T17: Complex multi-stage heat treatments
This tutorial was created on
MatCalc version 5.23 rel 1.026
license: free
database: mc_sample_fe.tdb; ; mc_sample_fe.ddb
In this tutorial, we simulate the precipitation of NbC in the solid state during the continuous casting of steel and the subsequent austenitization treatment. The austenite / ferrite transformations of the matrix phases are taken into account. The continuous casting simulation starts at 1400 C with linear cooling to room temperature. the austenitization treatment is carried out at 1100 C for 2 hours. Heating and cooling rates are assumed to be 1 K/s. Furthermore, we assume that precipitation of NbC occurs only at austenite grain boundaries in the austenite during continuous casting. After transformation to ferrite, we assume that precipitation occurs at grain boundaries and dislocations.
Contents:
- Definition of complex heat treatments
- The heat treatment editor
- Multiple precipitation domains / matrix phase transformations
1. Setting up GUI, thermodynamics, precipitates and precipitation domains
Setup calculation
Create a workspace with the elements Fe, Nb and C and the phases
BCC_A2 and FCC_A1. Enter the composition 0.1 wt.% C, 0.7 wt.% Nb.
Create a precipitation domain named 'austenite' with the phase
FCC_A1 as its matrix, and a precipitation domain named 'ferrite' with the phase BCC_A2 as its matrix. Create a precipitate phase FCC_A1#01_P0. Enter
25 as the number of size classes for this phase, and attach it
to the 'austenite' domain. The phase status dialog should look somehow like the figure below. Leave all the other settings at their default values. Read in the
mobility data.

Please note that, on default, MatCalc suggests the value of the interfacial energy as 75% of the calculated interfacial energy of a planar boundary. The factor 0.75 takes into account the size correction for small nuclei with highly curved interfaces. Although this correction is a strong function of the critical nucleus size, the value of 0.75 has proven to be a useful first guess.
Setup GUI
Create a new XY-plot
window with four plots in it. Use a default x-axis and set the axis type to 'log'. Scale from '10..'. The axis title is 'time / s'. Insert series into the plots as follows:
- T$C (temperature in celsius), y-axis title 'temperature / C'.
- F$FCC_A1#01_P0 (phase fraction of NbC), y-axis title 'NbC phase fraction'.
- R_MEAN$FCC_A1#01_P0 (mean radius of NbC), y-axis title 'mean radius / nm', scaling '0.1..', log. Factor is 1e9 to display nm instead of m.
- NUM_PART$FCC_A1#01_p0 (number density of NbC), y-axis title 'number density / m<sup>-3</sup>'. axis is log and scaling is '1..'.
Your screen looks somehow like this:

2. Definition of the heat treatment
Open 'Global -> Heat treatments ...'. This dialog represents a very useful editor for definition of complex heat treatments by a sequence of linear heat treatment segments.
Firstly, create a new heat treatment 'New ...' with the name 'sample_ht'.
Since the present steel will transform from austenite to ferrite during the cooling process, we start with setting up a linear cooling segment from 1400 C to transformation temperature with a cooling rate of 1 K/s. Let us assume that this transformation occurs instantaneously at 600 C. Create a new segment with the button 'New segment'. Double-click the new line in the 'Data...' list box or highlight the line and press 'Edit'. In the following dialog, you can define the properties of the heat treatment segment. First of all, enter the start temperature 1400 C. Then, in the temperature definition mode combo box, you can select which data you want to provide to define the segment. Since we want to cool to RT and know the cooling rate, we select 'End temperature & Heat/Cooling rate'. End temperature is 600 C and Cooling rate is -1.
The next important setting is the definition of the number of states to store during the calculation. By default, each segment stores 25 states with linear interval distances. Optionally, you can select logarithmic. Remain with the default settings.
Finally, select the precipitation domain for the segment, in our case: Austenite. The dialog should now appear like this:

To set up the next segment, press the button. The start temperature for each following segment is automatically set to the end temperature of the previous segment, that is 600°C. Enter the new end temperature (25°C) and select ferrite for the precipitation domain. The second segment should look like this:

Continue to define the rest of the segments:
- Segment from RT to 850°C with 1 K/s heating rate. Since the precipitation domain does not change, select the 'inherit from previous segment' radio button. We assume that the ferrite to austenite transformation occurs at 850°C.
- Next segment from 850°C to 1100°C, however, with austenite as the precipitation domain.
- an isothermal segment for two hours at 1100 °C. This time, the temperature definition mode is 'End temperature & Delta-Time'. End temperature is 1100°C and delta_time is 7200 s.
- Define a cooling segment down to 600°C in austenite matrix.
- Finish with a segment from 600 to RT having ferrite as a matrix
If you have finished entering the segments, the entire heat treatment should look like this:

The last thing that we have to take care of is the changing nucleation sites for the NbC precipitates. According to our problem, we want to simulate NbC precipitation during cooling from continuous casting along the austenite grain boundaries. For all other parts of the heat treatment, we want to allow precipitation at grain boundaries and dislocations simultaneously.
This issue can be solved easily with the use of scripting commands that can be entered at the beginning and end of each of the heat treatment segments. Edit the first segment by double clicking it in the list. In the edit field for the pre-segment script, enter the command just as if you would do in the MatCalc console:
set-precipitation-parameter fcc_a1#01_p0 N S G
This command defines the (n)ucleation (s)ites of the NbC to be at grain boundaries. Since only grain boundaries are selected, please note that MatCalc will then use the diffusion geometry for grain boundary precipitates, which has been introduced MatCalc version 5.14. The following images show the two different diffusion geometries of MatCalc:
 
Since we want to continue with different nucleation sites after the first cooling segment, we define a post-segment script for the first segment reading
set-precipitation-parameter fcc_a1#01_p0 N S DG
This command will define dislocations AND grain boundaries as nucleation sites. MatCalc will then automatically use the spherical diffusion geometry again as shown in the left image.
The existence of pre-segment and post-segment scripts is indicated by the letter 'Y' in the heat treatment editor.
Save your file ('tut17.mcw').
3. Perform simulation
Start the precipitation simulation with 'Calc -> Precipitate kinetics ...'. In this dialog, the most important setting is the 'temperature control' selection. Select 'from heat treatment' and 'sample_ht'. It is not necessary to enter the simulation end time because MatCalc will automatically stop when reaching the end of the heat treatment segments.
Start the precipitation simulation with the 'Go' button.
After reaching the end of the heat treatment, the results look like follows:




The temperature plot on top shows the expected profile. The next plot with the NbC phase fraction shows a strong increase of the phase fraction at around 200 s, where the specimen reaches about 800°C on heating. Later, during austenitization, the phase fraction is decreased slightly because the solubility of the Nb and C is increased. The phase fraction remains almost constant during the rest of the process.
When looking at the plots for the mean radius and the number density of the NbC precipitates, interpretation of the results is more difficult. First, nucleation starts and proceeds until 100 s. The nucleation stops because there are no more available nucleation sites at the grain boundary. Up to approximately 800 s, the existing NbC precipitates only grow. After switching to ferrite and adding dislocations as additional nucleation sites, the nulber density quickly increases in a burst of nucleation events. At the same time, the mean radius drops drastically, which is at first sight unexpected. However, since the plot displays the mean radius of the precipitate population, generation of a large number of new and small precipitates will decrease the mean value to the value of the highest number of precipitates. Later, in two more steps, the radius increases again due to growth as well as dissolution of a part of the small precipitates generated in the second nucleation burst.
Apparently, interpretation of this kind of simulation suffers from the fact that two different kind of precipitate populations, namely the one on the austenite grain boundaries and the other on the dislocations are treated as one. In the following section, a method of separation of populations is used that can be very useful in complex simulations.
4. Simulation with separation of precipitate populations
On many occasion, it can be useful to separate populations of one and the same precipitate type to facilitate interpretation of the results. For the present example, this is easily done by introduction of an additional precipitate phase FCC_A1#01_P1. Create an additional precipitate based on the FCC_A1#01 parent phase in the 'phase status ....' dialog. Highlight the FCC_A1#01 phase and press 'Create ...' for a new precipitate phase.Go to the 'Precipitate' tab and initalize the new phase with 25 classes.
Note that the suffix '_P1' of the new phase indicates that the precipitate is identical to the '_P0' in terms of its nucleus composition, however, it contains precipitate classes that can have appeared at different stages of the heat treatment.

Let us now set up the simulation such that the _P0 phase can only nucleate in the first segment of the heat treatment, that is cooling in the austenite, while the _P1 population is not allowed to form. This can be done by defining nucleation sites as 'none'. For all consecutive segments, nucleation of further _P0 precipitates will be suppressed while the _P1 population can nucleate at grain boundaries and dislocations. Make the following changes to the pre-segment and post-segment scripts of the first segment in the heat treatment editor:


Run the simulation again and modify the plots to display the properties of both precipitate populations. The result should look like this:




Major advantage of simulations with separated precipitate populations is the ease of interpretation of the results. The second simulation clearly shows that the precipitates that are formed during cooling in the austenite grow to large size and remain almost unaltered during the later stages of the heat treatment. On the other hand, their phase fraction and number density is low, which indicates that their contribution to mechanical properties in terms of precipitation strengthening will be negligible. The second population appears in high number density and with small radius of approximately 10 nm. Moreover, the phase fraction is high, indicating a strong potential for precipitation strengthening of this second wave of NbC precipitates.
‹‹ to the Top ›› ‹‹ to
the Tutorial files ›› |