Showing papers on "Directional solidification published in 2004"

Quantitative phase-field model of alloy solidification.

Abstract: We present a detailed derivation and thin interface analysis of a phase-field model that can accurately simulate microstructural pattern formation for low-speed directional solidification of a dilute binary alloy. This advance with respect to previous phase-field models is achieved by the addition of a phenomenological "antitrapping" solute current in the mass conservation relation [Phys. Rev. Lett. 87, 115701 (2001)]]. This antitrapping current counterbalances the physical, albeit artificially large, solute trapping effect generated when a mesoscopic interface thickness is used to simulate the interface evolution on experimental length and time scales. Furthermore, it provides additional freedom in the model to suppress other spurious effects that scale with this thickness when the diffusivity is unequal in solid and liquid [SIAM J. Appl. Math. 59, 2086 (1999)]], which include surface diffusion and a curvature correction to the Stefan condition. This freedom can also be exploited to make the kinetic undercooling of the interface arbitrarily small even for mesoscopic values of both the interface thickness and the phase-field relaxation time, as for the solidification of pure melts [Phys. Rev. E 53, R3017 (1996)]]. The performance of the model is demonstrated by calculating accurately within a phase-field approach the Mullins-Sekerka stability spectrum of a planar interface and nonlinear cellular shapes for realistic alloy parameters and growth conditions.

Directional solidification of large superalloy castings with radiation and liquid-metal cooling: A comparative assessment

Abstract: A columnar-grain variant of single-crystal RENE N4 has been directionally solidified (DS) over a range of conditions in order to assess the possible benefits of the use of liquid metal-enhanced cooling for large cross-sectional castings. Castings were solidified at a rate of 2.5 mm/min using conventional radiation cooling and at rates between 2.5 and 8.5 mm/min using liquid-metal cooling (LMC) with tin as a cooling medium. Thermocouples inserted in the casting directly measured thermal gradients during solidification. The LMC process exhibited higher gradients at all withdrawal rates. The higher thermal gradients resulted in a refined structure measurable by the finer dendrite-arm spacing. Additionally, the conventionally cast material exhibited several freckle-type defects, while none were observed in the liquid-metal-cooled castings.

Grain structure development in directional solidification of nickel-base superalloys

Abstract: The microstructures of three single crystal superalloys (CMSX4, CM186LC and CMSX10) that exhibit quite different casting properties have been characterised quantitatively following quenched directional solidification to identify variations in the grain selection mechanisms. No significant differences in the dendrite morphologies of the alloys were observed. Detailed observation of dendrites in directionally solidified bicrystals of CMSX4 with well-controlled misorientations showed significant modification of the growth of secondary dendrites at the developing seeded grain boundary. The generally accepted criterion of overgrowth by secondary dendrites cannot account for the present results. It is proposed that the diffuse textures that are frequently produced in second and third generation superalloys are a consequence of the inhibition of secondary dendrite development due to competing solute diffusion fields.

Interflake spacings and undercoolings in Al–Si irregular eutectic alloy

Abstract: Aluminium–silicon irregular eutectic alloy was melted in a graphite crucible in vacuum. This alloy was directionally solidified at a constant growth rate, V (8.3m/s) and at different temperature gradients, G (2.0–7.8 K/mm) and also with a constant G (7.8 K/mm) and different V (8.3–498.7m/s) in the Bridgman type directional solidification furnace. The interflake spacings, λi, were measured from both transverse and longitudinal sections of the specimens. The relationships between interflake spacings, λi and solidification parameters V and G were obtained by linear regression analysis method. The variations of interflake spacings, λi with V, G and undercoolings, � Ti, were investigated and the relationships between them were examined. Operating parameters φ and η which reflect the spacing adjustment mechanism were obtained.

Fabrication of Lotus‐type Porous Metals and their Physical Properties

Abstract: Lotus-type porous metals whose long cylindrical pores are aligned in one direction were fabricated by unidirectional solidification in a pressurized gas atmosphere. The pores are formed as a result of precipitation of supersaturated gas when liquid metal is solidified. The lotus-type porous metals with homogeneous size and porosity of the evolved pores produced by a mould casting technique are limited to the metals with high thermal conductivity. On the other hand, the pores with inhomogeneous pore size and porosity are evolved for metals and alloys with low thermal conductivity such as stainless steel. In order to obtain uniform pore size and porosity, a new “continuous zone melting technique” was developed to fabricate long rod- and plate-shape porous metals and alloys even with low thermal conductivity. Mechanical properties of tensile and compressive strength of lotus-type porous metals and alloys are described together with internal friction, elasticity, thermal conductivity and sound absorption characteristics. All the physical properties exhibit significant anisotropy. Lotus-type porous iron fabricated using a pressurized nitrogen gas instead of hydrogen exhibits superior strength.

Three-dimensional phase-field simulations of directional solidification

Abstract: The phase-field method has become in recent years the method of choice for simulating microstructural pattern formation during solidification. One of its main advantages is that time-dependent three-dimensional simulations become feasible. This makes it possible to address long-standing questions of pattern stability. Here, we investigate the stability of hexagonal cells and eutectic lamellae. For cells, it is shown that the geometry of the relevant instability modes is determined by the symmetry of the steady-state pattern, and that the stability limits strongly depend on the strength of the crystalline anisotropy, as was previously found in two dimensions. For eutectics, preliminary investigations of lamella breakup instabilities are presented. The latter are carried out with a newly developed phase-field model of two-phase solidification which offers superior convergence properties.

Influence of melt convection on dendritic spacings of downward unsteady-state directionally solidified Al-Cu alloys

Abstract: The dendritic spacings are important microstructural parameters involved in solidification processes. They can affect not only microsegregation profiles but also the formation of secondary phases within interdendritic regions, which influences mechanical properties of cast structures. A small number of studies have been carried out in order to analyze the effects of melt convection within the interdendritic region or to verify the influence of growth direction in the dendritic arm spacings. In this work, a combined theoretical and experimental approach is developed to quantitatively determine solidification thermal variables such as transient metal/mold heat transfer coefficients, tip growth rates, thermal gradients, tip cooling rates and local solidification time during downward unsteady-state solidification of hypoeutectic Al–Cu alloys. These solidification thermal variables are correlated with dendritic spacings, which have been measured along cross and longitudinal sections of ingots solidified under downward unsteady-state heat-flow conditions. Predictive theoretical models for dendritic spacings have been compared with experimental observations. A comparison between upward and downward unsteady-state results for dendritic spacings has also been conducted.

Simulation of weld solidification microstructure and its coupling to the macroscopic heat and fluid flow modelling

Abstract: The microstructure exerts a strong influence on the mechanical properties and on the integrity of welded joints. Prediction of the formation of the microstructure during welding and of other solidification processes may be an important and supporting factor for technology optimization. Nowadays, increasing computing power allows direct simulations of the dendritic and cell morphology of columnar grains in the molten zone for specific temperature conditions. Modelling is carried out, on the one hand, with the finite difference—cellular automata and, on the other hand, with the phase field method. Determination of the solidification conditions during fusion welding (temperature gradient, local solidification rate, weld pool shape) is carried out with a numerical macroscopic finite element modelling calculation of the weld pool fluid flow and of the temperature distribution, as presented in this paper. As with the use of accurate physical models, the simulations are carried out with a spatial resolution of the microstructure, and many assumptions and restrictions from traditional, analytical or phenomenological models may be eliminated. The possibilities of using numerical algorithms for generation and visualization of microstructure formation during solidification are demonstrated. The spectrum of applications extends from welding and casting to processes with rapid solidification. In particular, computer simulations of the solidification conditions and the formation of a dendritic morphology during the directional solidification in gas–tungsten-arc welding are described. Moreover, the simulation results are compared with the experimental findings.

A stabilized volume-averaging finite element method for flow in porous media and binary alloy solidification processes

Abstract: A stabilized equal-order velocity-pressure finite element algorithm is presented for the analysis of flow in porous media and in the solidification of binary alloys. The adopted governing macroscopic conservation equations of momentum, energy and species transport are derived from their microscopic counterparts using the volume-averaging method. The analysis is performed in a single domain with a fixed numerical grid. The fluid flow scheme developed includes SUPG (streamline-upwind/Petrov-Galerkin), PSPG (pressure stabilizing/Petrov-Galerkin) and DSPG (Darcy stabilizing/Petrov-Galerkin) stabilization terms in a variable porosity medium. For the energy and species equations a classical SUPG-based finite element method is employed. The developed algorithms were tested extensively with bilinear elements and were shown to perform stably and with nearly quadratic convergence in high Rayleigh number flows in varying porosity media. Examples are shown in natural and double diffusive convection in porous media and in the directional solidification of a binary-alloy.

Effect of Zr and B on castability of Ni-based superalloy IN792

Abstract: The effect of Zr and B on hot tearing susceptibility of the Ni-based superalloy IN792 during directional solidification (DS) was studied. The Zr and B concentrations in the experimental alloys ranged from 0 to ∼550 ppm. The results indicate that Zr or B does not influence the castability when added individually. However, when both Zr and B are present in the alloy, high hot tearing susceptibility was found, the effect being particularly strong if Zr concentration was high. The castability results cannot be explained by simple solidification characteristics such as total freezing range (obtained from differential scanning calorimetry (DSC)) or by the amount of eutectic liquid (derived from the fraction of interdendritic γ/γ′ obtained from quantitative metallography). However, the present results can be interpreted in terms of formation of continuous films of liquid at grain boundaries (GBs) during the final stages of solidification rather than enclosed pockets. Such thin films of liquid may reduce GB cohesion and promote hot tearing.

Crossover scaling of wavelength selection in directional solidification of binary alloys

Abstract: We simulate cellular and dendritic growth in directional solidification in dilute binary alloys using a phase-field model solved with adaptive-mesh refinement. The spacing of primary branches is examined for a wide range of thermal gradients and alloy compositions and is found to undergo a maximum as a function of pulling velocity, in agreement with experimental observations. We demonstrate that wavelength selection is unambiguously described by a nontrivial crossover scaling function from the emergence of cellular growth to the onset of dendritic fingers. This result is further validated using published experimental data, which obeys the same scaling function.

The effect of solidification variables on tertiary dendrite arm spacing in unsteady-state directional solidification of Sn–Pb and Al–Cu alloys

Abstract: Solidification thermal variables, i.e., transient metal/mold heat transfer coefficient and tip cooling rate, and tertiary dendrite arm spacings have been measured in Sn–Pb and Al–Cu alloys directionally solidified under unsteady-state heat flow conditions. The tertiary arms seem to initiate from the secondary branches only when a certain value of a parametric factor ( δ= T /C 0 ) relating cooling rate and alloy solute content is attained. It was observed that a −0.55 power law characterizes the tertiary spacing variation with the cooling rate, for any hypoeutectic alloy experimentally examined. The influence of initial alloy composition on tertiary dendritic spacing is also analyzed. The insertion of analytical expressions for cooling rate into the resulting experimental equations permitting to establish empirical formulae relating tertiary dendrite spacing with unsteady-state solidification parameters like: melt superheat, type of mold and transient metal/mold heat transfer coefficient is proposed.

Sound absorption characteristics of lotus-type porous copper fabricated by unidirectional solidification

Abstract: Lotus-type porous copper with large number of unidirectional cylindrical pores was fabricated by unidirectional solidification of melt dissolving hydrogen in a pressurized hydrogen atmosphere. The sound absorption coefficient of the porous copper plate, which has many open pores, was measured by standing-wave method in the frequency range up to 4 kHz. The absorption coefficient increases with increasing frequency. The absorption coefficient increases with increasing porosity and specimen thickness, while it decreases with increasing pore diameter. In addition, it was understood that the absorption coefficient of lotus-type porous materials could be evaluated by using the attenuation constant.

Cumulative mechanical moments and microstructure deformation induced by growth shape in columnar solidification.

Abstract: The dynamical interaction between columnar interface microstructure and self-stress, resulting in unforeseen mechanical deformation phenomena, is brought to light by means of in situ and real-time synchrotron x-ray topography during directional solidification of dilute aluminum alloys. Beyond long-known local mechanical stresses, global mechanical constraints are found to be active. In particular, column rotation results from deformation caused by the mechanical moments associated with the very growth shape, namely, the cumulative torque acting together with the cumulative bending moment under gravity. A basic model allowing for a qualitative explanation of the observed distinctive features of the self-stress effects on microstructure dynamics is proposed.

Analytical, numerical, and experimental analysis of inverse macrosegregation during upward unidirectional solidification of Al-Cu alloys

Abstract: The present work focuses on the influence of alloy solute content, melt superheat, and metal/mold heat transfer on inverse segregation during upward solidification of Al-Cu alloys. The experimental segregation profiles of Al 4.5 wt pct Cu, 6.2 wt pct Cu, and 8.1 wt pct Cu alloys are compared with theoretical predictions furnished by analytical and numerical models, with transient hi profiles being determined in each experiment. The analytical model is based on an analytical heat-transfer model coupled with the classical local solute redistribution equation proposed by Flemings and Nereo. The numerical model is that proposed by Voller, with some changes introduced to take into account different thermophysical properties for the liquid and solid phases, time variable metal/mold interface heat-transfer coefficient, and a variable space grid to assure the accuracy of results without raising the number of nodes. It was observed that the numerical predictions generally conform with the experimental segregation measurements and that the predicted analytical segregation, despite its simplicity, also compares favorably with the experimental scatter except for high melt superheat.

A review of directionally solidified intermetallic composites for high-temperature structural applications

Abstract: Alloys based on intermetallics have been considered for high temperature structural applications However, many of these alloys suffer from intrinsic brittleness and low fracture toughness at ambient temperature Therefore, ductile-phase-toughened intermetallic composites are being investigated as a means to improve the fracture toughness A subset of this class of materials is in-situ composites produced by directional solidification of intermetallic eutectics In this paper, we review recent developments related to the processing and properties of these composites

Removal of Metal Impurities in Molten Silicon by Directional Solidification with Electron Beam Heating

Abstract: An industrial-scale pyrometallurgical method of removing metallic impurities from metallurgical grade silicon (MG-Si) was developed as an element technology in a sequential purification process for manufacturing high-purity silicon for solar grade silicon (SOG-Si) by segregation of metallic impurities during solidification. Metallic impurities were removed from MG-Si using an electron beam heating equipment. Molten silicon was supplied continuously at a constant mass to a water-cooled copper mold and was allowed to solidify gradually in an unidirectional manner from the bottom upward. This process is termed directional solidification. The iron concentration after solidification can be expressed by Pfann’s and Burton’s equations, and was reduced from an initial 1500 mass ppm to below 10 mass ppm. Aluminum removal was excessive, presumably due to vaporization to the gas phase. Above a certain height in the ingot, it became impossible to remove metallic impurities by partition during directional solidification. This phenomenon showed a correlation with the concentration of enriched iron in the silicon pool. The mechanism of metallic impurity removal was estimated based on visual examination of the solidified structure and EPMA. The iron concentration profile of ingots and critical purification height were estimated experimentally using a 20 kg scale device and verified as being applicable on an industrial scale in experiments with 150 kg scale equipment. Solar grade silicon was test-produced by this process and showed satisfactory quality for solar cell use.

Effect of growth rate and lamellar spacing on microhardness in the directionally solidified Pb-Cd, Sn-Zn and Bi-Cd eutectic alloys

Abstract: Lead-cadmium, Zinc-tin and Bismuth-cadmium of (99.99%) high purity eutectic alloys were melted in a graphite crucible under vacuum atmosphere. These eutectic alloys were directionally solidified upward with a constant temperature gradient G and different growth rates V in the Bridgman type directional solidification furnace. The lamellar spacings λ and microhardness H V were measured from both transverse section and longitudinal section of the specimen. The variations of H V with respect to V and λ have been determined by using the linear regression analysis method. H V values increase with the increasing values of V and decrease with the increasing λ values. The Hall-petch type relationships obtained in this work have been compared with the previous works.

Plastic deformation of NiMnGa polycrystals

Abstract: Ferromagnetic materials based on the Heusler alloy Ni 2 MnGa have been recognized as interesting actuating materials. Large strains can be obtained by applying an external magnetic field acting on the reorientation of the mesoscopic structure of martensite. Even if a great part of the investigation has been performed on single crystals, an interest exists for the development of polycrystalline technology. It has been recognized that, in order to balance the strong uncoupling effect due to the large number of fixed interfaces (e.g. the grain boundaries), the polycrystalline sample should have some texture. This should result in some pre-orientation of the twinned martensitic structure and, if possible, in a modification of the random distribution of the easy axis orientation within the material. Strong material texturing can be obtained basically by using directional solidification, rapid solidification techniques or plastic deformation. The effects of directional solidification, and of melt spinning have been evaluated in the past. In the present work, we report on successfully plastic deformation of polycrystalline NiMnGa alloys. In literature, there are few (if any) papers devoted to this topic. The great brittleness of the alloy at room temperature is well known. The rare attempts performed to deform the material are reported as failures. The approach used here is based on the hot working of NiMnGa ingots in special metallic cans filled with Argon and sealed. Hot deformation of a 7×7×40 mm 3 small slab down to 1.25×11.9×130 mm 3 was successful. Even after this severe plastic deformation, it was possible to easily remove the deformed material from the special can. The structural and functional characterization of the final product, which maintained the martensitic transformation, will be presented and discussed.