T11: Simulation
of solidification of 0.7C 3Mn steel
This tutorial was created on
MatCalc version 5.23 rel 1.026
license: free
database: mc_sample_fe.tdb
Contents:
- Scheil calculation
- Back-Diffusion
- Composition set
- Solid-solid transformation
The Scheil-Gulliver method allows calculating the fraction and composition
of all phases during solidification step by step from the liquidus temperature
to the temperature where solidification of the residual liquid phase occurs [1-3].
The particular residual fraction at final solidification is dependent on the
cooling rate. Generally, the fraction is higher, the higher the cooling rate is.
At slow cooling rates, the liquid film can become very thin and the residual
liquid enriches more than in the case of higher fraction residual liquid at solidification.
According to the Scheil-Gulliver hypothesis, illustrated in the figure below
(Fig.1), a solidifying liquid with the initial composition C0 is
slightly undercooled. Consequently, a certain fraction of solid is formed with
a composition of CS,1
with the remaining liquid phase with the composition CL,1. Both phases
are in local equilibrium following the lever rule. From that instant on, the composition
of the solid phase with regard to the substitutional atoms is frozen due to the Scheil-Gulliver assumption
of very slow (and therefore negligible) diffusion in the solid phase. The interstitial elements boron, carbon
and nitrogen are assumed to be nevertheless highly mobile in the liquid phase
as well as the solid phase. Therefore, these elements are assumed to be able to establish equilibrium
between the liquid and solid phases due to back-diffusion of enriched solute atoms from the liquid phase into the
solid phase. This process occurs repeatedly, enriching the solid phase as
well as the liquid phase with solute during cooling (Fig.1:CL,i and
CS,i).

Fig.1: Scheme of Scheil solidification of a hypothetic Fe-C alloy. During solidification
the actual liquid phase, beginning with C0, is undercooled and solidifies according
to the lever rule enriching the liquid phase with solute atoms
When solidification is finished, the microstructure of the solid phase shows
a composition gradient from the regions where the solidification started (centre
of the dendrite) to the areas where the last liquid solidified (outer shell of
the dendrite). The composition of the residual liquid at final solidification
corresponds to the composition of the interdendritic regions. It should be noted
that the Scheil-Gulliver analysis yields an upper limit of segregation since
the substitutional elements also have a finite mobility and have some potential
of back-diffusion.
Scheil-type calculations in multi-component systems have proven to be a useful
method to simulate solidification processes. The present example shows how to
carry out this type of simulation with MatCalc and demonstrates the effect of
carbon back-diffusion on the solidification process. Moreover, the influence of solid-solid phase transformations, i.e. the peritectic transformation, is analyzed.
Step 1: Setup the thermodynamic system (see also Tutorial
T2)
Create a new workspace file. From a suitable database (mc_sample_fe.tdb) define
the elements Fe, Mn and C and
the phases liquid, BCC_A2 (ferrite), FCC_A1 (austenite)
and Cementite.

Enter the system composition in weight percent as listed in the subsequent
figure selecting 'Global Composition ...' or
pressing the
F7 key.

Set initial values with 'Equilibrium-Set start
values' or Ctrl+Shift+F.
Calculate equilibrium at 1600°C. The results in the 'Phase
summary' window
are
LIQUID * act 1,00000e+000 dfm: +0,00000e+000
### inactive ###
BCC_A2 - OK - 0,00000e+000 dfm: -1,02442e+003
FCC_A1 - OK - 0,00000e+000 dfm: -1,08259e+003
CEMENTITE - OK - 0,00000e+000 dfm: -1,27830e+004
Step 2: Carry out a Scheil calculation
Since we expect austenite to be the first phase to form on solidification, let us first
look for the solubility temperature of this phase. Select 'Calc
- Search phase boundary ...' or press Ctrl+Shift+T and
select FCC_A1 as
target phase.

Press 'Go':
Tsol 'FCC_A1': 1471,11 C (1744,27 K) iter: 4, time used: 0,03 s
The first solid phase becomes stable at 1471.11°C.
So let us start with the Scheil simulation at 1500°C and go down to 1000°C in steps of 10. Open the Scheil-calculation dialog with 'Calc
- Scheil calculation ...' or press Ctrl+H.

Press 'Go' to start the simulation. In order
to be able to remove the equilibrium content of solid phases from the system
after each temperature step, MatCalc needs to create copies
of all phases except the dependent (liquid) phase. MatCalc therefore asks

Click 'Yes'. MatCalc then creates 3 new phases
with the name of the original phase plus the suffix '_S'. This suffix denotes
that the corresponding phase is a 'solid' phase.
The result in the 'Output' window looks as follows
Checking solid phases ... - OK -
Searching initial equilibrium ...
1, 0,11 s, 1500,00 C (1773,16 K), its 2, f=1,00000000, LIQUID
...
3, 0,13 s, 1480,00 C (1753,16 K), its 2, f=1,00000000, LIQUID
4, 0,13 s, 1470,00 C (1743,16 K), its 5, f=0,96984216, LIQUID FCC_A1
...
12, 0,20 s, 1390,00 C (1663,16 K), its 6, f=0,25223958, LIQUID FCC_A1
13, 0,22 s, 1380,00 C (1653,16 K), its 6, f=0,22786302, LIQUID FCC_A1
14, 0,22 s, 1370,00 C (1643,16 K), its 6, f=0,20736865, LIQUID FCC_A1
15, 0,23 s, 1360,00 C (1633,16 K), its 6, f=0,18993180, LIQUID FCC_A1
...
39, 0,45 s, 1120,00 C (1393,16 K), its 5, f=0,05684036, LIQUID FCC_A1
40, 0,47 s, 1110,00 C (1383,16 K), its 107, f=0,00000000, FCC_A1
fraction of phase 'LIQUID' smaller than 1e-006. Finishing in equilibrium mode ...
41, 0,48 s, 1100,00 C (1373,16 K), its 2, f=0,00000000, FCC_A1
...
51, 0,56 s, 1000,00 C (1273,16 K), its 2, f=0,00000000, FCC_A1
Steps: 52, CalcTime: 0,58 s
AktStepVal: 1273,160000
- OK -
The current value of the fraction liquid at each temperature step is displayed with 'f=xxx' in
each line. The final eutectic is reached at T=1110°C. When the fraction liquid
comes below 1e-6 (minimum liquid fraction) , the
dependent phase is dissolved and the calculation is finished.
Let's now look at the result.
Create a XY-data plot that shows the fraction
of residual liquid as a function of temperature. The correct variable is F$LIQUID,
you have to change the default x-data to T$C in
the options window to show °C instead of K. Rescale the x-axis from 1100°C
to 1500°C.
A few other settings were made until the result looks as follows

Step 3: Add a Scheil calculation with back-diffusion of carbon
The solidification of the current steel as calculated by the Scheil model predicts final solidification at too low temperature. In
reality, carbon atoms are fast enough not only in the liquid but also in the solid to be able to equilibrate
between the solid and liquid phases. Therefore, to get more
realistic simulation results, we must allow for back-diffusion
of carbon. First, in order
not to loose the results of the previous simulation, rename the current buffer
to 'Scheil' and create a new one with the name 'Scheil
with BD of C'. Open the
Scheil calculation dialog with 'Calc - Scheil calculation
...' or press
Ctrl+H. Highlight carbon in the list box and press 'Toggle'.

Press 'Go' to start the simulation. After each
temperature step, MatCalc sets up a paraequilibrium calculation, where all elements
without back-diffusion have fixed composition variables and only
the elements with back-diffusion are unconstrained.
By that means, carbon is always brought back into equilibrium with regard to the solid
and liquid phases after a regular Scheil simulation step is carried out.
We are going to display the Scheil curve with and without back-diffusion in
one window. Therefore, first, lock the previous Scheil calculation, which is
still displayed in the diagram window and name it 'Scheil'.

Then, we make sure that the just created buffer ('Scheil
with BD of C') is selected as current buffer and drag and drop
the 'F$LIQUID' variable
into the plot (note that alternatively you can use the 'Lock and duplicate series' option accessible via the right mouse button or the 'View' menu). Rename the new series to 'Scheil with BD of
C'. The new diagram looks
like the following figure.

Step 4: Add the equilibrium solidification path
Let us finally add the solidification temperatures for thermodynamic equilibrium conditions. To speed up the calculations, we suspend all 'solid' phases which were needed for the Scheil calculations. Open the 'Phase status' dialog (F8). Set the 'suspended' flag for each 'solid' phase.

Create a new buffer with the name 'Equilibrium'. Open
the stepped calculation dialog (Ctrl+T).
Calculate a stepped calculation with temperature as the variable between 1500°C
and 1350°C in steps of
5. Press 'Go' to
start the calculation.

Change the buffer to be used in the diagram window to 'Equilibrium'and
drag and drop the 'F$LIQUID' variable into the
plot after locking the previous series as done before. Rename the current series
and the diagram looks like this:

On changing the 'y-axis' type to 'log' and scaling from 0.01, the results finally display as
From this diagram, and with the assumption that all residual liquid freezes (solidifies) when 1% residual liquid is reached, the predicted solidification temperatures using the classical Scheil model, Scheil with back-diffusion and full thermodynamic equilibrium can be read as 1110, 1335 and 1380°C, respectively. Probably, 1335°C comes closest to the real, experimentally observed solidification temperature for this alloy composition.
References
[1] E. Kozeschnik, W. Rindler and B. Buchmayr, „Scheil-Gulliver simulation with partial redistribution of fast diffusers and simultaneous solid-solid phase transformations“, Int. J. Mater. Res., 98 (9), 2007, 826-831.
[2] W. Rindler, E. Kozeschnik and B. Buchmayr, “Computer simulation of the brittle temperature range (BTR) for hot cracking in steels”, Steel Res., 2000, 71 (11), 460-465.
[3] E. Kozeschnik, “A Scheil-Gulliver Model with Back-Diffusion Applied to the Micro Segregation of Chromium in Fe-Cr-C Alloys”, Met. Mater. Trans., 2000, 31A, 1682-1684.
‹‹ to the Top ›› ‹‹ to
the Tutorial files ›› |