Driving force for f.c.c. → b.c.c. martensites in FeX alloys

PII: S1359-6454(96)00308-4

DRIVING

FORCE

FOR

f.c.c.4b.c.c. ALLOYS

A. BORGENSTAM Division

of Physical

Metallurgy,

Dept.

(Received

Materials

14 March

Acta muler. Vol. 45, No. 5, pp. 2079-2091. 1997 c’) 1997 Acta Metallurrica Inc. Published by Elsevier S&&e Ltd Printed in Great Britain. All rights reserved 1359-6454197 $17.00 + 0.00

MARTENSITES

IN Fe-X

and M. HILLERT

Science and Engineering, Sweden

KTH,

S-100 44 Stockholm,

1996; accepted 24 July 1996)

Abstract-Information on M,, the starting temperature for formation of martensite, is reviewed and one M, line each for lath and plate martensite are drawn in a number of Fe-X phase diagrams. A reasonable interpretation of the data indicates the possibility that the distance between the two lines may vary linearly with temperature and be independent of the choice of alloying element. Using thermodynamic descriptions of the binary systems, the driving force for the start of the formation of the two kinds of martensite is calculated from the same interpretation of data. When plotted against temperature the results indicate that the driving force for martensite may not be much affected by solution hardening but may mainly be a function of temperature. For plate martensite it may have a fairly constant value of about 2100 J/mol. For lath martensite it may vary linearlv, possiblv from 500 Jjmol at 8OO’C to 2100 J/mol at 25O’C. 0 1997 Acta Metallurgica-Inc. . . _ .

1. AIM OF PRESENT

WORK

In order to understand the mechanism of the f.c.c.--+b.c.c. martensitic transformation in Fe alloys it is essential to know its driving force and how it varies with the alloy content. It has been evaluated many times by combining experimental information on the A4, line with descriptions of the Gibbs energy of the f.c.c. and b.c.c. phases, usually denoted y and a and called austenite and ferrite. In such work it is important to define the M, line in a correct way and to judge the accuracy of the thermodynamic descriptions in a realistic way. Almost 30 years ago [l] there were indications of two separate MS lines in some Fe-X systems and later studies have produced more information of the same kind. However, most evaluations of the driving force are still based on a single M, line, the only exceptions being papers by Shteynberg et al. [2], Wilson [3], Mirzayev et al. [4] and Zhao and Jin [5]. In the present work the existence of two M, lines will be accepted and they will be evaluated from experimental information on the martensitic plateaux, i.e. constant A4, values in some range of cooling rates, observed in very rapid quenching experiments. It is evident that the two M, lines approach each other as they go to lower temperatures at higher alloy contents. It has been suggested that the two lines intersect [6]. In the present work we shall study the consequences of accepting that they actually intersect. In particular, we shall attempt to rationalize the resulting values of the driving force for several alloying elements by plotting the values as a function of the temperature in a common diagram. Almost all information on alloy contents cited in the present work is originally given in mass %. It will

and % will be used to be quoted as given originally mean mass %. Atom % will be used in all the diagrams and sometimes in the text. 2. TWO

TYPES OF THE MARTENSITIC TRANSFORMATION y-m

In the light optical microscope one can distinguish between two kinds of martensite: lath and plate. Lath is usually formed at low alloy contents and plate at high contents and a mixture in between. The typical martensite plate has a midrib which is visible after some kind of etching. In the transmission electron microscope one can see that lath martensite is dislocation rich and it might have formed by slip. The midrib of plate martensite is heavily twinned and it might have formed by a twinning mechanism. The outer part of a martensite plate is often dislocation rich and without twins and sometimes it even resembles lath martensite in the optical microscope. In Fe-Ni alloys of about 2&30% Ni it is evident that the twinned region is very thin at the lower Ni contents but widens at higher Ni contents and finally covers the whole plate [7]. Lahteenkorva [8] and Patterson and Wayman [9] have observed that in a junction of plates, formed in the same burst. the second plate to form grows until it hits the twinned region in the plate formed first. Evidently the plates then grow thicker, indicating that the thickening is slower than the initial growth of the twinned parts. In spite of the presence of these two modes of martensite formation, it is common to draw a single line for the starting temperature, M,, in binary phase diagrams. Much work has been done to assess the factors determining the type of martensite. The influence of

2079

2080

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and HILLERT:

DRIVING FORCE FOR f.c.c.4b.c.c.

temperature, composition, magnetic character of the austenite, quench rate, stacking fault energy, shear strength of the austenite and driving force for the martensite formation have been discussed. The discussion gets even more complicated when one includes rapid cooling experiments, since plate martensite can be formed at relatively high temperatures and low alloy contents if the cooling rate is high. In 1971 Morozov et al. [6] studied the transformations in Fe with 0.01% C from low to very high cooling rates. When plotting the arrest temperatures vs the cooling rate they found four plateaux and denoted them I, II, III and IV. They identified plateau III with the formation of martensite by slip (lath martensite) and plateau IV with the formation of martensite by twinning (plate martensite). The present work will be based on the following picture. Only lath martensite can form between plateaux III and IV when the former is observed above the latter. After the intersection of the two M, lines the martensitic transformation will start by the twinning mechanism yielding thin midribs, but on thickening the slip mechanism may take over very soon at alloy contents close to the intersection, but later on at higher alloy contents as mentioned above. When trying to draw curves for the two M, temperatures for various alloying elements in an attempt to evaluate the driving forces, we shall mainly rely on information from plateaux obtained in very rapid cooling experiments. However, there are regions of alloy content where the rapid cooling information is too meagre or completely missing and classical information on M, will then be used. We shall not pay much regard to the microscopic information because it may be very difficult to distinguish a small amount of one kind of martensite in a background of the other. Another problem is that plate martensite may form at alloy contents lower than the intersection point if the cooling rate is high enough. Despite the uncertainties it might still be interesting to compare the microscopic information with the intersection points chosen below. The selected M, lines will be presented in Figs l-7 and will there be denoted III and IV in order to emphasize that they are mainly based on information on plateau temperatures. Lines will also be included for plateaux I and II. Furthermore To, the temperature where LYand y of the same composition would have the same Gibbs energy, will be included as obtained by calculation from the SGTE (Scientific Group Thermodata Europe) solution database [lo] except for the Fe-Ni system where To is calculated with the Steel Research Group Martensite Database developed at the Northwestern University [ll]. Plateau I is mainly due to the formation of incoherent equiaxed CI and plateau II is mainly caused by the transformation to acicular GI,Widmanstatten CI. The following temperatures for the four plateaux in pure Fe will be accepted: I:SOO, 11:760, III:545 and IV:42O”C [6, 121. A similar study of the two ill, lines

MARTENSITES

was recently made by Zhao [13] but in some parts he trusted classical information on M, more whereas the present work was mainly based on information from rapid cooling experiments. The conclusions are thus different for some systems. 3. SELECTION OF M, LINES In the discussion of various alloy systems it will soon become evident that the information is not always good enough to allow the intersection of the two M, lines to be determined very accurately. Table 1 reproduces the temperatures of the intersection according to various authors. It shows that Mirzayev et al. have reported different intersection temperatures in the Fe-C system. In 1973 they drew the lines according to data from Gulyayev [14] giving a value of 342°C [ 151. In a paper from 1979 [16] they drew the lines according to their own experimental data and obtained 284°C. In a paper from 1987 [ 171 they did not include their own data for plateau III and instead relied on other experimental information, obtaining 252°C. They did not give any explanation why they disregarded their own data in that work. The scatter of values in Table 1 is considerable, in particular for the Fe-Ni system. In view of this scatter it does not seem meaningful to make separate choices for the various systems. The constructions for all the systems will thus be based on the choice of a common temperature of intersection, 250°C. Of course, this strategy will have consequences on the final result of the analysis and will thus be discussed again towards the end of the paper. It may be mentioned that the very high value by Zhao and Jin [5] for Fe-Cu was obtained by extrapolation. 3.1.

The Fe-C

system

By varying the cooling rate it has been possible to observe a plateau. The first ones to do this seem to be Wever and Engel [22] in 1930 who achieved cooling rates up to 9470 K/s. In 1933 their results were confirmed by Esser et al. [23] for carbon contents above 0.2%. Greninger [24] in 1942 used cooling rates up to 3 100 K/s and reported M, values independent of cooling rate. In 1979 Mirzayev et al. [ 161 studied a series of Fe-C alloys with cooling rates up to 500,000 K/s and observed two plateaux in each alloy up to 0.4% C. From 0.58% up to 0.89% C only one plateau was observed. A large number of authors have studied M, in Fe-C alloys using a single moderately high cooling rate. The works by Digges [25], Greninger and Troiano [26], Oka and Okamoto [27] and Hsu et al. [28] are often cited. In the present discussion the results of Oka and Okamoto and of Hsu et al. will be included because they give information on MS at carbon contents above the range studied by Mirzayev et al. The data are collected in Fig. 1. Following the suggestion by Morozov et al. [6] in 1971 we have

BORGENSTAM

and HILLERT:

DRIVING

FORCE

FOR f.c.c.+b.c.c.

MARTENSITES

208 1

connected the high carbon information on M, with the information on plateau IV. The data on plateau III from Mirzayev et al. are well represented by a straight line intersecting the other line at 250°C and 0.71% C, (3.22 at.%). In the region 0.3990.95% C, (1.7994.27 at.%), the MS values from several authors fall above the two lines selected in Fig. 1. Zhao [ 131 chose to trust these points when drawing the line for plateau III, yielding a small deviation from the line drawn by us. The composition regions for lath or plate martensite in Fe-C have been determined in many microscopical studies, e.g. by Kelly and Nutting [29], Marder and Krauss [30], Speich and Leslie [31] and Maki et al. [32]. These observations agree well with an intersection point at 0.71% C, as chosen in this work. A mixed structure of plate and lath martensite has been observed at slightly lower carbon contents, which is reasonable since the two M, lines are very close in temperature there.

3.2.

The Fe-Ni

system

Information on rapid continuous cooling in Fe-Ni has been discussed by us previously [21] up to 15 at.% Ni and here only data for higher Ni contents will be discussed in detail. In 1956 Kaufman and Cohen [33] measured MS temperatures using as low cooling rates as 5 K/min in alloys between 9.5 and 33.0 at.% Ni. Their data are discarded below 15 at.% Ni because they probably concern plateaux I and II. In 1963 Yeo [34] measured the M, temperatures in a series of air cooled Ni alloys between 19.8 and 29.55% Ni with a carbon content up to 0.009%. In 1964 Goldman and Robertson [35] determined the M, temperature for a 29.9% Ni alloy with 0.004% carbon using a very low cooling rate, l-2 K/min. These values confirm the values given by Kaufman and Cohen at high Ni contents. Banerjee and Hauser [36] determined the MS temperature in a series of alloys with more than 15 at.% Ni and these values also confirm earlier measurements. In 1970 Izumiyama et al. [37] used cooling rates up to 60,000 K/s and observed a plateau in an alloy with 19.6 at.% Ni. This value is in good agreement with other measurements. In 1970 Davies and Magee [38] measured the M, temperature at high Ni contents, and these values confirm earlier measurements. Mirzayev et al. [15] used cooling rates up to 330,000 K/s in alloys with 0.008-0.009% C and up to 29% Ni. Above 9.8% Ni only plateau IV was reported. All these data are collected in Fig. 2. The lines for plateaux III and IV have been drawn previously [21] and those lines are accepted here and the line for plateau IV is now extended to higher Ni contents. The intersection between the two lines at 250°C falls at 16.1% Ni, (15.4 at.%). The lines for plateaux I and II from the previous assessment [21] are also included in Fig. 2 but without giving the experimental information.

2082

BORGENSTAM

DRIVING

and HILLERT:

FORCE

FOR f.c.c.+b.c.c.

MARTENSITES

800 700

?? Greninger (24) 0 Minayev et al. (16) and Okamoto (27) + Hsu et al. (28)

800

VOka

600

700 ,u

500 ?? a m 400 8 g g 300

,u

i

600

# 500 g

200 100

3

2

4

5

6

7

8

9

’

10

0

m

2

temperatures

as functions

of carbon

content.

For this system the selection of lines differs much from those reported by Zhao [13] who trusted the microscopic information and did not make the two M, lines intersect until 29% Ni. The microscopic evidence of the transition between lath and plate martensite is quite uncertain [7, 9, 31, 39461. However, it should be stressed that the intersection point for plateaux III and IV chosen in the present study is at 16.1% Ni, which is much lower than the Ni content where plate martensite has been observed. A possible explanation to this discrepancy was given in Section 2. 3.3.

The Fe-Cr

system

For the Fe-Cr system we accept the lines as drawn for plateaux I and II in the previous assessment [21] (see Fig. 3). However, for plateau II there is another alternative. The previous assessment was based on

information mainly from Wilson [I]. Izumiyama’s [50] results are quite different and in Fig. 3 a dashed line represents his data whereas the solid line for plateau II is reproduced from the previous assessment. The information from Pascover and Radcliffe [49] and Mirzayev et al. [51] fall in between the two lines. In 1986 Mirzayev et a/. [19] showed how the plateau values vary with carbon content in three FeeCr-C alloys, 4.3, 6.6 and 9.4% Cr. These data can be represented reasonably well by a straight line for each plateau and an intersection of the lines for plateaux III and IV at 250°C. The results for 9.4% Cr are presented in Fig. 4. By extrapolating these lines back to 0% C, values for Fe-Cr were obtained and they have been included in Fig. 3 and the line for plateau IV was drawn in accordance with the data by

I

I

I

I I I Qirzaycv et al. (19)

and Robertson (35) y Banerjee and Hauser (36) V Izumiyama et al. (37) Davies and Magee (38) Mirzayev et al. (15)

600

12

10

Fig. 3. Plateau temperatures as functions of chromium content. The dashed line indicates an alternative shape for line II.

600 800

8

at%-Cr

at%-c Fig. 1. Plateau

6

4

X From F&r,

Fig. 3.

,u 2 g

400

& $

200

0

d

-200 A

0

5

10

lzt,;O

25

30

250 A

35 0.2

Fig. 2. Plateau temperatures as functions of nickel content, Up to 15 at.% Ni the lines are accepted from Ref. [21] and here the extension of plateau IV to higher Ni contents is shown.

0.4

0.6

0.8

1.0

1.2

1.4

at% C Fig. 4. Plateau temperatures as functions of carbon content in an alloy with 9.4% Cr. Points from the FeeCr system are included for 0% C.

BORGENSTAM

and HILLERT:

DRIVING

(52) CJMirzayev et al. (18) A lzumiyama et al. (SO)

1

2

3

4

5

6

Fig. 5. Plateau temperatures as functions of copper content.

Mirzayev et al. Also the line for plateau III was redrawn to represent available data better. It may be added that the values for plateau II obtained by extrapolating the Fe-Cr-C data support the results reported by Wilson and the full line in Fig. 3. The lines for plateaux I, II and III differ from the lines reported by Zhao [13], who drew these lines with similar curvature as the calculated 7’” line. For plateau IV our line is slightly steeper than his. In passing it may be mentioned that the slope of line IV, in the three Fe-Cr-C alloys, representing the dependence of plateau IV on the C content at various Cr contents, seems to vary linearly with the Cr content. The Fee&

2083

MARTENSITES

better than the values given by Izumiyama

3.5. The Fe-Co system

at%-Cu

3.4.

FOR f.c.c.+b.c.c.

R&ken et al.

?? RBstien

0

FORCE

system

In 1969 RlsLnen [52] reported transformation temperatures in FeeCu. From dilatometric curves he found two different transformation temperatures for alloys with up to 0.007% C by using a cooling rate of 840 K/s. In 1970 Izumiyama et al. [50] studied a series of Fe-Cu alloys with the sum of carbon and nitrogen <0.005% by using cooling rates up to 50,000 K/s. In all alloys examined only one plateau was observed and these values confirm the lower values measured by Rkgnen, and probably concern plateau II. Mirzayev et al. [ 181achieved cooling rates up to 280,000 K/s and could observe all four plateaux at 1.2 and 2.7 at.% Cu but only plateaux I, III and IV at 4.8 at.% Cu. The carbon impurity fluctuated from 0.003 to 0.006%. It is straightforward to draw the lines for plateaux I, III, IV and for plateau II up to 3.5% (see Fig. 5). To continue the line for plateau II the values reported by Izumiyama et al. were trusted rather than the values reported by Rlslnen, because his values only represent ordinary M, values and not plateau values. The lines for plateaux I, III and IV agree well with the lines given by Zhao [13]. For plateau II Zhao chose a straight line, describing the values by

Fe-Co differs from the other systems discussed since Co increases the M, temperature for both lath and plate martensite. In 1967 Parr [53], using cooling rates up to 97,000 K/s, observed two plateaux for alloys with 0. I, 0.25 and 0.5% Co but at higher alloy contents only one plateau was observed. The carbon impurity in the alloys used was 0.009%. In 1970 et ul. [50] used cooling rates up to Izumiyama 50,000 K/s to study Fe-Co alloys up to 60% Co with the sum of carbon and nitrogen impurity <0.008%. Only one plateau was observed and Izumiyama et al. explained the difference from Parr as resulting from the high carbon impurity in the alloys used by Parr. Mirzayev et al. [ 181 reported values for plateaux I-IV in one alloy with 2.8% Co and the carbon impurity in the region 0.003~0.006%. At higher cobalt contents only plateaux I, III and IV were observed. They achieved cooling rates up to 500,000 K/s. The reported temperatures for plateaux I, III and IV fall close to each other except for two values reported by Izumiyama et al. for 6.0 and 14.4% Co and two values reported by Parr for 3.0 and 6.0% Co. They fall between values reported for plateaux I and III by Mirzayev et al. Nevertheless, it seems straightforward to draw the lines for plateaux 1, III and IV and the lines agree well with the lines drawn by Zhao [13]. For plateau II the situation is more complicated. Several points by Parr give a strong indication of a very steep line, presumably the line for plateau II. A single point by Mirzayev et al. may refer to plateau II but indicates that the line should be less steep. Both alternatives are shown in Fig. 6. The points by Parr are represented by a full line and the

900

600

A Parr (53)

500

?? hmuyama et al (50) 0 Mirzayev et al. (18)

A

4ooL

1

I

I

I

I

I

o

10

20

,Eco

40

50

60

Fig. 6. Plateau temperatures as functions of cobalt content. For plateau II two alternatives are shown; the dashed line is drawn according to data from Mirzayev ef ul. [18], and the solid line according

to data

by Parr [53].

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DRIVING FORCE FOR f.c.c.+b.c.c.

25OC and 5.3% Mn, (5.4at.%) (Fig. 7). Lath martensite has been observed at much higher manganese contents, and the situation is similar to the one discussed for nickel. The explanation may be the same. This is another case where Zhao [13] judged the data quite differently. He drew the two M, lines almost parallel and without any intersection. Holden et al. [58] observed t martensite at 12% Mn but not at 10%. Thus, Fig. 7 only concerns data up to 10 at. % Mn. Zhao [ 131 instead interpreted the data at high Mn contents as representing lath and plate martensite and disregarded the fact that f martensite is formed.

800

,u 600 g$ 500 E” g 400 300

3.7. Summary

100 &&

O

2

4

&lMn

*

lo

l2

Fig. 7. Plateau temperatures as functions of manganese content.

single point by Mirzayev by a dashed line. It should be emphasized that the results by Parr may be influenced by the fairly high C impurity. These two lines for plateau II differ appreciably from the lines drawn by Zhao who instead chose to trust the points reported by Izumiyama ef al., and drew a line with positive slope. 3.6.

The Fe-Mn

MARTENSITES

system

M, in Fe-Mn alloys has been studied by several authors using a single, moderately high cooling rate. The works by Troiano and McGuire [54], Jones and Pumphrey [55] and Schumann [56] are often cited but are not included in Fig. 7 since they did not observe plateaux. Gomersall and Parr [57] in 1965 were the first to report plateau temperatures in FeeMn. By using cooling rates up to 48,000 K/s they observed a plateau in alloys between 1 and 10 at.% Mn with carbon impurities around 0.009%. In 1970 Izumiyama et al. [50] used cooling rates up to 46,000 K/s to study a series of manganese alloys with carbon impurities around 0.003%. At 1.1 at.% Mn they gave values that probably concern plateaux I and II but at higher contents only plateau II was observed. In 1977 et al. [2] studied a series of manganese Shteynberg alloys with cooling rates up to 200,000 K/s with 0.003% C. They gave values for four plateaux up to 2.0% Mn, and for 4.1 and 7.5% Mn they reported plateaux I, II and IV and for 9.8% Mn only plateaux I and IV. Their values for plateau I fall close to the value for plateau I at 1.1% given by Izumiyama et al. For 4.1% Mn it is possible that plateaux III and IV are so close in temperature that it is difficult to distinguish them and that the plateaux observed by Shteynberg et al. are actually plateaux I, II and III. The lines for the different plateaux are drawn according to the data discussed above and the lines for plateaux III and IV are forced to intersect at

of information

on M,

The general impression of the diagrams is that the lines for plateaux III and IV approach each other at lower temperatures but move away from each other at higher temperatures. One way to illustrate this without using any additional information or interpretation would be to plot T,,, - T,, vs (T,,, + T,,)/ 2 (see Fig. 8). This diagram gives a strong impression of a correlation between these two quantities. Of course, it should be realized that the good agreement for C, Mn, Ni and Cu mainly depends on the fact that the same temperature of intersection between the two plateau lines was chosen. However, it is very interesting that the line for Co has almost the same slope although it goes to higher temperatures. The value of T,,, - T,,, is closely related to the difference in driving force for the start of the martensite transformation according to the two modes. Figure 8 thus seems to indicate that this difference is mainly a function of temperature, here given as (r,,, + T,,)/2. For a deeper analysis one should study how the driving force for each kind of martensite formation

*O”-

Fig. 8. Mean value of temperatures for plateaux III and IV as a function of temperature difference. The fairly straight line indicates that the difference in driving force for the formation of lath and plate martensite is mainly a function of temperature since the temperature difference is closely related to the difference in driving force.

BORGENSTAM

DRIVING

and HILLERT:

- -- -- Cohen et al. (59) - - - - Gilbert and Owen (47) (60) -.-.-Bell and Owen (61)

Imaietal.

. . ..-...---Bhadeshia (62) - Mirzayev et al. (4) - Zhaoand k(5) Ghosh and Olson (63)

FORCE

FOR f.c.c.+b.c.c.

,

2600,

2085

MARTENSITES

,

,

,

,

,

,

,

,

-

1800 j h

1600

-*a 1400 ..--..... Halden

1000

et al. (58)

- - - - Shteynberg

800

’ 1

0

’ 2

’ 3

’ 4

’ 6

et al. (2)

’ 7

’ 8

’ 9

10

at%-Mn (d)

800

I

2200, 2500

’ 5

I

I

I I ““~~~“~~~’ Kaufman -.-._ -

-

I

I

I

and Cohen Zbao and Jin (5) -Wilson (3)

I

-----ZhaoandJin(5) (73)

A O

5

lo

at%_&

l5

(e)

3500,

,

,

,

,

(

,

,

,

,

,

2000 1800 ---1

.

______.

1600

..r

,.,..__....‘.

;=;E1400 .._,>_.<.C ..... ....‘1.> , _’ / _ -8 1200~~/,‘~~~ , >--1000 E

--I’

Fig. 9. Driving force for calculated with the SGTE M, lines drawn in Fig. 1 evaluations of the driving

_--:

formation of lath and plate martensite as functions of alloy content. The thick solid lines are solution database [lo] and the thinner solid lines with the Northwestern database [l l] using the for (a), Fig. 2 for (b), Fig. 3 for (c), Fig. 7 for (d), Fig. 5 for (e) and Fig. 6 for (f). Previous force for the formation of martensite are included. The difference in values is due to the use . ^ -

2086

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DRIVING FORCE FOR f.c.c.+b.c.c.

varies with temperature. It is then necessary to have information on the thermodynamic properties. Such information is available and evaluations have been made many times but the results scatter considerably. It will now be attempted again. The present results are compared with previous results in Fig. 9(a))(f). Due to the uncertainty in the thermodynamic descriptions, the present work made use of two different databases, the SGTE solution database [lo] and the Northwestern database [l 11. The former results are plotted with thick solid lines and the latter ones with thin solid lines.

4. DRIVING

FORCE

IN THE Fe-C SYSTEM

The main part of the lines for the Fe-C system in Fig. 9(a) were based on classical M, information and they all start from a value of about 1200 J/mol for lath martensite in pure Fe. Some of these lines are almost horizontal but some have a strong positive slope. The main reason for this difference is the difference in the thermodynamic descriptions but to some degree it depends on different shapes of the M, line chosen. It is thus important to discuss the thermodynamics of the martensite transformation in the Fe-C system. Johansson in 1937 [64] was the first to publish a thermodynamic analysis of the c( and y phases in the Fe-C system. He also discussed the martensitic transformation, presuming that martensite cannot form at the temperature where c( and y have the same Gibbs energy but needs further undercooling. He explained the extra driving force needed for the martensitic transformation as resulting from the C atoms of martensite being frozen in positions inherited from the parent y, and he believed that those positions would give a higher energy as well as a lower entropy than in c( with a random distribution of the C atoms. Zener [65] instead assumed that martensite, which is tetragonal at higher C contents because of the non-random positions of the C atoms, would have a lower energy because the C atoms there collaborate and thus minimize the strain energy caused by the presence of C atoms in interstitial sites of insufficient size. He even proposed that there is a temperaturecomposition region where the tetragonal martensite with the non-random distribution of C atoms would have a lower Gibbs energy than CI with a random distribution. He developed a simple theory of ordering and by minimizing the Gibbs energy it was possible to predict the degree of order at equilibrium. When evaluating the driving force for the martensitic transformation he assumed that martensite would have those equilibrium properties. Fisher [66] accepted Zener’s picture and made a more thorough analysis of the Gibbs energy of the ordered c( phase when he evaluated the driving force for martensite formation. It was also accepted by Bell

MARTENSITES

and Owen [61] and by Kaufman et al. [67], for instance, and many evaluations of the driving force for martensite formation in Fe-C alloys have been published over the years with most of them taking Zener ordering into account. The work by Kaufman et al. also contains a thorough discussion of the solution of C in the y phase where the deviation from Henry’s law is explained with the excluded sites model, which assumes that neighbouring sites are rarely or never occupied, an idea which seems to originate from Darken [68]. It is important to notice that this model implies that the distribution of C atoms is already far from random in the y phase. The present evaluation of the driving force for martensite was based upon Gustafson’s description of the Fe-C system [69], which is purely formal but seems to reproduce rather well all the available experimental information on equilibria. His choice of description of the y phase is not very critical for the final result. The description of the x phase is much more uncertain because the direct experimental information on its equilibrium properties is limited to very low C contents. That information can only be used to evaluate the slope according to Henry’s law. However, there have been many attempts to go further and to evaluate an interaction energy between neighbouring C atoms. Recently, it has been realized that this is not possible because the equilibrium information is limited to very low contents in the CI phase [70, 711. Thus, the present evaluation will be based on the Henrian description proposed by Gustafson but with an addition of the effect of the non-random distribution of the C atoms, because they have inherited their positions from the parent y phase. The energy term for this ordering as developed by Zener and by Fisher will be used. In contrast to previous applications of Zener ordering, it will here be assumed that there is complete ordering of C in martensite rather than a slightly lower degree of order which is predicted at equilibrium, or no order at all above a critical temperature. The C atoms are thus assumed to inherit their positions from the parent y. The difference in Gibbs energy according to these two models is demonstrated in Fig. 10 and is not very large. It should further be emphasized that accepting that the C atoms inherit their positions directly from the parent y, one should omit all the contribution from configurational entropy in a and y when calculating the driving force. If the excluded sites model is correct for the y phase, then the same sites should also be excluded in the martensite and the driving force should probably be somewhat lower than calculated. It should be emphasized that the i&a of C atoms inheriting their positions from the parent y is based on the assumption that the rate of transformation is so high that there is not enough time for C to redistribute during the actual transformation. It seems possible that this could apply to the edgewise growth of plate martensite but possibly not to lath

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be based on the results obtained with the SGTE solution database after adding the effect of ordering (thick lines).

5. DRIVING FORCE IN OTHER Fe-X SYSTEMS

Fig. 10. Contribution to Gibbs energy of martensite due to Zener ordering as a function of carbon content and temperature calculated with the model presented by Fisher. The dashed line is calculated assuming complete ordering of martensite at all temperatures and all carbon contents and the solid line is calculated from the equilibrium degree of ordering suggested by Zener.

In that case, the equilibrium degree of order should be used for lath martensite. Furthermore, at very high growth rates there is not even time for the reaction heat to diffuse away and the temperature will be higher at the r/cc interface than in the rest of the system [72]. A calculation based on adiabatic conditions would give much lower values than the isothermal conditions assumed in all the calculations presented in Fig. 9(a). Another uncertainty in the description of the Gibbs energy of the c( phase comes from the effect of C on the ferromagnetic transition in the c( phase. The analysis of the properties of the c1 phase made by Gustafson and by most other researchers is made under the assumption that the magnetic properties are not affected by C. The two databases used in the present work both give a strong positive slope for lath martensite [thin and thick solid lines starting from about 1200 J/mol in Fig. 9(a)]. For plate martensite they have different slopes but are much more horizontal (thin and thick lines starting from about 2000 Jjmol). It is evident that a single M, line, which would actually represent lath martensite at low contents and plate martensite at high, would start with a positive slope and bend in the region of mixed structures and then become more horizontal and even get a negative slope. This may explain the maximum in some of the curves published previously but it is surprising that most of the published lines are more or less straight. The general impression of Fig. 9(a) is quite confusing, in particular for lath martensite. However, the more recent studies seem to agree that there should be a strong slope. Further analysis of the Fe-C system will

martensite.

The driving force obtained for the FeeNi system is presented in Fig. 9(b). The line presented by Kaufman and Cohen [73] starts from a very low value for pure Fe. However, that line refers to a series of different transformations because a constant and rather low rate of cooling was used. Of the other lines, the upper group refers to plate martensite and the lower group to lath martensite. The thick solid lines were obtained in the present work using the SGTE solution database. For plate martensite it goes to zero, which implies that the A4, line should intersect the To line. This is evidently incorrect and it must be emphasized that this thermodynamic description is based on equilibrium information at low Ni contents and high temperature. The extrapolation to the A4, temperatures at high Ni contents is very uncertain and requires an estimate of the ferromagnetic properties of s( as well as y at these Ni contents. This is probably difficult to do and, as a consequence, it is very difficult to predict the size of the driving force. The other database used in the present work gives a less drastic decrease up to 25 at.% Ni but then a very steep slope. The diagram for FeeCr, Fig. 9(c), also has a curve starting from a very low value for pure Fe. It should be disregarded because it probably refers to a series of different transformations. All the other curves are rather horizontal because the two M, lines are rather parallel to the To line. For FeeMn and FeeCu [Fig. 9(d) and (e)]. the difference between the lines obtained in various studies is mainly caused by differences in the thermodynamic descriptions. It is interesting to note that the lines, obtained in the present study using two different databases, are more or less parallel and the distance between them originates from different descriptions of pure Fe. Of course, this difference is common to all the binary systems discussed in the present work. When comparing the driving forces for different alloying elements it will thus be necessary to use a single description of pure Fe. The result for FeeCo [Fig. 9(f)] looks very different because Co increases the M, temperatures. The thermodynamic properties involved have thus been obtained without drastic extrapolations from experimental information on equilibria. As a consequence, these evaluations of the driving force are probably safer than for the other alloying elements. 6. VARIATION

IN DRIVING FORCE WITH TEMPERATURE

In view temperature

of the strong correlation between and the difference between the driving

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forces for plate and lath martensite, indicated by Fig. 8, the driving forces now calculated for various alloying elements were plotted vs temperature in Fig. 11. The values obtained using the SGTE solution database were selected here. For each kind of martensite all the lines start from a point representing pure Fe, 1250 J/mol at 545°C for lath martensite and 2100 J/mol at 420°C for plate martensite. For lath martensite the point representing pure iron falls at 545°C and the effect of Co is described by an almost straight line up to 800°C. The other elements decrease the MS temperature and the general tendency is that they increase the driving force. As already emphasized, there is a strong uncertainty in these values due to the uncertain thermodynamic descriptions. This is particularly true for Ni as already discussed in connection with Fig. 9(b). By using the Northwestern database [resulting in the thin lines in Fig. 9(b)] the line for Ni in Fig. 11 would have a slope much closer to that of C. The large deviation for Cu may partly be due to the small range of composition examined in that system. The line for plateau III in Fig. 5 could easily be given a steeper slope by trusting the point given by Mirzayev et al. [18] at 4.8 at.% Cu. The Cu line for lath martensite in Fig. 11 would then fall close to the line for carbon. Anyway, accepting the lines for C and Mn as typical, it would be almost possible to describe the effect of temperature with a single straight line from 800 to 250°C (see sloping dashed line in Fig. 11). The dashed lines for lath martensite may be within the experimental uncertainty for most of the information and it is an interesting possibility that the same

900 800 700 600 500 400 300 200 100 0

500

1000

1500

2000

2500

AGm J/mol Fig. 11. Driving force for formation for martensite from Figs 9(a)-(f) as a function of formation temperature calculated with the SGTE solution database [lo]. For lath martensite it is almost possible to describe the relation between driving force and temperature with a single line (see the dashed line with negative slope). For plate martensite the driving force is more independent of temperature (see vertical dashed line).

FORCE

FOR f.c.c.+b.c.c. 8OOt

,

,

0.5

1.0

MARTENSITES

,

,

,

,

2.5

3.0

,

,

,

,

3.5 4.0

4.5

5.0

650

600

550

500 -0

1.5 2.0

at% Fig. 12. Line for plateau II as a function of alloy content of Ni, Cr, Cu, Co, Mn and MO in Fe. For Cr and Co two different alternatives are included.

line should hold approximately for all alloying elements. Accepting the sloping dashed line in Fig. 11 for lath martensite and 250°C as the intersection between the two M, lines, one can draw the corresponding line for plate martensite through that point of intersection and the point for pure Fe. The resulting line is almost vertical (see second dashed line in Fig. 11). The results for the individual elements differ from this line about as much as for lath martensite. This is a consequence of the suggestion that the two MS lines intersect at the same temperature for all Fe-X systems. In any case, it is evident that the driving force for plate martensite varies with temperature much less than for lath martensite. The effect of alloying elements on plateau II, demonstrated in Figs l-7, will now be discussed without a detailed thermodynamic analysis. Those transformation temperatures are collected in Fig. 12. Also a line for MO is included, drawn according to plateau values given by Izumiyama et al. [50]. The initial slopes of all the lines, with the possible exception of Cr, are much steeper than the initial slope of the respective To line and the lines for the other plateaux. In particular, the initial slopes of the lines for Mn, Ni, Cu and MO are fairly similar and Co would belong to this category if the data by Parr can be trusted (solid line in Fig. 12). The line for Cr would also be fairly steep if the alternative based on Izumiyama’s data can be trusted (dashed line), which seems less probable, though. In the previous study [21] the steep initial slope for plateau II in Fe-Ni was explained as an effect of an interaction between the solute and the moving phase interface (a kind of solute drag). The information now gathered for Mn, Co, Cu and MO may be taken as further support for the existence of such an effect.

DRIVING FORCE FOR f.c.c.+b.c.c.

and HILLERT:

BORGENSTAM

7. DISCUSSION

The prevailing idea about the effect of alloying elements on the M, temperature, and thus on the need of a driving force, is that they cause solution hardening. This has been proposed by Hornbogen [74] and developed in detail by Ghosh and Olson [63, 751. However, in order to explain the decrease in driving force caused by Co they had to postulate a softening due to an effect on the elastic modulus. It is not evident why Co of all elements would have such an effect. That kind of explanation is no longer needed if it is accepted that there is a negative effect of temperature on the requirement for a driving force. Ghosh and Olson supported the idea of solution hardening both in substitutional and interstitial alloys and they actually obtained parabolic curves for the driving force as function of alloy content. This is shown by their curves for the driving force as a function of the C and Cr contents for lath martensite, included in Fig. 9(a) and (c). It is not evident how well that construction is supported by the information used and, above all, the information seems too uncertain to allow conclusions to be drawn from the fact that they obtained parabolic curves. Accepting that there should be some line in Fig. 11 representing the effect of temperature on lath martensite, one should expect then to add a positive effect of solution hardening for each alloying element as one moves away from the value for pure Fe at 545°C. This would make the line for Co steeper than the dashed line and for all the other elements the lines would be more horizontal, as illustrated schematically in Fig. 13. Such a difference between the lines for Co, on the one hand, and the other elements on 900,

I

800

’ In

I \

I

1

I

\

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2089

the other is not shown by Fig. 11. It is difficult to avoid concluding that the effect of solution hardening is too weak to be noticed and that the main effect is caused by the temperature. Accepting the two dashed lines in Fig. 1 I as representative of the effect of various alloy elements, one should primarily look for an explanation of the different temperature dependence for lath and plate martensite. It is generally agreed that the driving force is required in order to overcome mechanical resistance, whether in “J, c( or the interface. Since the microscopic difference between lath and plate martensite is coupled to their different internal structures, which in turn indicates different mechanisms of the shape accommodation inside the a phase, by slip and twinning, respectively, it is natural to assume that the most important mechanical resistance is caused by the rx phase. From the slopes of the two dashed curves in Fig. 11 one could then conclude that shape accommodation of the z phase by twinning requires a fairly strong driving force at high temperatures and about the same at lower temperatures. On the other hand, shape accommodation of the c( phase by slip requires a much smaller driving force at high temperatures but it increases rapidly at lower temperatures. This would be in qualitative agreement with the known facts that the critical shear stress for slip in c( varies greatly with temperature but not for twinning. It should be emphasized that the thermodynamic description of pure Fe at low temperatures, preferred by Ghosh and Olson [63,75] and used in their database, would change the slope of all the lines, including the dashed lines, but the difference in slope between the two dashed lines would be essentially the same. One would still have to find an explanation of the difference in the effect of temperature on the two kinds of martensite. It has been mentioned already that microscopic evidence favours the intersection between the two M, lines in the FeeNi and Fe-Mn systems being moved to a higher alloy content and a lower temperature. If that was the general tendency for all alloy elements, then the dashed line for lath martensite would have to be modified. The dotted line in Fig. 13 shows this modification schematically if it is assumed that the M, line for lath martensite will never intersect the other line but approach it asymptotically. It is evident that the general conclusions would not be affected. 8. CONCLUSIONS

Fig. 13. Schematic diagram showing how solid solution hardening should affect the temperature dependence of the driving force for formation of lath or plate martensite. The two dashed lines should change in the direction shown by the dashed-dotted line. The dotted line shows the modification schematically if it is assumed that the line for plateau 111 approaches the line for plateau IV asymptotically.

Accepting different M, lines for lath and plate martensite one finds that they tend to intersect at some low temperature except for Co which increases both M, temperatures and Cr which increases hl, for lath martensite. It is possible to account for most of the experimental information on the effect of C. Mn, Ni and Cu by accepting that the temperature of intersection is 250 C for all of them. On the other

2090

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300 200 t 100 A

b

5;o

Ii

J,l5j

2;o;

25bo

m Fig. 14. Illustration of conditions for martensitic transformation. The solid curves are calculated for some alloys. The intersection with a dashed line gives the M, temperature as indicated by an arrow.

hand, one should not completely rule out the possibility that M, for lath martensite starts to bend, when it approaches the other MS line, and thus moves the point of intersection to higher alloy content and lower temperature, as suggested for the Fe-Ni and Fe-Mn systems by Zhao [13]. There are certainly some microscopic observations supporting his choice. However, it is not evident by what mechanism the two M, lines could do this if they represent two different kinds of transformation. The calculation of the driving force for the start of martensite formation is rather uncertain due to uncertainties in the thermodynamic descriptions of the binary Fe-X systems at low temperatures and high alloy contents. However, the results seem to indicate that the dependence of the driving force on the alloy content is mainly an effect of temperature and less an effect of solution hardening. It is proposed that this should hold for multicomponent alloys if it holds for binary alloys. With the description of the Gibbs energy of pure Fe, preferred in the present work, the driving force for plate martensite is approximately constant, 2100 J/mol, i.e. independent of the solute content. For lath martensite the need for a driving force increases, approximately linearly from 500 J/mol at 800°C to 2100 J/mol at 25O’C. It should be emphasized that this result depends on the choice of 25O.C as the temperature of intersection between the two MS lines but the line is a reasonable linear continuation of the line for Co at higher temperatures. In view of the considerable uncertainties involved, the result should be regarded as an interesting possibility rather than a proven fact. Certainly, during its formation martensite must overcome several barriers. The conclusion from the present examination is that the main barriers are already present in pure Fe. They may be connected

FORCE

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MARTENSITES

to the structure of the interface or to the mechanism of deformation. It is known that twinning plays an important role for plate martensite and slip for lath martensite. A very simple and probably too nai’ve suggestion of the difference in behaviour of the driving force for the two kinds of martensite would be that the driving force for twinning is high but relatively independent of temperature and the driving force for slip is lower at high temperatures but increases drastically at lower temperatures. Accepting the present results, the conditions for martensite transformation in a series of Fe-Co and Fe-C alloys can be described with the use of Fig. 14. The curve for each alloy shows G& - CL as function of temperature. When a curve intersects a dashed line, the available driving force, Gj,, - G&, is sufficient to overcome the resistance, represented by the dashed lines, and a martensitic transformation may occur. The M, temperature can be evaluated from the intersection (see arrows in Fig. 14). The curve for 0.77% C, (3.5 at.%) predicts plate martensite; all the other curves intersect line III and predict lath martensite. However, by very rapid cooling one may suppress lath martensite and reach the intersection with the line for plate martensite, line IV.

Ackno+vledgements-This work was supported by a special grant from the Royal Institute of Technology and NUTEK. Thanks are also due to Professor John Agren for his advice and encouragement.

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