A meshless numerical solution of thermo-mechanics of hot-rolled steel bars on a cooling bed

A meshless numerical solution of thermo-mechanics of hot-rolled steel bars on a cooling bed

VUGA Gašper, MAVRIČ Boštjan, HANOGLU Umut, ŠARLER Božidar

download PDF

Abstract. After the continuous hot-rolling process, steel bars are immediately placed on the cooling bed. At the beginning of the cooling, the material is at high temperatures, and the yield strength is low. Due to thermal load, yield strength can be exceeded, and permanent plastic strains start accumulating, resulting in possible unwanted shape changes and residual stresses. The present paper aims to develop a thermo-mechanical model for studying and eliminating undesirable phenomena before the products leave the cooling bed. The governing equations are solved for the two-dimensional slice in a strong form, and a modified version of the radial basis function generated finite difference (RBF-FD) method [1]. The initial bar geometry is obtained from the existing meshless hot-rolling simulation system [2]. The thermal and mechanical models are one-way coupled, i.e. the temperature solution represents a driving force for the stress and strain solution. The temperature field is obtained with explicit propagation in time. The convective and radiative heat fluxes on the boundary are updated at each time step using the ray tracing procedure to determine the radiative heat flux. The mechanical part is solved by considering the small strain elasto-plasticity, where the isotropic von Mises temperature-dependent hardening is employed. The global system of nonlinear equations of the mechanical part is solved by the Newton-Raphson method. The closest point projection method is used to solve the constitutive relations. A sensitivity study is performed on the influence of cooling intensity on a rectangular steel bar’s temperature, stress and strain field. We defined the most influential factors for defect formation. For the first time, a novel meshless RBF-FD method is successfully used for solving such a complex industrial problem. The model will be perspectively upgraded from the slice to the three-dimensional model to enable also bending.

Cooling Bed, Steel Bars, Thermo-Mechanics, Strong Form Meshless Method

Published online 4/19/2023, 10 pages
Copyright © 2023 by the author(s)
Published under license by Materials Research Forum LLC., Millersville PA, USA

Citation: VUGA Gašper, MAVRIČ Boštjan, HANOGLU Umut, ŠARLER Božidar, A meshless numerical solution of thermo-mechanics of hot-rolled steel bars on a cooling bed, Materials Research Proceedings, Vol. 28, pp 1611-1620, 2023

DOI: https://doi.org/10.21741/9781644902479-174

The article was published as article 174 of the book Material Forming

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

[1] R. Vertnik, B. Šarler, Meshless local radial basis function collocation method for convective-diffusive solid-liquid phase change problems, Int. J. Numer. Meth. Heat Fluid Flow 16 (2006) 617-640. https://doi.org/10.1108/09615530610669148
[2] U. Hanoglu, B. Šarler, Multi-pass hot-rolling simulation using a meshless method, Comput. Struct. 194 (2018) 1-14. https://doi.org/10.1016/j.compstruc.2017.08.012
[3] K. Mramor, R. Vertnik, B. Šarler, Simulation of Natural Convection Influenced by Magnetic Field with Explicit Local Radial Basis Function Collocation Method, CMES – Comput. Model. Eng. Sci. 92 (2013) 327-352.
[4] K. Mramor, R. Vertnik, B. Šarler, Meshless approach to the large-eddy simulation of the continuous casting process, Eng. Anal. Bound. Elem. 138 (2022) 319-338. https://doi.org/10.1016/j.enganabound.2022.03.001
[5] B. Šarler, R. Vertnik, A. Lorbiecka, I. Vušanović, B. Senčič, A multiscale slice model for continuous casting of steel, IOP Conf. Ser. Mater. Sci. Eng. 33 (2012). https://doi.org/10.1088/1757-899X/33/1/012021
[6] B. Mavrič, T. Dobravec, R. Vertnik, B. Šarler, A meshless thermomechanical travelling-slice model of continuous casting of steel, IOP Conf. Ser. Mater. Sci. Eng. 861 (2020) 012018. https://doi.org/10.1088/1757-899x/861/1/012018
[7] U. Hanoglu, B. Šarler, Hot Rolling Simulation System for Steel Based on Advanced Meshless Solution, Metals 9 (2019) 788. https://doi.org/10.3390/met9070788
[8] U. Hanoglu, B. Šarler, Developments towards a Multiscale Meshless Rolling Simulation System, Materials 14 (2021) 4277. https://doi.org/10.3390/ma14154277
[9] L.V. Nikitin, F.D. Fischer, E.R. Oberaigner, F.G. Rammerstorfer, M. Seitzberger, R.I. Mogilevsky, On the frictional behaviour of thermally loaded beams resting on a plane, Int. J. Mech. Sci. 38 (1996) 1219-1229. https://doi.org/10.1016/0020-7403(96)00009
[10] J. Basu, S.L. Srimani, D.S. Gupta, Rail behaviour during cooling after hot rolling, J. Strain Anal. Eng. Des. 39 (2004) 15-24. https://doi.org/10.1177/030932470403900102
[11] A. Pernía-Espinoza, F.J. Ascacibar, E. Martínez-de-Pisón, J. Blanco, Analysis of rail cooling strategies through numerical simulation with instant calculation of thermal expansion coefficient, Rev. Metal. 46 (2010). https://doi.org/10.3989/revmetalm.0911
[12] M. Abouaf, J.-L. Chenot, J.-L. Marcelin, A two-dimensional finite element idealization for thermo-elastic deflection in beams, Int. J. Numer. Methods Eng. 19 (1983) 1453-1465. https://doi.org/10.1002/nme.1620191004
[13] I.I. Boyadjiev, P.F. Thomson, Y.C. Lam, Prediction of the deflection and residual stress in controlled cooling of hot-rolled steel beams including load and arbitrary support: Part I. Computational model, J. Mater. Process. Technol. 147 (2004) 370-376. https://doi.org/10.1016/j.jmatprotec.2004.01.009
[14] A. Jaklič, F. Vode, T. Kolenko, Online simulation model of the slab-reheating process in a pusher-type furnace, Appl. Therm. Eng. 27 (2007) 1105-1114. https://doi.org/10.1016/j.applthermaleng.2006.07.033
[15] G.E. Fasshauer, Meshfree Approximation Methods with Matlab: (With CD-ROM), World Scientific 6 (2007). https://doi.org/10.1142/6437