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Abstract

  1. Top of page
  2. Abstract
  3. 1 Introduction
  4. 2 Data Base for Ms Temperature
  5. 3 The Classical Ms Relations
  6. 4 The Extended Ms Relation
  7. 5 Comparison of the Extended Relation with the Classical Ones
  8. 6 Conclusions

A new relation for the Ms temperature prediction is proposed. The composition ranges covered by the new model are enlarged compared to the classical relations. This new relation is obtained from a data base of almost 1000 different compositions. The predictive ability of this new relation is compared to the classical ones.

1 Introduction

  1. Top of page
  2. Abstract
  3. 1 Introduction
  4. 2 Data Base for Ms Temperature
  5. 3 The Classical Ms Relations
  6. 4 The Extended Ms Relation
  7. 5 Comparison of the Extended Relation with the Classical Ones
  8. 6 Conclusions

The use of martensitic structures becomes more and more common in advanced high strength steels (AHSS). The design of these structures, and more precisely of the chemistry, involves the determination of the martensite start (Ms) temperature.

Several parameters control the Ms temperature: chemistry, austenitic grain size, hydrostatic pressure, applied stress. Among these parameters, the effect of chemistry is of first importance. Several relations are available in the literature in order to determine the Ms temperature from the chemistry. These relations can be divided in different types of equations linking the alloying element contents to the Ms temperature:

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    Relations based on linear regressions,[1-8] among which the well known Andrews and Steven & Haynes ones,
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    Relations taking into account the interactions between some alloying elements,[9, 10]
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    Relations based on non-linear regressions.[11, 12]

Most of these relations differ from their validity domain and the alloying elements they take into account. Two other approaches are also considered in the literature to determine the Ms temperature:

  • -
    Thermodynamic calculations based on transformation energies.[13] This method seems very powerful but quite heavy for rapid alloy design,
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    Artificial Neural Network (ANN) methods. These approaches have been already widely used and developed to predict the martensite start temperature as a function of the chemistry,[14-25] even considering binary interaction between alloying elements [26, 27] or prior austenitic grain size.[28] The output models from ANN generally lead to very complex interactions between alloying elements. As for the thermodynamic based model, theses methods are very efficient for Ms prediction, but not easy to use for rapid alloy design purpose.

The present study aims at presenting a new empirical relation to determine the Ms temperature, with extended validity domain and more alloying elements taken into account. This new relation is evaluated and compared to the existing ones.

2 Data Base for Ms Temperature

  1. Top of page
  2. Abstract
  3. 1 Introduction
  4. 2 Data Base for Ms Temperature
  5. 3 The Classical Ms Relations
  6. 4 The Extended Ms Relation
  7. 5 Comparison of the Extended Relation with the Classical Ones
  8. 6 Conclusions

A data base of 1000 chemistries and their related Ms temperatures has been set up. These data has been either selected from the literature or obtained by dedicated experiments using dilatometry trials performed with a Bähr 805 A/D dilatometer. To ensure the data consistency, two criteria have been used for the data gathering and the new experiments: (i) all the alloying elements should be in solid solution (ii) the austenitic grain size should be high enough in order to avoid any effect on the Ms temperature. These two criteria ensure that the Ms temperature is a function of only the alloying elements in solid solution. The austenitization temperature has been chosen to a minimum value of 1200 °C. The data from the literature having a temperature below 1200 °C have been excluded. This temperature ensures that the strong carbide former elements such as Ti, Nb, Cr or V remain available in solid solution. Moreover, this temperature guarantees a large austenitic grain size, i.e. superior to 10 µm. It has been shown in fact that over 10 µm, the martensite start temperature is independent from the austenitic grain size.[29, 30] The range of investigated elements and composition ranges are presented in Table 1.

Table 1. Investigated elements and composition ranges
 CMnSiCrNiMoVCoAlCuNbTiB
Min, wt.%0.002000000000000
Max, wt.%1.8610.241.917.9829.555.41.1916.083.0072.170.111.6140.004

3 The Classical Ms Relations

  1. Top of page
  2. Abstract
  3. 1 Introduction
  4. 2 Data Base for Ms Temperature
  5. 3 The Classical Ms Relations
  6. 4 The Extended Ms Relation
  7. 5 Comparison of the Extended Relation with the Classical Ones
  8. 6 Conclusions

The following Ms relations were considered in this study:

* Steven & Haynes [8]

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*Andrews [1]

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*Andrews polynomial [1]

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*Nehrenberg [5]

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*Rowland and Lyle [7]

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*Grange and Stewart [3]

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*Kung and Rayment [4]

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*Payson and Savage [6]

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*Eldis [2]

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*Eicheman and Hull [9]

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*Sverdlin and ness [10]

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*Carapella [11]

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*Van Bohemen [12]

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These equations present two main limitations (i) regarding the considered alloying elements (no effect of Ti, Al, Nb…) and (ii) regarding the validity domain (generally below 5% for Ni or Mn, which is a crucial limitation regarding the current development of medium Mn or AHSS α' steels).

4 The Extended Ms Relation

  1. Top of page
  2. Abstract
  3. 1 Introduction
  4. 2 Data Base for Ms Temperature
  5. 3 The Classical Ms Relations
  6. 4 The Extended Ms Relation
  7. 5 Comparison of the Extended Relation with the Classical Ones
  8. 6 Conclusions

As already identified in,[12, 13] the Ms temperature presents an exponential %C dependence. The evolution of Ms temperature against the %C content, over the 1000 chemistries of the database, is plotted Figure 1, confirming this exponential trend. Inspired from the work of Van Bohemen,[12] and based on this exponential dependence on %C, the following expression is used to describe the composition dependence of Ms temperature:

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Figure 1. Evolution of the Ms temperature with the %C content.

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A0 being the transformation temperature of pure iron under extremely rapid cooling (A0 = 545 °C [31]), i the alloying element weighted by Bi, D and E the parameters associated to effect of carbon. The parameters Bi, D and E are identified by linear regression on the complete data base, conducting to the following equation:

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The identified parameters for C, Mn, Si, Cr, Ni and Mo on the resulting decrease of Ms temperature are in close agreement with those obtained in the relations presented in 3-. The nature of this effect, i.e. the decrease of the Ms temperature with the increase of (C, Mn, Si, Cr, Ni, Mo) content is consistent with the thermodynamic analysis performed by several authors as Cool and Bhadeshia,[21] Wang et al.[32] and more recently Strormvinter et al..[13] Addition of (C, Mn, Si, Cr, Ni, Mo) increases the required driving force for martensite transformation, leading to a decrease of the Ms transformation temperature.

The effects of the less conventional alloying elements taken into account in this new relation are illustrated on Figure 2, where the experimental Ms values from the database are plotted as a function of the alloy content for different steels compositions:

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    Vanadium (Figure 2a) seems to increase the Ms temperature, even if its effect seems negligible in some cases,
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    Cobalt (Figure 2b) clearly increases the Ms temperature, as already proposed in,[4, 11] but with a different intensity,
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    Aluminum (Figure 2c) has almost no effect in the range of investigated composition,
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    Copper (Figure 2d) clearly decreases the Ms temperature,
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    Niobium (Figure 2e) seems to a have a strong decreasing effect on the Ms temperature, even in small quantity (maximum Nb content investigated: 0.1 wt.%). It has been checked that it is a direct chemical effect of Nb. In fact, Nb is well known for decreasing the austenitic grain size, and as a consequence the Ms temperature. But in this case, experiments were performed with large γ grains.
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    Titanium (Figure 2f) effect remains un-clear. For content below 0.5 wt.%, it strongly decrease the Ms temperature. But for content over 0.5 wt.%, Ms temperature increase. As already mentioned, not all the experimental conditions were available. This non-linear effect of Ti maybe linked to ferrite forming effect of Ti. Anyway, it has been found on the complete set of data that Ti has a slight decreasing effect on Ms temperature.
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    Boron (Figure 2g) in small quantities tends to strongly the Ms temperature.
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Figure 2. Experimental data on the effect of (a) V (b) Co (c) Al (d) Cu (e) Nb (f) Ti and (g) B on the Ms temperature for different steel compositions.

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It is clear that from these observations, the new relation is able to describe mean effect of elements such as Ti, Nb and B, but further investigations are required for a fine description, especially for non linear effects.

5 Comparison of the Extended Relation with the Classical Ones

  1. Top of page
  2. Abstract
  3. 1 Introduction
  4. 2 Data Base for Ms Temperature
  5. 3 The Classical Ms Relations
  6. 4 The Extended Ms Relation
  7. 5 Comparison of the Extended Relation with the Classical Ones
  8. 6 Conclusions

The different relations are applied on the complete data base in order to assess their predictive capability. Figure 3 presents the predicted Ms temperatures versus the experimental ones for all the relations. To complete these comparisons, the Table 2 gives the correlation coefficients for all the relations between the predicted and experimental Ms temperatures. Most of the relations give rather acceptable average predictions. Among the classical relations, the one from Van Bohemen[12] gives a very good correlation, slightly below the one from the extended relation.

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Figure 3. Application of the different relations to the complete data base.

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Table 2. Calculated correlation coefficient for the different Ms relations
RelationCorrelation coefficient
Extended Ms relation0.964
Stevens and Haynes0.915
Andrews0.935
Andrews polynomial0.862
Carapella0.832
Nehremberg0.898
Rowland and Lyle0.884
Grange and Stewart0.843
Van Bohemen0.957
Einchelman and Hull0.899
Kung and Rayment0.931
Payson and Savage0.878
Eldis0.927
Sverdlin and Ness0.861

These two relations are further compared on the same basis, i.e. by excluding the data from the basis having non common alloying elements (Co, V, Al, Ti, Cu, Nb, B). Figure 4 presents a comparison of the predicted Ms temperatures by the extended relation and the Van Bohemen one,[12] performed on the same alloying basis. Both relations give very good prediction on the whole Ms temperature range. But on this common alloys basis, the extended relation gives a more narrow distribution around the experimental Ms values.

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Figure 4. Comparison of the predicted Ms temperatures obtained with the extended and Van Bohemen [12] relations on the same composition basis.

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Finally, the Table 3 presents the covered alloying elements by the new Ms relation compared to the existing ones. Most of the relations take into account the same classical elements, i.e. C, Mn, Si, Cr, Ni and Mo. Few relations describe the effect of a single non-conventional element, such as W [6, 7, 11] or Cu.[10] The proposed relation covered a larger range of elements, including major ones regarding the developments of the new Advanced High Strength Steels, such as Ti, Nb, B and V.[33-35] All these elements are here taken into account in a single relation.

Table 3. Covered alloying element by the different Ms relations
 CMnSiCrNiMoVCoAlCuNbTiBNW
New relationadem201300116-gra-0001adem201300116-gra-0001adem201300116-gra-0001adem201300116-gra-0001adem201300116-gra-0001adem201300116-gra-0001adem201300116-gra-0001adem201300116-gra-0001adem201300116-gra-0001adem201300116-gra-0001adem201300116-gra-0001adem201300116-gra-0001adem201300116-gra-0001  
Steven & Haynes [8]adem201300116-gra-0001adem201300116-gra-0001adem201300116-gra-0001adem201300116-gra-0001adem201300116-gra-0001adem201300116-gra-0001         
Andrews [1]adem201300116-gra-0001adem201300116-gra-0001adem201300116-gra-0001adem201300116-gra-0001adem201300116-gra-0001adem201300116-gra-0001         
Andrews polynomial [1]adem201300116-gra-0001adem201300116-gra-0001adem201300116-gra-0001adem201300116-gra-0001adem201300116-gra-0001adem201300116-gra-0001         
Nehrenberg [5]adem201300116-gra-0001adem201300116-gra-0001adem201300116-gra-0001adem201300116-gra-0001adem201300116-gra-0001adem201300116-gra-0001         
Rowland and Lyle [7]adem201300116-gra-0001adem201300116-gra-0001adem201300116-gra-0001adem201300116-gra-0001adem201300116-gra-0001adem201300116-gra-0001        adem201300116-gra-0001
Grange and Stewart [3]adem201300116-gra-0001adem201300116-gra-0001adem201300116-gra-0001adem201300116-gra-0001adem201300116-gra-0001adem201300116-gra-0001         
Kung and Rayment [4]adem201300116-gra-0001adem201300116-gra-0001adem201300116-gra-0001adem201300116-gra-0001adem201300116-gra-0001adem201300116-gra-0001 adem201300116-gra-0001       
Payson and Savage [6]adem201300116-gra-0001adem201300116-gra-0001adem201300116-gra-0001adem201300116-gra-0001adem201300116-gra-0001adem201300116-gra-0001        adem201300116-gra-0001
Eldis [2]adem201300116-gra-0001adem201300116-gra-0001adem201300116-gra-0001adem201300116-gra-0001           
Eicheman and Hull [9]adem201300116-gra-0001adem201300116-gra-0001adem201300116-gra-0001adem201300116-gra-0001         adem201300116-gra-0001 
Sverdlin and ness [10]adem201300116-gra-0001adem201300116-gra-0001adem201300116-gra-0001adem201300116-gra-0001adem201300116-gra-0001adem201300116-gra-0001   adem201300116-gra-0001     
Carapella [11]adem201300116-gra-0001adem201300116-gra-0001adem201300116-gra-0001adem201300116-gra-0001adem201300116-gra-0001adem201300116-gra-0001 adem201300116-gra-0001      adem201300116-gra-0001
Van Bohemen [12]adem201300116-gra-0001adem201300116-gra-0001adem201300116-gra-0001adem201300116-gra-0001adem201300116-gra-0001adem201300116-gra-0001         

6 Conclusions

  1. Top of page
  2. Abstract
  3. 1 Introduction
  4. 2 Data Base for Ms Temperature
  5. 3 The Classical Ms Relations
  6. 4 The Extended Ms Relation
  7. 5 Comparison of the Extended Relation with the Classical Ones
  8. 6 Conclusions

The proposed new relation for the Ms temperature give improved prediction in comparison to the classical ones. The effect of new alloying elements has been introduced. Nevertheless, further experiments should be performed to precisely assess the effect of Ti, Nb and B which are for now described on average. But some results tend to show that the effect of Ti seems not to be linear and monotonous. Further improvement could also concern the introduction of the austenitic grain size which has a strong effect on the Ms temperature.