T22: Recrystallization on subgrain boundaries

This tutorial was tested on
MatCalc version 6.00 rel 0.282
license: free
database: mc_fe.tdb; mc_fe.ddb

Complimentary files

Click here to view the script for this tutorial

Contents:

  • Activation of recrystallization model
  • Kinetic simulation of recrystallization process

Deformation of the material introduces new dislocations into the microstructure. These surplus dislocations will create the substructure by ordering themselves into the subgrain walls during the recovery process. MatCalc includes a model describing the transformation of the newly subgrains into the new recrystallized grains, as described at Buken et al. This tutorial shows the procedure to activate the recrystallization model, presents the typical result of the recrystallization kinetics simulation and discusses the output values of the parameters obtained during the simulation.

Setting up the system

Create a new workspace and open the 'mc_fe.tdb' database. Select the elements 'Fe' and 'C', together with the 'FCC_A1' phase. Click on 'Read' instead of 'Read & Close', as the subsequent step is to read the diffusion database in this window. Select 'Diffusion data' on the left side and read the 'mc_fe.ddb' database. Enter the composition of 0.2 wt.% C. Click on 'Set start values' and calculate an initial equilibrium at 1200°C.

Precipitation domains and phases

Create a precipitation domain called 'matrix' in the 'Precipitation domains …' window. Select FCC_A1 as the thermodynamic matrix phase.

 MatCalc plot

In the current recrystallization model, the newly recrystallized grains form from subgrain created during the recovery process following the material deformation. First, the subgrain formation and size evolution will be investigated. The subgrains are generated by the ordering of the excess dislocations introduced during the deformation process. Hence, the next thing to do will be to activate the substructure evolution model. Switch to the 'MS Evolution' tab, select 'Substructure' tab inside and choose '1-param - Sherstnev-Lang-Kozeschnik - 'ABC' ' as the model for the substructure evolution.

 MatCalc plot

In this tutorial, the default model parameters will be used for the demonstration so click on 'OK' to close this window.

Thermo-mechanical treatment

Now, define the thermo-mechanical treatment which will consist of the deformation segment and the subsequent annealing segment. For the sake of simplicity, the whole simulation will be performed at the constant temperature of 1200°C. In 'Global''Thermo-mech. treatments …' create a new treatment with the name 'tmt'. Next, create a segment in which the austenite domain will be deformed to the accumulated strain value of '0,1'. In 'MS Evolution' tab, set the 'eps-dot' (strain rate) value to '1'. Back in 'General' tab, the 'Start temperature' is to be set to '1200°C'.

 MatCalc plot

 MatCalc plot

In the next segment, the material will be held isothermally at 1200°C. Select “Heat/Cooling Rate & Delta-Time” in “Ramp control” field and set the rate to '0' and the segment time to '10000' seconds.

 MatCalc plot

The settings for the whole treatment are summarized below.

 MatCalc plot

Close the editor window by clicking 'OK'.

Kinetics simulation of the deformation process

With all the setup procedures done, perform the kinetics simulation. Click on 'Calc' → 'Precipitation kinetics'. Select the 'tmt' treatment in the 'Temperature control …' area and click on 'Go'.

 MatCalc plot

Once the calculation is completed, create a plot visualizing the dislocation density. In menu 'View', click on 'Create new window…' and select '(p1) Plot core: XY-data' plot type. Drag and drop 'DD_TOT$matrix' variable which is located in the 'prec_domain struct sc' group in 'variables' window. Set the x- and y-axis to logarithmic scale and start the x-axis scaling at 1e-5. Rename the x-axis to 'Time [s]' and the y-axis to 'Dislocation density [m-2]'. Switch on the major grids for both axes.

 MatCalc plot

As might be expected, the plot shows an increase of the dislocation density during the deformation segment which lasts up to 0,1 second. Afterwards, the dislocation density falls down to approx. 2e12 which corresponds to the recovery process during the subsequent isothermal holding at 1200°C. In order to investigate the effect on the size of the forming subgrains, create a new plot depicting the 'SGD$matrix”' variable which represents the subgrain diameter. 'SGD$matrix' variable can be also found in the 'prec_domain struct sc' group.

 MatCalc plot

The subgrain diameters drops initially from about 100 micrometers down to about 7 micrometers at 0,1 seconds. Afterwards, it rises again reaching the initial value. The stage of subgrain decrease is not to be interpreted directly, as the subgrains are formed during recovery rather than during deformation stage. It is a consequence of the MatCalc setting which sets the initial value of subgrain diameter equal to the initial value of the grain diameter. Then, the subgrain size is calculated inversely to the square root of the dislocation density, in accordance with the similitude principle. As the recovery process starts, it is assumed that the subgrains are immediately formed with the predicted size of 7 micrometers. These sugrains grow afterwards in a similar way as the grains would do - there is a model which correlates the growth rate with the inverse of the subgrain diameter. During the recovery step, the rising subgrain size corresponds to the falling dislocation density. After almost 3 seconds, the subgrain size reaches the initial value of 100 micrometers and cannot grow further as the limiting grain size remains at this value. The dislocation density decreases further down to about 2-3e12 m-2. After reaching this value at about 35 seconds, it remains steady till the end of the simulation.

One might ask, why the dislocation density remains at this value rather than decreasing further to the initial value of 1e11 m-2. This happens as MatCalc proceeds with the dislocation annihilation till the equilibrium wall dislocation density value is reached, as defined in the substructure model setting. The last simulation was performed on the default setting which sets this value to the one required for the presence of the subgrains with the given size, as proposed by Read and Shockley. In the last case, the subgrains could not grow beyond 100 micrometers. It was already mentioned before, that the subgrain size is calculated from the dislocation density on the basis of the similitude principle which relates these two parameters. In the same manner, it is possible to calculate dislocation density which are geometrically needed for the given subgrain size and the given misorientation angle between the neighboring subgrains. As might be recalled from the substructure model settings, the misorientation angle of 3 degrees was used in the last calculation. The limiting value of the dislocation density coming from the discussed geometrical constraint is represented by the variable 'DD_EQU_RS$austenite'. Drag and drop this this variable on the dislocation density plot. The first observation is that the initial value for the limiting density is above the simulated actual density value. As mentioned above, this stage is not to be directly interpreted, as the subgrains are not forming during the deformation yet. During the recovery period, the limit value proceeds according to the subgrain size and reaches a plateau at about 3 seconds, when the subgrains do not grow anymore. The limit density curve is joined by the actual density one at about 35 seconds, after which nothing more happens in the system.

 MatCalc plot

Introducing grain growth

In the next simulation, the grain growth model will be activated, so that the constraint on the subgrain growth will be removed. In 'Precipitation domains' window, select the 'MS Evolution tab' and click on 'Grainstructure' tab there. In the field 'Grainsize evolution model' select 'Single class model'. Leave all parameters on default value.

 MatCalc plot

By clicking on 'Global' → 'Buffers' → 'Rename', rename the current buffer to 'deformation_only'. Next, in 'Global' → 'Buffers' click on 'Create' and name the new buffer as 'deformation&growth'. Create a new plot showing the grain diameter. Rename the y-axis to 'Grain diameter [<html>&mu;m]', set the factor to '1e6' and switch the y-axis to logarithmic type. Drag and drop the variable 'GD$matrix' on the plot. At the moment, only a straight line is visible, as the grain growth was kept constant in the last simulation. Right click on the plot and click on 'Duplicate and lock all series'. Afterwards, repeat the calculation by clicking on 'Calc' → 'Precipitation kinetics…' and clicking 'OK' in the appearing window.

After the calculation is done, switch the buffer relevant to the plots to the current one. In the 'options' window, select 'deformation&growth' in the 'core buffer' field. One can immediately notice the difference in the curves at the recovery stage. Increasing grain diameter allows for the further growth of the subgrains. This results in the further decrease of the dislocation density.

 MatCalc plot

 MatCalc plot

 MatCalc plot

Introducing recrystallization

It is time to activate the recrystallization model. In 'Precipitation domain' window, select again the 'MS Evolution' and 'Grainstructure' tab there. In the 'Recrystallization control…' section put a checkmark in 'Allow rexx' field.

 MatCalc plot

In 'Global' → 'Buffers' click on 'Create' and create a new buffer named 'Recrystallization'. Next, create three more plots in the plot window. Use the following y-axis settings for the plots:

  • Title: Nucl. rate of rex. grains [m-3s-1], type: log
  • Title: Number density of grains [m-3], type: log
  • Title: Recrystallized fraction

Drag and drop the following series on the plot:

  • 'RX_NUCL_RATE$matrix' (can be found in 'prec_domain ms evolution' variables group)
  • 'NG$matrix', 'NG_DEF$matrix', 'NG_RX$matrix' (can be found in 'prec_domain struct sc' variables group)
  • 'X_RX$matrix' (can be found in 'prec_domain struct sc' variables group)

Additionally, add the series 'GD_DEF$matrix' and 'GD_RX$matrix' to the plot of grain diameters.

With all these plots present, perform once again a kinetic simulation. Once it is completed, a picture of the recrystallization progress in the system is available. Looking at the last plot of recrystallized fraction for the matrix, one can notice that the structure is fully recrystallized. The process seems to happen between the 0,1 and 10 seconds.

 MatCalc plot

Looking on diagram showing the grain number densities, one can notice that the “old” microstructure of the deformed grains, represented with the variable 'NG_DEF$matrix', with the initial density of slightly above 1e12 m-3 decreases gradually and vanishes at the end of the recrystallization process. The curve representing the number of the recrystallized grains (variable 'NG_RX$matrix') appears already before 0,1 seconds and grows fast, showing a maximum value at about 1e14 m-3 and then continues to decrease to the end of the simulation. This analysis is supported by the plot of nucleation rates of recrystallized grains, which shows that the nucleation phase for the recrystallized grains starts around the time of 0,05 seconds and lasts to about 1,5 seconds. The end of the nucleation phase coincides obviously with the maximum observed for the number density of the recrystallized grains. The total number density of grains, represented by the variable 'NG$matrix' is just a superposition of the two previous values

 MatCalc plot

 MatCalc plot

The plot representing the grain diameter (with y-axis scaling limited to 2000 micrometers) gives some further information. The curve 'GD_DEF$matrix' representing the size of the deformed (“old”) grains initializes at 100 micrometers. The curve 'GD_RX$matrix' representing the size of the recrystallized (“new”) grains initializes at some high value and decreases down to about 13 micrometers. Obviously, a physical interpretation for the recrystallized grain size is reasonable only for the process time when such grains are present at all, i.e. once the number density of recrystallized grains gets a positive value. The mean value for the grain diameter observed in the microstructure ('GD$matrix' curve) decreases gradually from the deformed value towards the recrystallized value. Growth process of the recrystallized grain can be observed after the deformation process ends. On the contrary, the diameter of the deformed grain decreases a little, as these grains are “consumed” by the newly formed structure. Of course, there is again no interpretation possible for the deformed grain size for the simulation time with zero number density of these grains. Once the microstructure is fully recrystallized, a grain growth is observed. This coincides with the reduction of the nucleation density representing an occurrence of the grain impingement.

 MatCalc plot

Interestingly, the results for the subgrain size and dislocation density are similar to the ones obtained in the simulation without grain growth. The subgrain size seems to be limited again short below 100 micrometers and the dislocation density remains steady at the according value. To interpret this outcome correctly, one needs to keep in mind that the subgrains are assumed to exist only in the deformed grains in the applied single class model. The first consequence of this fact is that the interpretation of the calculated subgrain size is relevant only for the time periods when the deformed grain is present in the system, i.e. till the microstructure is fully recrystallized. The other consequence is the limitation of the subgrain size which cannot get a value greater than the size of the deformed grain. As the deformed grain size did decrease during the simulation, the subgrain size growth also stops around 95 micrometers. The dislocation density remained also at the value corresponding to the simulated subgrain diameter.

 MatCalc plot

 MatCalc plot

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tutorials/t22.txt · Last modified: 2017/11/08 11:12 by pwarczok