Mf temperature depends on complete transformation of austenite. It also depends on chemical composition. For some steels it could be 0 K and obtain more complete transformation cryogenic treatments are used.

One point in your experimental measurements. When K type sample is used at high temperature is looses accuracy in time. Better for steel applications are S or R types. 

Thanks for your answer.

I will try with S type thermocouple for further tests. But more specifically I am wondering if Mf temperature can be found on a classical thermal curve assuming a heat absorption (or release) sufficient to be detected on the curve. Actually, I know that dilatometry or DSC techniques are more appropriate for such a measurment but nitrogen quenching is not possible with the availabe devices. So if you or someone else already experienced such a measurement, I'm interested.

The same curve yield quite easily the Ms point probably due to the significant heat release occuring when martensitic transformation begins, but I did not find relevant information about the heat (release or absorption) at the end of martensitic transformation. I also try the first derivative curve but it is not very clear.

Hi Jerome, did you figure this out? Did you publish the results anywhere, or may I have access to them?

Do you know of any source for Mf temperatures for a variety of compositions, particularly for stainless steels?

 Hi Clinton,

Actually, the results have not been published yet and it is important to say that the studied alloys are more like HSS which are different from stainless steels due to their high carbon content, and the presence of numerous carbides within the microstructure.

In addition, you should find strain induced martensite transformation in stainless steels, the plastic deformation process supplying the necessary energy for martensite transformation. This is not usual (let's say more difficult to achieve) in HSS grades. That is the reason why in addition to the conventional Ms point used to set the start of the martensitic transformation (which depends only on the chemical composition of the alloy), another concept is often used for stainless steel under deformation, which is given by the Md point.

Just to fix it, for an austenitic stainless steel alloy of AISI 316 grade for example, the Ms point is very low (-186°C), which is close to the liquid nitrogen temperature), while the Md point can be achieved at room temperature (around 6°C). The same equation give a Ms point of -82°C for an AISI 304 grade while the Md point is set at 47°C.  

You may keep in mind that Md point is defined a little bit differently from Ms.

The true equation is set as Md (30/50) in °C that means the temperature at which 50% of the martensite is formed after achieving 30% of true deformation within the material.

And to come out with your query about the end point of the martensitic transformation, of course other formulae exist for the Mf point that also depends on the chemical composition.

My finding is that all the empirical equations, either those concerning Ms or those with Mf points, cannot be applied as such, because the actual composition of the austenite that will undergo martensitic transformation is different from the initial composition of the alloy. In fact, a certain amount of C with other alloying elements is retained within the carbides that are form during the solidification, but also lather in the solid state, including the tempering stage. That is the reason why you may always find a gap between the predicted value and the actual one, depending on the composition of the prior austenitic grains. Another finding concern the variation within the Ms point itself for the material, because there is a chemical gradient between the center and the grain boundary due to microsegregations, each composition corresponding to a specific start point for the martensitic transformation within a single austenitic grain.

To come back now to austenitic stainless steels, when considering the Mf point with the empirical equation that concern only the martensitic transforation induced by thermal activation, you should find a point that is very low, even below liquid nitrogen temperature. That is to say the parent austenite in the austenitic stainless steel has a high thermal stability. But taking into account strain or external stress can strongly modified this stability thus helping increasing the temperature at which the martensite can form from austenite. But there are no formula for the finish point of the martensite transformation when considering the strain-induced martensite. This is probably because other phenomena take place during the deformation, such as work hardening. Other parameters may also be considered that influence the progress of the strain-induced martensite transformation which are the strain rate and the Stacking Fault Energy (SFE), this latter parameter influencing the stability of the austenite.

But numerous works have be done on this topic which yield to the definition of constitutive or kinetics models for the formation of strain-induced martensite transformation (SIMT). Just take a look on the following papers: Olson and Cohen in [Met. Trans., Vol. 6A (1975), p.791], Hallberg et al. in [Int. Jrn. Plast.,Vol. 23 (2007), p. 1213] and Zaera et al. in [Int. Jrn. Plast., Vol. 29 (2012), p. 77].

The influence of strain rate and other parameters on the kinetic of SMIT in discussed in the following papers: Talonen et al. in [Met. Mat. Trans., Vol. 36A (2005), p. 421] and Parnian and Parsa in [Proc. Mat. Sci., Vol. 11 (2015), p. 24] .

And finally, the following review paper by Lo et al. in [Mat. Sci. Eng. R, Vol. 65 (2009), p. 39] who work on stainless steels, gives an interesting overview on Deformation-induced martensite (subsection 4 in the paper), with the remind of the main empirical equations for the determination of Ms points, and the formulae of other parameters accounting for austenite stabilization such as Ni equivalent number and SFE (subsection 5 in the paper).

Hope this will be helpful.

Regards,

P.S: Direct links to Research Gate online publications of the sources quoted in my message have been mentioned.

Article Kinetics of Strain-Induced Martensitic Nucleation

Article A constitutive model for the formation of martensite in aust...

Article A constitutive model for analyzing martensite formation in a...

Article Formation of shear bands and strain-induced martensite durin...

Article The Effect of Strain Rate on Ultra-fine Grained Structure of...

Article Recent developments in stainless steels

The following answer may complete the previous one.

If you are working on austenitic stainless steels, it will be difficult to get the Mf point even if you perform a quenching in liquid nitrogen.

That is because the termally activated martensitic transformation involved both Ms and Mf points that are very low on the temperature scale, even lower than the liquid nitrogen temperature for Mf in particular.

Of course, depending on the sizes and the design of the part, the strain-induced martensite sometimes occurs under quenching or rapid cooling because the distortions due to the thermal gradient yield a strain (or internal residual stresses) that can activate the begining of the transformation.

But such a strain is not sufficient to achieve a large amount of transformation under deformation.

For my own samples, I manage to get the Mf temperature during liquid nitrogen quenching but the related Ms point (between 150 and 250°C) was well above that of the austenitic stainless steels,

Best regards

Dear Jerome, thanks for setting up such an interesting debate! I´m currently correcting one of my articles, and the reviewer is asking for Mf temperature. I´m working with a martensitic stainless steel (only Cr, not Ni) to which I apply different cryogenic treatments. I´ve found Andrews equations for estimating Ms, but I´m not having the same luck for Mf. 

Any help would be appreciated ;)

Thanks!

Dear German,

Usually many equations can be find which make it possible to estimate the value of the starting point of both the bainitic (hereinafter referred to as Bs point) and the martensitic transformations (hereinafter referred to as Ms point), based on the original chemical compositions of the alloys [1-3, 5].  The most common are those for which a constant coefficient is attributed to the main alloying elements in the form of a general linear equation. However, some studies have tried to consider not an individual influence, but the possibility of interaction (binary or more) between elements [2, 3, 6]. Such an approach involving the introduction of binary interaction terms together with the use of the product square root of the concentrations instead of the direct product for alloying elements contributions improves the prediction accuracy, compared to Andrew’s product formula (the linear formula). But there is also another formula from Andrew that is nonlinear, because it includes binary interaction terms.

Linear equations are preferred due to their simplicity, but it is important to remember that this is essentially a descriptive and non-predictive approach. As a result, the validity of the formula is based primarily on the size and the quality of the sampling under consideration, which was the case in the work done by Grange & Stewart [4] who studied about 14 steel alloys with their carbon content ranging between 0.3 and 1.0 wt-%. However, these alloys cannot be considered representative of all steels grades especially those that are highly alloyed and those that contain very few carbon such as low alloyed steels or certain stainless steels. In addition, special care must be taken for Ms point calculation under linear-like formula for low alloy steels providing that the austenitizing temperatures used are sufficiently high to permit dissolution of all the carbides inside the steel [5]. The assumption of the complete solution of all the alloying elements including carbon within the parent austenitic phase is a prerequisite which is clearly stated in almost all the earlier works which led to the establishment of empirical formulas [6], even if this statement is sometimes not properly taken into consideration today. In addition, the existence of different linear-type formulas for the Ms point may be due to the different steels grades that were studied in order to determine experimentally the critical point for the martensitic transformation. As a corollary, it should be remind that every empirical formula for the Ms point strongly depend on the range of compositions for the studied alloys, and on the same time, the accuracy on Ms point will decrease when increasing the contents of alloying elements especially carbon beyond 0.5 wt-%.  

The problem of high alloy steels which contain a high amount of both carbon and alloying elements is that they can form different types of carbides including solidification carbides and those which precipitate later in the solid state, either during last step of the cooling of during subsequent heat treatments. Most of the carbides should remain undissolved thus modifying to a greater or lesser extent the chemical composition of the austenitic matrix that is supposed to be transformed into martensite. Depending on the progress of the dissolution of carbides within the matrix (parent austenite) and also on the local micro-segregation (chemical gradient) that can occur especially at grain boundaries due to the presence of solidification carbides, the so-called splitting phenomenon corresponding to the existence of at least two different starting points for the martensite transformation can occur. Such a phenomenon when it occurs, is strongly influence by the chemical gradient that exist between the center of the grain that may contain a certain amount of fine (secondary or tertiary) carbides and the grain boundaries where precipitation free zone exist. Such a statement has been clearly set in one of my recent paper with the enhancement of the role of the fine carbides on the strengthening behavior of a High Chromium Cast Steel [7].

In addition, the equations which give the value of the Ms point assume amounts of alloying elements that are similar to the initial chemical composition. This is a very important source of error in high alloyed steels because a single alloy can present a very large variation in the value of the point Ms due to the changes in the composition of the parent austenitic matrix that could be associated to more or less carbides of different types, located either inside grains or at grain boundaries. It has been reported that only Andrew’s linear equation and Stevens & Hayne’s equation give reasonable fits when predicting Ms Temperature [6].

Moreover, in addition to the change within the chemical composition other phenomena such as heat treatment and plastic deformation should be taken into account when we consider the martensitic transformation occur after the destabilization of the parent (austenite) phase, [8]. The same authors also show that neural model can be more interesting than the empirical equations to better understand the influence of every single alloying element in the stabilization of the parent austenite.

Furthermore, from the thermodynamic approach, martensitic transformation is said to be triggered when the chemical driving force (free energy change for transformation of austenite gamma into martensite alpha', DeltaG(gamma-alpha') reaches a critical value at Ms (DeltaGMs(gamma-alpha') without a composition change [8, 9]. This critical value is obtained from an equation where the square root of every single alloying element in mole fraction is associated with a constant value that has been determined by Ghosh and Olson when establishing the square root dependence and fitting over a wide range of compositions, the maximum concentrations being around 2 wt-% for C and N, 0.9 wt-% V, and about 2-28 wt-% for all other alloying elements [10]. The thermodynamic approach is based on an artificial neural network which purpose is to model (predict) the Ms point of engineering steels based on their chemical composition and the austenite grain size [8, 11].

It has been admitted for a long time that Ms point is the key parameter to be set for the martensitic transformation because the range for the completion of the transformation is almost constant, between 150 ° and 300 ° C. The length of the temperature range depends on the alloy especially on its Carbon content. For low-Ni martensitic stainless steels containing about 12% Cr and 0.1% C, studies have shown that the martensitic transformation range extends about 150 to 200 ° C below the Ms point that is set around 300 ° C [12] But in the same review, Pickering also mentioned a lower Ms point for the so-called controlled transformation stainless steels that contain between 14 and 19 wt_% of Cr, with an enhanced Ni content (up to 7 wt-%) so as to allow a fully austenitic phase at room temperature. For such an alloy, cryogenic quenching is required to complete the martensitic transformation. A typical controlled transformation stainless steel having a composition of 0.1C-17Cr-4Ni exhibits a Ms point just below the room temperature with a Ms-Mf range  in the order of 100-140°C  that  set the Mf point between -80 and -120°C.

The Koisitinen-Marburger equation is known to determine the total size of the transformation interval from the knowledge of any two points of this interval, including Ms and another point which set an intermediate stage of the transformation [13]. However, this equation qualitatively describes the martensitic transformation, without taking into account the kinetics which can be strongly influenced by the cooling rates [14] or by both the athermal frictional work [15] and the interfacial friction [16] for the heterogeneous martensitic nucleation in particular.

In practice, we will not find a reliable equation capable of giving the point Mf. In a very old study on the quenching of commercial steels (14 grades with a carbon concentration varying between 0.3 and wt- 1%), Grange and Stewart [4] demonstrated that it is difficult to determine with precision the position of the Mf point which corresponds to the end of the martensitic transformation. Indeed, the curves which show the progress of the martensitic transformation exhibit a very pronounced asymptotic curvature when approaching the transformation rate of 95%. The same result was obtained by Payon & Savage [5] who studied the influence of elements other than C on the martensitic transformation. They considered 17 steel grades having a constant C amount of 0.5 wt-% with various contents in Mn, Si, Ni, Cr, Mo and W.  The Mf point remains approximated and its determination carried out under metallographic inspection was admitted to be less reliable than that of the starting point.

However, the Mf point can be determined with a certain accuracy under a dilatometric test providing the fact that the equipment which is used is capable of following the evolution of the expansion/contraction under fast cooling rates within the temperature ranges where the critical transformation points may appear.

To come back to your alloy, if the Ni content is low then passing through the d-ferrite field during solidification is expected, and maybe such a phase is still present at room temperature. d-ferrite may promote toughness within the material but at the same time, such a phase inherited from the solidification could not be transformed into austenite, then reducing the amount of phase that can undergo martensitic transformation. Otherwise, Ni addition up to 3 wt-% is required either to avoid the passing through d-ferrite formation during solidification or to allow peritectic transformation that yield a fully austenitic phase within the matrix in the solid state, this later phase being prompt to be transformed into martensite under quenching.

Regarding the determination of Bs in particular, the paper from Van Bohemen [3] is quite interesting because typical values obtained from a new empirical expression that is derived from 60 steels always lead to positive temperatures. The batch of the samples that are considered in this paper contain alloys of Enxxx series that are similar to the one you are dealing with. In addition, the Ms temperature of a given alloy as determined in the same paper is always lower than the Bs temperature.

So to come out with the issue about your paper reviewing process, let me know if you can provide some information about the following questions.

1. Have you been working with a standard alloy for which the composition or grade can be disclosed? If yes just remind the standard designation of you alloy (according to Pickering review paper [12])?

2. Which one between the linear or the nonlinear Andrew’s formula did you use (according to the paper from Kung and Rayment [6])?

3. Have you had the possibility to determine experimentally the position of the Ms point (eg dilatometry, or literature with the same alloy that you use)

4. Why did you carried out cryogenic quenching? Is it because the Ms is below or closed to the room temperature or what is only to be sure about the completion of the martensitic transformation?

Regards

P.S: Only the available DOI have been mentioned. Let me know if you need one of the quoted papers of my reference list.

Reference list

1. Bates, C. E., Totten, G. E., & Brennan, R. L. (1991). Quenching of steel. ASM International, ASM Handbook., 4, 67-120.

2. Wang, J., van der Wolk, P. J., & van der Zwaag, S. (2000). Determination of martensite start temperature in engineering steels part I. Empirical relations describing the effect of steel chemistry. Materials transactions, JIM, 41(7), 761-768. http://doi.org/10.2320/matertrans1989.41.761

3. Van Bohemen, S. M. C. (2012). Bainite and martensite start temperature calculated with exponential carbon dependence. Materials Science and Technology, 28(4), 487-495. http://dx.doi.org/10.1179/1743284711Y.0000000097

4. Grange, R. A., & Stewart, H. M. (1946). The temperature range of martensite formation. Trans. AIME, 167, 467-501.

5. Payson, P., & Savage, C. H. (1944). Martensite reactions in alloy steels. Trans. ASM, 33, 261-280.

6. Kung, C. Y., & Rayment, J. J. (1982). An examination of the validity of existing empirical formulae for the calculation of Ms temperature. Metallurgical Transactions A, 13(2), 328-331. http://dx.doi.org/10.1007/BF02643327

7. Tchuindjang, J. T., Torres, I. N., Flores, P., Habraken, A. M., & Lecomte-Beckers, J. (2015). Phase transformations and crack initiation in a high-chromium cast steel under hot compression tests. Journal of Materials Engineering and Performance, 24(5), 2025-2041. http://dx.doi.org/10.1007/s11665-015-1464-7

8. Capdevila, C., Caballero, F. G., & García de Andrés, C. (2003). Analysis of effect of alloying elements on martensite start temperature of steels. Materials science and technology, 19(5), 581-586. http://dx.doi.org/10.1179/026708303225001902

9. Yang, H. S., Jang, J. H., Bhadeshia, H. K. D. H., & Suh, D. W. (2012). Critical assessment: Martensite-start temperature for the γ→ ε transformation. Calphad, 36, 16-22. http://dx.doi.org/10.1016/j.calphad.2011.10.008

10. Olson, G. B., & Cohen, M. (1976). A general mechanism of martensitic nucleation: Part III. Kinetics of martensitic nucleation. Metallurgical Transactions A, 7(12), 1915-1923. http://dx.doi.org/10.1007/BF02659824

11. Wang, J., van der Wolk, P. J., & van der Zwaag, S. (2000). Determination of Martensite Start Temperature for Engineering Steels Part II. Correlation between Critical Driving Force and Ms Temperature. Materials Transactions, JIM, 41(7), 769-776. http://doi.org/10.2320/matertrans1989.41.769

12. Pickering, F. B. (1976). Physical metallurgy of stainless steel developments. Int. Met. Rev., Dec. 1976, 21, 227-268.

13. Koistinen, D. P., & Marburger, R. E. (1959). A general equation prescribing the extent of the austenite-martensite transformation in pure iron-carbon alloys and plain carbon steels. acta metallurgica, 7(1), 59-60

14. Zhou, X., Liu, C., Yu, L., Liu, Y., & Li, H. (2015). Phase transformation behavior and microstructural control of high-Cr martensitic/ferritic heat-resistant steels for power and nuclear plants: a review. Journal of Materials Science & Technology, 31(3), 235-242. http://dx.doi.org/10.1016/j.jmst.2014.12.001

15. Ghosh, G., & Olson, G. B. (1994). Kinetics of FCC→ BCC heterogeneous martensitic nucleation—I. The critical driving force for athermal nucleation. Acta Metallurgica et Materialia, 42(10), 3361-3370. http://dx.doi.org/10.1016/0956-7151(94)90468-5

16. Ghosh, G., & Olson, G. B. (1994). Kinetics of Fcc→ bcc heterogeneous martensitic nucleation—II. Thermal activation. Acta Metallurgica et Materialia, 42(10), 3371-3379. http://dx.doi.org/10.1016/0956-7151(94)90469-3

How to get the Mf point (finish temperature) of the martensitic transformation of an alloyed steel from the thermal curve during cryogenic quenching? - ResearchGate. Available from: https://www.researchgate.net/post/How_to_get_the_Mf_point_finish_temperature_of_the_martensitic_transformation_of_an_alloyed_steel_from_the_thermal_curve_during_cryogenic_quenching [accessed Mar 6, 2017].

http://doi.org/10.2320/matertrans1989.41.761

http://dx.doi.org/10.1007/BF02643327

http://dx.doi.org/10.1007/s11665-015-1464-7

http://dx.doi.org/10.1179/026708303225001902

http://dx.doi.org/10.1016/j.calphad.2011.10.008

http://dx.doi.org/10.1007/BF02659824

http://doi.org/10.2320/matertrans1989.41.769

http://dx.doi.org/10.1016/j.jmst.2014.12.001

http://dx.doi.org/10.1016/0956-7151(94)90468-5

http://dx.doi.org/10.1016/0956-7151(94)90469-3

Dear Jerome, I truly apologize for not answering back before, I missed the RG notification completely :(

Thank you very much for taking so much time and effort in answering me, you have gave me a lot to read and think about! Regarding your questions:

1. Yes, it is a low-carbon AISI 420 (0,17 C - 12.9 Cr).

2. I´ve used the Andrews´ linear equation.

3. No, I wasn´t able to do experimental determinations of Ms or Mf temperatures.

4. In this steel, you can strongly modify the carbide size and distribution by means of cryogenic treatments, and this enhances its mechanical and tribological properties, so we´re not so interested in retained austenite. But in some side projects we´re working with other treatments and alloys, so we´re interested in being able to estimate Ms and Mf in a simple manner. 

Thank you!!

Dear jeromy useT.T.T curve to find Mf.

Dear Jeromy u mean theoratically or experimentally?