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— | tutorials:t10 [2019/05/20 18:11] – pwarczok |
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| ===== T10: T0-temperature in Fe-Cr-C ===== |
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| //This tutorial was tested on\\ |
| MatCalc version 6.01 rel 1.003\\ |
| license: free\\ |
| database: mc_fe.tdb// |
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| ==== Complimentary files ==== |
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| Click {{:tutorials:t10:script:t10_6021003.mcs|here}} to view the script for this tutorial. |
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| Click {{:tutorials:t10:script:t0_exp_temperatures.xls|here for .xls}} or {{:tutorials:t10:script:t0_exp_temperatures.txt|here for .txt}} table, respectively. |
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| ==== Contents: ==== |
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| * 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 |
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| 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. |
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| ===== Step 1: Define the thermodynamic system (see also Tutorial T2) ===== |
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| 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**. |
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| ===== Step 2: Calculate the T<sub>0</sub>-temperature ===== |
| FIXME |
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| 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 |
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| <code>Tsol 'BCC_A2': 857,21 C (1130,36 K) iter: 12, time used: 0,02 s</code> |
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| 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...'**. |
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| {{:tutorials:t10:img:t10_globalmenu_2016.png| MatCalc global menu}} |
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| {{:tutorials:t10:img:t10_create_a_new_calc_state_2016.png| MatCalc calc states }} |
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| 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: |
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| {{:tutorials:t10:img:t10_phase_boundary_2016.png| MatCalc search phase boundary}} |
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| 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 |
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| <code> |
| T0(FCC_A1/BCC_A2): 791,461 C (1064,61 K) |
| iter: 2, time used: 0,00 s |
| - OK - |
| </code> |
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| The phase details window shows: |
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| <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 |
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| ### inactive ### |
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| #### /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> |
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| 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. |
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| ===== Step 3: Evaluate T<sub>0</sub>- temperature as a function of chromium content ===== |
| FIXME |
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| 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. |
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| {{:tutorials:t10:img:t10_step_equilibrium_1_6011003.png| MatCalc step equilibrium}} |
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| 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. |
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| {{:tutorials:t10:img:t10_plot1_first_result_2_2016.png?650| MatCalc plot}} |
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| ===== Step 4: Evaluate T<sub>0</sub>-temperature as a function of carbon content ===== |
| FIXME |
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| 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'**. |
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| {{:tutorials:t10:img:t10_step_equilibrium_2_6011003.png| MatCalc step equilibrium}} |
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| 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**. |
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| {{:tutorials:t10:img:t10_options_window_6011003.png| MatCalc options window}} |
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| Afterwards, the x- and y-axes must be rescaled and in the case of the x-axis renamed. So the result looks as follows. |
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| {{:tutorials:t10:img:t10_plot_07_second_result_2_2016.png?650| MatCalc plot}} |
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| 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. |
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| =====Step 5: Add some experimental data on martensite start temperatures ===== |
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| 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'**. |
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| {{:tutorials:t10:img:t10_new_table_2016.png| MatCalc options window}} |
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| 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)}}). |
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| ^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| |
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| 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]]). |
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| {{:tutorials:t10:img:t10_connecting_table_data_2016.png| MatCalc options window}} |
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| Edit the legend and the series names. The result looks as follows. |
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| {{:tutorials:t10:img:t10_plot2_third_result_2_2016.png?650| MatCalc plot}} |
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| 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. |
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| 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: |
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| {{:tutorials:t10:img:t10_step_equilibrium_3_2016.png| MatCalc step equilibrium}} |
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| 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. |
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| {{:tutorials:t10:img:t10_plot3_fourth_result_2_2016.png?650| MatCalc plot}} |
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| 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. |
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| ===== Consecutive articles ===== |
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| The tutorial is continued in article [[tutorials:T11 | T11 - Simulation of solidification of 0.7C 3Mn steel]] |
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| Go to [[:tutorials|MatCalc tutorial index]]. |
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