# Analysis of Solidification and Thermal-Mechanical Behaviors in Continuous Casting

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## Abstract

Continuous casting (CC) is the most utilized steel making process today, but knowledge on the many complex phenomena that occur within the process could be gained. Issues such as transient flow patterns and immoderate amounts of localized stress can result in internal or external defects such as surface cracks. With the advancement in computational power, computational fluid dynamics (CFD) can provide significant insights into solidification and solid stress within CC. This work will focus on solidification of the shell within the mold, and the stresses that occur within the solidified shell. Excessive stress on a thinning portion of the shell is one of the main catalysts in the case of a breakout so it is important to understand its behavior and overall impact. Solidification and thermal-mechanical models were developed using the commercial CFD and FEM software STAR-CCM+™. The main objective of this paper is to create a simplistic method for analyzing stress in a solidifying shell that takes into account temperature distribution from the melt.

## Keywords

Continuous casting Solidification Solid stress CFD## Nomenclature

*k*The turbulence kinetic energy

- \( \omega \)
The specific dissipation rate

*ρ*Density

- \( {\vec{u}} \)
Velocity

- \( \mu \)
Viscosity

- \( \sigma_{k} \)
Model value

- \( \mu_{\text{t}} \)
The turbulent eddy viscosity

- \( f_{{\beta^{ *} }} \)
Free-shear modification factor

- \( \omega_{0} \)
Ambient turbulence value

- \( k_{0} \)
Ambient turbulence value

*T*Temperature

- \( \alpha^{*} \)
Model coefficient

*S*Energy source per unit volume

- \( {\vec{u}}_{\text{pull}} \)
Casting velocity

*h*The enthalpy of the liquid-solid phase

- \( h_{\text{s}} \)
The sensible heat

*L*The latent heat of fusion

- \( f_{\text{s}} \)
The relative solid volume fraction

- \( f_{\text{cr}} \)
The critical relative solid volume fraction

- \( T^{*} \)
The normalized temperature

- \( T_{\text{s}} \)
The solid temperature

- \( T_{\text{l}} \)
The liquid temperature

- \( \mu \)
The effective viscosity of the mixture

- \( \mu_{l} \)
The dynamic viscosity of the liquid

*A*The crystal characteristics of the growths

*F*Non-dimensional switching function

*c*The shape factor for the dendritic growth

- \( \sigma \)
Stress

*E*Young’s Modulus

- \( \varepsilon_{\text{i}} \)
Inelastic strain

- \( \varepsilon_{\text{el}} \)
Elastic strain

- \( \varepsilon_{\text{pl}} \)
Plastic strain

- \( \varepsilon_{\text{th}} \)
Thermal strain

## Notes

### Acknowledgements

The authors would like to thank the Steel Manufacturing Simulation and Visualization Consortium (SMSVC) members for funding this project. The Center for Innovation through Visualization and Simulation (CIVS) at Purdue University Northwest is also gratefully acknowledged for providing all the resources required for this work.

## References

- 1.Birat JP et al (2010) The making, shaping and treating of steel: casting volume, 11th edn. Association for Iron & Steel Technology, WarrendaleGoogle Scholar
- 2.Thomas BG (2018) Intro to continuous casting—CCC—U of I. Continuous Casting Consortium. http://ccc.illinois.edu/introduction/basicphenom.html
- 3.Thomas BG (2003) Chapter 14—fluid flow in the mold. In: AISE steel foundation, Pittsburg, PennsylvaniaGoogle Scholar
- 4.Weiner JH, Boley BA (1963) Elasto-plastic thermal stresses in a solidifying body. J Mech Phys Solids 11:145–154CrossRefGoogle Scholar
- 5.Seyedein SH, Hasan M (1977) A 3-D numerical prediction of turbulent flow, heat transfer and solidification in a continuous slab caster for steel. Can J Metall Mater Sci 37(3–4):213–228Google Scholar
- 6.Pfeiler C (2008) Modeling of turbulent particle/gas dispersion in the mold region and particle entrapment into the solid shell of a continuous caster. Ph.D. Thesis, Montanuniversität LeobenGoogle Scholar
- 7.Richmond O, Tien RH (1971) Theory of thermal stresses and air-gap formation during the early stages of solidification in a rectangular mold. J Mech Phys Solids 19:273–284CrossRefGoogle Scholar
- 8.Park JK, Thomas BG, Samarasekera IV (2002) Analysis of thermomechanical behavior in billet casting with different mould corner radii. Ironmaking Steelmaking 29(5):359–375. https://doi.org/10.1179/030192302225004601CrossRefGoogle Scholar
- 9.Koric S, Thomas BG (2007) Thermo-mechanical model of solidification processes with Abaqus. In: Paper presented at 2007 Abaqus users conference, 22–24 May 2007Google Scholar
- 10.Koric S, Thomas BG (2006) Efficient thermos-mechanical model for solidification processes. Int J Numer Meth Eng 66:1955–1989CrossRefGoogle Scholar
- 11.Koric S et al (2008) Explicit coupled thermos-mechanical finite element model of steel solidification. Int J Numer Meth Eng 2009, 78:1–31Google Scholar
- 12.Li C, Thomas BG (2004) Thermomechanical finite-element model of shell behavior in continuous casting of steel. Metall Mater Trans 35B:1151–1172CrossRefGoogle Scholar
- 13.Schwerdtfeger K et al (1998) Stress formation in solidifying bodies. Solidification in a round continuous casting mold. Metall Mater Trans B 29B(5):1057–1068Google Scholar
- 14.Menter FR (1994) Two-equation eddy-viscosity turbulence models for engineering applications. AIAA J 32(8):1598–1605CrossRefGoogle Scholar
- 15.Metzner AB (1985) Rheology of suspensions in polymeric liquids. J Rheol New York, New York 29(6):739–775Google Scholar
- 16.Carman PC (1997) Fluid flow through granular beds. Chem Eng Res Des 75:S32–S48CrossRefGoogle Scholar
- 17.Thomas BG, Stone D (1998) Measurement of temperature, solidification, and microstructure in a continuous cast thin slabGoogle Scholar
- 18.Liu Z, Li B, Zhang L, Xu G (2014) Analysis of transient transport and entrapment of particle in continuous casting mold. ISIJ Int 54(10):2324–2333Google Scholar
- 19.STAR-CCM+
^{™}(2019) User’s ManualGoogle Scholar - 20.Thomas BG, Li G, Moitra A, Habing D (1998) Analysis of thermal and mechanical behavior of copper molds during continuous casting of steel slabs. In: Presented at 80th Steelmaking Conference, Chicago, pp. 1–19, 1998Google Scholar
- 21.MatWeb (2019) AISI 1020 Steel, as Rolled. MatWeb. http://www.matweb.com/search/datasheet.aspx?MatGUID=a2eed65d6e5e4b66b7315a1b30f4b391&ckck=1
- 22.Zapulla MLS et al (2019) 3D thermal-mechanical model of solidifying steel strand. In: Presented at AISTech 2019—proceedings of the iron & steel technology conference 6–9 May 2019. 10.1000.377.224Google Scholar