ZHANG Lei, ZHAO Honglei, ZHU Mingfang. SIMULATION OF SOLIDIFICATION MICROSTRUC-TURE OF SPHEROIDAL GRAPHITE CAST IRON USING A CELLULAR AUTOMATON METHOD. Acta Metall Sin, 2015, 51(2): 148-158.
Spheroidal graphite (SG) cast iron is characterized by the presence of spherical graphite nodules distributed in the metallic matrix. The performance of castings is primarily dependent on the solidification microstructures. In this work, a two dimensional (2D) multi-phase cellular automaton (MCA) model previously proposed by the present authors is improved to simulate the microstructure evolution of SG cast iron during divorced eutectic solidification. The present model adopts a local solutal equilibrium approach to calculate the driving force for the growth of both graphite and austenite phases. The density difference between iron and graphite is also taken into account. The diffusion of solute in the simulation domain is calculated using a finite difference method (FDM). The present model is applied to simulate the evolution of microstructure and carbon concentration field during solidification for hypereutectic SG cast irons. The results show that the present model can reasonably describe the typical features of divorced eutectic solidification, involving the independent nucleation and growth of primary graphite and austenite dendrites in liquid, the competitive growth of adjacent graphite nodules, engulfment of graphite nodules by austenite dendrites, the isotropic growth of the austenite shells that envelop the graphite nodules, the austenite to graphite eutectic phase transition controlled by carbon diffusion through the solid austenite shell, and multiple graphite nodules encapsulated in each austenite grain at the end of eutectic solidification. The simulated volume fraction and average diameter for graphite nodules are compared reasonably well with the experimental data and level rule calculation. The interactive and competitive growth behavior between austenite dendrites and graphite nodules is studied in detail. It is found that the growth of a graphite nodule is promoted by the approaching austenite. However, after embedded by an austenite dendrite, the growth velocity of graphite decreases rapidly because of lower carbon diffusivity in austenite than that in liquid. In addition, the effect of cooling rate on the size of graphite nodules is also investigated. The results show that with cooling rate increasing, the size distribution of graphite nodules varies from two peaks to one peak, and the average diameter of nodules decreases. The simulation results compare reasonably well with the experimental data reported in literature, demonstrating the validity of the present model。
Table 1 Physical properties used in the simulation[19]
Fig.1 Simulated and experimental morphologies for a hypereutectic spheroidal graphite (SG) cast iron with an initial concentration C0=4.71% at T=1253 ℃ with fs=1% (a), T=1163 ℃ with fs=3% (b), T=1165 ℃ with fs=6% (c), T=1156 ℃ with fs=35% (d), T=1117 ℃ with fs=91% (e), T=1123 ℃ with fs=97% (f), T=740 ℃ with fs=100% (g) and experiment result of Fe-3.86%C-2.82%Si[22] (h) (Numbers in the figures show the local carbon concentration, and fs is the total solid fraction)
Fig.2 Volume fractions of solid, austenite and graphite vary with temperature for a hypereutectic SG cast iron with C0= 4.71%
Method
Graphite volume fraction / %
Average radius / mm
Simulation result of program calculation
14.16
21.24
Simulation result of Imagetool measurement
14.10
21.19
Lever rule calculation
14.59
21.55
Experimental result of Imagetool measurement[22]
11.44
18.52
Table 2 Comparisons of simulation, lever rule and experiment for the graphite volume fraction and average radius of a hypereutectic SG cast iron with C0=4.71%
Fig.3 Interactive and competitive growth between austenite dendrite and graphite nodules for a hypereutectic SG cast iron of C0=4.65% at solidification times of 1 s (a), 6 s (b), 11 s (c), 12 s (d), 13 s (e), 19 s (f), 20 s (g) and 22 s (h) (Numbers in the figures show the local carbon concentration)
Fig.4 Time evolution of growth rate (a) and radius (b) of nodules I, II and III in Fig.3
Fig.5 Simulated nodule size distribution for a SG iron of C0=4.31% at 740 ℃ with extraction rates of 16 ℃/s for 4 mm plate (a) and 21 ℃/s for 1.5 mm plate (b)
Fig.6 Simulated microstructures for a SG cast iron of C0=4.31% with heat extraction rates of 16 ℃/s (a) and 21 ℃/s (b)
Fig.7 Comparison of the average graphite radius as a function of solidification time between simulation (C0=4.31%) and experiment (Fe-3.57%C-2.64%Si)[23] results
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