Dear Madukhar,

Before answering your questions, it is important to point out that you must always indicate the references you have considered for the formulas used in the calculation of the different transformation points (Ac1, Ac3, Bs, Ms, etc.). Indeed, the empirical equations for the critical points of phase transformations in steels are numerous. I later posted an explicit answer on methods for estimating the Ms point and the thermal range of the martensitic transformation on another thread on this site (see the link below). The topic involved concerns martensitic stainless steels martensitic, but all that has been said there remains valid in your case.

Reference to the equation source is important because there are critical analyzes of the key formulas that highlight the limitations of their use. It should be noted that the empirical formulas are above all descriptive and non-predictive equations. Moreover, almost all the formulas are based on a specific sampling, which consists of a limited number of alloys having close chemical compositions. However, the chemical composition alone is not sufficient to predict the microstructure of an alloy, because the latter is also influenced by thermomechanical history, especially during solidification (cooling rate and undercooling phenomenon) and subsequent thermal and thermomechanical treatments. The occurrence of internal (residual) stresses can also significantly modify, either by promoting or inhibiting both bainitic and martensitic transformations [1, 2]. In the paper [2] I recently published on the study of internal damage in a High-chromium cast steel (HCCS), an extensive synthesis on the initiation and the growth of the Stress induced bainitic transformation is proposed. Moreover, a particular phenomenon is often not taken into account in the empirical equations which give the transformation points that correspond to undissolved carbides, which may originated either from the solidification or subsequent solid state transformations. The carbides, when present, fix alloying elements and especially carbon, leading to a significant modification within the chemical composition of the (austenitic) matrix. As a result, the actual composition of the matrix becomes significantly different from that of the original alloy, and so is its behavior when considering the possible bainitic or martensitic transformations for which the critical starting points are determined while using element amounts similar to those of the original alloy!

I would also like to point out that you must keep a critical eye on the results you had obtained. Indeed, it is normally not possible to have a point Bs lower than the point Ms. In addition, the negative values for the point Bs are improbable.

Below are links to two interesting articles that review different formulas for the calculation of Bs, each proposing a modified equation that allows to adjust to the experimental cases observed on several tens of steel alloys [3, 4]. Both formulas can be used on your alloys, especially those having a small amount of carbon and alloy element contents (Cr, Ni, Mn, Mo, etc.) of less than 5 wt-% (grade EN8 in your case). On the other hand, for Cr amounts above 5 wt-% and C contents greater than or equal to 1 wt-%, undissolved (solidification) carbides such as M7C3 Cr-rich primary or eutectic type should be present within the cast material (grades D2, 440A and 440C in your case). Depending on their original size (several tens of microns sometimes), they can remain present even after hot forming. Their presence may strongly influence the chemical composition of the austenitic matrix, since they contain in addition to carbon, a significant amount of Cr and possibly Mo and V. The alloying elements are thus "trapped" inside carbides, thus influencing not only the hardenability the alloy, but also the position of critical transformation points and the shape of transformation fields within both TTT and CCT diagrams. In addition to the undissolved solidification carbides, it is also possible to find finer carbides which have precipitated later in solid state inside grains or at grain boundaries during subsequent heat treatments. Once again, the presence of even fine carbides inside the matrix will modify the chemical composition of the latter, thus influencing the position of the transformation points. An important achievement of my study was to set the influence of different types of carbides on the internal damage mechanism in High-chromium cast steels [2]. In another conference paper that focuses on the influence of heat treatment on the microstructure of the same HCCS alloy, the effects of the variation of the composition of the matrix (from different austenitizing temperatures that lead to more or less dissolution of secondary intragranular carbides) on the Ms point has been highlighted [5].

So ta make it clear, I strongly recommend you to read the two review papers that focused on empirical equations for Bs point determination. The first one written by Zhao et al [3] evaluates several empirical formulas for Bs before suggesting a new equation that is independent of Carbon (as for Ae point), but is linear in the other elements. This equation was set after performing a regression on more than 80 plain carbon steels (Carbon content between 0.14 and 0.55 wt-%, with little Cr and Mo contents below 4 %). Moreover, the distinction between the theoretical starting point of the bainite transformation (Bo) and the practical point (Bs) is made, thus justifying why Bs always lies below Bo, with a constant deviation around 50-55°C. Finally, the authors showed that the experimental point Bs is around 500°C for low and medium carbon steels, while the same point is estimated at 630°C by the empirical formula.

The second interesting study has been carried out by Lee [4] who also compared several established empirical formulas to determine the starting point of the bainitic transformation under isothermal conditions. This approach considered data from TTT diagrams of 69 standard steels with a carbon content between 0.1 and 0.8 wt-%, and alloying elements with a maximum content of less than 5%, in order to establish from a regressive law. This led to a new equation that takes into account the C content and that have linear terms for the main alloying elements, but which additionally contains two polynomial terms (power of 2) for both Cr and Mo. This new formula allows a better fitting between experimental and predicted Bs values. The authors emphasize that in some cases the empirical formulas return negative values of Bs, and these are improbable!

For the point Ms, I refer you to the answer I made on another thread within RG (see the link below). You will also find interesting links on the equations for the estimation of the point Ms and the validity limits of these equations. Contrary to Bs, the negative values for the point Ms are commonl, especially for steels having their austenite stabilized by gamma promoters such a Ni and Mn. This is the case for austenitic stainless steel (AISI 300 series), but also for certain alloy steels containing high Ni or Mn contents. And finally, Carbon also tends to stabilize austenite when it remains in solid solution, thus lowering the point Ms below the ambient temperature.

Reference list

[1]. Nikravesh, M., Naderi, M., & Akbari, G. H. (2012). Influence of hot plastic deformation and cooling rate on martensite and bainite start temperatures in 22MnB5 steel. Materials Science and Engineering: A, 540, 24-29.  http://dx.doi.org/10.1016/j.msea.2012.01.018

[2]. 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://doi.org/10.1007/s11665-015-1464-7

[3]. Zhao, Z., Liu, C., Liu, Y., & Northwood, D. O. (2001). A new empirical formula for the bainite upper temperature limit of steel. Journal of Materials Science, 36(20), 5045-5056.

http://doi.org/10.1023/A:1011874708194

[4]. Lee, Y. K. (2002). Empirical formula of isothermal bainite start temperature of steels. Journal of Materials Science Letters, 21(16), 1253-1255. http://doi.org/10.1023/A:1016555119230

[5]. Tchuindjang, J. T., Habraken, A. M., & Lecomte-Beckers, J. (2015). Study of the Crystallization Behavior and the Subsequent Martensitic Transformation in a High Chromium Cast Steel submitted to Different Austenitization Temperatures. EUROMAT 2015, September 20-24, Symposium C4:1, Warsaw (Poland).

https://www.researchgate.net/publication/282571490_Study_of_the_Crystallization_Behavior_and_the_Subsequent_Martensitic_Transformation_in_a_High_Chromium_Cast_Steel_submitted_to_Different_Austenitization_Temperatures

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

Conference Paper Study of the Crystallization Behavior and the Subsequent Mar...

One more paper that gives estimated Bs and Ms points for alloys similar to your own grades. Regardless of the empirical equation that is used, you should never find negative values for Bs point. In addition, Ms is always lower than Bs temperature for a given alloy.

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