kung (1992)

Kung (1992) — Metallurgical Transactions A, 23:

  Ms (°C) = 539 − 423×%C − 30.4×%Mn − 7.5×%Si
              − 17.7×%Ni − 12.1×%Cr − 7.5×%Mo
              − 7.5×%W − 10×%Cu

  Identical to Andrews for elements without W and Cu.
  Adds W (−7.5°C/%) and Cu (−10°C/%) terms.
  Useful for tungsten-containing tool steels and Cu-bearing HSLA steels.

  Note: W coefficient of −7.5°C/% is relatively small — at typical
  M2 W content of 6.4%, this contributes only −48°C to Ms suppression,
  less than the carbon contribution of ~270°C.

Koistinen–Marburger Equation: Martensite Fraction and Retained Austenite

The Koistinen–Marburger (K–M) equation (1959) describes the athermal kinetics of martensitic transformation — the fraction of martensite formed at any temperature between Ms and Mf, without the time-dependence characteristic of diffusional transformations. It is one of the most widely validated empirical equations in physical metallurgy and is implemented in virtually all commercial phase transformation simulation software (Thermo-Calc TC-PRISMA, JMatPro, SYSWELD).

Koistinen–Marburger Equation (1959):

  Martensite fraction:
  f_M(T) = 1 − exp[−α × (Ms − T)]

  Retained austenite fraction:
  f_γ(T) = 1 − f_M = exp[−α × (Ms − T)]

  Where:
    T  = temperature at which fraction is evaluated [°C]
    Ms = martensite start temperature [°C]  (from empirical equation)
    α  = rate constant = 0.011 °C⁻¹ (Koistinen–Marburger original)

  Alternative α values reported in literature:
    α = 0.011: plain carbon and low-alloy steels (original KM)
    α = 0.008–0.010: high-alloy steels (Cr-Ni austenitic compositions)
    α = 0.013–0.015: some Fe-Ni alloys

  Retained austenite after quenching to ambient (Tq = 25°C):
  f_γ(25) = exp[−0.011 × (Ms − 25)]

  Examples:
    Ms = 400°C: f_γ = exp(−4.12) = 0.016 ≈ 2% RA
    Ms = 300°C: f_γ = exp(−3.025) = 0.049 ≈ 5% RA
    Ms = 200°C: f_γ = exp(−1.925) = 0.146 ≈ 15% RA
    Ms = 100°C: f_γ = exp(−0.825) = 0.439 ≈ 44% RA

  Sub-zero treatment benefit (quench to −80°C):
  At Ms = 200°C, Tq = −80°C:
  f_γ = exp(−0.011 × 280) = exp(−3.08) = 0.046 ≈ 5% RA (vs 15% at 25°C)

  Deep cryogenic treatment (−196°C, LN₂):
  At Ms = 200°C, Tq = −196°C:
  f_γ = exp(−0.011 × 396) = exp(−4.36) = 0.013 ≈ 1% RA

Why retained austenite matters: Retained austenite (RA) in as-quenched tool steels reduces hardness below the carbon-content maximum (soft austenite islands in a hard martensite matrix), creates dimensional instability when RA subsequently transforms to martensite during service or tempering, and reduces fatigue resistance in bearing and gear steels. The dimensional change on RA transformation is approximately 0.4 × %RA × 0.001 linear — a 15% RA steel bearing ring can expand by 0.006% (6 μm on a 100 mm bore) if RA converts in service, causing bearing seizure. Sub-zero treatment at −60 to −80 °C, or cryogenic at −196 °C, before the first temper converts the majority of RA and is mandatory for precision bearing, die, and gauge steel applications.

As-Quenched Hardness Prediction

As-quenched martensite hardness is primarily governed by the carbon content dissolved in austenite before quenching. Alloying elements (Cr, Ni, Mo, Mn) that reduce Ms improve hardenability (depth of hardening) but do not significantly increase the maximum attainable hardness at a given carbon content. The relationship between carbon content and maximum as-quenched Vickers hardness in fully martensitic steel is well established.

As-Quenched Hardness — Seyffarth Equation (fully martensitic):

  HV = 127 + 949×%C + 27×%Si + 11×%Mn + 8×%Ni + 16×%Cr + 21×%Mo
       (valid for fully martensitic microstructure, no bainite or ferrite)

  Simplified carbon-only approximation (±20 HV):
  HV_max ≈ 127 + 949×%C

  HRC conversion (approximate, valid HRC 20–65):
  HRC ≈ (HV − 80) / 10.3  [rough; use official conversion tables for precision]

  Carbon vs. maximum hardness:
    0.10%C: HV ≈ 222  (HRC ≈ 14)  — case-hardened steel base
    0.20%C: HV ≈ 317  (HRC ≈ 23)
    0.30%C: HV ≈ 412  (HRC ≈ 32)
    0.40%C: HV ≈ 507  (HRC ≈ 41)
    0.50%C: HV ≈ 601  (HRC ≈ 50)
    0.60%C: HV ≈ 696  (HRC ≈ 59)
    0.80%C: HV ≈ 886  (HRC ≈ 62, limited by RA)
    1.00%C: HV ≈ 1076 (HRC ≈ 65, limited by RA)

  NOTE: Above ~0.6%C, actual measured hardness falls short of
  the fully-martensitic prediction because retained austenite
  (soft phase) accumulates. The Seyffarth equation gives the
  theoretical fully-martensitic value — the actual value is
  approximately HV_actual ≈ HV_max × (1 − f_γ) + HV_γ × f_γ
  where HV_γ ≈ 150–300 HV for austenite.

Engineering Significance of Ms Temperature by Steel Category

Steel Grade / Type	Typical Ms (°C)	Typical Mf (°C)	RA at 25°C quench	Sub-zero needed?	Engineering implication
Plain C (0.2%C)	430–450	220–240	<1%	No	Very low RA; transformation complete at ambient. Low HV (≈320).
S355 / A572 structural	420–460	210–250	<2%	No	Martensite in HAZ on fast cooling; preheat to slow cooling and temper HAZ
4140 (42CrMo4)	310–370	100–160	3–5%	No (optional)	Good hardenability; Mf near ambient; minimal RA. Target 50–55 HRC
4340	290–330	80–120	5–8%	No (optional)	Deep hardening; Mf just above ambient; low RA in sections below 75 mm
H13 (0.40%C, 5Cr)	310–360	100–150	3–6%	No	Low RA acceptable; double temper removes remainder
D2 (1.55%C, 12Cr)	220–280	10–70	10–18%	Recommended	High RA from high C and Cr; sub-zero before first temper for precision tooling
M2 (austenitised at 1220°C)	180–240	−35 to +25	15–30%	Yes (mandatory for precision)	Very high RA; triple temper required; sub-zero preferred before first temper
P91 (9Cr-1Mo-V)	400–440	190–230	<2%	No	Low RA; Ms relatively high. Preheat 200°C minimum in welding (ASME B31.1)
17-4 PH SS	100–130	−90 to −120	30–45%	Yes (for condition A)	Very low Ms from high Ni+Cr; substantial RA in as-quenched condition; transforms on ageing
Maraging 250	−30 to +20	−200 to −240	50–90%	Critical	Austenitic above ambient; martensite on cooling; strengthened by intermetallic precipitation not C

Table 1 — Typical Ms, Mf, and retained austenite for common engineering steels. D2 and M2 compositions are given for the austenitised (dissolved) condition — actual values vary with austenitising temperature and time. All Ms values are estimates using the Andrews equation; verify experimentally for critical applications.

Worked Example: SAE 4140 Steel

SAE 4140 (42CrMo4) is one of the most widely used alloy engineering steels. A typical heat from a steel mill has the following composition (by OES): 0.41%C, 0.84%Mn, 0.23%Si, 0.98%Cr, 0.21%Ni, 0.19%Mo. Calculate Ms, Mf, retained austenite at 25 °C and at −80 °C, and as-quenched hardness.

SAE 4140 — Complete Ms Calculation

Composition: 0.41C, 0.84Mn, 0.23Si, 0.98Cr, 0.21Ni, 0.19Mo

Andrews (1965):
  Ms = 539 − 423(0.41) − 30.4(0.84) − 17.7(0.21) − 12.1(0.98) − 7.5(0.19) − 7.5(0.23)
     = 539 − 173.4 − 25.5 − 3.7 − 11.9 − 1.4 − 1.7
     = 539 − 217.6
     = 321°C

Steven–Haynes (1956):
  Ms = 561 − 474(0.41) − 33(0.84) − 17(0.21) − 17(0.98) − 21(0.19)
     = 561 − 194.3 − 27.7 − 3.6 − 16.7 − 4.0
     = 561 − 246.3
     = 315°C

Barbier (2012):
  Carbon term: 600×(1−exp(−0.96×0.41)) = 600×(1−exp(−0.394)) = 600×0.325 = 194.9
  Ms = 565 − 194.9 − 31(0.84) − 13(0.98) − 9(0.19) − 18(0.21)
     = 565 − 194.9 − 26.0 − 12.7 − 1.7 − 3.8
     = 565 − 239.1
     = 326°C

Mean Ms = (321 + 315 + 326) / 3 = 321°C  (use this for Mf and RA)

Mf estimate:
  Mf = Ms − 215 = 321 − 215 = 106°C

Retained austenite — Koistinen–Marburger:
  At 25°C: f_γ = exp[−0.011×(321−25)] = exp[−0.011×296] = exp(−3.256) = 0.038 ≈ 4% RA
  At −80°C: f_γ = exp[−0.011×(321−(−80))] = exp[−0.011×401] = exp(−4.411) = 0.012 ≈ 1% RA

As-quenched hardness (Seyffarth, fully martensitic):
  HV = 127 + 949(0.41) + 27(0.23) + 11(0.84) + 8(0.21) + 16(0.98) + 21(0.19)
     = 127 + 389.1 + 6.2 + 9.2 + 1.7 + 15.7 + 4.0
     = 553 HV  ≈ 53 HRC

  Corrected for RA at 25°C quench:
  HV_actual ≈ 553 × (1−0.038) + 200 × 0.038 = 553 × 0.962 + 7.6 = 540 HV ≈ 52 HRC

Preheat assessment:
  CE(IIW) = 0.41 + 0.84/6 + (0.98+0.19)/5 + 0.21/15
           = 0.41 + 0.140 + 0.234 + 0.014 = 0.798
  Minimum preheat (Dearden-O’Neill): 150–200°C (CE > 0.6 → preheat mandatory)

Fig. 2 — Left: Ms temperature vs carbon content for three empirical equations with all other alloying elements set to zero. The Andrews and Steven–Haynes equations are linear in carbon and diverge from the non-linear Barbier equation above 0.5 wt%C, with Andrews overestimating the carbon suppression effect at high carbon content. Right: Retained austenite fraction after quenching to 25 °C (ambient) as a function of Ms temperature, calculated by the Koistinen–Marburger equation. Steels with Ms below approximately 240 °C will contain more than 10% retained austenite after an ambient quench and should be considered for sub-zero treatment. © metallurgyzone.com

Application to Welding: Ms Temperature and Preheat Calculation

Ms temperature is a critical input for weld preheat determination because it governs both the susceptibility to hydrogen-assisted cold cracking (HACC) and the minimum preheat temperature needed to prevent it. The connection is indirect: the empirical carbon equivalent (CE) formulas used in preheat calculations are linear combinations of alloying elements that also appear in Ms equations — because both properties respond to the same fundamental microstructural variable, hardenability. High hardenability (low Ms) means the HAZ forms martensite at faster cooling rates, and martensite is the microstructure most susceptible to HACC.

Carbon Equivalent Formulas for Preheat Determination:

  CE(IIW) = %C + %Mn/6 + (%Cr + %Mo + %V)/5 + (%Ni + %Cu)/15

  Pcm (Ito-Bessyo, better for C < 0.18%):
  Pcm = %C + %Si/30 + (%Mn+%Cu+%Cr)/20 + %Ni/60 + %Mo/15 + %V/10 + 5%B

  Relationship to Ms (Graville’s Pcm approach):
  Minimum preheat T_p (°C) ≈ 1440 × Pcm − 392 (approximate guide)

  Connection to Ms:
  Lower CE ↜ higher Ms ↜ martensite forms at higher temperature
                ↜ faster H diffusion during transformation
                ↜ less H accumulation at the time of martensite formation
                ↜ lower cracking susceptibility

  Practical guidance from ASME B31.1 preheat table:
  P91/Grade 91 (CE ≈ 0.80): T_p = 200°C minimum; Ms ≈ 420°C
  4140 (CE ≈ 0.80):          T_p = 150–200°C; Ms ≈ 330°C
  S355 (CE ≈ 0.45):          T_p = 50–100°C (thin sections: none)
  304L SS (austenitic):         No martensite; no preheat required for HAC

Frequently Asked Questions

What is the Andrews (1965) equation for martensite start temperature?

The Andrews (1965) empirical equation is: Ms (°C) = 539 − 423×%C − 30.4×%Mn − 17.7×%Ni − 12.1×%Cr − 7.5×%Mo + 10×%Co − 7.5×%Si. It was derived by multiple linear regression on 66 steels with compositions in the ranges 0.03–0.64%C, 0.17–1.96%Mn, 0–4.89%Ni, 0–9.41%Cr, 0–4.27%Mo, 0–9.0%Co. Andrews reported a standard deviation of ±17°C. Carbon is the dominant depressant (−423°C per 1%C); cobalt is unique in raising Ms (+10°C per 1%Co). The equation is less accurate above 0.6%C and for high-alloy or stainless steels outside its calibration range.

What is the Koistinen-Marburger equation and how is it used to predict retained austenite?

The Koistinen–Marburger (1959) equation describes martensite fraction at any temperature below Ms: f_M = 1 − exp[−0.011 × (Ms − T)]. Retained austenite fraction is f_γ = 1 − f_M = exp[−0.011 × (Ms − T)]. After quenching to ambient (T_q = 25°C): f_γ = exp[−0.011 × (Ms − 25)]. For M2 high-speed steel (Ms ≈ 220°C), RA ≈ 15% after ambient quench. Sub-zero treatment at −80°C reduces this to ≈5%. The constant 0.011 °C⁻¹ applies to low-alloy steels; some high-alloy steels require 0.008–0.015 for accuracy.

How does carbon content affect the martensite start temperature?

Carbon is the most powerful Ms depressant. In the Andrews equation, each 0.1% increase in carbon reduces Ms by approximately 42°C. The Barbier equation uses a non-linear carbon term that more accurately captures the diminishing effect at high carbon concentrations: above 0.5%C the linear Andrews equation overestimates how much carbon suppresses Ms. At 1.0%C (tool steel range), Ms ≈ 115°C using Andrews and Mf ≈ −100°C — so 25–35% retained austenite forms in as-quenched high-carbon tool steels. The physical basis is that dissolved carbon creates tetragonal BCT lattice distortion requiring greater undercooling to supply the free energy for the diffusionless shear transformation.

How is the martensite start temperature used to design preheat for welding?

Ms governs cold cracking susceptibility: low Ms means the HAZ martensite forms at a low temperature where hydrogen diffusivity is slow, increasing the risk that trapped hydrogen causes cracking. Preheat slows the cooling rate, extending the time above Ms during which hydrogen can diffuse away from the HAZ. Carbon equivalent (CE_IIW or Pcm) formulas used to determine preheat temperature use the same alloying elements as Ms equations because both respond to hardenability. P91 with CE ≈ 0.80 and Ms ≈ 420°C requires 200°C minimum preheat (ASME B31.1); S355 with CE ≈ 0.45 and Ms ≈ 440°C may require only 50–100°C depending on heat input and hydrogen potential.

What is the Mf temperature and why is it important for heat treatment design?

Mf (martensite finish) is where martensite transformation is approximately complete — defined at ≈95–99% completion, approximately Mf ≈ Ms − 150 to Ms − 215°C. If Mf lies above room temperature, minimal retained austenite forms on ambient quenching. If Mf is below ambient (as for high-carbon and high-alloy steels), significant RA remains and sub-zero treatment at −60 to −80°C (or cryogenic at −196°C) is needed to convert additional austenite. For tool steels and bearing steels where Mf ≪ 0°C, triple tempering cycles are used instead of completing transformation before the first temper, progressively converting RA through each temper cycle.

How is as-quenched hardness related to Ms temperature and carbon content?

As-quenched martensite hardness is primarily a function of dissolved carbon content, not of the alloy additions that reduce Ms. The Seyffarth equation gives: HV = 127 + 949×%C + 27×%Si + 11×%Mn + 8×%Ni + 16×%Cr + 21×%Mo for fully martensitic microstructure. Above about 0.6%C, actual measured hardness falls short of the theoretical maximum because retained austenite (HV ≈ 150–300) dilutes the hard martensite. Alloying elements like Cr, Ni, Mo improve hardenability (depth of hardening through-section) but do not significantly increase the surface hardness at a given carbon level.

Which Ms equation is most accurate for high-alloy and stainless steels?

For conventional low-alloy steels (C < 0.5%, total alloy < 5%), Andrews (1965) and Steven–Haynes (1956) are adequate (±20–30°C). For high-alloy steels (9–12%Cr, high-C tool steels), the Barbier (2012) equation provides significantly better accuracy due to its non-linear carbon term and broader calibration dataset (780 steels). For martensitic stainless steels (440C, 17-4 PH), none of the above equations is accurate without specific calibration — CALPHAD thermodynamic calculation (Thermo-Calc with TCFE) provides the most reliable Ms prediction for complex multicomponent alloys.

What is the effect of austenite grain size on the martensite start temperature?

Austenite grain size has a small but measurable effect on Ms: finer grains (ASTM 8–10) typically show Ms 5–15°C lower than coarse grains (ASTM 3–5) at the same composition, because fine grains provide more grain boundary constraint on the martensitic shear. This shift is small compared with the compositional effects (42°C per 0.1%C). More significant is the grain size effect on martensite morphology: coarse prior-austenite grains produce plate martensite (with twin substructure) at high carbon; fine grains favour lath martensite (with dislocation substructure and higher toughness). The empirical Ms equations do not include grain size as a variable; they predict Ms for a standard austenitising condition.

Recommended References

📚

Steels: Microstructure and Properties — Bhadeshia & Honeycombe (4th Ed.)

Graduate-level treatment of martensite transformation kinetics, Ms prediction, Koistinen-Marburger equation, retained austenite, and carbon effect on martensite hardness.

View on Amazon

📚

Mechanical Metallurgy — Dieter

Classic graduate text covering martensite crystallography, transformation thermodynamics, hardness-carbon relationships, and the physical basis of Ms temperature in steel.

View on Amazon

📚

ASM Handbook Vol. 4 — Heat Treating

Comprehensive reference for quench and temper heat treatment cycles, hardness-carbon relationships, retained austenite measurement, and sub-zero treatment procedures.

View on Amazon

📚

Steels: Processing, Structure and Performance — Krauss

Authoritative reference on martensite morphology, lath vs plate martensite, carbon distribution, and the relationship between Ms temperature, carbon content, and as-quenched hardness.

View on Amazon

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Martensite Start Temperature Calculator — Ms Temperature from Steel Composition

Martensite Start Temperature Calculator — Ms, Mf, Retained Austenite, and Hardness from Steel Composition

Key Takeaways

The Four Empirical Ms Equations: Derivation and Accuracy

Andrews (1965) — The Standard Reference

Steven and Haynes (1956)

Barbier (2012) — Non-Linear Carbon Treatment

Kung (1992)

Koistinen–Marburger Equation: Martensite Fraction and Retained Austenite

As-Quenched Hardness Prediction

Engineering Significance of Ms Temperature by Steel Category

Worked Example: SAE 4140 Steel

Application to Welding: Ms Temperature and Preheat Calculation

Frequently Asked Questions

Recommended References

Further Reading