Austenite transformation kinetics: In situ characterization and physical based modeling

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Chemical Analysis of the cementite particle compositions

The TEM was operated at 200 kV. Composition measurements were performed with a BRUKER XFlash EDXS Silicon Drift Detector with a chemical resolution of 127 eV and a collector plate of 30 mm². The measurements presented in the following have been obtained with a probe size of 1 nm (1000 times finer than a conventional Castaing microprobe). Accounting for the thickness of the foil and contrary to SEM, there is no enlargement of the excitation volumes within the sample. The analyzed volume is thus limited to the probe size diameter.
EDXS measurements are by nature punctual, but repeating the measurements along lines and columns permits to reconstruct composition profiles or maps. A minimum spatial step of 5 nm was chosen to provide suitable compromise between spatial resolution and X-ray counts, in order to obtain statistically meaningful results in a reasonable period of time.
Detection of light chemical species like carbon is not possible by EDXS method because of the energy resolution. For this reason, it has been carried out only for major substitutional elements for Fe like Mn, Cr and Si. The measured concentrations are given by the Desktop Spectrum Analyzer (DTSA) in relative atomic site-fraction. As carbon is not considered in the balance, the measurements correspond to the u-fractions for each element. The typical relative error for measured substitutional concentrations was calculated using standard statistical techniques and does not exceed 5% (relative value). An Electron Energy Loss Spectroscopy (EELS) detector has also been used to estimate the local thickness of the foil. For each studied state, about 5 particles have been studied in detail (composition profiles). These particles were located in pearlite islands (not isolated at a ferrite grain boundary) to obtain a possible correlation with our thermodynamic prediction. However, it is not possible to tell with certainty that they are located in a microsegregated band.

High Energy X-Ray Diffraction (HEXRD)

Experimental set-up

In situ High Energy X-Ray Diffraction experiments have been conducted on Petra III-P07 line (EH3 hutch) at the Deutsches Elektronen SYnchrotron (DESY) facilities in Hamburg (Germany). The experimental configuration is schematized in Figure 1.9(a) and the experimental setup is illustrated in b and c. 63 in situ High Energy X-Ray Diffraction (HEXRD) experiments were carried out on lamellar samples 10 x 5 x 1.2 mm3, cut down from the industrial cold-rolled ferrite pearlite DP600 product.
The monochromatic incident X-Ray beam is diffracted when passing through the lamellar sample (oriented perpendicularly to the beam, according the dn vector, cf. Fig. 1.5). This technique permits to investigate in transmission larger volumes (700 x 700 x 1200 µm3) compared to the microscopy technique detailed above. The high energy of the incident beam (wavelength λ=0.124 nm) produces low Bragg’s diffraction angles. The fine grain size in the studied microstructures enables the production of continuous diffracted beam cones. These diffracted beams generate Debye Scherrer (DS) ring patterns on the planar CCD detector. The used Perkin Elmer detector shows a low ratio between background noise over signal intensity. The combination between the brightness of the beam, the energy and the quality of the detector has permitted to reach acquisition frequency rates up to 10 Hz.
The position of the detector relative to the samples was measured by laser and then determined precisely during the calibration procedure. This procedure consists in analyzing with Fit2D software a single diffraction pattern of LaB6 powder. A capillary filled with strain-free powder is put at the place of the steel sample and a diffraction pattern is recorded. As the lattice parameter of the LaB6 is well known at room temperature, it permits to determine the exact position of the incident beam on the detector, its distance and also its parallelism. The values determined are then used to correct and interpret systematically all the diffraction patterns obtained on steels. As explained below, the second interest of this calibration procedure is to estimate the natural broadening tendency of the set-up.
The heat treatments were performed by mean of a modified 805 A/D Bähr dilatometer as shown in Figure 1.10. The thermal schedules will be detailed in Chapter 4 and 5 respectively. As diffraction patterns can be obtained at the same time as the sample is heated, we are speaking about in situ experiments.
The temperature was measured in real time using K-type thermocouple that was spot welded on the dl side (as shown in Figure 1.9). The intrinsic uncertainty on temperature measurement associated with such thermocouple is ±2.2°C and must be added to that due to thermocouple connectors (±1°C). An additional temperature uncertainty is induced with the fast acquisition mode due to their intrinsic response times (0.1ms). This uncertainty ΔT is then estimated as ΔT = ± 0.1 x heating rate [ESI’04, NAK’04]. For a heating rate of 30°C/s, the temperature uncertainty is thus about ± 3°C. These temperature uncertainties will be taken into account during the exploitation of the results.
Not less than 7000 patterns were produced per experiment. The diffraction patterns have thus been analyzed using automated tools. In this Chapter, we will present the procedure which has been followed to perform our conventional Rietveld refinements (circular integration of DS rings and refinement). However, this analysis is not sufficient to obtain information about the recrystallization state of our material. A new analyzing technique has thus been developed and exploited. This latter will be discussed in Chapter 4.

Circular integration

When necessary, the intensity of the DS rings is integrated over the circular length of the rings (using Fit2D software) to produce 1D – 2θ intensity profiles (cf. Fig. 1.11). There are as many 1D-profiles produced as the number of recorded 2D patterns. Reliable integration requires an accurate instrumental calibration.

Phase quantification by Rietveld refinement

After circular integration, the patterns are analyzed by multiphase Rietveld refinement using the Fullprof software developed by Carvajal et al. [CAR’93]. The Rietveld approach consists in simulating theoretical 1D profiles, calculated from instrumental and structural parameters, to determine the phase fractions (in %weight). The simulated profiles are assessed upon minimizing the weight squared difference between the observed intensity yi,exp and the calculated one yi,rietveld. The function to be minimized is termed “chi-2”, expressed by (1.1):
being wi a factor inversely proportional to the variance, such that wi = 1 / σi². Thus, the standard deviation σi permits to establish the phase fraction uncertainty (error bar). The reader is referred to the work of Rietveld [RIE’69] for a detailed description of the numerical approach which relates the phase fractions to the diffracted intensities.
In the present study, the 1D profiles were integrated in batch-mode within the 2.7 – 7.2° 2θ range, discretized in 0.003751° steps, in such a manner to include only full rings. The mathematical form chosen to reproduce the experimental peaks is based on pseudo-Voigt functions. The refinement worked on the following phase structural parameters: lattice parameters, scale factors, peak widths, strains and overall isotropic temperature factor. Figure 1.12 is a screenshot taken from manual refinement (ferrite + austenite), where the experimental profile is plotted in red while that obtained from refinement appears in black.
The adjustment of the experimental peak width is essential, since it results from different contributions that must be deconvoluted: experimental broadening and density of crystalline defects in particular. In the Rietveld numerical procedure, the Full Width Half Maximum (FWHM) is determined by the calculation of three variables denoted U, V, W, related to the FWHM (termed βhkl) by the Caglioti formula (1.2):
where θ is the half 2θ angle and ℎ the FWHM. As evoked previously, the LaB6 calibration enables the instrumental peak broadening determination. This is due to a particular feature of the LaB6 material: the FWHM remains constant as function of the 2θ angle. The instrumental broadening in then subtracted from the experimental one using the relation (1.3):
being βexp , βinst the measured FWHM and the instrumental broadening measured with LaB6 calibration.
An additional type of analysis was realized in frame of ferrite recrystallization in-situ characterization. The ring intensity of the (200)α DS as function of the azimuthal angle ring was surveyed. The purpose of the method is presented in detail in the relevant Chapter 4, dedicated to recrystallization during heating.

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Thermodynamic approach and Thermocalc/DICTRA modeling tool

Analytical treatment of diffusive and moving interface problems

In Fe-C-X steels, X being a substitutional alloy component, the phase transformation kinetics is simultaneously controlled by the solute diffusion inside the phases and the transfer of carbon and alloy elements at the interface. In many diffusive problems, the interface is reduced to a mathematical surface according the seminal work of Gibbs [GIB’48]. More complex models for the interface are possible (see e.g. [HIL’99, GOU’15]). The phase transformation taken as example for the following is austenite to ferrite. The interface migration rate v verifies the continuity equation [HIL’04]:
The determination of the chemical potentials as function of phase compositions and temperature is made possible thanks to the CALPHAD method, detailed in the subsequent part.

Table of contents :

1 Experimental and Simulation Methods
1.1 Studied material
1.2 Electron Probe MicroAnalyser (EPMA)
1.3 Dilatometer trials
1.3.1 Rapid Cycle Dilatometer (RCD)
1.3.2 Bähr DIL 805
1.4 Scanning Electron Microscopy
1.4.1 Metallographic preparation
1.4.2 SEM microstructural observations
1.5 Image Analysis
1.5.1 Pearlite and ferrite grain size
1.5.2 Phase fraction
1.5.3 Carbide morphology and size
1.6 Transmission Electron Microscopy (TEM)
1.6.1 Thin foil preparation
1.6.2 Chemical Analysis of the cementite particle compositions
1.7 High Energy X-Ray Diffraction (HEXRD)
1.7.1 Experimental set-up
1.7.2 Circular integration
1.7.3 Phase quantification by Rietveld refinement
1.8 Thermodynamic approach and Thermocalc/DICTRA modeling tool
1.8.1 Analytical treatment of diffusive and moving interface problems
1.8.2 CALPHAD method for calculation of thermodynamic equilibria
1.8.3 Diffusive problem modeling with DICTRA
1.8.4 Mobility databases
2 Morphogenesis of ferrite-austenite microstructures during intercritical annealing
2.1 Literature review: Morphogenesis of ferrite/austenite microstructures during annealing
2.1.1 Formation of cold-rolled ferrite-pearlite microstructures
2.1.2 Interactions between recrystallization and austenitization
2.1.3 Discussion: austenite nucleation and growth
2.1.4 Effect of cold-rolling and recrystallization
2.2 Microstructure characterization
2.2.1 Sample preparation and nomenclature
2.2.2 Characterization of the HR state before cold-rolling
2.2.3 Characterization of the CR state prior to annealing
2.2.4 Microstructure evolution during heating below Ac1
2.2.5 Austenite transformation
2.3 Summary and discussion
2.3.1 Summary
2.3.2 Discussion
2.4 Conclusion
3 Evolution of cementite composition along the processing of cold-rolled and annealed Dual-Phase steels
3.1 Experiments: TEM observations and compositions measurements
3.1.1 Sampling plan
3.1.2 TEM observations conditions
3.1.3 Carbide composition after pearlite transformation (HR sample)
3.1.4 As received state (CR sample)
3.1.5 Heating to 700°C
3.1.6 Intermediate conclusion
3.2 Discussion and modeling
3.2.1 Manganese partition during pearlite transformation
3.2.2 Ripening process of cementite during coiling and annealing
3.3 Finite Difference (FD) model
3.3.1 FD Model’s description
3.3.2 Interface modeling
3.3.3 Calibration of the model and initialization of the calculation
3.3.4 Results
3.3.5 Discussions
3.4 Conclusion
4 Recovery and Recrystallization
4.1 Bibliographic study
4.1.1 Recovery
4.1.2 Recovery modelling
4.1.3 Recrystallization
4.1.4 Recrystallization modeling
4.2 Experimental Results
4.2.1 Introduction
4.2.2 Recovery
4.2.3 Recrystallization
4.2.4 Discussions
4.3 Modeling
4.3.1 Recovery
4.3.2 Recrystallization
4.4 Summary and conclusions
5 Austenite transformation kinetics: In situ characterization and physical based modeling
5.1 Literature review
5.1.1 Austenite transformation global kinetics
5.1.2 Thermo-kinetic analyses
5.1.3 Kinetic simulations
5.2 Austenite transformation kinetics: in situ HEXRD characterization
5.2.1 Experiments
5.2.2 Austenite transformation kinetics: slow heating (800H3 sample)
5.2.3 Austenite transformation kinetics: fast heating (800H30 and 800H100 samples)
5.2.4 Discussion
5.3 DICTRA modeling strategy
5.3.1 Thermodynamic hypotheses, diffusivity data
5.3.2 Geometrical representation of the microstructure
5.3.3 Austenite nucleation
5.3.4 Cell sizes and compositions
5.4 Simulation of austenite transformation during slow and fast heating
5.4.1 Isolated Carbide dissolution: sub-system I
5.4.2 Pearlite transformation: sub-system P
5.4.3 Austenite growth from former pearlite: sub-system A
5.4.4 Discussion on DICTRA simulations
5.5 Comparison between simulations and experiments
5.5.1 Calculation of global kinetics from specific kinetics in I, P, A cells
5.5.2 Slow heating
5.5.3 Fast heating
5.5.4 Discussion
5.6 Conclusion
Conclusion and Outlooks


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