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tutorials:t10 [2018/08/01 13:21] – [Step 4: Evaluate T<sub>0</sub>-temperature as a function of carbon content] pwarczok
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 +===== T10: T0-temperature in Fe-Cr-C =====
 +
 +
 +//This tutorial was tested on\\
 +MatCalc version 6.01 rel 1.003\\
 +license: free\\
 +database: mc_fe.tdb//
 +
 +==== Complimentary files ====
 +
 +Click {{:tutorials:t10:script:t10_2013.mcs|here}} to view the script for this tutorial. 
 +
 +Click {{:tutorials:t10:script:t0_exp_temperatures.xls|here for .xls}} or {{:tutorials:t10:script:t0_exp_temperatures.txt|here for .txt}} table, respectively.
 + 
 +
 +==== Contents: ====
 +
 +  * T<sub>0</sub>- temperature calculation
 +  * Martensite / Bainite transformation
 +  * Variation of T<sub>0</sub>- temperature with carbon and chromium content
 +  * Import and display of experimental data into plots
 +
 +The **T<sub>0</sub>-temperature** is defined as the temperature where two phases of identical chemical composition have the same molar Gibbs free energy. This temperature is an important quantity in the field of **diffusionless phase transformations**, i.e. the bainitic and martensitic transformation. In the present example, we will discuss some thermodynamic aspects of the austenite/martensite transformation and apply T<sub>0</sub>-temperature calculations to the evaluation of transformation temperatures.
 +
 +===== Step 1: Define the thermodynamic system (see also Tutorial T2) =====
 +
 +Create a new workspace file. From a suitable database (mc_fe.tdb) define the elements **Fe**, **Cr** and **C** as well as the phases **BCC_A2** (ferrite) and **FCC_A1** (austenite). Enter the system composition in weight percent with **wp(C) = 0.1** and **wp(Cr)=1.0**. Set initial values with **'Calc' -> 'Set start values'** or **Ctrl+Shift+F**. Calculate an equilibrium at **800°C**.
 + 
 +===== Step 2: Calculate the T<sub>0</sub>-temperature ===== 
 +FIXME
 +
 +Before evaluation of the T<sub>0</sub>-temperature, an equilibrium located in the **one-phase region** of the parent phase must be calculated in order **to set the composition of one of the phases equal to the system composition**. The parent phase is austenite so the solubility temperature of BCC_A2 will be evaluated with **'Calc' -> 'Search phase boundary...'** or **Ctrl+Shift+T**. Set **'Temperature'** as type and **'BCC_A2'** as target phase, then click on 'Go'. As a result, MatCalc displays in the **'console'** window
 + 
 +<code>Tsol 'BCC_A2': 857,21 C (1130,36 K) iter: 12, time used: 0,02 s</code>
 + 
 +In the **'Phase summary'** and **'Phase details'** window, only the FCC_A1 phase is denoted as active (mole fracton = 1). We can now proceed with this initial condition. For convenience, store this (current) state in a calculation state with the name **'Start austenite'** by selecting **'Global' -> 'CalcStates' -> 'Create...'**.
 +
 +{{:tutorials:t10:img:t10_globalmenu_2016.png| MatCalc global menu}}
 +
 +{{:tutorials:t10:img:t10_create_a_new_calc_state_2016.png| MatCalc calc states }}
 +
 +
 +We can now evaluate the T<sub>0</sub>-temperature for austenite and ferrite with **'Calc' -> 'Search phase boundary...'** or **Ctrl+Shift+T**. The following, well-known, dialog box appears:
 +
 +{{:tutorials:t10:img:t10_phase_boundary_2016.png| MatCalc search phase boundary}}
 +
 +Select **'T<sub>0</sub>-temperature'** in the type listbox, **'BCC_A2'** as target phase and **'FCC_A1'** as parent phase. The check box **'Force target to have parent composition'** must be chosen, because the composition of BCC_A2 wil be adjusted according to the parent composition. The energy difference (**DFM offset**) can be left as default (zero). Press **'Go'** to start the calculation. The result is shown below
 + 
 +<code>
 +T0(FCC_A1/BCC_A2):  791,461 C (1064,61 K)
 +iter: 2, time used: 0,00 s
 +- OK -
 +</code>
 + 
 +The phase details window shows:
 + 
 +<code>
 +#### /FCC_A1/ moles: 1, gm: -46908,9 (-46908,9)
 +Phasestatus: entered - active
 +FE +9,84677e-001  CR +1,06937e-002   C +4,62933e-003  
 +
 +
 +### inactive ###
 +
 +#### /BCC_A2/ moles: 0, gm: -46908,9 (-46908,9)
 +Phasestatus: entered - not active (dfm=2,4156e-009)
 +FE +9,84677e-001  CR +1,06937e-002   C +4,62933e-003
 +</code>
 + 
 +It is thus clear that, at the temperature of 791,461°C, FCC_A1 and BCC_A2 of the same composition have the same molar Gibbs free energy of gm = -46908.9 J/mole.
 + 
 +
 +===== Step 3: Evaluate T<sub>0</sub>- temperature as a function of chromium content =====
 +FIXME
 +
 +Let us now investigate how the T<sub>0</sub>- temperature for ferrite and austenite varies with the chromium content. From the menu select **'Calc' -> 'Stepped calculation…'**or press **Ctrl+T**. In the left listbox of the **'Step equilibrium ...'** window, select type **'T<sub>0</sub> temperature'**. Select **'FCC_A1'** for the parent phase and **'BCC_A2'** for the target phase. Don't forget to select chromium as the independent element. Enter the chromium range between **'0'** and **'10'** weight percent in steps of **'0.5'** and don't forget to mark the **'Force identical composition'** box. The **'Step equilibrium ...'** window looks now as follows.
 +
 +{{:tutorials:t10:img:t10_step_equilibrium_1_6011003.png| MatCalc step equilibrium}}
 +
 +Press **'Go'** to start the calculation. The result can be displayed in the well known **'XY-data'** plot. Create the plot and drag and drop the **T$c** variable from the variables window into the plot. Edit the **'x-axis'**, **'y-axis'** and **'legend'** (see also [[tutorials:T4 | Tutorial 4]] or [[tutorials:T5 | Tutorial 5]]) such that the result of the stepped T<sub>0</sub>- temperature calculation looks as follows.
 +
 +{{:tutorials:t10:img:t10_plot1_first_result_2_2016.png?650| MatCalc plot}}
 +
 +===== Step 4: Evaluate T<sub>0</sub>-temperature as a function of carbon content =====
 +FIXME
 +
 +In the same way, similar to the evaluation of the dependence of the T<sub>0</sub>- temperature on the chromium content, it is possible to calculate the T<sub>0</sub>- temperature as a function of the carbon content. Therefore, rename the **'_default_'** buffer selecting **'Global' -> 'Buffers' -> 'Rename...'** and give it the name **'T0-chromium'**. Then create a new buffer (**'Global' -> 'Buffers' -> 'Create...'**) with the name **'T0-carbon'** and load the calculation state **'Start austenite'** (make sure that the current buffer is the **'T0-carbon'**). Analogously to the calculation before, carry out a stepped calculation. Press **'Calc' -> 'Stepped calculation ...'** or press **Ctrl+T**, enter the following settings and press **'Go'**.
 +
 +{{:tutorials:t10:img:t10_step_equilibrium_2_6011003.png| MatCalc step equilibrium}}
 +
 +There is no need to create a new plot in order to display the graph for the T<sub>0</sub>-temperature dependence for varying carbon content. The T<sub>0</sub>- temperature line in the figure can be simply changed by **switching** from **'T0-chromium'** buffer to the **'T0-carbon'** buffer **in the options window**.
 +
 +{{:tutorials:t10:img:t10_options_window_6011003.png| MatCalc options window}}
 +
 +Afterwards, the x- and y-axes must be rescaled and in the case of the x-axis renamed. So the result looks as follows.
 +
 +{{:tutorials:t10:img:t10_plot_07_second_result_2_2016.png?650| MatCalc plot}}
 +
 +The strong dependence of the T<sub>0</sub>- temperature on the carbon content is evident. This is reflected in the strong influence of carbon on the martensite start temperature.
 +
 +=====Step 5: Add some experimental data on martensite start temperatures =====
 +
 +The experimental data, which will be added to the recent plot, are taken from ref. ((**References**\\
 +[1] Z. Jicheng and J. Zhanpeng, Acta met. mater. 38 (1990) 425-431.)). Before doing so, we must create a new buffer. So, none of the former results will be lost. Name the new buffer as **'T0 with offset'** (further calculations with various dfm-offsets will be done ...) and create a table selecting **'Global' -> 'Tables and Arrays'**. Press **'New ...'** and call the table **'Exp. data'**.
 +
 +{{:tutorials:t10:img:t10_new_table_2016.png| MatCalc options window}}
 +
 + After selecting **'Edit ...'**, enter the following measured martensite start temperatures into the table or copy them from a file ({{:tutorials:t10:script:t0_exp_temperatures.xls|the file is here}}, or here {{:tutorials:t10:script:t0_exp_temperatures.txt|(.txt)}}).
 +
 +
 +^Carbon content[wt%] ^Martensite start temperature|
 +|0|540|
 +|0.086|510|
 +|0.1936|475|
 +|0.2409|480|
 +|0.2495|470|
 +|0.2581|440|
 +|0.3011|430|
 +|0.3226|410|
 +|0.3871|410|
 +|0.3871|400|
 +|0.3871|395|
 +|0.4560|405|
 +|0.4947|355|
 +|0.5054|375|
 +|0.6022|330|
 +|0.6022|320|
 +|0.7097|280|
 +|0.7312|280|
 +|0.7743|265|
 +|0.8173|240|
 +|0.8603|225|
 +
 +Press **'OK'** twice and insert the experimental data into the plot as a new series (right-click in **'options'** window and select **'New series' -> 'table experimental data'**) and switch to **'Exp. data'** in **'connected to'** box (see also [[tutorials:T5 | Tutorial 5]]).
 +
 +{{:tutorials:t10:img:t10_connecting_table_data_2016.png| MatCalc options window}}
 +
 +Edit the legend and the series names. The result looks as follows.
 +
 +{{:tutorials:t10:img:t10_plot2_third_result_2_2016.png?650| MatCalc plot}}
 +
 +Apparently, the calculated T<sub>0</sub>- temperature does not fit the experimental data, however the curve runs parallel to it with the calculated temperatures being higher. The reason is that a certain amount of driving force is required to start the martensite transformation. This extra energy, or extra driving force, is of the order of 1.2 to 2.5 kJ/mol (depending on the composition of the alloy) and can be defined in the field **dfm-offset**. Default value for this parameter is zero.
 +
 +To evaluate how high this extra energy is as a function of carbon content, stepped calculations with different dfm-offsets can be performed. Carry out two simulations, one as a steped T<sub>0</sub>- temperature calculation with a **dfm-offset** of **1200 J/mole** and one with **1700 J/mole**. Before starting, lock the first series (T<sub>0</sub>- dfm=0 J/mole). So the first graph will be conserved for further comparison. Select **'Calc' -> 'Stepped calculation ...'**and complete the dialog box as follows:
 +
 +{{:tutorials:t10:img:t10_step_equilibrium_3_2016.png| MatCalc step equilibrium}}
 +
 +Change the plot buffer to **'T<sub>0</sub> with offset'** in the **'options'** window. Drag and drop the **'T$c'** variable again into the plot and rename the series to **T<sub>0</sub> - dfm=1200 J/mole**. Lock the curve afterwards. Repeat these operations to obtain a curve for a dfm-offset of 1700 J/mole.  The plot now looks like follows.
 +
 +{{:tutorials:t10:img:t10_plot3_fourth_result_2_2016.png?650| MatCalc plot}}
 +
 +A dfm-offset in the range of 1200-1700 J/mole can be used to obtain reasonable agreement between the calculations and the experimental data.
 +
 +
 +===== Consecutive articles =====
 +
 +The tutorial is continued in article [[tutorials:T11 | T11 - Simulation of solidification of 0.7C 3Mn steel]]
 +
 +Go to [[:tutorials|MatCalc tutorial index]].
 +
  
tutorials/t10.txt · Last modified: 2023/08/02 20:54 by jasmin
 
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