Simulation and analysis of the solidification characteristics of a Si-Mo ductile iron

High silicon and molybdenum ductile cast irons (Si-Mo alloys) are commonly used as exhaust manifold materials suffering from high temperature-oxidation and thermal-mechanical fatigue. The structural integrity of cast Si-Mo alloys under these service conditions is attributed to their microstructure consisting of spheroidal graphite and Mo-rich carbide embedded in a ferritic matrix. However, the cast structure includes also pearlite structure having a detrimental effect on the mechanical properties, therefore the cast matrix needs to be heat treated. In this study, the solidification of a Si-Mo ductile iron was investigated using (i) thermodynamic and kinetic calculations by Thermo-Calc and DICTRA software and (ii) thermal analysis in order to reveal out the sequence of phase formation and the phase transformations during solidification and (iii) microanalysis by energy dispersive spectrometer in order to determine elemental segregation and compare with the calculated values. The solidified structure was also characterized and all microstructural features were specified.


Introduction
Today's environmental protection and fuel economy regulations push the manufacturers to design the engines in order to increase power density with reduced emission and improved fuel economy. Increased power density causes higher operating temperatures from the engine to the exhaust system consisting of well-known components, i.e. manifold, catalytic converters, flexible bellow, muffler, resonator, connecting pipes, flanges and tailpipe [1][2][3][4][5]. Among these components, the manifold is exposed to the highest temperature and subjected to higher thermal and thermomechanical loads due to increased power density [6]. Therefore, it is necessary to design exhaust manifold with appropriate material which provides good high temperature strength, resistance to high temperature corrosion, resistance to microstructural changes, stable physical properties at higher temperatures, thermal shock resistance and resistance to thermomechanical fatigue [6 -8]. Although there is an increasing trend in designing new austenitic iron-based alloys [1,9], high silicon and molybdenum ductile cast iron (SiMo), with ferritic matrix, is one of the strongest candidate materials due to its low cost and good castability besides its high oxidation resistance and high-temperature strength [10]. The microstructure of Si-Mo alloys consists of spherical graphite and Mo-rich carbide embedded in a ferritic matrix [6,10]. Ekström et al. indicate that SiMo has lower expansion coefficient, higher thermal conductivity and higher strength than austenitic cast alloys by means of its ferritic matrix [6,11]. In the matrix design of SiMo cast iron, the amount of Si and Mo plays an important role on the properties of cast alloy, used preferably as high temperature material.
The addition of silicon not only enhances the mechanical properties but also improves the oxidation resistance of ductile cast irons due to the formation of complex Si-Fe-O based films, inhibiting further oxygen diffusion into the substrate at elevated temperature [7,12,13].
Molybdenum increases the strength and hardness of cast irons by suppressing the pearlite transformation kinetics and it also increases elevated temperature strength and creep resistance [4,7,11].
Currently, there is a trend to add alloying elements, i.e. Al, Ni, Cr etc., in order to vary the critical temperatures. This may be very effective in enhancing the properties at elevated temperatures [6,8,12,[14][15][16]. Although there are several studies reporting mechanical [6,12,14] and corrosion properties [4,8,15], microstructural features [6,10] of SiMo cast iron as well as microstructural properties of ductile cast irons [17,18], research on microsegregation, stability of phases and partition of elements in the phases of SiMo ductile cast iron is very limited. It is important to understand (i) the effect of alloying elements on solidification and final microstructure, (ii) macro/microsegregation, (iii) stability of phases and (iv) partitioning of elements in the phases during solidification in order to improve the Si-Mo ductile cast iron to be used as manifold material by means of controlled microstructure.
Therefore, the objective of this research is to investigate the effect of alloying elements on solidified microstructure of SiMo cast iron and give insight to the spatial distribution of the precipitated phases. For this purpose, the effects of elements were calculated by using the CALPHAD (CALculation of PHAse Diagrams) approach and the microstructure was investigated experimentally in order to compare the calculations with the experimental results.

Computational method
Thermo-Calc software which is based on the CALPHAD approach can perform the necessary thermodynamic calculations for various phases in any system [19][20][21]. For the Fe-C-Si-Mo system under consideration, the thermodynamic database, TCFE6, for ferrous alloys was used.
According to several reports, during the solidification the liquid phase transforms into a structure consisting of globular graphite (GR), austenite (γ) and Mo-rich M6C type carbide [10,11]. With further cooling below the temperature at which ferrite starts to form (TF), until the room temperature, austenite will eventually transform into ferrite (α) and cementite. The On the 2 nd stage, the phase transformations and the elemental microsegregations were simulated by the computational kinetics software DICTRA, using the MOBFE2 mobility database for ferrous alloys. The DICTRA homogenization model for 1D multiphase diffusional simulations was employed using a hollow spherical geometry, where the center of the cell corresponds to zero (Fig.1). The distance of the inner interface from the center of cell was taken equal to 10 μm and corresponds to the radius of globular graphite based on the experimental results of the current cast iron used in this study. It was assumed that austenite nucleates and grows along the globular graphite interface, therefore the distance between the inner and outer interface of the spherical cell corresponds to the radius of austenite phase, and was taken equal to 50 μm based on the experimental results. Due to the fact that graphite in the DICTRA software is considered as a diffusion none phase, a typical moving boundary problem approach cannot be adopted in this study. For this reason, an approach for carburization models [22] was applied, in which the boundary conditions set on the inner interface of the cell are where is the activity of carbon, and is the concentration gradient of element (mol/m 4 ).
The system is considered closed for all the elements except carbon, since the fluxes (mol/m 2 s) are equal to zero. The fluxes can be described by Fick-Onsager law for a multicomponent system with elements, where is the diffusion coefficient matrix (m 2 /s). For the outer interface, the system is considered closed for all elements and the boundary conditions are M6C carbide, ferrite (α) and cementite were considered as dispersed phases in austenite matrix phase (γ). It should be noted that for the current cast iron used in this study, the flux of carbon in the inner interface can also take negative values, which means that graphite can act as a point sink of carbon in the system. In addition, graphite volume fraction was not included to the total volume of the system since it was regarded as a boundary condition.
Throughout the simulations (i) diffusion was assumed to take place only in the matrix phase, (ii) the dispersed phases acted as point sinks or sources of solute atoms in the simulation and (iii) local equilibrium conditions were imposed at all interfaces. The Hashin-Shtrikman bounds model with prescibed matrix was selected for the description of the homogenization function of the dispersed phases, which is suitable when diffusion data are known [23].

Experimental procedure
The studied high silicon and molybdenum ductile cast iron (SiMo) was produced as Y block by sand mold casting according to DIN EN 1563:2012-03 standard at Gedik Casting Co., Turkey. The chemical composition of the SiMo cast iron is given in Table 1. In order to validate the computational results in terms of (i) the formation of the phases during solidification, (ii) critical temperatures of the studied alloy and (iii) microsegregation of the elements, both microstructural examinations and thermal analysis were applied to the SiMo cast iron.

Solidification sequence and phase transformations
Phase equilibria and Scheil solidification sequence for the given composition were calculated in order to identify critical temperatures and major phases in the solidified structure. For this purpose, the C isopleth and solidification path were constructed for the SiMo composition ( Figure 2). The critical temperatures were also computed according to equilibrium and values are listed in Table 2. For the solidification sequence, the simulation starts from the liquid phase at casting temperature (TC=1500 ºC). The solidification path indicates that the solidification begins at liquidus temperature (TL=1209 ºC) and ends at solidus temperature (TS=1094 ºC).
The sequence of solid phase formation during solidification is L → L + GR (graphite) → L + GR + FCC (austenite) → L + GR + FCC + M6C (Fig. 2b). After solidification, FCC phase transforms to BCC phase between TF (865.41 °C) and A1 (823.91 °C) temperatures (Fig. 2a).  In order to experimentally validate the calculated results, thermal analysis was applied to the SiMo cast iron. The thermogram obtained from DTA analysis is given in Figure 3.  [24]. According to calculation results given in Figure 2 and the thermogram (Fig. 3), the matrix is expected to consist of ferrite, graphite, M6C carbides and cementite. In order to clarify the microstructure, LM (Fig. 4a) and SEM (Fig. 4b and c) micrographs showing the cast structure of SiMo alloy are given. As indicated in the micrographs, the cast microstructure of SiMo consists of globular graphite (GR), eutectic carbide (EC), granular cementite (GC) and ferritic matrix as suggested by the calculations (Fig. 2) and thermal analysis (Fig. 3). EDS results obtained from eutectic carbide in Figure 4c indicates that this eutectic

Evolution of microsegregation and phase fraction
Microsegregation of elements and phases were calculated in two stages, stated above. The simulation region is a unit spherical cell, where the inner grain boundary corresponds to 10 μm, and the outer grain boundary corresponds to the end of the cell at 60 μm (Fig. 1). In the 1 st stage, the microsegregation of the elements in austenite, as well as the fractions of M6C carbide were computed at the end of the solidification at TS with the Scheil module of Thermo-Calc.
The mole fraction of M6C carbide, in the austenite is depicted in Figure 5. The mole fraction of graphite according to Scheil calculations, takes a value around 0.082, which approximates the image analysis results. M6C carbide precipitates only near the boundary, due to carbon segregation. According to solidification studies in the literature, graphite forms from liquid and intercepts the austenite grains [19,20] while M6C carbide precipitates at the boundaries due to the microsegregation of the elements [10].
The presence of elemental microsegregation in austenite phase can be calculated at the end of the solidification by Scheil module. Figure 6 shows the compositional profiles for the elements C, Si, Mo, Mn, Ni and Fe. It can be observed that Si and Ni exhibit negative segregation whereas the composition of the other elements (C, Mo, Mn, Fe) increased towards the grain boundary. In the concentration profiles, a knee at the curve exists at about 45 µm away from the grain center where M6C begins to form, thus an increase of the mole fraction of C, Mo and Mn and a decrease of Si and Ni, enables the formation of M6C close to the grain boundary [13].
Such a formation is also indicated by Figure 5. These findings are in good agreement with the microstructural feature given in Figure 4a, since globular graphite is observed around the middle of the solidified phase whereas M6C appears at the grain boundaries.

Validation of calculations by quantitative analysis
In this section, initially a methodology is described shortly and then multi EDS analyses results in the solidified structure are given, in order to validate the calculations on microsegregation for the 2 nd stage mentioned in Section 3.2.
A general view is obtained by SEM using topographic contrast as shown in Figure 10, diameter of grain structure is marked by a line and 50 µm radius is shown. The EDS analyses were carried out in a large number of grains, from globular graphite until grain boundaries, in order to get statistically reliable results.
The EDS profiles of elements are plotted as a function of distance (Fig. 11). The calculated profiles at the end of the 2 nd stage (Fig.8) and the experimentally determined profiles (Fig.11) show

Conclusion
In this study, both solidification characteristics and microstructural features of SiMo cast iron as one of the strongest candidate materials for exhaust manifolds were studied by using the CALPHAD approach and metallurgical analyses on cast alloy. Calculations revealed the solidification sequence as the formation of graphite from liquid followed by austenite and M6C carbide. After solidification, the austenite phase transformed to ferrite phase at about 824 °C which limits its use at higher temperature. All predicted phases were determined within the ferritic cast structure where graphite and Mo-rich M6C carbides exist at intercellular regions.
Critical temperatures were determined experimentally by DTA and findings supported the calculated results.
In order to follow the microsegregation of the elements, Scheil module of Thermo-Calc, was            Table 1. Chemical composition of the SiMo alloy (wt. %) Table 2. Critical temperatures (°C) obtained from Thermo-Calc software for the studied alloy.