Kinetics analysis of two-stage austenitization in supermartensitic stainless steel

The martensite-to-austenite transformation in X4CrNiMo16-5-1 supermartensitic stainless steel was followed in-situ during isochronal heating at 2, 6 and 18 K.min -1 applying energy-dispersive synchrotron X-ray diffraction at the BESSY II facility. Austenitization occurred in two stages, separated by a temperature region in which the transformation was strongly decelerated. The region of limited transformation was more concise and occurred at higher austenite phase fractions and temperatures for higher heating rates. The two-step kinetics was reproduced by kinetics modeling in DICTRA. The model indicates that the austenitization kinetics is governed by Ni-diffusion and that slow transformation kinetics separating the two stages is caused by soft impingement in the martensite phase. Increasing the lath ACCEPTED MANUSCRIPT

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Introduction
Supermartensitic stainless steels are low carbon lath martensitic steels based on the Fe-Cr-Ni system [1,2]. This class of steels has gained popularity in the oil and gas sector as a low cost alternative to highly alloyed duplex stainless steels in pipeline applications [3].
The excellent strength and toughness properties are obtained through inter-critical annealing (tempering below A 3 temperature) to promote the formation of lamellar reversed austenite on high-and low-angle boundaries of lath martensite [4][5][6][7]. The annealing leads to an effective decrease of the average grain size and to a "composite structure" of hard tempered martensite and soft austenite. During plastic deformation, such a structure hinders dislocation movement over long distances. Reversed austenite was furthermore reported to strengthen the material during plastic deformation by transformation induced plasticity (TRIP) [8][9][10][11].
The formation of lamellar austenite was reported to be promoted by the establishment of an energetically favorable phase-interface (Kurdjumov-Sachs [12][13][14][15]), and might be affected by residual stress of the martensite transformation and grain-boundary segregation [16]. Partitioning of Ni is a well-documented mechanism of stabilizing reversed austenite to room temperature [8,[17][18][19][20]. Furthermore, the internal substructure of austenite [8] and the size and shape distributions of the austenite regions [10], were suggested to affect thermal stability. With increasing A C C E P T E D M A N U S C R I P T 4 annealing temperature, the austenite was reported to approach a coarser, spherodized morphology, which decreases the phase stability upon cooling [10].
Studies on isochronal heating of different steel alloys have shown that austenitization can occur in multiple stages [21][22][23][24][25][26][27]. In all these cases two-stage austenitization was found to be based on a given or evolving inhomogeneous microstructure during heating, which gave rise to locally varying driving forces for austenite formation, dissolution of phases and related diffusion or shear processes.
Bojack et al. showed in a comprehensive in-situ study that also 13Cr6Ni2Mo supermartensitic stainless steel exhibits two distinct stages of austenite formation during isochronal heating [23]. In a later study the two-stage austenitization kinetics was analyzed with a Kissinger-like method applying a range of heating rates [22]. It was suggested that the two-step kinetics was a result of solute redistribution during the growth of austenite. The first stage was assumed to be mainly caused by partitioning of Ni and Mn and the second stage by dissolution of carbides and increased diffusivity of Ni and Mn. Two-stage austenitization kinetics was also observed for austenitization of X4CrNiMo16-5-1 (EN 1.4418) supermartensitic stainless steel by dilatometry and in-situ synchrotron X-ray diffraction [28].
The kinetics of the two transformation stages in both investigated supermartensitic stainless steels depended on heating rate, thus it appears as if they are governed by a thermally activated process [18]. From the listed investigations on the multi-stage austenitization kinetics in different steel alloys, all thermally activated A C C E P T E D M A N U S C R I P T 5 transformations were identified as diffusion controlled. Therefore it appears as if the responsible mechanisms for two stage austenitization can be identified from kinetics modeling of the diffusion process.
As part of a physics-based modeling framework Galindo-Nava et al. modelled diffusion controlled reversion of austenite from lath martensite during isothermal holding based on transformation of a single lath [29]. was interrupted at 650 °C. The sample was a thin foil which was thinned by electrolytic twin-jet polishing in 10 % perchloric acid dissolved in ethanol at -20 °C.

Energy dispersive synchrotron X-ray diffraction
The investigation was carried out at the EDDI-beamline at the synchrotron facility HZB-BESSY II [30]. It consisted of a series of isochronal heating tests at applied heating rates 2, 6 and 18 K.min -1 within the temperature interval 25 -920 °C. reflections are acquired simultaneously, which enables accurate quantitative phase analysis over temperature. Diffraction peaks occur for certain energies E hkl , which are a function of the respective interplanar spacing, d hkl , and the fixed scattering angle, [31]. The diffraction peaks were fitted with a Pseudo-Voigt profile and the phase fractions were determined by the direct comparison method [32]. Detailed descriptions of the procedures applied for peak fitting and quantitative phase analysis are reported in [28].

Transmission Kikuchi Diffraction
Transmission Kikuchi Diffraction (TKD) was carried out on electro-polished thin foils in an FEI Nova NanoLab 600 scanning electron microscope. The Kikuchi patterns were acquired with a Bruker e-Flash EBSD detector, configured with a horizontal OPTIMUS TKD detector head. No tilt was applied to the sample. The working distance was 3 mm, the acceleration voltage 30 kV, the beam current 1.7 nA and the step-size in-between successive TKD patterns was 16 nm. The orientation data were cleaned and smoothed by a minimum grain-size criterion and a smoothing spline filter by using the texture analysis software MTEX [33].
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Energy dispersive synchrotron X-ray diffraction
The measured transformation curves in Figure 1a show

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9 the transformation kinetics with dilatometry for heating rates 2-100 K.min -1 consistently yielded two-stage transformation kinetics [28].

Transmission Kikuchi diffraction
The microstructure from a dilatometry experiment, in which isochronal heating at

Kinetics modeling
In order to elucidate the mechanism responsible for the observed two-step kinetics, the austenitization was modeled with DICTRA, a software package for simulation of diffusion controlled reactions in multi-component alloy systems [37]. In contrast to Kissinger-like methods, which require fitting to an Arrhenius type of transformation and yield effective activation energies for heterogeneous transformations [38], the analysis with kinetics modeling is carried out with direct forward modeling based on constitutive equations and the thermodynamics and kinetics databases TCFE6 [39] and MOB2 [40]. Austenitization was modeled using the moving phase-boundary model within DICTRA.
A comprehensive description on the foundation of the DICTRA software is given in Ref. [37]. A short summary of the governing equations is given in the following.
Diffusion in DICTRA is modelled based on Fick's second law (1) where is the concentration, and It is noted that the factors are purely kinetic quantities, whereas the chemical potential gradients are purely thermodynamic quantities. The basic data for computation of these parameters are obtained from experimental data and are stored in kinetics and thermodynamics databases, respectively. The composition dependence of the parameters is determined by a Redlich-Kister expansion [41].
In the moving boundary model single-phase regions are separated by an interface, which migrates based on the rate of diffusion to and from the interface. For each time

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A C C E P T E D M A N U S C R I P T 13 step the boundary condition at the phase interface is calculated by assuming local equilibrium and the diffusion problem is solved for each single-phase region.
Migration of the interface between two phases α and  is then calculated by solving a flux balance equation for n-1 components [42] ( where is the interface velocity. The moving phase boundary model in DICTRA is based on the formation and evolution of a single grain of austenite and does not include a classic nucleation model. Other models, as the Thermo-Calc precipitation module [46], are available and well suited for analyzing nucleation and competitive growth, but do not treat the diffusion controlled evolution of two phases, which is the purpose of this investigation. DICTRA does however allow for input of a critical driving force for precipitation of austenite, which makes it possible to account for a nucleation barrier. Since the nucleation mechanism of reversed austenite has not been determined unequivocally by experimental means (see general discussion section), the model was Simulations were performed for different heating rates to investigate whether the presented approach yielded results, which are consistent with the experimental data.
The system was limited to Fe, Cr and Ni to increase numerical stability.

Results and interpretation
Kinetics modeling predicted for all heating rates an effective start temperature of the transformation, i.e. a temperature at which the transformation rate is discernable within the range of experimental measurement accuracy, at approx. 575 °C ( Figure   1b). This is in close agreement with the results obtained from XRD ( Figure 1a). On

(i) Nucleation and initial growth
Diffusion profile (i) shows austenite growing from the left-hand side of the diffusion domain immediately after nucleation ( Figure 4). The segment appears at approx. 623, 635 and 647 °C for heating with 2, 6, and 18 K.min -1 (Figure 1b).
According to the model, considerable partitioning of Ni and some depletion in Cr occurs at the nucleation and initial growth stage of austenite at these temperatures.

(ii) Growth in stage 1
Diffusion profile (ii) shows the Ni and Cr content at the maximum rate of transformation in the first stage of austenitization ( Figure 4). The segment appears at 695, 711 and 726 °C for the heating rates 2, 6, and 18 K.min -1 (Figure 1b). Martensite

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19 is locally depleted in Ni at the interface, but provides excess Ni from the bulk to maintain the transformation. The transformation is at its maximum rate, enabled by increasing driving force for formation of austenite and increasing diffusivities with increasing temperature. The predicted transformation rates in this segment are in good agreement with the measured transformation rates (Figure 1)

(iii) Deceleration of the transformation kinetics
Diffusion profile (iii) shows the contents of Ni and Cr, at which deceleration of the transformation occurs. This segment appears at 713, 725, and 736 °C for the heating rates 2, 6, and 18 K.min -1 , respectively (Figure 1b). It is evident that the transformation is halted because impingement of the diffusion field with the model boundary causes the gradients in Ni and Cr content in martensite virtually to vanish.
In the actual microstructure this mechanism corresponds to the situation in which the diffusion field of the simulated austenite particle starts to overlap with the diffusion field of the adjacent austenite particle (see inset b in Figure 3). Then, continued growth of the austenite phase fraction is mainly achieved by a change of Ni profile in austenite close to the interface with martensite, while some redistribution of Ni in fcc commences (compare profiles (iii) and (iv) in Figure 4). Soft impingement in martensite occurred at higher phase fractions for higher heating rates (Figure 1b). The predictions of the phase fractions and temperatures where soft impingement occurs are in fair agreement with the onsets of the plateaus of the experimental transformation curves (Figure 1a).

(iv) Growth in stage 2
Diffusion profile (iv) corresponds to the Ni and Cr distribution at the onset of the second stage of austenitization ( Figure 4). The segment appears at approx. 770, 785 and 821 °C for the heating rates 2, 6, and 18 K.min -1 (Figure 1b).

Governing mechanisms
The rate-determining mechanism for the first stage of austenitization was identified -It is still unclear whether austenite nucleates or, rather, grows from thin layers of inter-lath retained austenite. The dispute revolves around the austenite memory effect, which describes the inheritance of the orientation of reversed austenite from prior austenite grains. The orientation inheritance could indicate a variant selection mechanism [12] or growth from inter-lath retained austenite [13,47]. In the prior case, grain-boundaries are potentially decorated by solute from grain boundary segregation prior to the nucleation of austenite [48]. In the latter case, substantial diffusion towards retained austenite could activate the growth. Regardless of the actual mechanism it is expected that an enrichment in solute would enable premature formation of reversed austenite.
-It is anticipated that the driving force for the nucleation of austenite is increased by the release of residual stresses from metastable lath martensite [49]. It was evident that the nucleation barrier did not affect the overall two-step kinetics strongly. Figure 6b shows that transformation with nucleation barrier leads to an increased fraction of austenite compared to the transformation without barrier just after nucleation, and that this divergence fades away on continued heating. This might seem counterintuitive, but is caused by less partitioning during formation of austenite at slightly more elevated temperatures. Thus, more austenite can be formed instantly at nucleation. Since the concentration gradient in austenite during heating is subject to homogenization, this marginal initial difference disappears upon further heating. Ultimately the time and temperature interval spent from nucleation to diffusion-controlled growth for the two-step kinetics is sufficiently large that the overall kinetics are not strongly affected by the nucleation mechanism.

Conclusions
The conclusions of the in-situ observation of two-stage austenitization and the modeling of austenitization with the kinetics model DICTRA are: -Austenitization of X4CrNiMo16-5-1 super martensitic stainless steel during isochronal heating at 2 -18 K.min -1 occurs in two stages.
-Two-stage austenitization kinetics are predicted from kinetics modeling of multi-component diffusion in DICTRA based on the transformation of a single martensite lath to austenite and nucleation without nucleation barrier.

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27 -The mechanism for the deceleration of the transformation after the first stage is identified as soft impingement in the martensite phase.
-Ni-diffusion in the bcc lattice is rate-determining for the first stage of austenitization, where Ni diffuses from martensite towards the phase-interface.
-Ni-diffusion in the fcc lattice is rate-determining for the second stage of austenitization, where austenite, which is heavily enriched in Ni due to partitioning in the initial growth stage, is required to homogenize in order to supply solute to the phase-interface. This requires the build-up of a concentration gradient.
-The martensite lath width, corresponding to two times the diffusion distance in the model, has a similar effect on the austenitization kinetics as the heating rate.

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