Numerical Modeling of Carbide Redistribution during Centrifugal Casting of HSS Shell Rolls

Abstract

A numerical model was further developed and applied in this work to understand and optimize the carbide redistribution during centrifugal casting process used in manufacturing of high speed steel (HSS) shell rolls. This model will help to further understand the complex solidification behavior of the HSS roll. Performance of the HSS roll requires proper formation and distribution of the VC, (V, Mo)C, and Mo₂C carbides as well as the eutectic carbides, which is shown by dimensional analysis to be dominated by centrifugal buoyancy effects and solidification and carbide kinetics. The model includes a rheology-viscosity sub-model to address the interference between different moving particles or classes of particles of different sizes. The carbide redistribution model was successfully validated against experimental work. A parametric study was performed to determine the key variables that influence the distribution of the VC, (V, Mo)C, and Mo₂C carbides and refine the HSS microstructure including the wash (coating) material, superheat, C content of the shell material and mold temperature.

1. Introduction

The centrifugal casting processing (vertical or horizontal) is the method of choice for producing HSS shells with improved mechanical performance. However, the centrifugal casting process is complex and difficult to control^1,2,3,4) and therefore, numerical modeling is an important tool for understanding and improving the centrifugal casting of high speed steel (HSS) rolls. Several analytical and numerical models were previously developed to predict the particle distribution during centrifugal casting of metal-matrix-composites (MMC)^4,5,6,7) (see a more complete list of references including work on pushing/engulment/entrapment transition in Ref. 1)).

An HSS shell alloy was investigated via DTA analysis to understand the formation of the carbides in the HSS shell. DTA analysis was performed at the University of Alabama, Solidification Laboratory. Also, a test coupon was developed to reproduce similar solidification conditions as in the shell processing. This helped to further understand the solidification behavior of the HSS roll. From the DTA analysis, it was determined that the formation temperature of the VC carbides is above the liquidus temperature of the HSS alloy under current investigation (see Fig. A1 in Appendix I). This fact is also confirmed by JMatPro calculations⁸⁾ based on the chemical composition of the same HSS alloy. This means that the VC carbides can redistribute during the centrifugal casting of HSS alloys and therefore careful process parameters have to be developed to minimize their segregation. The main objective of this paper is to describe the carbide segregation model, further validate it and then apply it to minimize the carbide segregation in the HSS shell rolls.

2. Model Description

A comprehensive 1-D axisymmetric computer model previously developed¹⁾ was adapted in this work to understand and optimize the centrifugal casting process for manufacturing the HSS rolls. Performance of these components requires proper formation and distribution of the VC, (V, Mo)C, and Mo₂C primary carbides as well as of the eutectic network carbides, which is shown by dimensional analysis (see Appendix I) to be dominated by centrifugal buoyancy effects and solidification and carbide kinetics. The model includes a rheology-viscosity sub-model to address the interference between different moving particles or classes of particles of different sizes. The metal/mold interface heat flux boundary conditions were determined based on the experimental temperature measurements and previous knowledge with alumina coating material, which is used at the metal-mold/shell interface.

From a modeling point of view, the centrifugal casting process can be summarized in two important stages. The first is the pouring phase, which includes phenomena from the beginning of pouring to the end of mold filling. The second stage starts at the end of filling and continues to the end of solidification. It is assumed that the outer layer of metal is instantly picked up by the spinning mold and that during the pouring phase the incoming molten material is evenly distributed along the inside of the casting. Also, it was assumed that the VC carbides are typically formed above the liquid temperature of the HSS alloy. This is confirmed by the DTA analysis and JMatPro calculations. Based on the above assumptions, the carbide (e.g., particle) redistribution model can be described as a 1-D axis-symmetric system in cylindrical coordinates. The particle segregation model is summarized below (see more details and validation of the current model in¹⁾):

2.1. Particle Motion

  

$$v_{pr}=-\frac{d_p^2{\omega }^{2}r}{18\mu }({\rho }_p-{\rho }_l)$$(1)

where ρ_p and ρ_l are the densities of the particle and liquid metal, respectively, ω is the mold spinning angular velocity, d_p is the particle size, v_pr is the particle velocity, and μ is the liquid-metal effective viscosity including the effects of particle interaction and solid fraction (Einstein's equation for viscosity^9,10,11)):   

$$\mu ={\mu }_l{\left(1-\frac{f_s+f_p}{C_{\mu }}\right)}^{-2}$$(2)

where μ_l is molecular viscosity of molten metal; f_s is metal solid fraction; and C_μ is an empirical constant that is set to be the maximum random packing volume fraction of particles (068–0.74). Note that when (f_s + f_p) approaches C_μ, the effective viscosity, μ, tends to infinity; therefore the particle motion will be completely stopped.

2.2. Particle Volume Conservation

  

$$\frac{\partial f_p}{\partial t}+\frac{1}{r}\frac{\partial }{\partial r}\left(r{v}_{pr}{f}_p\right)=0$$(3)

The initial and boundary conditions required to solve for Eq. (3) are as follows:

Constant Initial Condition for Particle Volume Fraction:   

$$f_p=constant\hspace{1em}\text{At t}=\text{0}$$(4)

Zero Velocity Condition for Particle Motion:   

$$v_{pr}=0\hspace{1em}\text{At casting inner and outer surfaces}$$(5)

Zero-Gradient Condition for Particle Volume Fraction:   

$$\frac{\partial f_p}{\partial r}=0\hspace{1em}\text{At casting inner and outer surfaces}$$(6)

2.3. Particle Clustering and Agglomeration

Clustering and agglomeration of particles in the liquid change particle motion, usually making particles move faster. The effects of particle clustering and agglomeration have been investigated in Refs. 12), 13), 14), 15). There are two key factors that should be considered: (i) the particles in clusters or agglomerates move together and thus e, the effective sizes of particles are much larger than those of individual particles and (ii) when a cluster or agglomerate moves, the entrapped molten alloy inside the cluster or agglomerate moves as well. This modifies the effective density of the cluster or agglomerate. These two factors are taken into account in this model by using the following relations:^12,14,15)   

$$v_{pr}=-\frac{d_p^2 {\omega }^{2}r}{18 \mu }({\rho }_p-{\rho }_l)\mathrm{\hspace{0.17em} }{\left(1-\frac{f_p}{k}\right)}^n$$(7)

  

$${\rho }_p=k{\rho }_{pm}+(1-k)\mathrm{\hspace{0.17em} }\left[\left(1-f_s\right){\rho }_l+f_s{\rho }_s\right]$$(8)

Note that the “particle density”, ρ_p, in Eq. (7) is evaluated in Eq. (8), replacing particle material density with a value for the alloy/agglomerate combination. It is usually called “effective particle density.” Similarly, the particle size, d_p, in Eq. (7) is termed the effective particle size; it includes contributions of individual particles, clusters, and agglomerates. The effective particle size will be discussed in detail in the next section.

In Eqs. (7) and (8), ρ_pm is the particle materials density; k is the volume ratio of particles in clusters or agglomerates; and n is a constant, empirically determined to be 4.65 for most of the particle suspension systems.^12,14,15) The volume ratio of particles in clusters or agglomerates, k, is process and materials dependent.^15,16,17) For the SiC/A356 alloy system, k varies from 0.18¹⁶⁾ to 0.65.¹⁷⁾ In Ref. 15), k is shown to be 0.42 for particles with an average effective size of 14 μm. In the previous work,¹⁾ a distribution of k is assumed and illustrated in Fig. 1 in Ref. 1) for both the SiC/A356 and the TiC/Bronze alloy systems. For VC/HSS system, no data are reported in the open literature.

Fig. 1.

Schematic of 1-D heat transfer model for centrifugal casting system.

2.4. Particle Size Distribution

During the centrifugal casting process, the centrifugal force increases with effective particle size. Therefore, larger particles move closer to the inner or outer boundary of the fluid. In addition, the particle-free region increases with effective particle size. It was found that the largest particles (low-density cases (VC and (V, Mo)C)) were closest to the inner surface of the casting and smaller particles were further away. It was also found that the largest particles (high-density case (Mo₂C)) were closest to the outer surface of the casting and smaller particles were further away. The effect of particle size distribution has been taken into account by the particle segregation model. Clusters and agglomerates are treated as single particles with the effective particle density specified by Eq. (7). The term “particle size” is defined as the effective particle size including individual VC particles, clusters, and agglomerates.

2.5. Heat Transfer and Solidification Model

The 1-D heat conduction equation in cylindrical coordinates is used to model the temperature evolution in the 1-D centrifugal casting model:   

$${\rho }_c{C}_c\frac{\partial T}{\partial t}=k_c\left(\frac{{\partial }^{2}T}{\partial r^2}+\frac{1}{r}\frac{\partial T}{\partial r}\right)$$(9)

Figure 1 shows the 1-D centrifugal casting model. The casting equipment consists of a mold and a mold wash. The mold itself spins on two sets of wheels. The liquid region consists of liquid metal and partially solidified metal where particle motion is still present. The solid region consists of completely frozen metal and partially frozen metal where particle motion has ceased. An air gap formed at the interface of the mold wash and solidified metal. During solidification, heat is conducted away from the liquid metal through the solid metal, mold wash, and mold. At the inner surface of the cast cylinder, heat is radiated to the environment. The heat conduction equation is solved in the mold, solid casting, and liquid casting regions. In the mold regions, the material properties of the mold are used. In the solid and liquid regions of the casting, composite material properties are used.

2.6. Composite Material Properties

Maxwell’s thermal conductivity model (as referred by Sundstrom and Lee in Ref. 18)) for randomly distributed and non-interacting spheres in a continuous medium was chosen for calculating the thermal conductivity (k_c) of HSS/VC system:   

$$\begin{array}{l}{k}_c=\left[\left(1-f_s\right)k_l+f_s{k}_s\right]\\ \frac{k_p+2\left[\left(1-f_s\right)k_l+f_s{k}_s\right]+2f_p\left\{k_p-\left[\left(1-f_s\right)k_l+f_s{k}_s\right]\right\}}{k_p+2\left[\left(1-f_s\right)k_l+f_s{k}_s\right]-f_p\left\{k_p-\left[\left(1-f_s\right)k_l+f_s{k}_s\right]\right\}}\end{array}$$(10)

where k_c is the thermal conductivity of composite, k_l and k_s are the thermal conductivities of the liquid and solid metal, respectively, f_s is the metal solid fraction, and k_p is the particle thermal conductivity. Note that the particle volume fraction is a function of both time and location.

Density (ρ_c) and specific heat (C_c) of the composite can be estimated by the rule of mixtures:¹⁹⁾   

$${\rho }_c=(1-f_p)\left[\left(1-f_s\right){\rho }_l+f_s{\rho }_s\right]+f_p{\rho }_p$$(11)

  

$$C_c=(1-f_p)\left[\left(1-f_s\right)C_l+f_s{C}_s\right]+f_p{C}_p$$(12)

where C_l, C_s, and C_p represent the specific heat of liquid metal, solid metal, and particles, respectively, and ρ_s represents the density of solid metal.

In the mushy zone, an effective specific heat is applied to account for latent heat of solidification of the matrix metal:   

$$C_{effec}=C_c+\frac{L}{T_{liquidus}-T_{solidus}}(1-f_p)$$(13)

where C_effec is the specific heat of the composite within the mushy region, T is the temperature, and L is the latent heat of solidification.

2.7. Heat Transfer Boundary Conditions

The boundary conditions are described in detail in Ref. 1). On the outside of the mold and on inner surface of the casting, both convection and radiation boundary conditions are used: The type of mold wash material, along with the quality and thickness of the mold wash, affect the rate of heat transfer from the casting to the mold. Mold wash effect is accounted for in this model by using the following equivalent convective heat transfer coefficient (h_eq) is used to simulate mold wash effect:   

$$h_{eq}=\frac{h{k}_{mw}}{k_{mw}+lh}$$(14)

where h is the convective heat transfer coefficient between the casting and mold wash, k_mw is the thermal conductivity of the mold wash, and l is the mold wash thickness. The air gap due to casting contraction during solidification and solid state cooling introduces an additional h between the casting and mold, which varies with time. This effect is accounted for by varying h between the casting and mold during solidification:²⁰⁾   

$$h=h_0+(h_f-h_0)\mathrm{\hspace{0.17em} }\left\{1-{\left[min\left(1,\mathrm{\hspace{0.17em} }\frac{t_0}{t}\right)\right]}^{\alpha }\right\}$$(15)

where h₀ and h_f are the initial and final values of h during the solidification process, respectively; t₀ is the time to initiation of solidification, and α is a constant. Data obtained from strip casting experiments indicated that α is around 0.55.²⁰⁾

2.8. Numerical Methodology

The governing equations described by Eqs. (1), (3), and (7) through (13), are solved using the finite difference method with appropriate boundary and initial conditions, i.e., Eqs. (4), (5), (6) and Eqs. (14) to (15). Figure 2 outlines the solution methodology. Particle motion is computed first. From the particle velocity information, the particle volume fraction across the casting thickness is solved. Afterwards, the solidification front is updated. The solution iterates until the end of solidification has been reached.

Fig. 2.

Simulation methodology flowchart.

Note that particle entrapment is taken into account by using an effective viscosity defined in Ref. 1). Note also that the segregation of the alloying elements including Mo and V are not accounted for in the current model. Also, the complex interaction between the solidification structure and the evolving carbides in centrifugally-cast HSS shell rolls is not yet evaluated in the current work. These phenomena may have a strong impact on the formation and redistribution of some of the carbides that form later during the solidification stage (especially eutectic/network carbides) of the HSS cast rolls.

3. Simulation Results and Discussion

3.1. Model Validation

Comparison with the SiC/A356 Alloy System. The model results were first compared with experimental measurements performed on the centrifugal casting of SiC/A356 alloy by Lajoye and Suery.⁴⁾ More details about this comparison are shown in Ref. 1). As shown in Fig. 3, the simulated results are in reasonably close agreement with the experimental measurements in both the particle-“free” zone and in the remainder of the casting. However, it is not clear what causes the dip in the experimental curve near the outer surface of the casting. The complex interaction between microstructure and SiC particles in the A356/SiC alloy system is studied in Ref. 1). Much less interaction is expected in TiC/Bronze system because particle segregation usually occurs before the onset of solidification. Also, the particle pushing and engulfment play an important role in the modeling of microstructure. However, there is a relatively small effect for the final particle distribution profile on a macroscopic scale.²¹⁾

Fig. 3.

Comparison of simulated versus measured particle distribution in SiC/A356 MMC component.

Comparison with a Standard TiC/Bronze Drum. The model was applied to simulate the standard TiC/bronze drum.^1,2) More details about this comparison are described in Refs. 1) and 2). From the metallurgical analysis, two distinct layers (i.e., a particle-rich region and a particle-“free” region) were noted visually across the thickness of the drum. The average size of individual particles was determined to be about 4 μm and their shape was close to spherical. At mid-height of the drum, TiC particle volume fractions were determined at seven different radial locations, as shown in Fig. 4. Also shown in Fig. 4 are model predictions of the particle volume fractions. The following observations can be made from Fig. 4: (i) the model correctly predicts the transition between the particle-rich and particle-“free” zones; and (ii) the model predictions in the particle-rich zone are in better agreement with the experimental measurements than in the particle-“free” zone. The latter discrepancy is explained by the model assumption of uniform particle size. Metallurgical analysis revealed that particles have a smaller size in the particle-“free” zone.

Fig. 4.

Comparison of simulated and measured particle distributions in a standard TiC/Bronze drum.

3.2. Modeling of the Carbide/HSS Cast Shell Rolls

In this section, the modeling results of the redistribution of the carbide particles during horizontal centrifugal casting of HSS rolls are presented. Table 1 lists the relevant process parameters and simulation conditions. In Table 1, h₀ and h_f are the initial and final values of the heat transfer coefficient at the mold/shell interface, respectively (see Eq. (15)). The material properties of the casting and the mold used in this simulation are listed in Table 2. As shown in Table 2, the air temperature inside the mold is assumed to be the same as the mold preheat temperature, which is 340 K. The effect of the wash (coating) material is shown in Figs. 5 and 6. The coating material is accounted for by using different heat transfer coefficients at the mold/shell interface (see Table 2).

Table 1. Process parameters and simulation conditions for the carbide/HSS alloy system.

Parameter	Units	Value
Casting Inner Radius (rin)	(m)	0.3560
Casting Outer Radius (rout)	(m)	0.4515
Casting Thickness (rout - rin)	(m)	0.0955
Effective Particles Size (d)	(μm)	1
Initial Particle Volume Fraction - VC		0.085
Initial Particle Volume Fraction - Mo2C		0.04
Initial Particle Volume Fraction - (V, Mo)C		0.125
Mold Rotating Speed	(RPM)	1075
Mold Material		steel
Mold Temperature	(K)	340
Ambient Temperature	(K)	298
Initial Melt Temperature	(K)	1674
Air Temperature Inside the Mold	(K)	340
Mold Outer Radius (rm)	(m)	0.597
Heat Transfer Coefficient at Casting Inner Surface, hair	(W m–2 K–1)	10
Heat Transfer Coefficient at Mold Outer Surface, hamb	(W m–2 K–1)	10
Initial HTC* (alumina coating), h0	(W m–2 K–1)	3000
Final HTC (alumina coating), hf	(W m–2 K–1)	90
Initial HTC (alumina and graphite coating), h0	(W m–2 K–1)	6000
Final HTC (alumina and graphite coating), hf	(W m–2 K–1)	180

*  HTC is the heat transfer coefficient at mold/casting interface.

Table 2. Material properties used in modeling of carbide/HSS alloy system.

Property	HSS Alloy	Steel mold	VC	Mo2C	(V, Mo)C*
Liquidus Temperature (TL) (K)	1589
Solidus Temperature (TS) (K)	1423
Density (kg m–3)	6930 at TL 7250 at TS	7500	5390	8120	6264
Specific Heat (J kg–1 K–1)	725	725	710	290	500
Thermal Conductivity (W m–1 K–1)	159	30	17	51	34
Latent Heat of Fusion (J kg–1)	2.73×105
Viscosity, μ0 (N s m–2)	0.004

*  74.4% VC and 25.6.% MoC (MoC density is 8800 kg m^–3).

Fig. 5.

HSS shell 1-D axisymmetric modeling: Simulation Results at the end of solidification (t=2521 s) (alumina coating). (a) VC carbide distribution. (b) Temperature distribution in the mold and casting after 4, 6, 8, 12 and 42 min. (c) Time to reach liquidus (TimeL) and solidus (TimeS) temperatures. (d) Solid fraction of the shell as a function of time.

Fig. 6.

HSS shell 1-D axisymmetric modeling: Experimental validation shell thickness after 6 min (alumina coating).

Figures 5(a)–5(d) shows the key predictions for the HSS shell using the standard alumina coating material with a thickness of about 0.6 mm and 8.5 vol.% VC. These predictions include the VC carbides redistribution, time evolution of the temperature profile in the mold and in the shell, time to reach liquid and solidus temperatures, and the evolution of the solidified shell thickness as a function of time. It can be seen from Fig. 5(a) that the distribution of the VC carbides is non uniform with the VC carbides segregated toward the inner surface of the casting. The amount of VC carbides increases from about 4–5% in the first 80 mm of the shell to about 9% in the last 15 mm of the shell that is located near the inner surface. Note also that some small entrapment of the VC carbides due to solidification occurred near the outer wall of the shell. Figure 5(b) shows the time evolution of the temperature profile in both the mold and the shell. After the solidification of the shell (about 42 min), the temperature of the mold at the metal mold/shell interface reaches about 720 K, while the temperature of the shell at the shell/metal mold interface is about 1300 K. Also, the maximum temperature gradients in the shell and mold are about 140 K and 250 K, respectively, at time = 12 min. Figure 5(d) shows the time evolution of the solid fraction of the shell. After about 8 min (see also Fig. 5(c)), the shell is entirely mushy and at this time carbide segregation becomes more difficult. It can also be seen from Fig. 5(d) that at time = 8 min, the solidification of the shell also started from the inner wall in a very small rate.

Figure 6 shows a comparison between the predicted and experimental shell thickness after 6 min. The predicted shell thickness (42 mm) in Fig. 6 compared well with the experimental measurement (41 mm) obtained from a cast HSS shell. This means that the developed modeling approach including the process and material parameters is validated for HSS cast rolls.

Figure 7 shows the predicted VC carbide distribution for 5 different classes of carbides (their size and volume fraction are also shown in Fig. 7). The standard alumina coating material and 8.5 vol.% VC were used in this simulation. It can be seen form Fig. 7 that the distribution of the VC carbides is highly non-uniform across the shell and they segregate significantly toward the inner surface of the shell. This is because of the larger size and non-uniform distribution of the VC carbides used in this simulation. Thus, it is critical to have small and as uniform as possible VC carbide sizes (see Fig. 6(a), where uniform VC carbides with d = 1 μm were used).

Fig. 7.

HSS shell 1-D axisymmetric modeling: VC carbide distribution for 5 classes of carbides (alumina coating).

Figures 8(a)–8(d) shows the key predictions for the HSS shell assuming 8.5 vol.% VC and a two-layer coating material (graphite and alumina) with 0.75 mm thickness and with higher thermal conductivity than the standard alumina coating due to the use of the graphite material. The change in the coating material decreased the solidification time of the shell from 2521 s (Fig. 5) to 1710 s (Fig. 8). The decrease in the shell solidification time is beneficial since will decrease the grain size and also moderately improve the carbide distribution and uniformity in the shell (see Figs. 5(a) and 8(a)). After the solidification of the shell (about 28 min), the temperature of the mold at the metal mold/shell interface reaches about 810 K, while the temperature of the shell at the shell/metal mold interface is about 1220 K (see Fig. 8(b)). Also, the maximum temperature gradients in the shell and mold are about 240 K and 360 K, respectively, at time = 12 min. Thus, the thermal stresses in both the mold and casting because of these temperature gradients are higher than in the case when standard alumina coating is used (see Fig. 5(b)). As it can be seen from Fig. 8(d), the shell is entirely mushy after about 6 min (see also Fig. 8(c)), and concomitantly, the solidification of the shell also started from the inner wall. This solidification process is quicker than that shown in Figs. 5(c) and 5(d).

Fig. 8.

HSS shell 1-D axisymmetric modeling: Simulation Results at the end of solidification (t=1710 s) (combined alumina and graphite coatings). (a) VC carbide distribution. (b) Temperature distribution in the mold and casting after 4, 8, 12 and 28 min. (c) Time to reach liquidus (tL) and solidus (tS) temperatures. (d) Solid fraction of the shell as a function of time.

A comparison of carbide segregation profiles assuming two different type of carbides (12.5 vol.% (V, Mo)C or 8.5 vol.% VC plus 4.0 vol.% Mo₂C) and two different coatings (alumina (0.6 mm thickness) vs. graphite and alumina (0.75 mm thickness)) is illustrated in Fig. 9. For the (V, Mo)C case, it was assumed that the MoC will nucleate and grow quickly on the VC carbides near the TL of the HSS alloy. The composition of the (V, Mo)C is: 74.4% VC and 25.6.% MoC. Similarly, Mo₂C will precipitate close to the TL of the HSS alloy under current investigation. The overall behavior of the carbide distribution is to some extent similar for both types of carbides as well as for the coating materials. However, the distribution profile of these types of carbides is significantly improved when compared with VC carbide profile alone (see Figs. 5(a) and 8(a)). It can be also noted from Fig. 9 that the use of alumina and graphite coating strategy moderately improved the distribution of these carbides.

Fig. 9.

HSS shell 1-D axisymmetric Modeling: Comparison of carbide segregation profile (alumina coating (a) and (b) and alumina and graphite coatings (c) and (d)). (a) Carbide redistribution (separate formation of VC and Mo₂C) (initial volume fraction amounts of VC and Mo₂C were 8.5% and 4%; d = 1 μm). (b) (V, Mo)C redistribution (initial volume fraction amount was 12.5%; d = 1 μm). (c) Carbide redistribution (separate formation of VC and Mo₂C) (initial volume fraction amounts of VC and Mo₂C were 8.5% and 4%; d = 1 μm). (d) (V, Mo)C redistribution (initial volume fraction amount was 12.5%; d = 1 μm).

To minimize the remelting of the eutectic phase (where eutectic temperature, TE = 1425 K) from about 40% to about 20%, the C content of the intermediate layer material can be decreased from 2.7% to 2.2.%; TL (liquidus temperature) will thus increase from 1539 K to 1570 K. The decrease in C content will also improve the quality of the shell/intermediate layer material bonding area. The potential formation of the shrinkage porosities the shell/intermediate layer material interface is minimized too. The cooling rate distribution in the shell at TL and TE as a function of the shell thickness is shown in Fig. 10. From Fig. 10, an average cooling rate of about 0.1 K/s at TE is estimated for the standard practice (alumina coating). By assuming this cooling rate value, the temperature evolution of the shell/intermediate layer material area can further be estimated.

Fig. 10.

Cooling rate distribution at TL (dTdtL) and TE (dTdtS) in the HSS shell (alumina coating).

3.3. Summary of the Parametric Study: Carbide/HSS Cast Rolls

Figure 11 presented some of the key results of a parametric study showing the effects of the shell’s process and material parameters on the evolution of the shell thickness; this also impacts the bonding time of shell with the intermediate layer material and the final carbide distribution. The main studied variables were: coating material, superheat, carbon content of the shell (e.g., liquidus temperature), and the preheat mold temperature. Based on the results in Fig. 11, the first 3 variables have a significant impact on the shell thickness evolution. The preheat mold temperature (356 K vs. 311 K) slightly affect evolution of the shell thickness. The change in the coating material decreased the solidification time of the shell from 2521 s to 1710 s (see Fig. 11(a)). The decrease in the shell solidification time is beneficial since will decrease the grain size and also moderately improve the carbide distribution and uniformity in the shell.

Fig. 11.

Parametric Study: The effects of the process and material parameters on the solid fraction of the shell. (a) Coating material effect. (b) Superheat effect. (c) Carbon content effect. (d) Mold temperature effect.

The effects of process conditions and materials parameters are summarized as follows:

Superheat. Superheat has some effect on the evolution of the shell thickness and the final carbide distribution. The carbide distribution near the designed wear surface zone will not change very much. However, a low superheat may cause machining problems in later manufacturing processes by entrapping particles in non-desired regions. Also, because the casting defects related to high superheat are not critical to the friction drum application, high superheat will help avoid the casting defects related to a low superheat, such as incomplete filling. Therefore, a relatively high superheat is better for both carbide distribution and casting structure. A superheat of at least 80 K is recommended.

Mold Coating. Mold coating and thickness affect the shell thickness and final carbide distribution through the effect on casting interface/mold interface h. A two-layer coating (graphite and alumina) with a thickness of 0.75 mm is recommended. This will result in a moderate solidification time that allows completion of carbide segregation before matrix solidification starts.

Mold Preheat Temperature. Mold preheat temperature has little effect on the evolution of the shell thickness and final carbide distribution. However, a low mold temperature may decrease the life of steel molds due to thermal shock. Therefore, a moderate-to-high mold preheat temperature is recommended. No strict control of mold preheat temperature is needed.

Mold Materials. Selection of mold material has some effect on the evolution of the shell thickness, the bonding time and the final carbide distribution. Sand, graphite, and standard steels are acceptable. Reinforced sand molds and graphite molds are recommended for general purposes. However, it may be more beneficial to use high Cr ferritic stainless steel molds for large scale manufacturing because of their longer life than the standard steel molds.

Mold Cooling Methods. Minor effect of mold cooling methods on final carbide distribution was observed in the parametric study. Natural air-cooling is recommended at the outer surface of the mold.

Mold Rotating Speed. Mold rotating speed significantly affects both carbide particle motion and solidification. Higher mold rotating speed results in a stronger centrifugal buoyancy force and therefore gives rise to faster carbide particle segregation. Higher mold rotating speed also generates stronger pressing force at the casting/mold interface, and therefore results in stronger interfacial heat transfer and quicker solidification. These factors significantly influence final carbide distribution. A higher mold rotating speed is desired. A mold rotating speed equivalent to about 100G’s or larger is recommended.

Initial Carbide Volume Fraction. Initial carbide volume fraction has a significant effect on the final carbide distribution. An initial carbide volume fraction in the range of 0.085–0.125 (8.5–12.5 vol.%) is recommended.

Carbide Size. The carbide size significantly influences final carbide distribution. Smaller carbide particles, due to ineffective segregation, may be entrapped in non-desired region and cause problems in later machining process. Larger carbide particles segregate faster but may distribute non-uniformly if they are bigger than the dendritic arm spacing. To minimize carbide segregation across the shell thickness, an optimum effective carbide size of about 1 μm is recommended.

4. Conclusions and Future Work

A comprehensive computer model has been applied to simulate the centrifugal casting process for manufacturing carbide/HSS shell rolls. A dimensional analysis revealed that there are two fundamental, interactive phenomena that dominate the final carbide distribution in the centrifugal casting system; carbide motion due to centrifugal buoyancy effects, and solidification. Generally, it is important to ensure that carbide formation and segregation takes place before solidification starts. A well-defined carbide-rich region with small and uniform carbide distribution sizes is desired. After carbide segregation is completed, fast solidification is preferred to obtain optimum casting integrity and quality.

The model predictions were validated with available literature experimental data for SiC/A356 and TiC.Bronze systems. Then, the carbide redistribution model was successfully validated against the current experimental work (standard alumina coating case) in terms of the solidified shell thickness vs. time (see Fig. 6). It was found that (i) the coating material, superheat and C content of the shell material can have a relatively large effect on the shell solidification and (ii) the mold temperature can have only a relatively small effect on the shell solidification. It was determined that a two layer-coating (graphite and alumina with 0.75 mm thickness) strategy can moderately improve the distribution and uniformity of the (V, Mo)C, VC and Mo₂C carbides (see Figs. 9 and 11(a)) across the shell and decrease the HSS microstructure size. This is because of the decrease in the solidification time of the shell by about 30%. Also, to minimize carbide segregation across the shell thickness during HSS roll processing, an optimum effective carbide particle size of about 1 μm is recommended.

Future work will include an evaluation of a coating strategy based on other coating materials; and the development of an inoculation practice to enhance heterogeneous nucleation of the VC carbides.²²⁾ This should also improve the distribution of the carbides and decrease the size of VC carbides. Note also that the grain refinement due to enhanced inoculation should also improve the distribution and decrease the size of the eutectic/network carbides. In addition, the complex interaction between the solidification structure and the carbides in centrifugally-cast HSS shell rolls is being investigated and it will be reported soon. Efforts are currently directed toward developing a comprehensive model, comprising four components (see Refs. 23), 24), 25), 26), 27), 28), 29) for theoretical description of these models): (1) a macro-transport/solidification-kinetics (MT-SK) model to simulate heat transfer and solidification during the centrifugal casting; (2) a multi-component species transfer model to simulate the segregation of the alloying elements during solidification at both the micro and macro scale levels as well as the redistribution of the carbides during the centrifugal casting process of the HSS shell rolls; (3) a deterministic model to simulate the nucleation and growth of carbides as well as their distribution in the casting during solidification; and (4) a stochastic model to simulate the microstructure formation in the presence of the carbides.

Acknowledgement

The author would like to acknowledge Whemco (Kevin Marsden and Chris Hrizo) and United Rolls (Ray Schleiden) for their continuous support and useful comments and suggestions in developing this article.

Appendix I: Dimensional Analysis of Carbide Particle Motion

A dimensional analysis is performed in order to obtain an overall understanding of the centrifugal casting process and the relative importance of the physical phenomena involved in the horizontal centrifugal casting of HSS rolls. Based on the governing equations described in Ref. 1), representative values of important groups of variables can be calculated using typical casting conditions. Tables 1 and 2 lists the conditions and parameters used in the present calculations for carbide/HSS system and Table 3 lists the calculated results and physical meaning for the listed groups of variables. To demonstrate the generality of the particle motion behavior, results for the Carbide/HSS system are listed in Table 3 together with results for the TiC/Bronze and SiC/Al systems. As determined by DTA analysis, VC carbides are formed above the liquidus temperature of the HSS alloy under investigation and therefore they can redistribute during the centrifugal casting of HSS alloys (see Fig. A1). This fact is also confirmed by JMatPro calculations⁸⁾ based on the chemical composition of the same HSS alloy.

Table 3. Order of magnitude of characteristic groups of variables.

Group of Variables	TiC/Bronze System	SiC/A356 System	VC/HSS System	Physical Meaning
$\frac{CentrifugalForce}{InertialForce}$	>30	>30	>30	Centrifugal force is much stronger than inertial force
$\frac{DragForce}{InertialForce}$	~104	~104	~104	Drag force is much stronger than inertial force
$\frac{ParticleRadialSettlingVelocity}{CharacteristicVelocity}$	~6 × 10–4	~2 × 10–4	~3 × 10–4	Particle radial settling velocity is much smaller than characteristic velocity. Particle segregation takes much longer time than mold filling
$\frac{ParticleVerticalSettlingVelocity}{ParticleRadialSettlingVelocity}$	~10–2	~10–2	~5 × 10–3	Gravity effect is much smaller than centrifugal effect. Particle segregation in vertical direction takes much longer time than in radial direction
$\frac{ParticleStokes’RelaxationTime}{PouringTime}$	~10–6	~10–6	~10–6	Particles follow fluid flow very well
$\frac{ParticleSeparationTime}{PouringTime}$	~10	~10	~10	Mold filling takes place much faster than particle separation
$\frac{MetalSolidificationTime}{PouringTime}$	~10	~20	~30	Mold filling takes place much faster than solidification

Fig. A1.

DTA analysis of an HSS alloy showing relevant information related to the formation of the primary carbides.

The following statements may be drawn from Table 3: (1) during mold filling, carbide particles follow the molten metal flow closely and carbide particle segregation is negligible; (2) casting solidification takes place after the mold filling is completed and solidification effects can be separated from the mold filling effects; (3) carbide particle separation is dominated by centrifugal and drag forces and carbide particle inertia is negligible; and (4) carbide particle relative motion takes place only in a radial direction and therefore, carbide particle segregation can be simplified as a one-dimensional phenomenon.

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