# Thermal-mechanical finite element simulation of flat bar rolling coupled with a stochastic model of microstructure evolution

## Thermal-mechanical finite element simulation of flat bar rolling coupled with a stochastic model of microstructure evolution

Danuta Szeliga1, Natalia Czyżewska2, Jan Kusiak1, Roman Kuziak3, Paweł Morkisz2, Piotr Oprocha2, Maciej Pietrzyk1, Michał Piwowarczyk4, Łukasz Poloczek3, Paweł Przybyłowicz2, Łukasz Rauch1, Natalia Wolańska4

1AGH University of Science and Technology, Faculty of Metals Engineering and Industrial Computer Science, al. A. Mickiewicza 30, 30-059 Krakow, Poland.

2AGH University of Science and Technology, Faculty of Applied Mathematics, al. A. Mickiewicza 30, 30-059 Krakow, Poland.

3Łukasiewicz Research Network, Institute for Ferrous Metallurgy, ul. K. Miarki 12, 44-100 Gliwice, Poland.

4CMC Poland, ul. Piłsudzkiego 82, 42-400 Zawiercie, Poland.

DOI:

https://doi.org/10.7494/cmms.2022.3.0787

Abstract:

It is generally recognized that the kinetics of phase transformations during the cooling of steel products depends to a large extent on the state of the austenite after rolling. Austenite deformation (when recrystallization is not complete) and grain size have a strong influence on the nucleation and growth of low-temperature phases. Thus, the general objective of the present work was the formulation of a numerical model which simulates thermal, mechanical and microstructural phenomena during multipass hot rolling of flat bars. The simulation of flat bar rolling accounting for the evolution of a heterogeneous microstructure was the objective of the work. A conventional finite-element program was used to calculate the distribution of strains, stresses, and temperatures in the flat bar during rolling and during interpass times. The FE program was coupled with the stochastic model describing austenite microstructure evolution. In this model, the random character of the recrystallization was accounted for. Simulations supplied information about the distributions of the dislocation density and the grain size at various locations through the thickness of the bars.

Cite as:

Szeliga, D., Czyżewska, N., Kusiak, J., Kuziak, R., Morkisz, P., Oprocha, P., Pietrzyk, M., Piwowarczyk, M., Poloczek, Ł., Przybyłowicz, P., Rauch, Ł., & Wolańska, N. (2022). Thermal-mechanical finite element simulation of flat bar rolling coupled with a stochastic model of microstructure evolution. Computer Methods in Materials Science, 22(3), 137–148. https://doi.org/10.7494/cmms.2022.3.0787

Article (PDF):

Keywords:

References:

Chang, Y., Lin, M., Hangen, U., Richter, S., Haase, C. & Bleck, W. (2021). Revealing the relation between microstructural heterogeneities and local mechanical properties of complex-phase steel by correlative electron microscopy and nanoindentation characterization. Materials & Design, 203, 109620. https://doi.org/10.1016/j.matdes.2021.109620.

Chin, B., Nemes, J.A. & Yue, S. (1999). Influence of strain distribution on microstructure evolution during rod-rolling. International Journal of Mechanical Sciences, 41(9), 1111–1131. https://doi.org/10.1016/S0020-7403(98)00085-X.

Czyżewska, N., Kusiak, J., Morkisz, P., Oprocha, P., Pietrzyk, M., Przybyłowicz, P., Rauch, Ł. & Szeliga, D. (2022). On
mathematical aspects of evolution of dislocation density in metallic materials. IEEE Access, 10, 86793–86812. https://doi.org/10.1109/ACCESS.2022.3199006.

Davies, C.H.J. (1994). Dynamics of the evolution of dislocation populations. Scripta Metallurgica et Materialia, 30(3), 349–353. https://doi.org/10.1016/0956-716X(94)90387-5.

Estrin, Y. & Mecking, H. (1984). A unified phenomenological description of work hardening and creep based on one-parameter models. Acta Metallurgica, 32(1), 57–70. https://doi.org/10.1016/0001-6160(84)90202-5.

Glowacki, M., Kedzierski, Z., Kusiak, H., Madej, W. & Pietrzyk, M. (1992). Simulation of metal flow, heat transfer and structure evolution during hot rolling in square-oval-square series. Journal of Materials Processing Technology, 34(1–4), 509–516. https://doi.org/10.1016/0924-0136(92)90148-L.

Hassan, S.F. & Al-Wadei, H. (2020). Heterogeneous microstructure of low-carbon microalloyed steel and mechanical properties. Journal of Materials Engineering and Performance, 29(11), 7045–7051. https://doi.org/10.1007/s11665-020-05217-7.

Heibel, S., Dettinger, T., Nester, W., Clausmeyer, T. & Tekkaya, A.E. (2018). Damage mechanisms and mechanical properties of high-strength multi-phase steels. Materials, 11(5), 761. https://doi.org/10.3390/ma11050761.

Kang, J.-H. & Kim, S.-J. (2019). Critical Assessment 33: Dislocation density-based constitutive modelling for steels with austenite. Materials Science and Technology, 35(10), 1128–1132. https://doi.org/10.1080/02670836.2019.1618030.

Klimczak, K., Oprocha, P., Kusiak, J., Szeliga, D., Morkisz, P., Przybyłowicz, P., Czyżewska, N. & Pietrzyk M. (2022). Inverse problem in stochastic approach to modelling of microstructural parameters in metallic materials during processing. Mathematical Problems in Engineering, 9690742. https://doi.org/10.1155/2022/9690742.

Kobayashi, S., Oh, S.-I. & Altan, T. (1989). Metal Forming and the Finite Element Method. Oxford University Press.

Lahoti, G.D. & Pauskar, P.M. (2005). Flat, bar, and shape rolling. In S.L. Semiatin (Ed.), Metalworking: Bulk Forming
(pp. 459–479). ASM International, Materials Park.

Lee, Y. (2004). Rod and Bar Rolling: Theory and Application. Marcel Dekker.

Li, S., Vajragupta, N., Biswas, A., Tang, W., Wang, H., Kostka, A., Yang, X. & Hartmaier, A. (2022). Effect of microstructure heterogeneity on the mechanical properties of friction stir welded reduced activation ferritic/martensitic steel. Scripta Materialia, 207, 114306. https://doi.org/10.1016/j.scriptamat.2021.114306.

Mecking, H. & Kocks, U.F. (1981). Kinetics of flow and strain-hardening. Acta Metallurgica, 29(11), 1865–1875. https://doi.org/10.1016/0001-6160(81)90112-7.

Pietrzyk, M. (2000). Finite element simulation of large plastic deformation. Journal of Materials Processing Technology, 106(1–3), 223–229. https://doi.org/10.1016/S0924-0136(00)00618-X.

Piwowarczyk, M., Wolanska, N., Pietrzyk, M., Rauch, Ł., Kuziak, R. & Zalecki, W. (2022). Phase transformation model for adjusting the cooling conditions in Stelmor process to obtain the targeted structure of thermomechanically rolled wire rod used for fastener production. Metallurgical Research and Technology, 119, 517. https://doi.org/10.1051/metal/2022071.

Poloczek, Ł., Kuziak, R., Pidvysots’kyy, V., Szeliga, D., Kusiak, J. & Pietrzyk, M. (2022). Physical and numerical simulations to predict distribution of microstructural features during thermomechanical processing of steels. Materials, 15(5), 1660. https://doi.org/10.3390/ma15051660.

Riljak, S. (2006). Numerical Simulation of Shape Rolling [PhD thesis]. Royal Institute of Technology, Stockholm.
Roucoules, C., Pietrzyk, M. & Hodgson, P.D. (2003). Analysis of work hardening and recrystallization during the hot working of steel using a statistically based internal variable method. Materials Science and Engineering A, 339(1–2), 1–9. https://doi.org/10.1016/S0921-5093(02)00120-X.

Sandström, R. & Lagneborg, R. (1975). A model for hot working occurring by recrystallization. Acta Metallurgica, 23, 387–398. https://doi.org/10.1016/0001-6160(75)90132-7.

Sellars, C.M. (1979). Physical metallurgy of hot working. In C.M. Sellars, G.J. Davies (Eds.), Hot Working and Forming Processes (pp. 3–15). The Metals Society.

Szeliga, D., Czyżewska, N., Klimczak, K., Kusiak, J., Morkisz, P., Oprocha, P., Pietrzyk, M. & Przybyłowicz, P. (2021). Sensitivity analysis, identification and validation of the dislocation density based model for metallic materials. Metallurgical Research and Technology, 118(3), 317. https://doi.org/10.1051/metal/2021037 .

Szeliga, D., Czyżewska, N., Klimczak, K., Kusiak, J., Kuziak, R., Morkisz, P., Oprocha, P., Pidvysotsk’yy, V., Pietrzyk, M.
& Przybyłowicz, P. (2022a). Formulation, identification and validation of a stochastic internal variables model describing the evolution of metallic materials microstructure during hot forming. International Journal of Material Forming, 15, 53. https://doi.org/10.1007/s12289-022-01701-8.

Szeliga, D., Czyżewska, N., Klimczak, K., Kusiak, J., Kuziak, R., Morkisz, P., Oprocha, P., Pietrzyk, M., Poloczek, Ł.
& Przybyłowicz, P. (2022b). Stochastic model describing evolution of microstructural parameters during hot rolling
of steel plates and strips. Archives of Civil and Mechanical Engineering, 22(3), 139. https://doi.org/10.1007/s43452-022-00460-2.

Wisselink, H.H., Huétink, J., Dijk, M.H.H., van, & Leeuwen, A.J., van (2001). 3D FEM Simulations of a shape rolling process. In A.-M. Hebraken (Ed.), Proceedings of the 4th International ESAFORM Conference on Material Forming.

Liège, Belgium, April 23–25, 2001 (pp. 843–846). University of Liège.

Yanagimoto, J., Ito, T. & Liu, J. (2000). FE-based analysis for the rolling microstructure evolution in hot bar. ISIJ International, 40(1), 65–70. https://doi.org/10.2355/isijinternational.40.65.