Finite element modeling of macrosegregation coupled with shrinkage cavity in steel ingots using arbitrary Lagrangian-Eulerian model

Flemings M C. Our understanding of macrosegregation: past and present. ISIJ International, 2000, 40(9): 833–841.

Beckermann C. Modelling of macrosegregation: applications and future needs. International Materials Reviews, 2002, 47(5): 243–261.

Ma X P, Li D Z. Macrosegregation and its formation mechanism in steel ingot with designed local thermal control. ISIJ International, 2014, 54(2): 356–358.

Krane M J M, Incropera F P. Analysis of the effect of shrinkage on macrosegregation in alloy solidification. Metallurgical and Materials Transactions A, 1995, 26(9): 2329–2339.

Heinrich J C, Poirier D R. The effect of volume change during directional solidification of binary alloys. Modelling and Simulation in Materials Science and Engineering, 2004, 12(5): 881–899.

Samanta D, Zabaras N. Modelling convection in solidification processes using stabilized finite element techniques. International Journal for Numerical Methods in Engineering, 2005, 64(13): 1769–1799.

Chen K X, Shen H F. Numerical simulation of macrosegregation caused by thermal-solutal convection and solidification shrinkage using ALE model. Acta Metallurgica Sinica (English Letters), 2019, https://doi.org/10.1007/s40195-019-00897-0 .

Zhang S L, Yanke J R, Johnson D R, et al. Modeling defects in castings using a volume of fluid method. International Journal of Numerical Methods for Heat & Fluid Flow, 2014, 24(2): 468–482.

Zhang S L, Johnson D R, Krane M J M. Influence of riser design on macrosegregation in static castings. International Journal of Cast Metals Research, 2015, 28(1): 28–38.

Wang T M, Yao S, Zhang X G, et al. Modelling of the thermosolutal convection, shrinkage flow and grain movement during globular equiaxed solidification in a multi-phase system — I. Three-phase flow model. Acta Metallurgica Sinica, 2006, 42(6): 584–590. (In Chinese)

Wang T M, Li T J, Cao Z Q, et al. Modelling of the thermosolutal convection, shrinkage flow and grain movement during globular equiaxed solidification in a multi-phase system-II. Application of model. Acta Metallurgica Sinica, 2006, 42(6): 591–598. (In Chinese)

Wu M, Kharicha A, Ludwig A. Using four-phase Eulerian volume averaging approach to model macrosegregation and shrinkage cavity. In: IOP Conference Series: Materials Science and Engineering, IOP Publishing, 2015: 012006.

Wu M, Ludwig A, Kharicha A. A four phase model for the macrosegregation and shrinkage cavity during solidification of steel ingot. Applied Mathematical Modelling, 2017, 41: 102–120.

Ge H H, Ren F L, Li J, et al. Four-phase dendritic model for the prediction of macrosegregation, shrinkage cavity, and porosity in a 55-ton ingot. Metallurgical and Materials Transactions A, 2017, 48(3): 1–12.

Ren F L, Ge H H, Cai D X, et al. Simulation of macrosegregation and shrinkage cavity in an Al-4.5 wt pct Cu ingot using a four-phase model. Metallurgical and Materials Transactions A, 2018(12): 6243–6254.

Bellet M, Fachinotti V D. ALE method for solidification modelling. Computer Methods in Applied Mechanics and Engineering, 2004, 193(39–41): 4355–4381.

Bellet M, Jaouen O, Poitrault I. An ALE-FEM approach to the thermomechanics of solidification processes with application to the prediction of pipe shrinkage. International Journal of Numerical Methods for Heat and Fluid Flow, 2005, 15(2): 120–142.

Belytschko T, Liu W K, Moran B. Nonlinear finite elements for continua and structures. 2nd ed., West Sussex, UK, John Wiley & Sons Inc., 2014: 417–475.

Hebditch D J, Hunt J D. Observations of ingot macrosegregation on model systems. Metallurgical Transactions, 1974, 5(7): 1557–1564.

Ahmad N, Rappaz J, Desbiolles J L, et al. Numerical simulation of macrosegregation: a comparison between finite volume method and finite element method predictions and a confrontation with experiments. Metallurgical and Materials Transactions A, 1998, 29(2): 617–630.

Li W S, Shen H F, Liu B C. A response to numerical benchmark for solidification of binary alloys:macro-segregation with thermosolutal convection. China Foundry, 2012, 9(2): 171–177.

Combeau H, Založnik M, Hans S, et al. Prediction of macrosegregation in steel ingots: influence of the motion and the morphology of equiaxed grains. Metallurgical and Materials Transactions B, 2009, 40(3): 289–304.

Nguyen T T M, Gandin C A, Combeau H, et al. Finite element multi-scale modeling of chemical segregation in steel solidification taking into account the transport of equiaxed grains. Metallurgical and Materials Transactions A, 2018, 49(5): 1725–1748.