Solidification Theory Research Articles

Experimental and Numerical Simulation of Surface Segregation in Two-Phase Zone Continuous Casting Cu–Sn Alloy

Surface segregation exists in two-phase zone continuous casting (TZCC) alloy with wide solid–liquid two phase zone. The surface segregation formation cannot be explained by the traditional solidification theories. ProCAST software was used to simulate the TZCC process for preparing the Cu–4.7 wt%Sn alloy with wide solid–liquid two phase zone. The Sn solute distribution in TZCC Cu–4.7 wt%Sn alloy was investigated, and the surface segregation mechanism of TZCC Cu–4.7 wt%Sn alloy was analyzed. The results showed that numerical simulation results were agreed with that of experimental. TZCC Cu–4.7 wt%Sn alloy in the center firstly started to solidify and resulted in “Λ” shape inclined solid/liquid (S/L) interface near the mold. Therefore, a narrow gap between the wall of the two-phase zone mold and the S/L interface formed. On the one hand, while Cu–4.7 wt%Sn alloy solidified along the opposite continuous casting direction, the solute redistribution between the solid and the liquid occurred, which lead to Sn solute decreased in solid and enriched in front of S/L interface. Because the narrow gap lies in front of inclined S/L interface near the two-phase zone mold, Sn solute enriches in liquid of the narrow gap. On the other hand, during the TZCC process, solid grains nucleate on the wall of the two-phase zone mold, while the melt feeds into the two-phase zone mold which the temperature is in the two-phase zone of the Cu–4.7 wt%Sn alloy. The solute redistribution also occurs while the solid grains grow, thus lead to Sn content increases in front of S/L interface near the wall of the two-phase zone mold. The enriched Sn solute is too late to diffuse, and will quickly flows into the narrow gap, resulting in further increasing of Sn content in the narrow gap. The liquid with enriched Sn solute in the narrow gap will become the surface layer after solidification, which lead to surface segregation layer during the TZCC Cu–4.7 wt%Sn alloy.

Evolution of Phase Transition and Oxidation of Copper in Electrical Fires

Based on the theories of low-temperature plasma and metal solidification, the similarities and differences between anode melted marks (AMMs) and cathode melted marks (CMMs) in direct current (DC) short circuits were characterized, and the phase transition and oxidation of copper melted marks were analyzed. These data were used to ascertain which melted marks were suitable for identification of evidence of electrical fire materials. These parameters were assessed using metallographic microscopy, X-ray diffraction, laser micro-Raman spectroscopy, scanning electron microscopy and energy-dispersive spectrometry. The grain size of AMMs was 20–40nm and that of CMMs was 20–35nm at a DC of 600A. The oxygen: copper ratio on the three types of regions of AMM surfaces displayed an inverted U-shaped with increasing DC. The oxygen: copper ratio on rough surfaces was <1.3, on smooth surfaces were <0.8, and in gas holes were <1.2. Furthermore, the ratio on longitudinal sections of CMMs showed a similar trend, and was <0.8. Copper (I) oxide appeared only on the surfaces of SSMs (secondary short-circuited melted marks).

Effects of Groundwater Exploitation on Embankment for High-speed Railway Lines

Groundwater exploitation will cause significant subsidence to the ground, then influence the deformation of embankment for high-speed railway lines, which may threaten the safety of train operation. To study the law of embankment deformation aroused by groundwater exploitation near high-speed railway lines, a 3D fluid-solid coupling model is established based on infiltrating solidification theory and using finite element software ABAQUS, and embankment deformations caused by different pumping rates and pumping distance are analyzed. The results show that pumping rate and pumping distance are both of great influence on the deformations of embankment for high-speed railway lines. Therefore, in order to control the effects of groundwater exploitation on embankment, it should be forbidden to add new pumping well near the railway lines and groundwater exploitation should be strictly limited within the influence scope.

Austenite dendrite morphology in lamellar graphite iron

Primary austenite has been underestimated in general when the theories of nucleation, solidification, microstructure formation and mechanical properties were established for cast iron and particularly for lamellar cast iron. The present work aims to investigate the primary austenite morphology of as cast samples of a hypoeutectic lamellar cast iron produced with different cooling rates. Morphological parameters as the area fraction primary austenite, the secondary dendrite arm spacing, the dendrite envelope surface, the coarseness of the primary dendrite expressed as the relation between the volume of the dendrite and its envelope surface and the coarseness of the interdendritic space also known as the hydraulic diameter are measured. Furthermore, the role of the size of the investigation area is revealed to be sequential investigation. A strong relation between all measured morphological parameters and the solidification time has been established, except the volume fraction of primary austenite, which is constant for all cooling conditions.

Freeze-cast alumina pore networks: Effects of freezing conditions and dispersion medium

Alumina ceramics were freeze-cast from water- and camphene-based slurries under varying freezing conditions and examined using X-ray computed tomography (XCT). Pore network characteristics, i.e., porosity, pore size, geometric surface area, and tortuosity, were measured from XCT reconstructions and the data were used to develop a model to predict feature size from processing conditions. Classical solidification theory was used to examine relationships between pore size, temperature gradients, and freezing front velocity. Freezing front velocity was subsequently predicted from casting conditions via the two-phase Stefan problem. Resulting models for water-based samples agreed with solidification-based theories predicting lamellar spacing of binary eutectic alloys, and models for camphene-based samples concurred with those for dendritic growth. Relationships between freezing conditions and geometric surface area were also modeled by considering the inverse relationship between pore size and surface area. Tortuosity was determined to be dependent primarily on the type of dispersion medium.

Structure, Growth Process, and Growth Mechanism of Perovskite in High-Titanium-Bearing Blast Furnace Slag

The isothermal crystallization of perovskite in TiO2-CaO-SiO2-Al2O3-MgO high-titanium-bearing blast furnace slag was observed in situ at 1698 K (1425 °C) using a confocal scanning laser microscope. The dendrite structure of perovskite (CaTiO3) thus obtained showed vividly the primary dendrite trunks and secondary dendrite arms. Furthermore, the dendritic growth of perovskite in liquid slag was clearly observed on line. The results showed that the dendrite arrays in which the primary dendrite trunks observed on slag surface were parallel with each other grew toward the same direction. The secondary dendrite arms grew in the perpendicular direction with the primary trucks and stopped growing when they encounter. The perovskite dendrites showed a linear growth at two stages. The dendrites grew faster at early stage at about 5 to 7 μm/s and grew with a lower growth rate at about 1 to 2 μm/s in later stage. Finally, the growth mechanism of perovskite in melt was analyzed with the solidification theory. Based on the theoretical calculation of equilibrium phases in slag, the initial slag could be considered as a binary component system. One component was perovskite and the other component was the sum of all the other species that did not attend the crystallization of perovskite (included SiO2, Al2O3, and MgO, as well as CaO and TiO2 that were not involved in the solid formation). The formation of perovskite required the diffusion of CaO and TiO2 to the solid/liquid interface and the rejection of the other species from the interface. The solid/liquid equilibrium schematic diagram was made based on the calculation.

The development of non-equilibrium solidification theories

In recent years, the non-equilibrium solidification technology is developing very fast while the designing of solidification processes still relies on classical theories and empirical relations, which can no longer satisfy the increasing need for controlling of solidification conditions. The classical solidification theories are based on several major assumptions, such as linear liquidus/solidus, ideal solution, local equilibrium and they usually focus on model alloys instead of real industrial concentrated multi-component alloys. The discrepancies between classical theories and practical conditions demand us to abandon these classical assumptions so that the solidification theories can be applied to industrial processes. The current paper reviewed the recent development of non-equilibrium solidification theories for single-phase solid solution alloys. For dilute binary alloys, the microscopic interface kinetics, interface stability, dendrite growth and the micro-macro overall transformation kinetics were reviewed and the significances of nonlinear liquidus/solidus were illustrated. For concentrated binary and multi-component alloys, the interface kinetics, interface stability and dendrite growth were reviewed with an emphasis on the importance of interaction between the components. The newly-developed non-equilibrium theories can give more accurate description of complicated solidification processes, thus promote the application of the solidification theories to industrial processes.

Effect of Temperature Fields Heterogeneity in the Tundish on Primary Structure of Continuously Cast Ingots

AbstractThe formation of the cast strands’ primary structure is a very complex process in terms of the thermodynamics and physicochemical. It occurs during solidification and crystallization of the liquid steel in the crystallizer and in the secondary cooling zone of the CC device. On the basis of the experience gained in the industry and knowledge arising from theory of metals and alloys solidification it can be concluded, that substantial influence on the shape of cast strands primary structure have the temperature of overheating of the liquid steel above liquidus temperature and solidification velocity. A proper control of those casting parameters allows to obtain the cast strands with desired primary structure. In the one and two-way symmetric devices regulation like this is not problematic, in the multi-way devices - specially in the asymmetric - causes a series of problems. In those devices can occur a major temperature difference in each outlet zone of the tundish working space caused by i.e. the distance length diversity of liquid steel stream from the inlet to each outlet and by disadvantageous layout of liquid steel flow zones (turbulent flow zone, plug flow and dead zones) in working area of tundish. Particularly high values of those diversity can be expected in the asymmetric tundishes.The article presents results of laboratory research - model and industrial regarding impact of the liquid steel overheating temperature, but also heterogeneity of the temperature fields in the tundish on primary structure of the cast strands.

Directionally aligned macroporous SiOC via freeze casting of preceramic polymers

A commercially available polysiloxane was used as a preceramic polymer for solution freeze casting to obtain directionally aligned porous silicon oxycarbide. We show how choice of solvent, polymer concentration, and freezing rate can affect the final pore network of the freeze-cast ceramic. Solvents of cyclohexane and camphene resulted in dendritic pores, while tert-butyl alcohol (TBA) produced intersecting cellular pores in the freeze-cast ceramic. Characterization of pore size distribution by mercury intrusion porosimetry of ceramics produced from cyclohexane–polysiloxane solutions with varying polymer concentrations and freezing rates demonstrated trends consistent with solidification theory. Fourier transform infrared spectroscopy and X-ray diffraction were employed to confirm that the freeze-casting process resulted in silicon oxycarbide of comparable chemistry and crystallinity to that produced via traditional preceramic polymer processing techniques.

Compressive behavior of concrete filled steel tubular columns subjected to long-term loading

Despite many successes in concrete creep studies, its effect on the mechanical behavior of concrete members is far from a thorough understanding. For the members subjected to a long-term loading, the classical stress–strain models for the short-term behavior of confined or uniaxially loaded concrete are not suitable. An experiment procedure was designed to investigate the effect of long-term loading on the compressive strength, modulus of elasticity, and stress strain of confined concrete. Eight concrete filled steel tubular (CFT) columns were prepared, four of which were subjected to constant compressive loadings for 411 days then unloaded, and the other four were companion load-free specimens. After two weeks of creep recovery, the specimens were axially loaded in compression up to failure. Based on the microprestress solidification theory for concrete creep and a plasticity model for concrete, an analytical model was presented to predict the behavior of CFT columns after creep. The comparison between the model predictions and the experimental results shows a good agreement. Both the experimental and theoretical results indicate that after creep the elastic modulus of CFT columns increased, while the compressive strength slightly decreases.

Study on Pressurized Solidification Behavior and Microstructure Characteristics of Squeeze Casting Magnesium Alloy AZ91D

Squeeze casting technology for magnesium alloys has a great application potential in automobile manufacturing and has received increasing attention from both academic and industrial communities. In this study, the pressurized solidification behavior of magnesium alloy AZ91D in squeeze casting process was investigated using computer-aided cooling curve analysis (CA-CCA). It was found that the applied pressure increased both the start and end temperatures of primary α-Mg formation but had little effect on the sizes of temperature ranges. Moreover, the applied pressure increased the start temperature and decreased the end temperature of eutectic reaction during the solidification, resulting in a larger temperature range of eutectic reaction compared with solidification under atmospheric pressure. The grains were remarkably refined, and the eutectic fraction increased with increasing applied pressure. The dendritic microstructure with a larger secondary dendrite arm spacing (SDAS) was observed under a higher applied pressure at the central part of the experimental casting. By correlating the CA-CCA and SDAS data, it was found that SDAS and the cooling rate at the maximum α-Mg growth could be fit into the power law equation in classic solidification theories.

A Phase-Field Solidification Model of Almost Pure ITS-90 Fixed Points

A two-dimensional axisymmetric phase-field model of thermo-solutal solidification in freezing-point cells used for calibrating standard platinum resistance thermometers for realization and dissemination of the International Temperature Scale of 1990 is presented. The cell is essentially a graphite crucible containing an ingot of very pure metal (of order 99.9999 %). A graphite tube is inserted along the axis of the ingot to enable immersion of the thermometer in the metal. In this study, the metal is tin (freezing temperature of \(231.928\,^{\circ }\hbox {C}\)). During the freezing of these cells, a steady, reproducible temperature is realized, with a defined temperature that can be used to calibrate thermometers with uncertainties \({<}1\) mK. The model is applied to understand the effect of experimental parameters, such as initiation technique and furnace homogeneity, on the measured freezing curve. Results show that freezing curves whose behavior is consistent with the Scheil theory of solidification can be obtained with a specific furnace temperature profile, and provided that the freeze is of a long duration, the results are consistent with previous one-dimensional models and experiments. Morphological instability is observed with the inner interface initiation technique, causing the interface to adopt a cellular structure. This elevates the measured temperature, in accordance with the Gibbs–Thomson effect. In addition, the influence of initiation techniques on the solidification behavior is examined. The model indicates that an initially smooth inner mantle can ‘de-wet’ from the thermometer well-forming agglomerated solid droplets, following recalescence, under certain conditions. This manifests as a measured temperature depression due to the Gibbs–Thomson effect, with a magnitude of \(100\, {\upmu }\hbox {K}\) to \(200\,{\upmu }\hbox {K}\) in simulations. The temperature rises to that of the stable outer mantle as freezing progresses and the droplets re-melt. It is demonstrated that the effect occurs below a critical mantle thickness. A physical explanation for the origin of the effect is offered showing that it is consistent with solid-state de-wetting phenomena. Consideration is also given to the limitations of the current model configuration.

Microprestress–solidification theory of concrete creep: Reformulation and improvement

Concrete creep is strongly affected by the evolution of pore humidity and temperature, which depend on environmental conditions and on the geometry of the concrete member. One advanced model accounting for such phenomena is the extended version of the B3 model referred to as the microprestress–solidification theory. It postulates a differential equation governing microprestress relaxation and generation of additional microprestress caused by changes of temperature and humidity. Here, this equation is rewritten in terms of viscosity, which leads to a reduction of the number of parameters and their easier identification. Based on numerical simulations it is shown that the evolution of mechanical strain measured in creep tests at constant and monotonically increasing temperature can be captured properly by the original microprestress–solidification theory, but certain deficiencies are detected for repeated temperature cycles. An improved version is proposed, identification of new parameters is discussed and good agreement with experimental data is demonstrated.

Containerless Processing in the Study of Metastable Solids from Undercooled Melts

An undercooled melt possesses an enhanced free enthalpy that enables to crystallize metastable solids in competition with their stable counterparts. Crystal nucleation selects the crystallographic phase whereas the growth dynamics controls microstructure evolution. We apply containerless processing such as electromagnetic and electrostatic levitation to containerlesss undercool and solidify metallic melts. Heterogeneous nucleation on container-walls is completely avoided leading to large undercooling with the extra benefit that the freely suspended drop is direct accessible for in situ observation of crystallization far away from equilibrium. Results of investigations of maximum undercoolability on pure zirconium are presented showing the limit of maximum undercoolability set by the onset of homogeneous nucleation. Rapid dendrite growth is measured as a function of undercooling by a high-speed camera and analysed within extended theories of non-equilibrium solidification. In such both supersaturated solid solutions and disordered superlattice structure of intermetallics are formed at high growth velocities. A sharp interface theory of dendrite growth is capable to describe the non-equilibrium solidification phenomena during rapid crystallization of deeply undercooled melts.

Micromodeling of the Diffusion‐Controlled Equiaxed Peritectic Solidification

Principles of the statistical solidification theory are used for the mathematical formulation of the micro‐diffusion field modeling during the equiaxed grain growth controlled by diffusion. It is proposed to use the Averaged Voronoi Polyhedron concept for the representation of the domain of elementary diffusion field. This approach is applied for the peritectic transformation modeling with the assumption of a partial mixing of the intercrystalline liquid phase. The results of the evolution of the volume fractions of the liquid, austenite, and ferrite phases during primary solidification and the peritectic transformation simulation are presented as well as carbon concentration distribution along the grain radius in the ferrite and liquid phase at the instant of initiation of the peritectic solidification and in the austenite at the moment of peritectic solidification termination.

Progress and development trends in the numerical modeling of solidification

The history of development and current situation of the theoretical description and numerical modeling of the solidification process are reviewed. The status and problems of the related research are discussed, with the main focus being on the solidification theories associated with microstructure formation and the concurrent macro-/microcoupling methods used to simulate solidification. Furthermore, the development trends of the theoretical description and numerical modeling of solidification are discussed.

Application of ridge regression and factor analysis in design and production of alloy wheels

This study proposes using statistical approaches to help with both the design and manufacture of wheels. The quality of a wheel is represented by the mechanical properties of spokes. Variation in the mechanical properties of different wheels is attributed to two sources, i.e. between-model variation and within-model variation. The between-model variation is due to different shapes of different wheel models. To model the effect of shapes on the mechanical properties, we first specify eight shape variables potentially critical to the mechanical properties, and then we collect relevant data on 18-wheel models and perform ridge regression to find the effects of these variables on the mechanical properties. These results are linked to the solidification theory of the A356 alloy. The within-model variation is due to natural variability and process abnormality. We extract mechanical data of a particular wheel model from the database. Factor analysis is employed to analyze the data with a view to identifying the latent factors behind the mechanical properties. We then look into the microstructure of the alloy to corroborate the fact that these two latent factors are essentially the Si phase and the Mg2Si phase, respectively. These results can be used to efficiently identify the root cause when the manufacturing process goes wrong.

Research on Cladding Process of Metal Powder during Laser Additive Manufacturing

The process of laser additive manufacturing consists of depositing successive layers of molten metal powder to create a near-net shape. A high-power laser is used to melt incoming metal powder, which forms a molten pool on the surface. As the latter moves beneath the laser, this newly created molten pool solidifies. By properly controlling the trajectory of deposition tracks, one can create a diverse range of shapes with varying complexities. In nature, the laser additive manufacturing technology is a continuous multilayer laser cladding process under the control of computer. The microstructure morphology of cladding layer is essential for the performance of as-deposited metal parts, so the cladding process was studied through related experiment. Based on the solidification theory, the microstructure morphology and the evolution rule were comprehensively analyzed. The results indicate that the temperature gradient and the solidification rate are the primary factor determining the microstructure morphology of cladding layer.

Numerical Analysis of Temperature Field of Co-Based Alloy Coatings by Laser Cladding on the Mild Steel

In order to analyze temperature field of Co-based alloys laser cladding, the model of Co-based alloys laser cladding with preset-powder method has been made by finite element method. The temperature field of coatings was analyzed by SYSWELD software, and Experimental verification is done. The results showed that temperature field changed from non-steady-state to steady-state in the laser cladding process. Favorable metallurgy bonding with 8.26% dilution was obtained by scanning velocity was 5 mm/s, the temperature gradient of surface coatings is obviously decreased to 1/20 of bonding interface, the solidification rate of surface is nearly 70 times of bonding interface. Right power with 1.6 kW and 1.87 kW was found when scanning velocity was 3 mm/s and 4 mm/s by SYSWELD software. Based on solidification theory, shape factor of crystallization are analyzed, these are consistent with experimental results. These results provide reference and guide for parametric optimization and control dilution rate of laser cladding. Key words: Laser cladding, Co-based alloy, SYSWELD, Simulation

Phenomenological model of nonequilibrium solidification

The maximum entropy production principle is used as a foundation for the nonequilibrium solidification theory. Based on this principle, a new simple model of dendrite solidification is proposed. The model predicts the explicit dependency of a dendrite’s rate and tip size on supercooling. The obtained results are devoid of the contradictions of the previous models and show quantitative agreement with the recent experimental data for the SCN dendrite.