Solidification Model Research Articles

Fast-throughput simulations of laser-based additive manufacturing in metals to study the influence of processing parameters on mechanical properties

Laser-powder bed fusion additive manufacturing (LPBF-AM) of metals is rapidly becoming one of the most important materials processing pathways for next-generation metallic parts and components in a number of important applications. However, the large parametric space that characterizes laser-based LPBF-AM makes it challenging to understand what are the variables controlling the microstructural and mechanical property outcomes. Sensitivity studies based on direct LPBF-AM processing are costly and lengthy to conduct, and are subjected to the specifications and variability of each printer. Here we develop a fast-throughput numerical approach that simulates the LPBF-AM process using a cellular automaton model of dynamic solidification and grain growth. This is accompanied by a polycrystal plasticity model that captures grain boundary strengthening due to complex grain geometry and furnishes the stress-strain curves of the resulting microstructures. Our approach connects the processing stage with the mechanical testing stage, thus capturing the effect of processing variables such as the laser power, laser spot size, scan speed, and hatch width on the yield strength and tangent moduli of the processed materials. When applied to pure Cu and stainless 316L steel, we find that laser power and scan speed have the strongest influence on grain size in each material, respectively.

Anomalous Mitigation in Phase Evolution Impacting Thermal Stability in a Rapidly Solidified AA5182 Al–Mg Alloy via Continuous Thin‐Strip Casting

This study, for the first time, reports an anomalous phase evolution and its impact on the thermal and oxidation behavior of rapidly solidified AA5182 Al–Mg alloy strip fabricated using a novel thin‐strip (TS) continuous casting technique. The microstructural analysis reveals a through‐thickness gradient microstructure of distinct types, morphology, and fractions of nonequilibrium Al–Mn–Fe intermetallic and Al–Mg eutectic phases. The rapid solidification experienced in TS casting effectively mitigates the formation of phases, particularly with the Al–Mg (β‐Al3Mg2) eutectic, being nearly absent from the near‐surface regions. The total fraction of formed phases is considerably lower than that in the slowly cooled direct‐chill counterpart. The solute macrosegregation also shows an inverse Mg segregation profile toward the strip surface primarily due to a higher degree of matrix supersaturation closer to the strip surface. Modeling of solidification successfully predicts the influence of cooling rate on the fractions of the nonequilibrium eutectic phase, agreeing well with the experimental data obtained from image analysis. Heat treating the samples over a broad temperature range unveiled unexpected improvements in oxidation resistance and excellent thermal stability, attributed to the absence of the eutectic β‐phase in subsurface regions. The research findings have practical implications for improving the properties of sheet Al–Mg alloys.

Isotropic discretization methods of Laplacian and generalized divergence operators in phase field models

Phase field models have been extensively used to address various physical phenomena. However, discretization-induced anisotropy remains a longstanding challenge for phase field models. By using a hexagonal mesh in 2D, we describe isotropic discretization methods for the computation of Laplacian and generalized divergence operators. Quantitative analyses derived from discrete Fourier analysis prove that our methods are more isotropic than commonly used approaches, including isotropic methods for square mesh. To compare the performance of conventional and our discretization methods, a specific phase field model of alloy solidification was selected to perform benchmark simulations. Various 2D simulations using different discretization methods were carried out to verify the accuracy and efficiency of the improved numerical methods in a hexagonal mesh. We emphasize that the improved numerical methods using a hexagonal mesh are general and may be equally applied to other physical models that include the same operators.

Modeling of solidification via Galerkin method within storage unit utilizing nano-powders incorporating unsteady source term

The employed numerical method, which incorporates nanomaterial and fins, represents a noteworthy advancement in simulating enhanced freezing processes. This technique leverages an adaptive grid approach, providing a sophisticated framework for estimating the characteristics of the nanomaterial. A key innovation lies in considering the final material as a homogeneous mixture. Notably, the exclusion of gravity's influence on the freezing process, leading to the omission of velocity terms, adds to the precision of the model. This approach holds substantial promise for a range of applications requiring controlled and efficient freezing. The study's significance lies in its potential to revolutionize freezing technologies, offering improved outcomes across various industrial contexts. The analysis's physical outputs, demonstrating notable reductions in completion time, further underscore the method's efficacy in enhancing freezing processes. The Finite Element Method (FEM) has been employed to obtain a comprehensive solution, allowing for an assessment of the effect of the shape factor “m” and nanoparticle concentration (ϕ) on the freezing process. Notably, the introduction of nanoparticles leads to a significant acceleration of the process, resulting in a remarkable 26.77 % reduction in completion time. This finding underscores the crucial role that nanoparticle dispersion plays in enhancing the efficiency of the solidification process. This insight holds substantial promise for applications where controlled and rapid freezing is paramount. The choice of particles with higher “m” values leads to an enhancement in the conduction mode. Consequently, this results in a nearly 7 % reduction in completion time, demonstrating the efficiency of this selection. The fastest process achieves solidification in a mere 538.98 s, while in the absence of nanomaterial, the process with water alone takes significantly longer at 975.69 s. This showcases the substantial improvement that can be achieved with the incorporation of nanoparticles. This information is vital for industries where rapid, controlled solidification is critical.

Trace elements in IVA iron meteorites explained by limited solid–liquid equilibration during inward solidification

Iron meteorites are windows into the formation and evolution of planetesimal cores. The trace element compositions of IVA iron meteorites are enigmatic; specifically, to explain the fractionations of different elements requires various sulfur contents of the parent liquid. Here, we propose a possible solution to this problem. IVA irons are thought to sample an exposed core that underwent inward solidification. In an inward solidifying core, sulfur-rich liquids expelled by crystallization are buoyant and stably stratified in the interstices of the mushy solidification front, until they eventually solidify at the eutectic point. Solidification proceeds through in-situ dendritic crystallization of mushy parcels of identical compositions, with the absence of chemical fractionation. In order for fractionation to take place, “pristine” liquids must flow into the mushy front and react with solids, which would be possible if circulation is driven by external forcing, for example, collisions. In this picture, the fluid exchange (which enables fractionation) is driven by occasional events, and each incremental solid can react with only a limited amount of liquid during solidification. We develop a simple model to describe the fractionation associated with this limited solid–liquid equilibration. With this model, we can explain the concentrations of different elements satisfactorily with a single sulfur content (∼5wt%) of the IVA iron parent liquid. Assuming that the stirring is caused by collisions to the solidifying body, we combine the new model for element fractionation with a model for solidification (as a Stefan problem) to suggest a frequency on the order of once per few thousand years for collisions that are large enough to cause the required stirring.

Multiphase Solidification Modeling of Solidification Structure Evolution and Macrosegregation of Round Bloom Continuous Casting Process with Mold Electromagnetic Stirring and Final Electromagnetic Stirring

Based on Eulerian–Eulerian method, a 3D/2D multiphase solidification model, which takes into consideration the heat transfer and fluid flow with grains nucleation and crystal growth, is developed to predict the macrostructure evolution and macrosegregation in continuously cast round bloom. The results show that the mold electromagnetic stirring (M‐EMS) can accelerate superheat dissipation and promote grain nucleation, but the horizontal swirl induced by M‐EMS has a strong washing effect on the solidification front and leads to subsurface negative segregation. When the M‐EMS current intensity increases from 200 to 300 A, the subsurface negative segregation ratio decreases from 0.935 to 0.875. The final electromagnetic stirring (F‐EMS) not only improves the center segregation, but also leads to the formation of negative segregation zone near the round bloom center due to the enhancement of solute washing induced by F‐EMS. As the F‐EMS current intensity increases from 150 to 300 A, the center segregation ratio decreases from 1.148 to 1.075, and the negative segregation ratio near the strand center decreases from 0.985 to 0.977. Another phenomenon is found that the nucleation of equiaxed grain ahead of columnar tips restrains the solute diffusion and leads to a local macrosegregation in columnar‐to‐equiaxed transition zone.

Influence of multi-walled carbon nanotubes on the solidification process of an Al-12 %Si alloy

This paper investigates the influence of multi-walled carbon nanotubes (MWCNT) on the solidification process of an Al-12 %Si alloy. Amulti-phase Eulerian model of solidification is deployed to numerically handle the problem. The simulation determines the cooling curve and addresses the recalescence phenomena along with the estimation of the columnar and globular solid phases;precipitating silicon (PSP) phase and MWCNT phase distributions. The findings reveal that MWCNT significantly affects the cooling rate, leading to multiple recalescence phenomena, and influences the formation and evolution of the columnar and globular grains. MWCNT also impacts silicon segregation, causing fluctuations in silicon phases and redistribution. Furthermore, the study explores the distribution of MWCNT throughout the material and identifies a critical time period for their influence. Overall, the study enhances our understanding of the complex dynamics within the solidification process and provides insights into the role of MWCNT in shaping the microstructure through a mathematical model.

Research on Simulation of Coating Fusion and Solidification Process in Electro-Spark Deposition

As a surface-strengthening technology, electro-spark deposition (ESD) is widely used in the strengthening and repair of key components of high-end equipment. In this paper, a fusion and solidification model of ESD coating is established. The method of heat–fluid–solid interaction is adopted to simulate the material’s flow and fusion process in the droplet dropping into the molten pool. The distribution law of the coating-matrix material inside the coating was studied. Through the heat transfer between the molten material and the matrix material, the condensation and solidification process of the coating-matrix material is simulated, the temperature change in the coating area during the solidification process is analyzed, and the solidification law of the molten material is studied. The results show that the deposition time reaches 80 μs, and the content of electrode material at the bottom of the molten pool reaches 4.5%. The content of electrode material in the upper region of the material gushing out of the molten pool is higher than that in the bottom region. The material outside the molten pool solidifies first, and the molten material in the molten pool gradually solidifies from the bottom up; the shape of the solidification interface is similar to the boundary of the molten pool. Through the single-point deposition experiment of electro-spark deposition, the surface morphology of the deposition point was observed. The depth of the concave part of the contour can reach 16 μm. The difference between the two contour curves in the horizontal direction is not much; the error of the diameter is about 4%. The element distribution of the surface and the section of the deposition point are analyzed. The diffusion distance in the depth direction of the coating is about 4μm, and the transverse diffusion distance inside the coating is 364 μm. The error is 7.6% compared with the experimental results. The cross-section structure of the deposition point was observed, and the error between the experimental results and the simulation results in diameter is about 11%. It was found that the material distribution in the sedimentary area is basically consistent with the simulation results, and the simulation results are verified from the side.

Mesoscale Modeling of Extrusion and Solidification During Material Extrusion Additive Manufacturing

In this work, we apply a multiphysics approach to fused deposition modeling to simulate extrusion and solidification. Restricting the work to a single line scan, we focus on the application of polylactic acid. In addition to heat, momentum and mass transfer, the solid/liquid/vapor interface is simulated using a front-tracking, level-set method. The results focus on the evolving temperature, viscosity, and volume fraction and are cast within a set of parametric studies, to include the printing and extrusion speed, as well as the extrusion temperature. Among other findings, it was observed that fused deposition modeling can be effectively modeled using a front-tracking method (i.e. the level set method) in concert with a temperature dependent porosity function. The use of the level-set method for discriminating the phase change interface in this context is relatively new and offers considerable advantages over existing methods.

Gas entrapment and pore formation in metal droplet-based 3D printing

Gas entrapment behavior during metal droplet deposition tends to form pore defects and discourages interfacial bonding between droplets, resulting in lower densities and poorer performance of printed components. Moreover, the gas entrapment process is influenced by the interaction of gas-liquid two-phase flow and non-isothermal solidification, which makes the interfacial behavior of droplets challenging to identify. Therefore, gaining insight into the gas entrapment behavior and pore formation mechanism at the bottom of molten droplets is essential. This paper established a model of two-dimensional axisymmetric numerical by combining the fluid volume tracking method and heat transfer solidification model. Single metal molten droplet deposition experiments verified the accuracy of the model. The evolution of solid phase fraction, velocity field, pressure field, and contact surface heat flux during the deposition of the molten droplet at low Weber numbers (0.1-10) was investigated comprehensively. The mechanisms of gas entrapment and pore formation were revealed. The effects of molten droplet impact velocity, contact angle, and surface tension on the gas film evolution process and pore morphology were further investigated. The results show that decreasing the droplet impact velocity causes capillary waves to contact the substrate surface and form local solidification, allowing the gas disk to evolve into central and two peripheral pores. Moreover, the pore breaks away from the substrate and remains inside the droplet when decreasing the droplet contact angle to 50°. Furthermore, the rate of gas disk retraction decreases as surface tension reduces, which may accentuate the resistance effect of the contact surface solidification layer on the gas disk retraction, thus changing the final morphology of the pores. These findings elucidate the mechanism of pore formation at the bottom of molten metal droplets and further understand the interfacial behavior of droplets in 3D-printed metal structures.

Simulation of a sessile nanofluid droplet freezing with an immersed boundary-lattice Boltzmann model

The freezing process of a sessile nanofluid droplet has been reported to behave differently from a pure sessile water droplet in terms of freezing dynamics and the final shape of the ice droplet. When nanoparticles are added to the water droplet, instead of forming a pointed tip on the top, the completely frozen droplet exhibits a flat plateau shape. To investigate this unique scenario, we developed a lattice Boltzmann (LB) model that combines the multiphase solidification model (MSM) with the immersed boundary method (IBM). The MSM is based on our previous work of simulating the freezing of a pure droplet, while the IBM is used to handle the interaction forces between the suspended particles and the different phases in the freezing droplet. Using this LB model, we succeeded in simulating the formation process of the frozen plateau shape. The simulation takes into account the dynamics of the dispersed particles, including their expulsion from the propagation freezing front and their segregation, which brings the liquid water to the edge. We compared the simulated freezing shape profiles with the experimental images and found that the shape forms in a similar manner. We then used the developed model to explore more cases, considering the effects of droplet contact angles and particle volume concentration. Results show that the distribution of particles and final droplet height depend on the surface wettability, as the freezing front exhibits a concave/convex shape on hydrophilic/hydrophobic surfaces, resulting in different particle separation distributions on the freezing front interface. Furthermore, our simulation results confirm the experimental conclusion that the plateau size on the frozen top increases with particle concentration and appears to be independent of the initial droplet contact angle.

Review of the modeling approaches of phase change processes

In recent years, phase change materials have played an important role in the field of energy storage because of their flexibility and high efficiency in energy storage and release. However, most phase change processes are unsteady and highly nonlinear. The ways to obtain exact solutions are urgently needed. This study first summarizes the principles and characteristics of different methods to solve the phase transition process, including analytic methods, numerical methods, and CFD numerical methods. After that, the advantages of employing CFD software to simulate the phase change process are discussed, and the solidification and melting models in FLUENT are introduced. In particular, the influences and weights of natural convection and nanoparticles on the solidification/melting processes are revealed and enumerated in detail. Finally, the challenges and future developments in the solution methods, theoretical models, and numerical simulation applications of phase change materials are prospected. This review shows that most of the phase change heat transfer problems are solved by numerical methods. FLUENT is high-precision software commonly used in CFD software, its solidification and melting model is convenient to simulate the phase change process. Both natural convection and nanoparticles can shorten the melting time of phase change materials.

Study on the Effect of SEMS on the As-Cast Structure of Steel in Thin Slab Continuous Casting Using an Equiaxed-Columnar Solidification Model

Study on the Effect of SEMS on the As-Cast Structure of Steel in Thin Slab Continuous Casting Using an Equiaxed-Columnar Solidification Model

Model for particle capture by the solid-liquid interface during solidification of metal matrix nanocomposites

A sharp-interface model for solidification of nanocomposites with nanoparticle-interface interaction is presented. The main novelty of the work is that the engulfment or non-engulfment of nanoparticles is modelled as a function of the local interface velocity and a particle size-based critical velocity. This is incorporated through a variable partitioning coefficient while solving the nanoparticle conservation equation which is modelled similar to an alloying constituent. The movement of nanoparticles is governed by nanoparticle-interface interaction and by diffusion due to Brownian motion. The model couples a sharp-interface solidification model, species transport model and nanoparticle transport model. Thus, the engulfment and the resultant distribution of nanoparticles in the solidified region can be predicted for different combinations of initial undercooling and nanoparticle size. The effect of accumulated nanoparticles on the solute transport and solidification rate is also included in the model. Results show that the engulfment of smaller nanoparticles is very low resulting in high accumulation near the interface. This results in a high restriction to solute diffusion and solidification. Combined variation of initial undercooling and particle size shows that the average engulfment values for initial undercooling of 0.3, 0.5, and 0.7 are 2.75 %, 7.75 % and 21.50 % for r* = 0.1, 15.5 %, 53.5 %, and 82.5 % for r* = 0.5, and 38.0 %, 77.75 %, and 93.25 % for r* = 0.9. Thus, the engulfment of nanoparticles into the solid improves with increase in nanoparticle size and with the increase in solidification rate.

Shear Strength Behaviors of Aeolian Sand Solidified by Microbially Induced Calcite Precipitation and Basalt Fiber Reinforcement.

Aeolian sand flow is identified as the main factor in the formation of sandstorms. However, conventional sand fixation methods cannot meet the current development requirements of environmental protection. In this paper, the method using Microbially Induced Calcite Precipitation (MICP) combined with basalt fiber reinforcement (BFR) was adopted to solidify the aeolian sand. Consolidated undrained triaxial shear tests were carried out to analyze the influence of fiber content, fiber length, confining pressure, and other factors on stress-strain characteristics, peak strength, brittleness index, and shear strength of aeolian sand. A shear strength model of aeolian sand solidification using MICP-BFR and considering the effect of fiber length and fiber content is established according to the test results. The results show that the peak strength of aeolian sand solidified by MICP-BFR is remarkably higher than that of aeolian sand solidified by MICP alone, and the peak strength rises with the increasing fiber length, fiber content, and confining pressure. The application of fiber can effectively reduce the brittleness index of aeolian sand solidified by MICP and improve the sample ductility. As fiber content and fiber length increase, the cohesion of solidified aeolian sand increases while the internal friction angle changes relatively little. In the limited range set by the test, the fiber length of 12 mm and the fiber content of 1.0% constitute the optimum reinforcement condition. The test results coincide with the model prediction results, indicating that the new model is fitting for predicting the shear strength of aeolian sand solidified by MICP-BFR. The research results provide an important reference value for guiding the practice of wind prevention and sand fixation in desert areas.

On the primary silicon precipitation during the eutectic solidification of Al–Si alloys

During the Al–Si eutectic alloy solidification, silicon distribution throughout the melt is not homogeneous which causes silicon segregation. A four phase Eulerian model of solidification is developed and invoked in Ansys Fluent simulation software to track the silicon segregation location and to understand the distribution of the segregating silicon in the Al–Si metal matrix. The recalescence phenomena are also observed during the solidification process. It is found that the silicon segregation is nearly 1.08 volume %, and the silicon is mostly found near the top surface of the simulation domain. It is also revealed through the numerical simulation that the columnar solid phase grains grow rapidly towards the center of the casting in the early stage of the solidification and the segregating silicon phase is generated near the columnar phase. However, the globular solid phases are also observed at the center of the simulation domain. The above numerical predictions are satisfactorily validated with the in-house experiment conducted using a specific alloy known as eutectic Al–Si (LM6).

Comparative analysis of the thermal behavior of blooms and beam-blanks during continuous casting: Development and validation of a mathematical model for heat transfer

The present work explores the feasibility of producing blooms and beam blanks in a continuous casting machine using a single support rollers setup, aiming to eliminate the need for specialized setups for each geometry. The current practice requires frequent roll replacements during production switches, leading to reduced machine availability and safety risks.To assess the viability of the new approach, a 2D mathematical model for heat transfer and solidification was developed for both blooms and beam blanks. Simulations with the current and the new setup were performed, and their results analyzed. The model was validated with experiments during production campaigns at the steel melting shop. The model accurately predicts the casting process, with solid fraction deviation of 6% for blooms and 16% for beam blanks, and temperature difference between the model and thermal imaging measures values are between 20 °C and 70 °C.The heat transfer simulation results show that a single rollers setup can yield minimal variations in the temperature related operational parameters, supporting the feasibility of this approach. In addition to the thermal analysis performed in this work, mechanical stress and strain assessments need to be performed to further investigate the suggested solution and they will be the topic of future works.The findings provide valuable insights for the steel industry, as this type of feasibility study is a relatively unexplored area. Furthermore, the models developed can also be used to optimize process parameters, study defects formation during continuous casting and in the development of new products.

Structure and diffuseness model of solid-liquid interface for binary alloys

Using the morphological instability at the solid–liquid interface as a basis by the maximum entropy production rate principle (MEPR), a model is presented on the morphological structure and diffuseness of the interface during directional solidification of binary alloys. It is shown that, the independent diffuseness theory of Cahn and the Jackson roughness criterion can be unified at a limiting condition under this new MEPR solidification model. The model under the principle of MEPR is applied to describe the evolution of atomistically smooth and rough interfaces through the evaluation of the size of the solid–liquid interface and the of number atomic layers. The model is tested with data for binary alloys of aluminium, lead, and tin at varying solute concentrations. The results showed strong agreement with available data from experimental measurements.

Study on Flight Dynamics and Heat Transfer Solidification of Metal Droplets during Centrifugal Spray Deposition Forming Process

Centrifugal spray deposition forming technology, which is used in the preparation process of near-net-forming billets, not only reduces the macroscopic segregation and refines the microstructures of billets but also has the characteristics of a rapid solidification structure. The trajectory, velocity, heat transfer and solidification of metal droplets granulated by the centrifugal force during flight will affect the shape, precision and microstructure of the billet. Therefore, it is necessary to study the dynamics and thermal history of droplets in flight. In this study, a single droplet is taken as the object. Considering the resistance of ambient gas, Newton’s second law, classical nucleation theory, Newton’s cooling law and the energy conservation equation were used to establish a dynamic model and heat transfer solidification model of liquid metal droplets during flight. The influence of the centrifugal disc speed on the diameter of granulated droplets was analyzed. The variation law of droplet flight trajectory and velocity was explored. The supercooling degree in metal droplet nucleation was quantified, and the influence of droplet diameter, superheat and other factors on heat transfer and solidification was revealed. The results show that the numerical calculation results are basically consistent with the previous research results. The trajectory of the droplet is parabolic during flight. The initial velocity of the droplet, the environmental gas resistance and the convective heat transfer coefficient are positively correlated with the rotating speed of the centrifugal disc; however, the droplet diameter is negatively correlated with the rotating speed of the centrifugal disc. The super cooling degree at the time of droplet nucleation and the flight time required for solidification are negatively correlated with the droplet diameter. Among them, the droplet diameter has a linear relationship with the solidification start time and a quadratic curve relationship with the solidification end time. The effect of superheat on the heat transfer and solidification of droplets is not obvious. The conclusions obtained can provide a theoretical basis for the determination of the preparation process parameters.

Effect of electromagnetic stirring on the transient flow, solidification and inclusion movements in the continuous casting slab mold

PurposeThe purpose of this study is to explore how a time-varying electromagnetic stirring (EMS) affects the fluid flow and solidification behavior in a slab caster continuous casting mold. Further, the study of inclusion movements in the mold is carried out under the effect of a time-varying electromagnetic field.Design/methodology/approachA three-dimensional coupled numerical model of solidification and magnetohydrodynamics has been developed for slab caster mold to investigate the inclusions transport by discrete phase model with the use of user-defined functions. Enthalpy porosity and the Lagrangian approach are applied to analyze the behavior of solidification and inclusion.FindingsThe study shows that the magnetic field density distribution has a radial symmetry in relation to the stirrer’s center. As the EMS current intensity increases, the strength of the lower recirculation zone gradually decreases and nearly disappears at higher intensities. Additionally, the area of localized remelting zone expands in the solidification front with rising current intensity. The morphology of inclusions and EMS current intensity have a significant impact on the behavior and movement of inclusions within the molten steel.Practical implicationsBy using the model, one can optimize the EMS parameter to enhance the quality of steel casting through the elimination of impurities and by improving the microstructure of cast that mainly depend on solidification and flow patterns of molten steel.Originality/valueUntil now, the use of time-varying EMS in the slab caster mold to study solidification and inclusion behavior has not been explored.