Channel-type segregation is one of the defects in aluminum casting technology, particularly in the direct chill (DC) process, having a significant influence on the cast quality. Nevertheless, the formation mechanism of three-dimensional (3D) channel-type segregations remains poorly understood. In order to clarify the formation mechanism of defects of this type, we conducted a 3D numerical simulation of the DC casting process of an Al-Mg alloy billet considering the melt flow, heat and mass transfer, solidification, and the motion of the solidified ingot, coupled with the alloy phase diagram. The simulation results showed that the channel-type segregations have strip-patterns and formed easily at high casting speeds, being localized at a distance of a half-radius from the billet centerline. We also compared two-dimensional axisymmetric and 3D simulations, and the results indicated that a two-dimensional axisymmetric simulation is incapable of properly predicting the behavior of channel-type segregations.
This is a preview of subscription content,to check access.
Access this article
Similar content being viewed by others
E.F. Emley, Int. Metals Rev. 21, 75. (2013).
M. Jolly, and L. Katgerman, Progr. Mater. Sci. 2021, 100824. (2021).
R. Nadella, D.G. Eskin, Q. Du, and L. Katgerman, Progr. Mater. Sci. 53, 421. (2008).
D.G. Eskin, J. Zuidema, V.I. Savran, and L. Katgerman, Mater. Sci. Eng. A 384, 232. (2004).
D.G. Eskin, V.I. Savran, and L. Katgerman, Metall. Mater. Trans. A 36A, 1965. (2005).
D. Eskin, R. Nadella, and L. Katgerman, Acta Mater. 56, 1358. (2008).
S.R. Wagstaff, and A. Allanore, Metall. Mater. Trans. B 47, 3132. (2016).
H.-T. Li, P. Zhao, R. Yang, J.B. Patel, X. Chen, and Z. Fan, Metall. Mater. Trans. B 48, 2481. (2017).
A.V. Reddy, and C. Beckermann, Metall. Mater. Trans. B 28B, 479. (1997).
H.J. Thevik, A. Mo, and T. Rusten, Metall. Mater. Trans. B 30B, 135. (1999).
C.J. Vreeman, M.J.M. Krane, and F.P. Incropera, Int. J. Heat Mass Transf. 43, 677. (2000).
B.C.H. Venneker, and L. Katgerman, J. Light Metals 2, 149. (2002).
K. Fezi, A. Plotkowski, and M.J.M. Krane, Numer. Heat Transf. A Appl. 70, 939. (2016).
L. Heyvaert, M. Bedel, M. Založnik, and H. Combeau, Metall. Mater. Trans. A 48, 4713. (2017).
K.O. Tveito, A. Pakanati, M. M’Hamdi, H. Combeau, and M. Založnik, Metall. Mater. Trans. A 49, 2778. (2018).
C.J. Vreeman, and F.P. Incropera, Int. J. Heat Mass Transf. 43, 687. (2000).
C.J. Vreeman, J.D. Schloz, and M.J.M. Krane, J. Heat Transf. 124, 947. (2002).
M. Založnik, B. Šarler, and D. Gobin, Mater. Tehnol. 38, 249. (2004).
M. Založnik, and B. Šarler, Mater. Sci. Eng. A 413, 85–91. (2005).
M. Založnik, A. Kumar, H. Combeau, M. Bedel, P. Jarry, and E. Waz, Adv. Eng. Mater. 13, 570. (2011).
D.G. Eskin, Q. Du, and L. Katgerman, Metall. Mater. Trans. A 39, 1206. (2008).
A. Pakanati, M. M’Hamdi, H. Combeau, and M. Založnik, Metall. Mater. Trans. A 49, 4710. (2018).
A. Pakanati, K.O. Tveito, M. M’Hamdi, H. Combeau, and M. Založnik, Metall. Mater. Trans. A 50, 1773. (2019).
A. Pakanati, M. M’Hamdi, H. Combeau, and M. Založnik, IOP Conferemce Series: Materials Science and Engineering 861, 012040 (2020).
K. Fezi, and M.J.M. Krane, Int. J. Cast Metals Res. 30, 191. (2017).
J. Coleman, and M.J.M. Krane, Mater. Sci. Technol. 36, 393. (2020).
G.S.B. Lebon, G. Salloum-Abou-Jaoude, D. Eskin, I. Tzanakis, K. Pericleous, and P. Jarry, Ultrason. Sonochem. 54, 171. (2019).
G.S.B. Lebon, H.-T. Li, J.B. Patel, H. Assadi, and Z. Fan, Appl. Math. Model. 77, 1310. (2020).
T. Yamamoto, K. Kamiya, K. Fukawa, S. Yomogida, T. Kubo, M. Tsunekawa and S. Komarov, Metallurgical and Materials Transactions B. https://doi.org/10.1007/s11663-021-02320-5
A. Plotkowski, and M.M. Krane, Comput. Mater. Sci. 124, 238. (2016).
D.M. Stefanescu, Science and engineering of casting solidification (Springer, New York, 2008).
F. Rösler, and D. Brüggemann, Heat Mass Transf. 47, 1027. (2011).
C. Prakash, and V.R. Voller, Numer. Heat Transf. B Fundam. 15, 171. (1989).
T. Yamamoto, H. Mirsandi, X. Jin, Y. Takagi, Y. Okano, Y. Inatomi, Y. Hayakawa, and S. Dost, Numer. Heat Transf. B Fundam. 70, 441. (2016).
D.C. Weckman, and P. Niessen, Metall. Trans. B 13B, 593. (1982).
S. Komarov, and T. Yamamoto, Materials (Basel) 12, 3532. (2019).
T. Yamamoto, and S.V. Komarov, J. Mater. Process. Technol. 294, 117116. (2021).
Y. Du, Y.A. Chang, B. Huang, W. Gong, Z. Jin, H. Xu, Z. Yuan, Y. Liu, Y. He, and F.Y. Xie, Mater. Sci. Eng. A 363, 140. (2003).
M. Leitner, T. Leitner, A. Schmon, K. Aziz, and G. Pottlacher, Metall. Mater. Trans. A 48, 3036. (2017).
R.I. Issa, J. Comput. Phys. 62, 40. (1985).
M. Bellet, H. Combeau, Y. Fautrelle, D. Gobin, M. Rady, E. Arquis, O. Budenkova, B. Dussoubs, Y. Duterrail, A. Kumar, C.A. Gandin, B. Goyeau, S. Mosbah, and M. Založnik, Int. J. Therm. Sci. 48, 2013. (2009).
H. Combeau, M. Bellet, Y. Fautrelle, D. Gobin, E. Arquis, O. Budenkova, B. Dussoubs, Y. Du Terrail, A. Kumar, C.A. Gandin, B. Goyeau, S. Mosbah, T. Quatravaux, M. Rady, and M. Založnik, IOP Conference Series: Materials Science and Engineering 33, 012086 (2012).
Conflict of interest
There is no conflict of interest.
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Numerical model for thermodynamic relationship
The thermodynamic relationship was coupled with the governing equations through the numerical model proposed by Prakash and Voller.33 Through a linearized phase diagram, the mass fraction of liquid, fl, was calculated as:
where kp is the partition coefficient, Tm the melting temperature of pure aluminum, and Tliq the liquidus temperature, which is described as:
where Te is the eutectic temperature, and Ce the eutectic concentration. By rearranging Eq. A1, the following equation can be obtained:
A dependence of enthalpy on the liquid fraction can be given as:
where L is the latent heat. The discretized governing equations and thermodynamic relationship were coupled by using Eq. A3 and (A4) through outer iterations. By substituting Eq. A3 into Eq. A4, the following equation can be obtained at the n-th outer step:
Finally, Eq. A5 can be transformed into the following:
where a, b, and d are coefficients of the quadratic equation, which are described as:
Finally, the mass fraction at the n-th outer step was calculated as:
During the outer iterations, liquidus and solidus concentration and the physical properties were updated. By the outer iterations, the mass fraction was converged to a certain value. In this simulation, the convergence criterion of mass fraction was set to 1 × 10−6. The average number of outer iterations was approximately 7.
About this article
Cite this article
Yamamoto, T., Kamiya, K., Kubo, T. et al. Investigation on Three-Dimensional Morphology of Channel-Type Macrosegregation in DC Cast Al-Mg Billets Through Numerical Simulation. JOM 73, 3838–3847 (2021). https://doi.org/10.1007/s11837-021-04906-5