The isothermal martensite formation in a maraging steel: A magnetic study

Materials Science and Engineering A 481–482 (2008) 757–761

The isothermal martensite formation in a maraging steel: A magnetic study D. San Martin a,∗ , N.H. van Dijk b , E. Br¨uck c , S. van der Zwaag a a b

Fundamentals of Advanced Materials Group, Faculty of Aerospace Engineering, TU Delft, Kluyverweg 1, 2629 HS Delft, The Netherlands Fundamental Aspects of Materials and Energy Group, Faculty of Applied Sciences, TU Delft, Mekelweg 15, 2629 JB Delft, The Netherlands c Van der Waals-Zeeman Institute, University of Amsterdam, Valcknierstraat 65, 1018 XE Amsterdam, The Netherlands Received 22 May 2006; received in revised form 21 November 2006; accepted 21 November 2006

Abstract Maraging steels reach their extraordinary final mechanical properties from a combination of a fine martensitic microstructure and a high precipitate density. In the steel studied in this work, the starting metastable austenitic microstructure is transformed isothermally to martensite at 233 K. This work shows how the rate of the isothermal martensite formation in this steel can be significantly increased by an external magnetic field. In situ magnetization measurements have been used to characterize the phase transformation kinetics. A model of mixed physical–empirical nature is presented to support the observations. © 2007 Elsevier B.V. All rights reserved. Keywords: Stainless steel; Magnetic field; Kinetics; Modeling

1. Introduction Chromium alloyed maraging steels are low carbon steels developed in the 1960s for applications requiring ultra-high strength combined with good fracture toughness and corrosion resistance. Their remarkable properties are obtained through a process of martensite formation plus fine intermetallic precipitation. Kinetically, iron based alloys can undergo martensitic transformation under two main mechanisms: athermal or isothermal. The more common athermal martensite transforms during cooling as a function of temperature only. The isothermal transformation takes place as a function of temperature and time; an incubation time is needed for the transformation to start. The shape of the isothermal transformation curve is sigmoidal, as function of time; and shows a C-shape, as a function of temperature. Recently, Borgenstam and Hillert [1] have reviewed different experimental studies on Fe–Ni–Mn and Fe–Cr–Ni alloys regarding the isothermal formation of martensite. It is well known that phase transformations in steels are strongly influenced by external stimuli such as uniaxial stress, hydrostatic pressure or magnetic fields [2,3]. Some authors have shown that the martensite start temperature, MS , can be raised ∗

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0921-5093/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2006.11.177

in Fe–Ni and Fe–Mn alloys [3–5]. The isothermal martensitic transformation kinetics in Fe–Ni alloys can be accelerated by the effect of applied magnetic fields [6]. In this work the influence of applied magnetic fields on the isothermal martensitic transformation is evaluated in a Fe–12Cr–9Ni (wt.%) maraging steel. The strength of the magnetic field is varied from 2 to 9 T. It is shown that an applied magnetic field can significantly speed up the isothermal martensitic transformation in the steel studied. The analysis of the results is discussed with the aid of a mixed physical–empirical model. 2. Materials and experimental procedure The composition of the steel studied in this work is given in Table 1. The as-received material was delivered as plates of 31 mm width × 0.5 mm thickness. In the final stages of the processing, the material is heat-treated at around 1300 K and aircooled down to room temperature. The nose of the C-curve in this steel was determined to be around 233 K by Holmquist et al. [7]. The initial microstructure of the steel is composed of austenite, a small volume fraction of martensite and Chi-phase precipitates (Fe36 Cr12 Mo10 ). The austenite grain boundaries were revealed using the hot Lichtenegger–Bloch etching solution and the mean grain size was determined to be 6 ␮m using an image analyzer.

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Table 1 Chemical composition of the studied steel (wt.%) with balance Fe Cr 11.4

Ni 8.7

Mo 3.4

Ti 1.1

The influence of the magnetic field on the isothermal martensitic transformation was studied at the optimum transformation temperature of 233 K. For the reference study of the martensitic transformation behavior in the absence of an applied magnetic field, square samples of 10 mm length and 0.5 mm thickness were transformed for times up to 8 days using a Cryostat. Smaller rectangular samples of 2 mm × 3 mm and 0.5 mm thickness were held isothermally at 233 K under the influence of a magnetic field, using a MagLab system (Oxford Instruments). Four different samples were treated in magnetic fields of 2, 4, 6 and 9 T. A fifth sample was used to make a two-step magnetic field experiment, also at 233 K. In this experiment the sample was transformed for 5 h in an applied field of 4 T, after which the field was raised to 9 T and held for 14 h. The metallographic examination of the martensite in the zero field samples was done in the following way: samples were annealed at 823 K for 30 min, then mounted in bakelite and polished in the usual way, finishing in 1 ␮m diamond paste. Martensite was then revealed using Lichtenegger–Bloch etching solution. Determination of the martensite volume fraction was done by the point counting method. 3. Model, results and discussion 3.1. The model The kinetics of the isothermal martensitic transformation is mainly controlled by its nucleation rate. The transformation ˙ V¯ , where V¯ is the ˙ can thus be expressed as, ϕ˙ = N rate, ϕ, mean volume of martensitic units (constant, as a first approx˙ is the nucleation rate imation, during the transformation) and N of martensite in austenite per unit austenite volume. Assuming oblate spheroid like martensite units, with a relation between ¯ axis length c¯ /¯a = 10 and c¯ = L/2 (semi-major axis length), ¯ 3 /60 with L ¯ the the mean volume can be written as V¯ = πL ˙ = mean grain size. The nucleation rate can be described by N (N0 + pϕ)(ϕ0 − ϕ)n ν exp(−E/RT ), where N0 is the initial number of potential nucleation sites per unit volume of austenite at the start of the transformation, p is the autocatalytic factor [8]. The parameter ν is the attempt frequency (≈107 s−1 ) and E is the energy barrier of the process [9]. Parameter ϕ is the volume fraction of martensite transformed during the experiment and ϕ0 is the maximum amount of martensite that can form under the conditions imposed; it is dependent on the composition of the alloy. It is supposed that this value will not be affected by the magnetic field. For the steel grade studied in this work (Table 1) ϕ0 ≈ 0.7 [10]. Combining the previous equations yields the following expression,   π ¯3 E n ϕ˙ = L (N0 + pϕ)(ϕ0 − ϕ) ν exp − (1) 60 RT

Al 0.7

Si 0.3

Cu 2.5

Mn 0.3

C, N <0.01

3.2. Magnetic characterization of the microstructure It is well known that austenite is paramagnetic (small and positive susceptibility) and martensite is ferromagnetic (large and positive susceptibility); therefore it can be approximated that if both phases are present in the microstructure of a material, the total magnetization, as a result of an applied magnetic field, will be proportional to the amount of martensite present in the material. Thus, the volume fraction of martensite can be estimated from the magnetization saturation of the sample, MSat , if we know the saturation magnetization of the sample in the presence MAR ; ϕ = M /M MAR . of 100% of martensite MSat Sat Sat Unfortunately, the saturation magnetization of the steel is not known but it can be estimated by considering that Fe, Cr and Ni will have the strongest contribution to the average magnetic moment of the material and discarding the influence of the minor remaining alloying elements. Using the average magnetic moments of a Fe–12Cr alloy [11] and of pure Ni [12], μ ¯ Fe−12Cr (∼ 1.9 μB ) and μNi (∼ 0.6 μB ), respectively, with μB the Bohr magneton (9.27 × 10−24 A m2 ) and knowing the concentration of Fe, Cr and Ni in the steel (Table 1), the satMAR = 1.18 × uration magnetization can be estimated to be MSat 6 MAR 10 A m−1 (μ0 MSat = 1.49 T, where μ0 = 4π × 10−7 N A−2 is the permeability of vacuum). The magnetization curves of the five samples used in the study of the influence of the magnetic field on the martensitic transformation were measured at room temperature before the test (see Fig. 1(a)). The magnetization was found to increase rapidly for increasing applied magnetic fields until around 2 T, after which the slope of the curve approaches a constant value. In ferromagnetic phases like ferrite or martensite, the slope of this curve is nearly zero. In Fig. 1(a) it seems that there is a second contribution to the saturation magnetization of martensite. This contribution is thought to originate from the antiferromagnetic ␹ phase that is present in the initial microstructure [13]. In Fig. 1(b) a schematic representation of the contribution of each phase, martensite and ␹ phase, to the total magnetization of the sample is given. In order to find out the volume fraction of martensite, the contribution due to the ␹ phase has to be subtracted from the M corresponds to total magnetization curve. In Fig. 1(b), μ0 MSat the saturation magnetization of the martensite if the contribution C is also of the ␹ phase is removed. The apparent value, μ0 MSat shown. The volume fraction of martensite determined is given in Table 2. Table 2 Initial volume fraction of martensite, ϕi , in samples to be transformed under the influence of a magnetic field deduced from Fig. 1(a)

ϕi

S1 (2 T)

S2 (4 T)

S3 (6 T)

S4 (9 T)

S5 (4–9 T)

0.015

0.015

0.020

0.024

0.020

D.S. Martin et al. / Materials Science and Engineering A 481–482 (2008) 757–761

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Fig. 2. Time evolution of the volume fraction of martensite at 233 K. The experimental results (symbols) are compared with fits using Eq. (1) (solid lines).

Fig. 1. (a) Magnetization curves of the initial microstructure of samples to be tested under the influence of an applied magnetic fields and (b) illustration of the influence of the presence of the ␹ phase on the overall magnetization curve of the sample.

The magnetization curves could be used to calculate the volume fraction of the ␹ phase present in the microstructure. For the higher values of applied magnetic field (>2 T), the slope of the ˙ χ , is directly related to the volume fracmagnetization curves, M ˙ χ = ϕχ M ˙ χ,100% , tion of the ␹ phase, ϕ␹ , present in the sample: M ˙ where Mχ,100% is the slope corresponding to a microstructure with 100% of the ␹ phase present and it is known as the magnetic susceptibility of the antiferromagnetic ␹ phase. The average ˙ χ extracted from the curves in Fig. 1(b) is 3.3 × 10−3 . value of M Since the volume fraction of this phase in the steel is around 0.05 as estimated by optical/scanning electron microscopy, it can be ˙ χ,100% = 6.6 × 10−2 . From the work of Lai et al. deduce that M ˙ χ,100% ≈ 2.9 × 10−3 . This value [13], it can be deduced that M is lower than the one we have obtained and the reason for this disagreement is not clear. 3.3. In situ magnetization measurements In-situ magnetization measurements were carried out at a constant temperature of 233 K to study the progress of

the isothermal martensitic transformation as a function of the applied magnetic field for martensite fractions up to 0.2. Magnetization measurements were translated into martensite volume fractions as described in the previous section. The data are shown in Fig. 2 for transformed volume fractions. It is clear that applied magnetic fields reduce the transformation time to form martensite significantly (see also the t0.2 values in Table 3). Using the generally accepted concepts for isothermal martensite formation and taking into account how the relevant parameters are to be affected by the presence of a magnetic field, a model for the observation was constructed (as described in Section 3.1). First, free fitting on four parameters (N0 , n, p and E) on all experimental data points was done. It was found that a value of n = 2 (Austin–Rickett theory [14]) describes the transformation kinetics better than n = 1 (Avrami theory [15]). The so-called autocatalytic parameter, p, has been found to be close to zero suggesting that for this maraging steel the formation of martensite plates leads to very few new potential nucleation sites compared to the pre-existing ones (N0  pϕ). In contrast, values of the order of p = 1016 m−3 were reported for in Fe–Ni–Mn alloys [8]. A careful characterization of the martensitic microstructures obtained should be undertaken in order to clarify the absence of autocatalytic effects during the transformation. Imposing p = 0 and n = 2, a new fit procedure to of the experimental results was carried out. A range of possible values for N0 and E was found. Based on microstructural characterization of the microstructure, a value of N0 = 6.2 × 1016 m−3 was Table 3 Selective parameters E, N0 used for fitting the experimental values in Figs. 2 and 3 according to Eq. (1) μ0 H (T)

E (104 J mol−1 )

t0.2 (104 s)

0 2 4 6 9

5.66 5.37 5.18 5.06 4.80

34.9 7.8 4.0 1.9 0.5

The transformation time to form a volume fraction of martensite of 0.2 is also given.

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chosen. This value means that an average number of around 13 sites per austenite grain are present initially, which seems a reasonable value. Since austenite is paramagnetic, the initial number of pre-existing nuclei in austenite should not be affected by the magnetic field. Kakeshita and Shimizu showed that the influence of magnetic fields on austenite is important only for values higher than 20 T [5]. Therefore, N0 was kept constant to determine the value of E as a function of applied magnetic field (Table 3). The effective energy barrier for the martensitic transformation is much lower than the activation energy for self-diffusion of iron (E = 284 kJ mol−1 ). Olson and Cohen propose dislocation motion as the mechanism responsible for the activation of martensite formation [16]. According to Kajiwara [17] the expected value martensite nucleation should be E ∼ 165 kJ mol−1 in the absence of friction. Lower experimental values have been found experimentally by other authors (E = 30–140 kJ mol−1 ) in the presence of friction [18] which are in agreement with the values found in this work. As shown in Table 3, the effective energy barrier decreases as the magnetic field increases, indicating the influence of the magnetic field on lowering the energy barrier for the nucleation of martensite. Several studies have shown experimentally that this energy barrier is linearly related to the total free energy change per mole of the system, E(μ0 H = 0) = aGT + b [18,9,19,20]. With a and b empirical constants and GT the total driving force of the transformation. Therefore, to incorporate the influence of applied magnetic fields it can be suggested that: E = a(Gch + Gmag ) + b, where Gch and Gmag are the chemical and the magnetic contribution to the total driving force. From the zero field experiments it can be deduced that aGch + b = 56.6 kJ mol−1 (Table 3). Since this value is supposed to be constant with temperature for varying magnetic fields, we can deduce the magnetic contribution to the energy barrier from the plot [E(μ0 H)–E(μ0 H = 0)] versus μ0 H, which gives (aGmag ) = −1010μ0 H J mol−1 . On the other hand, the magnetic contribution to the total free energy can be calculated [2] by (Gmag ) = −Vm Mμ0 H = −8μ0 H J mol−1 . Assuming the validity of these expression and by comparing them, we get a ∼ 126 (with G in J mol−1 ). From the work of Ghosh and Raghavan (Fig. 7 in [18]) on a Fe–Ni–Mn alloy the following expression for E could be reconstructed: E = 140Gch + 290 kJ mol−1 , with a ∼ 140, which is comparable to the value obtained in this work. According to the work of Olson and Cohen [16], a is related to the activation volume of martensite, the density of atoms on the close-packed plane and the burgers vector. While the fit procedure is relatively crude and parameter sensitivity is not very high, we performed a two step experiment and described the resulting transformation curve taking the parameter values from single field experiments. Fig. 3 shows the result of this experiment; the sample was first transformed for 5 h in an applied field of 4 T, after which the field was raised to 9 T and held for 14 h. These results support the use of Eq. (1) to predict the volume fraction of martensite transformed during an isothermal holding in the presence of an external magnetic

Fig. 3. Time evolution of the volume fraction of martensite at 233 K during the two-step magnetic field experiment. Theoretical predictions are plotted along with the experimental results as solid lines.

field applied, and confirm the reliability of the fitting parameter values. 4. Conclusions Magnetization measurements have been used to study the magnetic microstructure of a maraging steel. The influence of an applied magnetic field on the isothermal martensitic transformation has been studied. It has been shown that applied magnetic fields can significantly increase the transformation rate of the isothermal martensitic transformation by more than two orders of magnitude. The results have been discussed based on a mixed physical–empirical model. Acknowledgements The authors are grateful to the Stichting voor Fundamenteel Onderzoek der Materie (FOM) and The Netherlands Institute for Metals Research (NIMR) (project number 02EMM30-3) in the Netherlands for providing financial support. References [1] A. Borgenstam, M. Hillert, Acta Mater. 45 (1997) 651–662. [2] H.D. Joo, J.K. Choi, S.U. Kim, N.S. Shin, Y.M. Koo, Metall. Mater. Trans. A 35 (2004) 1663. [3] T. Kakeshita, K. Shimizu, Mater. Trans. JIM 38 (1997) 668. [4] T. Kakeshita, Y. Sato, T. Saburi, K. Shimizu, Y. Matsuoka, K. Kindo, S. Endo, Mater. Trans. JIM 40 (1999) 107. [5] K. Shimizu, T. Kakeshita, ISIJ Int. 29 (1989) 97. [6] M.K. Korenko, M. Cohen (Eds.), Proceedings of the International Conference on Martensitic Transformations (ICOMAT-79), MIT Press, Cambridge, MA, USA, June 24–29, 1979, p. 388. [7] M. Holmquist, J.-O. Nilsson, A. Hultin Stigenberg, Scripta Metall. Mater. 33 (1995) 1367. [8] V. Raghavan, in: G.B. Olson, W.S. Owen (Eds.), Martensite, ASM International, Metals Park, OH, USA, 1992, p. 197. [9] S.R. Pati, M. Cohen, Acta Metall. 17 (1969) 189. [10] J. Post, On the constitutive Behaviour of Sandvik Nanoflex, Ph.D. Thesis, University of Twente, The Netherlands, 2004, p. 31. [11] C.G. Shull, M.K. Wilkinson, Phys. Rev. 97 (1955) 304. [12] T.J. Hicks, J. Phys. F: Metal Phys. 7 (1977) 481.

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