Modeling of the internal structure of a spherical graphite inclusion in ductile cast iron and its behavior under loading

The goal of this work is to develop a finite element model of a spherical graphite inclusion in ductile cast iron, modeling the process of its destruction under bilateral compression and verification of models by performing compression experiments.

A three‑dimensional model of a spherical graphite inclusion in ductile cast iron is developed and a finite element model that includes more than one million finite elements. It is constructed based on the assumption that in the center of the graphite inclusion there is a microscopic foreign spherical particle. According to one of the versions, it is a complex combination of oxides, sulfides and oxysulphides, the outer layer of this particle being coherent with the graphite lattice; according to another version, it is a particle of siliceous ferrite. This particle is framed by graphite, which has a polycrystalline sectoral structure in the form of pyramids with vertices diverging from the center of the particle; at the base of the pyramids are pentagons and hexagons. Each segment of the pyramid includes many graphite plates arranged parallel and layered on top of each other.

Numerical modeling of biaxial (quadrilateral) deformation of spherical graphite inclusion was carried out using the Ansys program. It is shown that the central particle is not deformed nor destroyed; the stresses in it do not exceed 53 MPa. It is demonstrated that destruction initially occurs along the boundaries of graphite pyramids, and at certain stages they are destroyed. In the longitudinal section, the displacement of the graphite planes inside the pyramids is also noticeable. The stresses in different parts of the pyramids differ by an order of magnitude and range from 14 MPa (mainly in the central part) to 192 MPa (at the edges of the graphite inclusion).

To verify the computer models, experiments were performed on the compression of ductile cast iron samples at a room temperature using a tensile testing machine. SEM studies have confirmed the sector‑pyramidal structure of a graphite inclusion with the presence of parallel planes inside the pyramids. It has been shown experimentally that, starting from a certain load, complete destruction of the pyramid‑shaped packets of graphite planes occurs. The results of modeling of quadrilateral compression adequately describe the behavior of a spherical graphite inclusion. In future, the obtained results will be used for comparison with the behavior of graphite at high‑temperature (900–1000 °C) deformation of cast iron.

1. Verkhovlyuk A. M., Shumikhin V. S., Nazarenko A. V. Osobennosti rosta sharovidnyh vklyuchenij grafita v chugune [Features of the growth of spherical graphite inclusions in cast iron]. Processy lit’ya = Casting processes, 2007, no. 5, pp. 11–18.

2. Skaland T., Grong F., Grong T. A model for the graphite formation in ductile cast iron. Part I. Inoculation mechanisms. Metallurgical Transactions A, 1993, vol. 24, pp. 2321–2345.

3. Pokrovsky A. I. Analiz himicheskogo sostava i morfologii grafitnyh vklyuchenij v vysokoprochnom chugune [Analysis of the chemical composition and morphology of graphite inclusions in high‑strength cast iron]. Sovremennye metody i tekhnologii sozdaniya i obrabotki materialov: sb. nauch. tr. v 2 kn. Kn. 1. Novye tekhnologii i materialy = Modern methods and technologies for creating and processing materials: collection. scientific tr. in 2 books. Book 1. New technologies and materials. Minsk: FTI NAN Belarusi Publ., 2021, pp. 224–234.

4. Stefanescu D. M. Solidification and modeling of cast iron – a short history of the defining moments. Materials Science and Engineering A, 2005, vol. 413–414, pp. 322–333.

5. Stefanescu D. M. Modeling of cast iron solidification – the defining moments. Metallurgical and Materials Transactions A, 2005, vol. 38, no. 7, pp. 1433–1447.

6. Stefanescu D. M. State of the art in solidification modeling of cast iron. Science and Processing of Cast Iron VIII, 2006, pp. 32–41.

7. Alonso G., Larrañaga P., Stefanescu D. M., De la Fuente E., Natxiondo A., Suarez R. Kinetics of nucleation and growth of graphite at different stages of solidification for spheroidal graphite iron. International Journal of Metalcasting, 2017, vol. 11, pp. 14–26.

8. Ghassemali E., Hernando J. C., Stefanescu D. M. [et al.] Revisiting the graphite nodule in ductile iron. Scripta Materialia, 2019, vol. 161, pp. 66–69.

9. Stefanescu D. M. The meritocratic ascendance of cast iron: from magic to virtual cast iron. International Journal of Metalcasting, 2019, vol. 13, iss. 4, pp. 726–752.

10. Alonso G., Stefanescu D. M., Larranaga P., Suarez R. Graphite nucleation in compacted graphite cast iron. International Journal of Metalcasting, 2020, vol. 14, pp. 1162–1171.

11. Stefanescu, D. M. Numerical micro‑modeling of solidification / D. M. Stefanescu // Science and Engineering of Casting Solidification. Edited by D. M. Stefanescu. – Springer, Boston, MA, 2009, pp. 1–44.

12. Catalina, A. V. A new analytical approach to predict spacing selection in lamellar and rod eutectic systems / A. V. Catalina, S. Sen, D. M. Stefanescu // Metallurgical and Materials Transactions A. – 2003. – Vol. 34, No. 2. – P. 383–394.

13. Beltran–Sanchez, L. A quantitative dendrite growth model and analysis of stability concepts / L. Beltran–Sanchez, D. M. Stefanescu // Metallurgical and Materials Transactions A. – 2004. – Vol. 35, No. 8. – P. 2471–2486.

14. Catalina, A. V. Prediction of room temperature microstructure and mechanical properties in lamellar iron castings / A. V. Catalina, X. Guo, D. M. Stefanescu, L. Chuzhoy, M.A. Pershing // AFS Transactions. – 2000. – Vol. 94. – P. 889–912.

15. Sotsenko O. V. Komp’yuternaya DLA‑model’ formirovaniya sharovidnogo grafita v vysokoprochnom chugune [Computer DLA model of the formation of spheroidal graphite in high‑strength cast iron]. Metall i lit’e Ukrainy = Metal and casting of Ukraine, 2009, no. 9, pp. 3–9.

16. Sotsenko O. V. Osobennosti agregativnogo mekhanizma formirovaniya struktury sharovidnogo i vermikulyarnogo grafita v modificirovannyh chugunah [Features of the aggregative mechanism of formation of the structure of spherical and vermicular graphite in modified cast irons]. Metall i lit’e Ukrainy = Metal and casting of Ukraine, 2012, no. 12, pp. 3–9.

17. Ostroumova G. M. Modelirovanie processa nukleacii uglerodnyh nanostruktur: dis. … kand. fiz.‑mat. nauk [Modeling the nucleation process of carbon nanostructures: dis. …cand. physics and mathematics sciences]. Dolgoprudny, 2020.