The fractal dimension analysis was applied to the evaluation of primary dendrite and several eutectic structure morphologies in the high speed steel type cast iron for rolls which have been produced by the centrifugal cast technique. Initially, the affine parameter of the dendrite morphology of transparent organic alloy was evaluated based on the self-affine fractal theory. Primary γ dendrite and several eutectic structures crystallize in the high carbon high alloying element roll specimen. The microstructural morphology of sliced γ dendrite was analyzed by the self-similar fractal technique. The fractal dimension of each part of two-dimensionally-sliced dendrite varies from 1.05 to 1.13, and that of aggregation of dendrite's parts increases to 1.30. The fractal dimension of the primary dendrite among eutectic phases varies depending on the analysis area, and decreases with in decreasing of volume fraction of primary dendrite. In the specimen contained relatively high alloying elements, the round shape of sliced dendrite and the reduction of area fraction of primary dendrite cause to the difficulty of analyses using secondary dendrite arm spacing and fractal dimension of primary dendrite. Therefore, the fractal dimension of primary γ and γ+MC eutectic structure were evaluated. The fractal dimension analysis reveals that the morphology of dendrite and eutectic structure in segregated region slightly increases in comparison with the normal microstructure, and decreasing with the cooling velocity. Lower equilibrium partition coefficient of alloying elements and centrifugal force could cause the micro segregation of outer dendrites in roll specimen and complicated primary dendrite and γ+MC eutectic structure.
Solidification structure of an alloy of grade Hastelloy G-2 was investigated by differential scanning calorimetry and electron probe microanalyzer. Small amount of Cr and Mo-enriched phase was observed at the final solidification region. Furthermore, the numerical simulation of solidification behavior of this alloy was conducted using the thermodynamic models such as the Scheil-Guillver model and the Partial Equilibrium model, and the Multi-Phase-Field (MPF) method. The simulation results of the MPF method were in good agreement with the experimental results. And the Cr and Mo-enriched phase formed at the final solidification region was predicted as the σ phase from the results of simulation. The MPF method is valuable tool to investigate the microsegregation and phase transformation during the solidification of the Ni-base alloys.
Influence of cooling rate on the development of solidification structure and microsegregation of multi-component white cast iron was investigated by using Fe-2mass%C-5mass%Cr-5mass%Mo-5.5mass%V alloy. Primary austenite(γ), MC and M2C carbides were crystallized at the cooling rates obtained by this experiment and the solidification process and structure were unchanged within the cooling rate of 5K/min to 351K/min. The amount of M2C carbide decreased with an increase in the cooling rate, while that of MC carbide was almost same level. Concentrations of alloying elements in the residual liquid during solidification varied greatly in line with the progress of crystallizing each phase. As the primary γ continued to crystallize, Cr, Mo and V contents in the residual liquid were increased. According to the crystallization of (γ+MC) eutectic, the V content decreased and both the Cr and Mo contents increased more in the residual liquid. In the final liquid highly concentrated with Mo, (γ+M2C) eutectic started to crystallize. The microsegregation can be estimated using the partition coefficient of elements to each phase and the diffusivity of alloying elements. The estimated results showed relatively good accordance with the experimental results. Since the apparent partition coefficient of alloying element in the residual liquid is varied by the cooling rate, the amount of M2C carbide crystallized in the final liquid enriched with Mo was changed. The estimated amount of M2C carbide decreased from 6.8% in volume at 5K/min to 5.2% at 20K/min, and the estimated and the experimental results were close each other.
The macrosegregation model that heat transfer, solidification, liquid flow and solute movement were considered was developed to simulate the generation of the center-line segregation in the casting of steel. The center of cast has negative segregation only under influence of the liquid flow with solidification shrinkage when calculated in a conventional model. It was necessary to consider the bulging of cast slab so that positive segregation was formed in the center of cast. This macrosegregation model considering three driving force of fluid flow; solute concentration, thermal expansion, and solidification shrinkage, calculated that positive segregation was generated in the center of cast by the bridging being formed to a solidifying shell in last stage of solidification. This simulation results show effect of driving force of solidification shrinkage with bridging is larger than the other driving force. And a mechanism of generating center-line segregation with bridging was suggested.
Macrosegregation is directly related to the performance of steel products. So many research works have been performed to tackle this problem. Quality of steel products have been increased remarkably, though, we have still some problems of macrosegregation. In this study, in order to investigate the relationship between solidified structure and macrosegregation, model experiments using Al-10 mass%Cu alloy have been carried out. A mold, which can form macrosegregation in the central region of the small ingot, has been newly developed. About 520 g of Al-10 mass%Cu alloy was used for experiment, changing casting temperature ranged from 650 °C to 850 °C. Areal fraction of eutectic structure was characterized for macrosegregation. When this value exceeded 0.23, which was evaluated using Scheil equation, it was defined that macrosegregation formed in the solidified shell. Primary crystals bridged together and free liquid flow was prevented near the chill plate. Therefore, the negative pressure increased and relatively high suction force acted through the mushy zone near the chill plates. Thus, remained liquid in the interdendritic region, which had high solute content, flew into the bottom area. After complete solidification, there remained large shrinkage and macrosegregation below the chill plated region. On the other hand, near or above the chill plate region, negative segregation and/or small porosity formed.
It is well-known that the degree of macrosegregation decreased with increasing the amount of equiaxed zone. However, the effect of size and morphology of equiaxed grains on the macrosegregation has not been understood. Thus, laboratory-scale experiments using Al-10 mass%Cu alloy have been carried out. The equiaxed structures can be easily obtained in aluminum alloy using modifier, which contains Ti and B, without changing the solidification condition, such as fluid flow. A mold, which can form macrosegregation in the central region of the ingot, has been developed and used in this study. Changing casting temperature and the amount of modifier, the central regions of the ingot have been metallographically analyzed. The degree of macrosegregation has been characterized by the areal fraction of eutectic structure. It was found that the diameter of equiaxed grains decreased with increasing the amount of modifier. Furthermore, the shrinkage and macrosegregation decreased with decreasing the diameter of equiaxed grains. Complexity of the equiaxed grain has been also characterized using fractal dimension. In case of the same diameter of equiaxed grains, the degree of macrosegregation in the ingot decreased with increasing the fractal dimension of the equiaxed grains. The reason of these may be that the flow of liquid phase in the mushy zone decreases when the equiaxed grains are fine and/or complex. Since the liquid flow in the final stage of solidification is inadequate, small shrinkages form in the interdendritic region and consequently the suction force becomes small. Therefore, neither large shrinkage nor macrosegregation forms.
To evaluate the permeability for columnar dendritic structures, three dimensional (3D) flow simulations of interdendritic liquid were carried out. The 3D columnar dendrites were made by means of the computer aided design (CAD), which were based on two-dimensional dendrite morphologies calculated by a phase-field method. The artificial 3D columnar dendrites were regularly-arranged, and six kinds of 3D columnar dendritic structures were obtained, which have different volume fractions of liquid between 0.56 and 0.95. For these columnar dendritic structures, the flows parallel and normal to the primary dendrite arms were calculated by the FLUENT, and the permeability for six 3D columnar dendritic structures and both flow directions were determined by using the Darcy law. The values of our simulated permeability were compared with those of the experimental permeability [K.Murakami, A.Shiraishi and T.Okamoto: Acta metall., 31 (1983), p.1417, 32 (1984), p.1423, C.Y.Liu, K.Murakami and T.Okamoto: Mater. Sci. Tech., 5 (1989), p.1148]. For both flow directions, our simulated permeability was in good agreement with their experimental permeability. Therefore, we confirmed that our 3D flow simulations are valid to obtain the permeability for columnar dendritic structures. Also, from these results, we discussed the marginal volume fraction of solid for interdendritic flow, and we suggest that it is effective to define the marginal permeability of interdendritic flow to estimate exactly the marginal volume fraction of solid for interdendritic flow considered the morphology of interdendritic structures.
Evolution of dendrite morphology in Fe-base ternary alloys (Fe-C-X : X=Cr, Mn, Mo, P, Si, V, W) was simulated by using the phasefield method with linking to the Thermo-Calc software. The complexity of the dendrite morphology of the alloys was evaluated by using fractal dimension and dimensionless perimeter. The values of evaluated fractal dimension and dimensionless perimeter lined as P>V>Si>Cr>Mo>W>Mn and this result demonstrates that the both parameters of the fractal dimension and the dimensionless perimeter are effective to evaluate the complexity of dendrites. Permeability of simulated dendrite arrays was estimated by using the fractal dimension and the dimensionless perimeter as the tortuosity factor of interdendritic liquid channels. Obtained permeability corresponded to reported values of the permeability when the dimensionless perimeter was used as the tortuosity factor.
Channel segregation behavior of a lateral directional Sn-20mass%Bi ingots was examined by X-ray computing tomography (X-ray CT) and three-dimensional numerical analysis. The channel segregation with string shape from near the cold wall side was observed by the X-ray CT and those segregation patterns could be reproduced by the numerical analysis. Low concentration regions also appeared above the channel segregation in both X-ray CT images and numerical analysis results. These results suggest that the proposed numerical method is a reasonable model to simulate the channel segregation. Detailed investigation of the effects of convection on the generation of channel segregation showed that a solidification-accelerated region (SA-region) and solidification-retarded region (SR-region) were formed by the fluid flow. At the SA-region, solidification was accelerated by the inflow of lower Bi concentrated liquid. On the other hand, in the SR-region, solidification was retarded by the inflow of the liquid with high Bi concentration from the SA-region. It was found that the SA-region (called donor part) and SR-region (called acceptor part) group into pairs, and generate the channel segregation.
In-situ observation of deformation in semi-solid alloys at the grain scale has been carried out using X-ray radiography. This paper characterizes the deformed microstructure in the semi-solid state by a quantitative analysis of solid motion from the image sequences obtained by the in-situ experiment on semi-solid Al-Cu alloys. A velocity of solid, a shear strain rate and a divergence of solid rate, which correspond to the change in solid fraction, were evaluated during a 0.5-1d (d: crystal size) increment of direct shear. The effect of solid morphology on the shear deformation was also examined by in-situ observation of deformation in water-polystyrene particle mixture where the polystyrene particles are spherical (shape factor~1) with diameter of 500 μm. The shear strain was localized in the vicinity of the shear domain and the localized area corresponds to the area where the solid fraction decreased both in semi-solid Al-Cu alloys and the water-particle mixture. The waterpolystyrene particle mixture showed a narrower localized area of the shear strain than that of Al-Cu alloys due to the difference in the solid shape.
In order to understand the role of angle of rotation axis, experimental work using organic substance has been performed. One of the advantageous points of the experimental equipment is that visual point (=the video camera) can be rotating with the glass cell, in which organic material was filled. In-situ observation has been carried out at the rotation rate of 250 rpm, changing the angle of rotation axis (η) at the interval of 30°, defining 0° as being horizontal to ground. In case of η<90°, the equiaxed grains formed in the middle of solidification process. Equiaxed grains oscillated with respect to the mold wall back and forth in accordance with rotation. Amplitude of oscillation decreased with increasing η. Equiaxed grains also travelled backward with respect to the rotation. Travelling length per revolution decreased with increasing η. Since the contribution of gravitational acceleration to the movement of solid/liquid mixture decreases with increasing η, the turbulence of the surface of liquid phase decreases with increasing η. In case of η=90°, the typical columnar dendrites grew from the mold and no equiaxed grains formed. The liquid phase is completely stabilized by centrifugal force, because the effect of acceleration due to gravity vanishes in this condition.
A centrifugal casting method is a key technology for producing high quality rolls which are used in a rolling process in steel industry. Because the surface quality of steel products highly depends on the roll quality and it is affected by liquid motion in the centrifugal casting method, control of the liquid motion is essential for supply of defect free rolls to the steel industry. In this research, liquid flow in the centrifugal casting method has been numerically calculated for clarification of difference of liquid motion in a horizontal type centrifugal casting method and a vertical one. The mainly obtained results are as follows. The center of the gravity periodically oscillates and its cycle is longer than the rotation cycle of the mold in the both cases of the horizontal and vertical types. Its time average in the horizontal type locates above the center axis of the mold while that in the vertical type is the same with the center axis. Increase in apparent viscosity in the vicinity of the mold wall accelerates the damping of the oscillating motion of the center of the gravity.
A centrifugal casting method is an important process for high quality steel production because rolls produced by this method have been used in a rolling process in steel industry. However, some problems to be solved such as segregation still remain. Thus optimization of the centrifugal casting method is essential for high quality steel production. In this investigation, numerical calculation of fluid motion in the horizontal type centrifugal casting method has been conducted for clarification of effect of the rotation velocity of the mold on the fluid motion. And the following results have been obtained. Center of the gravity of a liquid phase shifts to upward from the center axis of the mold rotation and it increases with decrease of the mold rotation velocity. And frequency of the periodical motion of the center of the gravity can be explained by superposition of the mold rotation and wave propagation on the liquid free surface. Furthermore, the critical diameter for breaking dendrite growing from the mold increases with increase of the mold rotation velocity when the dendrite length is constant.
Fluid flow and heat transfer analysis based on MPS method (Moving Particle Semi-implicit method; one of the particle method) was carried out, and its applicability to the centrifugal casting process was discussed. A rotation speed of the mold, a rotation center offset and a gravitational force were changed to discuss the influence of them on the flow pattern and the cooling curves. As a result, the flow pattern and the cooling curves could be summarized using dimensionless Froude number, and the results agreed well with experimental data in the past studies. In case of small Froude number, the gravitational force is relatively stronger than centrifugal force, and fluctuation of surface and temperature distribution, delay of internal flow compared with the mold rotation occur. In contrast, large Froude number case, flow and temperature distribution was stable and the thickness of the pipe is uniform. Finally, calculation time was discussed and it was shown that the particle method has high efficiency of parallelization.