On the formation of centreline shrinkage porosity in the continuous casting of steel
Tóm tắt
A recent asymptotic model for solidification shrinkage-induced macrosegregation in the continuous casting of binary alloys is extended for the purposes of understanding the link between solute segregation and centreline shrinkage porosity, a defect that commonly occurs in the continuous casting of steel. In particular, the analysis elucidates the relationship between microsegregation, mushy-zone permeability, heat transfer and centreline pressure, yielding an inequality that constitutes a criterion for whether or not centreline porosity will form. The possibilities for developing this approach to take account of gas porosity and the implementation of mechanical soft reduction to reduce macrosegregation and shrinkage porosity are also discussed.
Tài liệu tham khảo
Amberg G. Computation of macrosegregation in an iron carbon cast. Int J Heat Mass Transf. 1991;34:217–27.
Assunção M, Vynnycky M, Mitchell SL. On small-time similarity-solution behaviour in the solidification shrinkage of binary alloys. Eur J Appl Math. 2020. https://doi.org/10.1017/S0956792520000091. Accepted.
Brody HB, Flemings MC. Solute redistribution in dendritic solidification. Trans AIME. 1966;236:615–24.
Chung JD, Yoo HS. Similarity solution for peritectic solidification with shrinkage-induced flow. J Thermophys Heat Transf. 2003;17:481–7.
Clyne TW, Kurz W. Solute redistribution during solidification with rapid solid-state diffusion. Metall Trans A. 1981;12:965–71.
Dantzig JA, Rappaz M. Solidification. Lausanne: EPFL Press; 2009.
Domitner J, Wu M, Kharicha A, Ludwig A, Kaufmann B, Reiter J, Schaden T. Modeling the effects of strand surface bulging and mechanical softreduction on the macrosegregation formation in steel continuous casting. Metall Mater Trans A. 2014;45A:1415–34.
Du P. Numerical modeling of porosity and macrosegregation in continuous casting of steel [PhD thesis]. University of Iowa; 2013.
Fredriksson H, Åkerlind U. Materials processing during casting. New York: Wiley; 2006.
Gao Z, Jie W, Liu Y, Luo H. Solidification modelling for coupling prediction of porosity and segregation. Acta Mater. 2017;127:277–86.
Gao Z, Jie W, Liu Y, Luo H. Formation mechanism and coupling prediction of microporosity and inverse segregation: a review. Acta Metall Sin. 2018;54:717–26.
Hansen PN, Sahm PR. How to model and simulate the feeding process in casting to predict shrinkage and porosity formation. In: Modeling of casting, welding and advanced solidification processes IV. Warrendale: TMS-AIME; 1988. p. 33.
Heinrich JC, Poirier DR. Convection modeling in directional solidification. C R Mecanique. 2004;332:429–45.
Heinrich JC, Poirier DR, Nagelhout DF. Mesh generation and flow calculations in highly contorted geometries. Comput Methods Appl Mech Eng. 1996;133:79–92.
Jacobi HF. Investigation of centreline segregation and centreline porosity in CC slabs. Steel Res Int 2003;74:667–78.
Jones DRH, Ashby MF. Engineering materials 2: an introduction to microstructures, processing, and design. 2nd ed. Stoneham: Butterworth-Heinemann; 1998.
Khalajzadeh V, Carlson KD, Backman DG, Beckermann C. A pore-centric model for combined shrinkage and gas porosity in alloy solidification. Metall Mater Trans A. 2017;48A:1797–816.
Kubo K, Pehlke RD. Mathematical modeling of porosity formation in solidification. Metall Trans B. 1985;16:359–66.
Lee PD, Chirazi A, See D. Modeling microporosity in aluminum-silicon alloys: a review. J Light Metals. 2001;1:15–30.
Lee YW, Chang E, Chieu CF. Modeling of feeding-behavior of solidifying Al–7Si–0.3Mg alloy plate casting. Metall Mater Trans B. 1990;21:715–22.
Maples AL, Poirier DR. Convection in the 2-phase zone of solidifying alloys. Metall Trans B. 1984;15:163–72.
Mehrabian R, Keane M, Flemings MC. Interdendritic fluid flow and influence of gravity macrosegregation. Metall Trans. 1970;1:1209–20.
Miyazawa K, Schwerdtfeger K. Macrosegregation in continuously cast slabs: preliminary theoretical investigation on the effect of steady state bulging. Arch Eisenhüttenwes. 1981;52:415–22.
Natsume Y, Takahashi D, Kawashima K, Tanigawa E, Ohsasa K. Quantitative model to determine permeability for columnar dendritic structures. ISIJ Int. 2013;53:838–47.
Ni J, Beckermann C. A volume-averaged two-phase model for transport phenomena during solidification. Metall Mater Trans B. 1991;22B:349–61.
Nick AS, Vynnycky M, Fredriksson H. A theoretical analysis of the interaction between pores and inclusions during the continuous casting of steel. Metall Mater Trans A. 2016;47A:2985–99.
Niyama E, Uchida T, Morikawa M, Saito S. Predicting shrinkage in large steel castings from temperature-gradient calculations. Int Cast Met J. 1981;6:16–22.
Niyama E, Uchida T, Morikawa M, Saito S. A method of shrinkage prediction and its application to steel casting practice. Int Cast Met J. 1982;7:52–63.
Piwonka TS, Flemings MC. Pore formation in solidification. Trans Metall Soc AIME. 1966;236:1157–65.
Poirier DR. Permeability for flow of interdendritic liquid in columnar-dendritic alloys. Metall Trans B. 1987;18:245–55.
Poirier DR, Heinrich JC. Continuum model for predicting macrosegregation in dendritic alloys. Mater Charact. 1994;32:287–98.
Reddy AV, Beckermann C. Modeling of macrosegregation due to thermosolutal convection and contraction-driven flow in direct chill continuous casting of an Al–Cu round ingot. Metall Mater Trans B. 1997;28B:479–89.
Rogberg B, Ek L. Influence of soft reduction on the fluid flow, porosity and center segregation in CC high carbon- and stainless steel blooms. ISIJ Int. 2018;58:478–87.
Saleem S, Vynnycky M, Fredriksson H. The influence of peritectic reaction/transformation on crack susceptibility in the continuous casting of steels. Metall Mater Trans B. 2017;48B:1625–35.
Stefanescu DM. Computer simulation of shrinkage related defects in metal castings—a review. Int J Cast Met Res. 2005;18:129–43.
Swaminathan CR, Voller VR. Towards a general numerical scheme for solidification systems. Int J Heat Mass Transf. 1997;40:2859–68.
Thermo-Calc Software TCAL version 2.
Thevik HJ, Mo A, Rusten T. A mathematical model for surface segregation in aluminum direct chill casting. Metall Mater Trans B. 1999;39B:135–42.
Vynnycky M, Saleem S. On the explicit resolution of the mushy zone in the modelling of the continuous casting of alloys. Appl Math Model. 2017;50:544–68.
Vynnycky M, Saleem S, Fredriksson H. An asymptotic approach to solidification shrinkage-induced macrosegregation in the continuous casting of binary alloys. Appl Math Model. 2018;54:605–26.
Weimer HE, Jacobi H, Wunnenberg K. Influence of solidification structure and casting speed on the center porosity of different steels. Stahl Eisen. 1995;115:67–76.
West R. On the permeability of the 2-phase zone during solidification of alloys. Metall Trans A. 1985;16:693.
Wu M, Domitner J, Ludwig A. Using a two-phase columnar solidification model to study the principle of mechanical soft reduction in slab casting. Metall Mater Trans A. 2012;43A:945–64.