Modeling and experimental validation of ductile iron castings during solidification
Developing a micro model to simulate the microstructure formation of ductile iron casting during solidification. The density variation resulting from the eutectic transformation process of austenite and graphite. Mechanical properties calculation.
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Modeling and Experimental Validation of Ductile Iron Castings During Solidification Jianzheng Guo and Mark T. Samonds (Submitted September 17, 2007; in revised form March 28, 2008) Ductile irons are still important engineering materials due to their high strength and toughness, and relatively low price. In the foundries, ductile irons suffer from shrinkage porosity formation during solidification, which is detrimental to the mechanical properties. In order to minimize porosity formation, large risers are normally used in the design, which reduces porosity level sometimes but leads to a low yield.
In order to better understand the shrinkage behavior of ductile iron during solidification, a micro model was developed to simulate the microstructure formation. The density change during solidification and the room temperature mechanical properties can be calculated based on the microstructure. The simulation has been compared with the experimental results and found to be in good agreement.
Cast iron remains the most important casting material with over 70% of the total world tonnage (Ref 1). Based on the shape of graphite, cast iron can be lamellar (flake) graphite iron or spheroidal (nodular) graphite iron. In the last 40 years, many papers have been published on the modeling of ductile iron solidification. It started with the computational modeling by analytical heat transport and transformation kinetics calculations (Ref 2-8). The computer model can calculate the cooling curve with an analytical method, together with the kinetics calculation of carbon diffusion through the gamma phase shell. In 1985, Suet al. (Ref 9) first coupled heat transfer and solidification kinetics in a model using the finite difference method. After that, many papers have been published on micro modeling of ductile iron solidification (Ref 10-20). The carbon diffusion controlled growth through the gamma shell was treated. In those models, the nodule count, graphite radius, and austenite shell radius were calculated. Onsoien et al. (Ref 21-22) used the internal state variable approach to model the multiple phase changes occurring during solidification and subsequent cooling of near eutectic ductile cast iron. In their simulation, the effects on the microstructure evolution at various stages of the process due to alloy composition, graphite nucleation potential, and thermal progress were illuminated. The heat flow, fading effect, graphite/austenite eutectic transformation, ledeburite eutectic transformation, graphite growth in the austenite regime, and the eutectoid transformation were all modeled. There is one common assumption for all the models mentioned above. The thermo-physical properties, such as thermal conductivity and density, are constants. It is well known that density as well as thermal conductivity is strongly composition, temperature, and process dependent. Shrinkage porosity can form because of the density variation during solidification. For ductile iron, expansion can happen during solidification because of the graphite precipitation based on the composition, inoculation, and other processes.
The microstructure has been extensively studied so far but not the porosity formation because of the density variation of ductile cast iron during solidification. Chen et al. (Ref 20) calculated the densities of austenite, graphite, and liquid and the volume change as well as coupling the volume change model to the growth kinetic model. In their model the density of ledeburite phase was not included. Ledeburite phase can form when cooling is too fast or the inoculation is not good enough.
In their model, the density calculation was not coupled to the porosity prediction. In this article, a comprehensive micro model is developed which can give accurate microstructure information as well as the mechanical properties, such as yield strength, tensile strength, and hardness. The density of austenite, ferrite, pearlite, graphite, liquid, and ledeburite are all calculated. The prediction has been compared with the experimental results and found to be in good agreement.
1. Micro Modeling
1.1 Nucleation Model In this work, Oldfield_s nucleation model is applied
Bulk heterogeneous nucleation occurs at foreign sites which are already present within melt or intentionally added to the melt by inoculation. Where A is the nucleation constant, No is the nucleation number per unit volume, DT is the undercooling, and n is another constant which depends on the effectiveness of inoculation.
Jianzheng Guo, GE Global Research Center, One Research Circle, Niskayuna, NY 12309; and Mark T. Samonds, ESI US R&D, 6851 Oak Hall Lane, Ste 119, Columbia, MD 21045. Contact e-mail: email@example.com.
JMEPEG (2008) 17:831-837 _ASM International DOI: 10.1007/s11665-008-9246-0 1059-9495/$19.00 Journal of Materials Engineering and Performance Volume 17(6) December 2008--831
1.2 Fading Effect
Fading is the phenomenon whereby the effectiveness of inoculation diminishes as the time between inoculation and casting increases. It is believed that the nucleation of graphite occurs on small nonmetallic inclusions which are entrapped in the liquid after the inoculation (Ref 21). The small particles will grow with time. The particle diameter can be calculated by.
model microstructure iron solidification
1.3 Graphite/Austenite Eutectic Transformation
The eutectic growth process in ductile iron is a divorced growth of austenite and graphite, which do not grow concomitantly. At the beginning of the liquid/solid transformation, graphite nodules nucleate in the liquid and grow in the liquid to a small extent. The formation of graphite nodules and their limited growth in liquid depletes the carbon in the melt in the vicinity of the nodules. This facilitates the nucleation of austenite around the nodules, forming a shell. Further growth of these nodules is by diffusion of carbon from the melt through the austenitic shell. Once the austenite shell is formed around each nodule, the diffusion equation for carbon through the austenitic shell is solved in 1D spherical coordinates. The boundary conditions are known from the phase diagram because thermodynamic equilibrium is maintained locally. Conservation of mass and solute is maintained in each grain.
Because of the density variation resulting from the growth of austenite and graphite, the expansion/contraction of the grain is taken into account by allowing the final grain size to vary. Toward the end of solidification, the grains impinge on each other. This is taken into consideration by using the Johnson Mehl approximation.
Differentiation of the above two equations and using Ficks law in spherical coordinates leads to two equations for graphite and austenite growth rates following some manipulation.
1.4 Ledeburite Eutectic Transformation
When the temperature reaches below the metastable eutectic temperature, the metastable phase forms. The metastable cementite eutectic is also called ledeburite, in which small islands of austenite are dispelrsed in the carbide phase. It has both direct and indirect effects on the properties of ductile iron castings. It increases the yield strength but reduces the tensile strength with an increasing volume percent of the hard, brittle carbide. Following the assumptions from Onsoien (Ref 22), the graphite/austenite nodule distribution is approximated by that of a close-packed face-centered space lattice and the ledeburite eutectic appears in intermediate positions.
1.5 Eutectoid Transformation
The eutectoid reaction leads to the decomposition of austenite to ferrite and graphite for the case of the stable eutectoid, and to pearlite for the metastable eutectoid transformation.
Usually, the metastable eutectoid temperature is lower than the stable eutectoid temperature. Slower cooling rates result in more stable eutectoid structure. Following solidification, the solubility of carbon in austenite decreases with the drop in temperature until the stable eutectoid temperature is
reached. The rejected carbon migrates toward the graphite nodules, which are the carbon sinks. This results in carbon depleted regions in austenite around the graphite nodules. This provides favorable sites for ferrites to nucleate, which grow as a shell around the graphite nodules. If the complete transformation of austenite is not achieved when the metastable temperature is reached, pearlite forms and grows in competition with ferrite.
Even though ferrite can form either from the breakdown of pearlite or from the direct decomposition of austenite, it is assumed here that ferrite results from the latter source only. It is assumed that (1) the austenite to ferrite transformation occurs at steady state and is controlled by carbon diffusion, (2) thermodynamic equilibrium exists at graphite/ferrite and ferrite/austenite interface, and (3) diffusion from the ferrite/austenite interface toward austenite is neglected as diffusion coefficients and concentration gradients in austenite are small compared to those in ferrite.
Nucleation and Growth of Pearlite. The nucleation of pearlite usually occurs at austenite grain boundaries. It has been demonstrated that pearlite colonies grow either as spheres or hemispheres following nucleation. By the movement of high mobility incoherent interfaces, these colonies can grow edgewise or sidewise into the austenite. This means that pearlite grows in competition with ferrite until austenite is completely transformed. Transformation of austenite into pearlite is usually modeled with an Avrami equation because the study of nucleation of pearlite is difficult, especially under continuous cooling conditions. Also, pearlite grains impinge on each other at an early stage, especially at a relatively high cooling rate.
2. Density Calculation
Thermo-physical properties research is a very important part of materials science, particularly at the current times because such data are a critical input for the simulation of metals processing. There is little information about such properties for multicomponent alloys during solidification. A simple pairwise mixture model, which is similar to that used to model thermodynamic excess functions in multi-component alloys, is used to calculate the properties (Ref 23).
3. Mechanical Properties Calculation
The ultimate goal of process modeling is to predict the final mechanical properties. The mechanical properties (hardness,tensile strength, yield strength, and elongation) of ductile iron castings are function of composition and microstructure. The graphite shape, graphite structure, graphite amount, carbide content, and matrix structure (pearlite, ferrite) all affect the mechanical properties of ductile iron castings. Carbide content has direct and indirect effects on the properties of cast ductile irons. The hard brittle carbide increases the yield strength but decreases the tensile strength. As for the matrix structure, the increasing of pearlite amount increases the strength and hardness but reduces the elongation. Mixture rule is applied here to calculate the mechanical properties. For example, the hardness can be calculated by.
4. Case Studies
In order to show the capability of this model, solidification of a simple geometry ductile iron casting was investigated. The dimension of the casting is 10 10 200 cm and the geometry of the casting is shown in Fig. 1. On the left face, it is cooled by contacting a constant temperature media (15 _C) with a heat transfer coefficient of 500 W/m2 K. All the other faces are adiabatic. The initial melt temperature is 1400 _C. Figure 2 shows the solidification time at different distances from the cooling end. At the very left, the solidification time is less than 1 s. On the other hand, the solidification time at 10 cm from the cooling end is more than 100 s. Because of the different cooling rates, the nodule count varies and is shown in the same figure.
The metastable phase forms when the cooling is too fast. Fig. 1 Geometry for a test casting to show the ability of current Model Journal of Materials Engineering and Performance Volume 17(6) December 2008--833 Figure 3 shows the volume fraction of different phases at room temperature. On the very left end, there is around 90% volume fraction of metastable phase ledeburite thanks to the rapid cooling. The ledeburite phase reduces gradually from left to right until at 3 cm from the chill end, there is no more ledeburite. At the same time, as cooling decreases, the volume fraction of ferrite increases and that of pealite decreases.
Ledeburite is a very hard, brittle phase, harder than pearlite. The pearlite phase is harder than ferrite. Hence the ductility increases as the cooling rate decreases. From the micro modeling, the calculated grain and graphite radius at different distances from the chill are shown in Fig. 4. Faster cooling results in smaller grain and graphite sizes. The ratio of the radius of graphite and austenite increases as cooling decreases, but reaches a constant value of around 0.46 even though the radius of graphite and austenite still continue to increase. This constant ratio is determined by the initial carbon content. It can determine the expansion level during solidification. Based on the microstructure, the mechanical properties can be calculated. As mentioned above, carbide increases the yield strength but decreases the tensile strength. The yield strength Fig. 2 The relationship between solidification time and nodule count due to the different solidification rates at different distances from the chill Fig. 3 The relationship between phase fractions and the elongation of the casting at different distances from the chill Fig. 4 The relationship between the grain and graphite size of the casting because of the different cooling conditions at different distances from the chill Fig. 5 Mechanical properties of the casting at different distances from the chill Fig. 6 Density variations of the casting at different distances from the chill 834--Volume 17(6) December 2008 Journal of Materials Engineering and Performance and hardness continuously decrease as the cooling rate decreases. The yield strength is very high on the left because of the formation of carbide.
The results are shown in Fig. 5. Based on the volume fraction of different phases and the composition, the density variation with temperature can be predicted and is shown in Fig. 6. It can be seen that at x = 0, because of the formation of carbide, there is no expansion during solidification. The density continuously increases as temperature decreases. Dependent on the locations from the cooling end, the expansion levels are different based on the microstructure at that location. There is a secondary expansion during eutectoid reaction around 1000 K because of the phase transformation of austenite to ferrite and/or pearlite phase. The density variation for the liquid stage is the same at different location because the initial composition is uniform and macrosegregation is not included in this model. Different cooling will cause different solid density profile even with the same initial chemistry because of the different microstructure.
As a result, the porosity can be predicted accurately.
5. Experimental Validations
In order to validate the model, a series of experiments were performed (Ref 26). The three-part cast-iron foundry mouldcontaining the gating system is shown in Fig. 7. The casting is GGG60 ductile iron. The pouring temperature is 1400 _C, theinitial die temperature is 165 _C, and the initial sand temperature is 20 _C. Table 1 shows the chemistry of the casting. In order to investigate the micro structure of the casting and the morphology of the graphite, specimens were taken as shown in Fig. 8. The specimens were then grounded, polished, and etched for structure evaluation. It can be seen in the pictures of the microstructure that graphite was segregated in the form of spheroids. Because of the rapid cooling, a large amount of the metastable phase, ledeburite, was formed in the corners. The ledeburite phase reduces gradually as the cooling rate decreases. In the center of the casting, no ledeburite phase was found. The radius of the black graphite balls increases as cooling decreases.
Journal of Materials Engineering and Performance Volume 17(6) December 2008--835 dramatically based on the microstructure variation. On the other hand, hardness is an excellent indicator of microstructure and strength and relatively easy to measure. Figure 10 shows the hardness measurement points on the sample. Table 2 shows the comparison between the measurement and prediction results of the hardness at different locations. It can be concluded that the prediction matches the experiments very well.
A micro model was developed to simulate the microstructure formation of ductile iron. Based on the microstructure, the volume fraction of different phases, and the composition, the density variation with temperature can be predicted. Dependent on the cooling condition, the expansion levels are different because of the different microstructure at that location. Hence, different cooling will cause different solid density profile even with the same initial chemistry. As a result, the porosity can be predicted accurately. Based on the microstructure, the mechanical properties can be calculated as well. The simulation, such as hardness, has been compared with the experimental results and found to be in good agreement. Further microstructure prediction validation, such as graphite nodule size and nodule count, will be performed next.
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