Understanding the Influence of Neighbours on the Spheroidization of Finite 3-Dimensional Rods in a Lamellar Arrangement: Insights from Phase-Field Simulations
Understanding the microstructural phenomena during the production chain of steels is essential to improve the characteristic material properties. Besides experimental investigations, numerical methods have proven to be a powerful tool to yield property delineations. Therefore, a phase-field model incorporating free energies from CALPHAD database is employed to analyse curvature-driven shape-instabilities, in the absence of any phase transformations. Owing to the instabilities, morphological evolution occurs. In this study, previous works [1, 2] are extended to capture the influence of the neighbouring rods on the volume-diffusion governed transformation of finite 3-dimensional facetted rods. It is identified that the terminal rods strongly influence the carbon redistribution. Furthermore, we observe, in the later stages of transformation, that the neighbouring rods introduce a reverse mass transfer towards the terminal rods. The interplay of those two aforementioned effects causes a shift of the critical aspect ratio (\(w/t_p\)) of the rods, above which the spheroidization is accompanied by the breaking-up of rods (‘ovulation’).
KeywordsPhase-field modelling Spheroidization Shape-instabilities 3-dimensional rods Lamellar arrangement
The authors thank the German Research Foundation (DFG) for funding our investigations through the project with number AN 1245/1. This work was performed on the computational resource ForHLR II funded by the Ministry of Science, Research and the Arts Baden-Wuerttemberg and DFG. Authors acknowledge the primary guidance of Prof. Kumar Ankit, Dr. Avisor Bhattacharya and Dr. Fei Wang.
- 4.Qian, M., Baicheng, L., Runqi, L.: Thermodynamic considerations of the equilibrium shape of an infinitely long rod. Acta Metallurgica et Materialia 42, 4083–4086 (1994). http://www.sciencedirect.com/science/article/pii/0956715194901856CrossRefGoogle Scholar
- 6.Joshi, C., Abinandanan, T.A., Choudhury, A.: Phase field modelling of Rayleigh instabilities in the solid-state. Acta Materialia 109 (2016). http://www.sciencedirect.com/science/article/pii/S135964541630146XCrossRefGoogle Scholar
- 9.Ankit, K., Mukherjee, R. Mittnacht, T., Nestler, B.: Deviations from cooperative growth mode during eutectoid transformation: insights from a phase-field approach. Acta Materialia 81 (2014). http://www.sciencedirect.com/science/article/pii/S1359645414006168CrossRefGoogle Scholar
- 11.Choudhury, A., Nestler, B.: Grand-potential formulation for multicomponent phase transformations combined with thin-interface asymptotics of the double-obstacle potential. Phys. Rev. E 85 (2012).https://link.aps.org/doi/10.1103/PhysRevE.85.021602
- 12.Porter, D.A., Easterling, K.E., Sherif, M.: Phase Transformations in Metals and Alloys (Revised Reprint). CRC Press, Boca Raton (2009)Google Scholar
- 13.Zheng, S., Carpenter, J.S., Wang, J., Mara, N.A., Beyerlein, I.J.: An interface facet driven Rayleigh instability in high-aspect-ratio bimetallic nanolayered composites. Appl. Phys. Lett. 105 (2014) https://aip.scitation.org/doi/abs/10.1063/1.4895560CrossRefGoogle Scholar
- 14.Trepczyńska-Łent, M.: Rod and lamellar growth of eutectic. Arch. Foundry Eng. 10, 179–184 (2010)Google Scholar
- 16.Hoetzer, J., Reiter, A., Hierl, H., Steinmetz, P., Selzer, M., Nestler, B.:The parallel multi-physics phase-field framework Pace3D. J. Comput. Sci. 26 (2018). https://www.sciencedirect.com/science/article/pii/S1877750317310116