Ac1, Ac3, Ms & Mf: Four Temperatures Every Welding Metallurgist Should Know
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Quick Answer: Ac1 is the temperature at which austenite begins to form on heating; Ac3 is the temperature at which the transformation to austenite is complete. Ms is the temperature at which austenite begins transforming to martensite on cooling; Mf is where that transformation finishes. All four are composition-dependent, can be estimated from chemistry using empirical formulas such as Andrews’ equations, and directly govern preheat, interpass, and PWHT temperature selection in welding.
Every carbon and low-alloy steel weld goes through a heating and cooling cycle that repeatedly crosses a set of critical temperatures most welding engineers can name but few can calculate. Ac1, Ac3, Ms, and Mf are not arbitrary numbers on a metallurgy chart. They define exactly which microstructure a given point in the heat-affected zone will end up with, they set the ceiling for post-weld heat treatment, and they explain why some steels are far more prone to hydrogen cracking than others with a nearly identical carbon content.
This guide defines all four transformation temperatures, explains why each one matters specifically to a welding engineer rather than only to a heat treater, and includes a composition-based calculator using widely published empirical formulas so you can estimate all four for a specific steel chemistry.
- Ac1 and Ac3 mark the start and finish of austenite formation on heating; below Ac1, no austenite exists and no hardening can occur.
- Ms and Mf mark the start and finish of martensite formation on cooling from austenite; both fall as carbon and alloy content increase.
- PWHT must be held below Ac1, with margin, to avoid partially re-austenitizing the weldment during heat treatment.
- All four temperatures can be estimated from chemical composition using published empirical formulas, most commonly Andrews’ equations, though different formula sets can disagree, especially for leaner or unusual alloy compositions.
- A low Ms or Mf, driven by high carbon or alloy content, increases the risk of untempered, crack-sensitive martensite forming in the heat-affected zone during welding.
What Are Ac1, Ac3, Ms, and Mf?
Ac1, Ac3, Ms, and Mf are the four critical temperatures that bound the austenite phase field in steel: the first two on heating, the last two on cooling. Each has a precise metallurgical definition:
| Temperature | Direction | Definition |
|---|---|---|
| Ac1 | Heating | The temperature at which austenite begins to form from ferrite and pearlite (or ferrite and carbide) |
| Ac3 | Heating | The temperature at which transformation to austenite is complete, in hypoeutectoid (typical structural and pressure vessel) steels |
| Ms | Cooling | The temperature at which austenite begins transforming to martensite |
| Mf | Cooling | The temperature at which martensite transformation is essentially complete |
Why the “c” in Ac1 and Ac3: The letter c comes from the French chauffage (heating), denoting that these are the transformation points measured on heating. The corresponding cooling transformation points are labeled Ar1 and Ar3 (from refroidissement, cooling), and they occur at somewhat lower temperatures than Ac1 and Ac3 due to thermal lag (hysteresis) in the transformation. Ms and Mf do not carry this heating/cooling naming convention because martensite transformation only occurs on cooling.
Where These Temperatures Sit on the Iron-Carbon Diagram
On a simplified iron-carbon phase diagram, Ac1 corresponds to the eutectoid temperature line, roughly 727°C for plain carbon steel at the eutectoid composition, below which austenite cannot exist at equilibrium. Ac3 is a sloped line above Ac1 that falls as carbon content increases, reaching Ac1 itself at the eutectoid carbon content (approximately 0.8 percent carbon for plain carbon steel). Between Ac1 and Ac3, a hypoeutectoid steel exists as a mixture of ferrite and austenite; above Ac3, the steel is fully austenitic.
Alloying elements shift both lines. Carbon, manganese, and nickel are austenite stabilizers and generally lower Ac1 and Ac3. Chromium, molybdenum, silicon, and vanadium are ferrite stabilizers and generally raise Ac3, though their effect on Ac1 can go either direction depending on the specific element and its interaction with other alloying additions.
Ac1 / Ac3 / Ms / Mf Calculator
Enter the weight percent composition below to estimate all four transformation temperatures using Andrews’ widely published empirical equations. These are estimates, not measured values; actual transformation temperatures should be confirmed by dilatometry or CCT/TTT diagram data for critical applications.
Estimate Transformation Temperatures
Why These Temperatures Matter for Welding
- PWHT temperature selection: Post-weld heat treatment must stay below Ac1, with margin, to avoid partially re-austenitizing the weldment. Re-austenitizing even a portion of the microstructure during PWHT can produce fresh, untempered martensite on subsequent cooling, defeating the purpose of the heat treatment.
- Preheat and interpass control: Preheat and interpass temperature selection is informed by how close the HAZ gets to Ac1 during multi-pass welding, and by how low the Ms temperature is, since a lower Ms means martensite forms over a wider temperature range during cooling, extending the window in which hydrogen-assisted cracking can occur.
- HAZ microstructure prediction: Different regions of the HAZ reach different peak temperatures during welding. Material that peaks above Ac3 becomes fully austenitized and re-transforms on cooling (potentially to martensite, depending on cooling rate and hardenability); material that peaks between Ac1 and Ac3 is only partially transformed, producing the well-known intercritical HAZ with its own distinct, sometimes more crack-sensitive, microstructure.
- Hydrogen cracking risk assessment: A steel with a low Ms temperature is more likely to retain untempered martensite, or even some retained austenite, at room temperature immediately after welding, both of which are associated with increased susceptibility to hydrogen-assisted cold cracking.
Caution: Empirical Ac1/Ac3/Ms/Mf formulas are fits to specific historical datasets and do not perfectly represent every alloy system. Different published equations can disagree meaningfully, especially outside the composition range they were originally derived from. For a critical application, confirm with dilatometry testing or published CCT/TTT diagram data for the specific steel grade rather than relying on a formula alone.
Worked Example
Consider a low-alloy steel with the following composition: C = 0.20%, Mn = 1.20%, Si = 0.30%, Cr = 0.90%, Mo = 0.20%, Ni = 0%, V = 0%, Cu = 0%.
Quick Reference: Typical Values by Steel Type
| Steel Type | Approx. Ac1 | Approx. Ac3 | Approx. Ms |
|---|---|---|---|
| Plain low-carbon steel | ~725°C | ~840-870°C | ~400-450°C |
| Medium-carbon steel | ~720-730°C | ~790-820°C | ~320-380°C |
| Low-alloy Cr-Mo steel (e.g. 2-1/4Cr-1Mo) | ~750-770°C | ~830-870°C | ~380-420°C |
| High-carbon / higher-alloy steel | ~700-720°C | ~750-800°C | <300°C |
These ranges are general guidance to illustrate the trend; always use the calculator above, or measured data, for a specific chemistry rather than reading a single value off a general table.
Common Mistakes and Limitations
- Treating empirical formulas as exact. Andrews’ equations, and other published formula sets, are curve fits to specific datasets. They give useful estimates but can diverge from measured values, particularly for compositions outside their original derivation range.
- Ignoring heating and cooling rate effects. Ac1 and Ac3 shift upward with faster heating rates, and Ms/Mf can shift with cooling rate and prior austenite grain size; a single static number does not capture every real thermal cycle.
- Setting PWHT too close to Ac1 without margin. Given the uncertainty in estimated Ac1 values, a PWHT temperature set right at a calculated Ac1 risks partial re-austenitizing in practice; a safety margin below the estimated value is standard practice.
- Assuming Mf always reaches room temperature. In steels with sufficiently low Mf, some austenite can remain untransformed (retained austenite) at room temperature, which has its own implications for hardness, dimensional stability, and cracking susceptibility.
- Using one formula set without cross-checking. Where the calculated result matters for a real decision (a PWHT window, a hardness prediction), cross-check against at least one other published formula set or, ideally, measured dilatometry data for the actual heat of material.
Requirements and specific numeric limits depend on the material specification and welding procedure applicable to your project; confirm PWHT temperature windows and hardness acceptance criteria against the governing code and material specification.
Key Terms
- Ac1
- The temperature at which austenite begins to form from ferrite and pearlite on heating.
- Ac3
- The temperature at which transformation to austenite is complete on heating, in hypoeutectoid steel.
- Ms (Martensite Start)
- The temperature at which austenite begins transforming to martensite on cooling.
- Mf (Martensite Finish)
- The temperature at which martensite transformation is essentially complete on cooling.
- Intercritical HAZ
- The region of a weld heat-affected zone that peaks between Ac1 and Ac3 during welding, producing a partially transformed, mixed microstructure.
- Retained Austenite
- Austenite that remains untransformed at room temperature because the material’s Mf temperature is at or below room temperature.
- Andrews’ Equations
- A widely published set of empirical formulas relating steel composition to Ac1, Ac3, and Ms transformation temperatures.
Frequently Asked Questions
What is the difference between Ac1 and Ac3?
Ac1 is the temperature at which austenite begins to form on heating a steel. Ac3 is the higher temperature at which that transformation to austenite is complete, in hypoeutectoid steels. Between Ac1 and Ac3, the steel exists as a mixture of ferrite and austenite; below Ac1, no austenite is present at equilibrium.
Why must PWHT stay below Ac1?
If post-weld heat treatment temperature exceeds Ac1, part of the microstructure can transform back into austenite. On subsequent cooling from the PWHT cycle, that re-transformed material can form fresh, untempered martensite, which defeats the softening and stress-relief purpose of the heat treatment and can leave the joint harder and more crack-sensitive than before PWHT.
How accurate are empirical formulas like Andrews’ equations?
Empirical formulas provide useful estimates but are fits to specific historical datasets, so accuracy varies by how closely a given steel’s composition matches the range the formula was derived from. Different published formula sets can give meaningfully different results for the same composition, particularly for lean or unusual alloys, so measured dilatometry or CCT/TTT data is preferred for critical decisions.
What is retained austenite and why does Mf matter for it?
Retained austenite is austenite that has not transformed to martensite by the time the material reaches room temperature. If a steel’s Mf temperature is at or below room temperature, some austenite can remain untransformed, affecting hardness, dimensional stability, and potentially long-term microstructural stability of the component.
What is the intercritical HAZ and why is it significant?
The intercritical heat-affected zone is the region of a weld that reaches a peak temperature between Ac1 and Ac3 during welding, so it only partially transforms to austenite before cooling back down. This produces a distinct, often more crack-sensitive mixed microstructure compared to regions that fully austenitized above Ac3, making the intercritical HAZ a frequent focus of hardness surveys and cracking investigations.
Does a lower Ms temperature increase hydrogen cracking risk?
Generally, yes, indirectly. A lower Ms temperature, typically associated with higher carbon or alloy content, extends the temperature range over which martensite forms during cooling and is often associated with a harder, more crack-sensitive as-welded microstructure. This is one of the reasons preheat and interpass temperature control is more critical for higher-hardenability steels with lower Ms temperatures.
Is there a single universally accepted formula for Mf?
No. Unlike Ms, which has several well-established empirical formulas such as Andrews’ equation, Mf is less consistently modeled in published literature. A commonly cited rule of thumb places Mf roughly 150 to 250 degrees Celsius below Ms, but the actual offset varies by alloy, so measured data is preferred where Mf is critical to a design decision.
Standards and References
- Andrews, K.W., “Empirical Formulae for the Calculation of Some Transformation Temperatures,” Journal of the Iron and Steel Institute, 1965 – source of the widely cited Ac1, Ac3, and Ms empirical equations used in this guide’s calculator.
- ASME Boiler and Pressure Vessel Code, Section VIII Division 1 and Section I – PWHT temperature and hold time requirements by material group, which must be set with reference to the material’s Ac1 temperature.
- ASM Handbook, Volume 4, Heat Treating, ASM International – general reference for transformation temperature behavior and phase diagrams.
Conclusion
Ac1, Ac3, Ms, and Mf are not academic trivia; they are the four boundaries that determine what microstructure any given point in a weldment will end up with, on both heating and cooling. Knowing roughly where they sit for a specific steel chemistry lets a welding engineer set a PWHT window with real margin, anticipate whether the HAZ will fully or only partially transform, and judge how much martensite risk a given preheat and interpass strategy needs to manage. The empirical formulas in the calculator above give a fast, composition-based estimate; for anything safety-critical, back it up with measured dilatometry or CCT/TTT data for the actual heat of material. For related metallurgy topics, see the high-temperature material properties guide and the sigma phase guide on WeldFabWorld.
About This Guide: This article was prepared by the WeldFabWorld technical team from the references listed above. Empirical transformation temperature formulas are estimates, not measured values; verify critical design decisions against dilatometry testing or published CCT/TTT data for the specific steel grade and heat of material.