P_14: Grain Growth and the Zener Pinning Effect

This example demonstrates the simulation of normal grain growth and the pinning effect [1948Smi; 1998Man] of precipitated second-phase particles on the grain boundary motion.

To investigate the grain growth and Zener pinning effect, an Fe-0.2C (wt.%) binary alloy, with a BCC_A2 matrix phase and CEMENTITE precipitate phase, is simulated and uses the demonstration steel databases, FEDEMO and MFEDEMO. These databases are available to all users (i.e. you do not need a license for the Precipitation Module (TC-PRISMA)) and contain the necessary thermodynamic and kinetic data needed for the calculation.

For more details, see the theory described in Normal Grain Growth and Zener Pinning.

  • Folder: Precipitation Module - TC-PRISMA
  • File name: P_14_Precipitation_Fe-C-Ferrite-Grain_Growth_with_Zener_Pinning.tcu

Example Settings

System (System Definer)
Database package Demo: Steels and Fe-alloys (FEDEMO and MFEDEMO)
Elements Fe, C
Conditions (Precipitation Calculator)

Composition

Fe-0.2C Mass percent

Matrix phase

BCC_A2

  • Grain boundary energy (J/m2): 0.5
  • Grain boundary mobility: Prefactor(m4/Js): 2 x 10-15
  • Click to Edit grain size distribution. Then Initial grain size distribution: Hillert distribution with average radius of 3.2 x 10-6 m
  • Mobility adjustment: Same for all elements. Prefactor 0.08.

Precipitate phase

CEMENTITE

  • Zener pinning parameters: Cutoff size (m): 8.0 x 10-7
Calculation Type (Precipitation Calculator)
Calculation type

Isothermal
Temperature

722 °C

Simulation time

 35 hours
Datasets (Experimental File Reader)
[1975Hel] Data sets included with this example and imported to two Experimental File Readers.

Visualizations

This example is included as a Precipitation Module (TC-PRISMA) tutorial on our website and as part of the playlist on our YouTube channel.

Open the example project file to review the node setup on the Project window and the associated settings on the Configuration window for each node. For some types of projects, you can also adjust settings on the Plot Renderer Configuration window to preview results before performing the simulation. Click Perform Tree to generate plots and tables to see the results on the Visualizations window.

There is a variety of information shown in the Visualizations window that can be viewed during configuration and after performing the calculation.

  • Thermal Profile: When setting up a calculator on a Configuration window for Isothermal or Non-isothermal Calculation Types, you can preview the profile and adjust settings as needed. When you click a calculator node in the Project window, the matching name of the node is on the tab(s) displayed in the Visualizations window.

    For TTT Diagram and CCT Diagram calculations there is nothing shown for the Precipitation Calculator tab in the Visualizations window as there is no Thermal Profile to be defined.

  • Plot or Table results: After completing the set up and performing the calculation, to view the matching name of the node on tab(s) in the Visualizations window, either click a Plot Renderer or Table Renderer node in the Project window or click the tabs individually in the Visualizations window.

For this Isothermal example, its Thermal Profile is also displayed in the Visualizations window showing the constant temperature entered for this calculation type. The tab names match the node names in the Project window.

The calculated equilibrium volume fraction of CEMENTITE at 722 °C (0.02786), using FEDEMO, matches that (0.02787) of a Fe-0.2C-0.004S-0.0004O-0.001N-0.001Al (wt.%) multicomponent commercial alloy, calculated using the latest version of the TCS Steel and Fe-alloys Database (TCFE), an alloy that was studied by Hellman and Hillert [1975Hel]. The mobility adjustment assures the precipitation kinetics of CEMENTITE phase in Fe-C system matches that of experimental data [1975Hel] of the commercial counterpart (and shown in Figure 1)

The evolution of the mean radius of cementite comparing the experimental data from [1975Hel] with the Precipitation Calculator results.

Figure 1: The evolution of the mean radius of cementite comparing the experimental data from [1975Hel] with the Precipitation Calculator results.

The grain boundary energy was chosen to be a reasonable value of 0.5 J/m2. There is a large discrepancy, in several orders of magnitude, among experimental data regarding the grain boundary mobility. In the present calculation, a value of 2x10-15 m4/Js was chosen.

The evolution of the mean grain radius of ferrite comparing the experimental data from [1975Hel] with predictions made with and without Zener pinning from an evolving dispersion of cementite precipitates.

Figure 2: The evolution of the mean grain radius of ferrite comparing the experimental data from [1975Hel] with predictions made with and without Zener pinning from an evolving dispersion of cementite precipitates.

References

[1948Smi] C. S. Smith, Grains, Phases, and Interfaces - an Interpretation of Microstructure. Trans. AIME. 175, 15–51 (1948).

[1975Hel] P. Hellman, M. Hillert, On the Effect of Second-Phase Particles on Grain Growth. Scand. J. Metall. 4, 211–219 (1975).

[1998Man] P. A. Manohar, M. Ferry, T. Chandra, Five Decades of the Zener Equation. ISIJ Int. 38, 913–924 (1998).