T18: Plotting
a TTP diagram
This tutorial was created on
MatCalc version 5.23 rel 1.026
license: free
database: mc_sample_fe.tdb; ; mc_sample_fe.ddb
Contents:
- Calculating a TTP diagram for isothermal treatments
- Calculating a TTP diagram for continuous cooling
- Plotting the diagram
- Display options: absolute, relative or relative to maximum
phase fraction
A time-temperature-precipitation diagram is a plot consisting
of contours characterising the extent of a precipitation reaction
on axes of temperature versus time. In this tutorial, a TTP diagram
will be calculated for the precipitation of NbC in the austenite
single-phase region.
1. Setting up the system
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 precipitate phase FCC_A1#01_P0. Enter '25' as the number of size classes for this phase, and attach it
to the 'austenite' domain. Its precipitation sites should be dislocations.
Leave all the other settings at their default values. Read in the
mobility data.
Firstly, it is necessary to determine the extent of the austenite
single-phase region in which the TTP diagram is to be calculated.
To do this, first calculate an equilibrium at 1000°C and then
search for the BCC_A2 phase boundary (referring to Tutorial
7 if
necessary). This gives a temperature of 903.51°C for the zero-phase-fraction
boundary of BCC_A2. This is the upper boundary of the low-temperature
'alpha' form of ferrite. Next, calculate another equilibrium at
1200°C and repeat the procedure. This time, the temperature
value found is 1439.01°C, which is the lower boundary of the
high-temperature 'delta'-ferrite. Between these two limits, the
only stable matrix phase is austenite (FCC_A1).
2. TTP diagrams for isothermal heat treatments
Calculations of phase fraction for isothermal treatments
The plot below, obtained using a stepped equilibrium calculation,
shows the equilibrium phase fraction of NbC between 925 and 1425°C:

The plot below illustrates the origin of the typical C-shaped
curves of TTP plots. It was obtained using 'Calc > Precipitation
kinetics' to simulate an isothermal heat treatment at 925°C,
plotting the series F$FCC_A1#01_P0 on a logarithmic x-axis, then
duplicating and locking this series before making further calculations
in the same way at a selection of other temperatures.
At each value of temperature, the phase fraction of NbC increases
with time before reaching a plateau when the equilibrium phase
fraction of NbC at that temperature is attained.
It can be seen that, between 925 and 1250°C, the rate of reaction
first increases (characterised by a shift of the curve towards
the left), goes through a maximum, then decreases again.
TTP diagrams plot the time taken to reach a particular point in
a reaction at different temperature values. It can be seen from
the plot below that if, for example, the time taken to reach 90%
of the plateau value were plotted for each temperature on axes
of temperature versus time, the resulting curve would be C-shaped.
The TTP diagram calculation function of MatCalc allows automatic
calculation of curves of this type.

Automatic calculation of TTP diagrams
Open 'Calc > TTP-diagram' and enter '1425' as the start temperature
and '925' as the stop temperature. The end time should be sufficient
for the phase fraction to reach a plateau at all temperatures under
consideration. (This can be verified by creating an XY-plot of
F$FCC_A1#01_P0 versus time and monitoring this during the TTP diagram
calculation.)
In the 'Calculation method' area,
select 'isothermal' and enter
a value of 25 for 'delta T'. Calculations
will now be performed every 25 degrees between 1425 and 925°C.

Plotting the results
When the calculation has finished, create a new window of type
'(p6) Plot: TTP-diagram'. In the 'options' window,
expand the 'plots' section
and right-click in the area under 'plot#0' to
show the context menu. Select 'new series' and
choose 'ttp-curve' from the
sub-menu on the right. Next, it is necessary to decide on the type
of TTP contours required. The three options are:
- Absolute: the contours correspond to different values of the
phase fraction F$FCC_A1#01_P0.
- Relative: a contour with a value of 'x' for a particular temperature
denotes the time at which the ratio of F$FCC_A1#01_P0 to its
maximum value at that temperature is equal to 'x'. The maximum
values of F$FCC_A1#01_P0 are approximately equal to the equilibrium
phase fractions F$FCC_A1#01 shown above.
- Relative max f: in this case, contour values represent
ratios of F$FCC_A1#01_P0 to its maximum value overall. These
contours have a similar form to the 'absolute' contours, but
different numerical values.
Select 'relative' from
the 'refer
to f' drop-box at the top of
the 'options' window. Then expand
the 'series' section of 'options',
which should look as shown in the image below. Select the phase
FCC_A1#01_P0 from the 'phase' drop-box
and enter '0.05' into
the 'y-data' line.

Add two more series to show the contours for ratios of 0.5 and
0.95 on the same diagram. The resulting diagram should look like
this:

The following two plots are examples of the other types of TTP
diagram. (TIP - to create more than one type of TTP diagram in
the same plot window, lock all the series in the first diagram,
then change the diagram type in the 'refer
to f' drop-box to plot
the next diagram.)
Absolute
In the plot below, the contours correspond to different values
of the phase fraction F$FCC_A1#01_P0. Note that the higher values
are only attained at lower temperatures, because the equilibrium
value of F$FCC_A1#01 decreases with increasing temperature. The
maximum value of F$FCC_A1#01_P0 is around 7.8e-3.

Relative max f
This diagram has a similar appearance to the 'absolute' diagram
above, but the contours now represent different ratios of F$FCC_A1#01_P0
to its maximum value.

3. TTP diagrams for continuous cooling
TTP diagrams can also be calculated under conditions of a constant
rate of temperature change. The diagram below shows several curves
of phase fraction versus time for the temperature interval from
1425 to 925°C calculated
with different cooling rates. It can be seen that the fraction
precipitated is greater when cooling is slower, because the reaction
has more time in which to occur.

Continous-cooling TTP diagrams can be calculated as shown below.
Enter a large value for the end time, otherwise this may cause
the calculation to end before the stop-temperature is attained
when slow cooling rates are used. Select 'continuous' in
the 'calculation
method' section and enter the '0.0001' and '1000' as the minimum
and maximum cooling rates respectively, and '5' as the 'delta
Tdot factor'.
Click 'OK' to start the calculation.

In the same way, the results can be displayed as absolute, relative
or relative to the maximum phase fraction. The plot below shows contours
of absolute values of phase fraction. In this case, logarithmic
values have been used.

The image below is a 'relative'-type
plot, in which the contours represent the ratio of F$FCC_A1#01_P0
at a particular cooling rate to its maximum value attained at that
cooling rate.

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