Mushy Zone Research Articles

Modeling Dendrite Coarsening and Remelting during Directional Solidification of Al-06wt.%Cu Alloy.

Research efforts have been dedicated to predicting microstructural evolution during solidification processes. The main secondary arm spacing controls the mushy zone's permeability. The aim of the current work was to build a simple sub-grid model that describes the growth and coarsening of secondary side dendrite arms. The idea was to reduce the complexity of the curvature distribution with only two adjacent side arms in concurrence. The model was built and applied to the directional solidification of Al-06wt%Cu alloy in a Bridgman experiment. The model showed its effectiveness in predicting coarsening phenomena during the solidification of Al-06wt%Cu alloy. The results showed a rapid growth of both arms at an earlier stage of solidification, followed by the remelting of the smaller arm. In addition, the results are in good agreement with an available time-dependent expression which covers the growth and coarsening. Such model can be implemented as a sub-grid model in volume average models for the prediction of the evolution of the main secondary arms spacing during macroscopic solidification processes.

Prediction of the Secondary Arms Spacing Based on Dendrite Tip Kinetics and Cooling Rate.

Secondary dendrite arm spacing (SDAS) is one of the most important factors affecting macrosegregation and mechanical properties in solidification processes. Predicting SDAS is one of the major parameters in foundry technology. In order to predict the evolution of microstructures during the solidification process, we proposed a simple model which predicted the secondary dendrite arm spacing based solely on the tip velocity (related to the tip supersaturation) and cooling rate. The model consisted of a growing cylinder inside a liquid cylindrical envelope. Two important hypotheses were made: (1) Initially the cylinder radius was assumed to equal the dendrite tip radius and (2) the cylindrical envelope had a fixed radius in the order of the dendrite tip diffusion length. The numerical model was tested against experiments using various Pb-Sn alloys for a fixed temperature gradient. The results were found to be in excellent agreement with experimental measurements in terms of SDAS and dendrite tip velocity prediction. This simple model is naturally destined to be implemented as a sub-grid model in volume-averaging models to predict the local microstructure, which in turn directly controls the mushy zone permeability and macrosegregation phenomena.

Exploring mushy zone constant in enthalpy-porosity methodology for accurate modeling convection-diffusion solid-liquid phase change of calcium chloride hexahydrate

Mushy zone constant (Am) is a crucial parameter in the momentum source term of enthalpy-porosity technique for modeling convection-diffusion solid-liquid phase change. Literature survey on the computations of Am found that the oriented customizable approaches have not revealed it in detail. Although the literature conducted an attempt on Am relationship by investigating the unconstrained melting of Calcium Chloride Hexahydrate (CaCl2·6H2O), they failed to directly establish the correlation between Am and ΔT; where ΔT is the driving temperature difference, which denotes an excess temperature of the hot wall above melting point of the CaCl2·6H2O. In view of the shortcoming in the literature, the relationship between Am and ΔT is here explored by the dimensionless analysis of the CaCl2·6H2O melting. The analysis finds a perfect correlation of dimensionless mushy zone constant (A) in terms of Grashof number (Gr) and Stefan number (Ste), i.e., A=Gr0.639Ste−2.947. Hence, a quick calculating method concerning Am values is established successfully. Then, the numerical verifications and validations for Am values implemented in enthalpy-porosity model are carefully taken into account. In addition, the theoretical reasonability is confirmed for the extrapolated Am values, and two interesting solid shapes of “Cap” and “Umbrella” are presented. Considering all of the applicable conditions herein, a generalized expression for melting fraction vs. dimensionless time is finally proposed.

The Role of Solidified Phases on the Hot Cracking of a Large-Size GH4742 Superalloy Ingot.

The effect of solidified phases on the hot cracking behaviour of a large-size GH4742 superalloy ingot produced using vacuum induction melting (VIM) is investigated in order to improve the quality of the final product. The results show that the solidification order of the ingot is γ matrix, MC carbide, η phase and γ' phase. Among them, the MC carbide and the η phase solidified in the mushy zone. The volume fraction of both the η phase and the MC carbide in the cracked zone is higher than that in the non-cracked zone, and a significant number of η phases are distributed near the hot cracks. The formation of solidified phases not only induces stress concentration at η phase/γ matrix interfaces but also reduces the ability of liquid feeding during solidification, thus promoting hot crack formation. It is believed that by controlling the segregation degree of both Nb and Ti, the volume fraction of η phases and MC carbides can be reduced to prevent hot cracking of the GH4742 superalloy VIM ingot.

Climate related phase transitions with moving boundaries by virtue of mushy zone investigation in Al–Cu: Experiment and phase‐field modeling

Studying Arctic ice formation stays in the focus of research groups over the past decades in the context of ice cover changes, thermal budget and climate agenda in general. Nevertheless, the phenomenon's underlying mechanisms are still not completely understood and described. The main reason for the lack in understanding is the limited experimental access to the field data when it comes to the processes that occur below the ice floe. Thus, there is a need to build competent analogies between the natural (ocean water–ice) and laboratory (here: binary alloy) conditions of the experiment as a step of data preparation for the verification of the mathematical model. In the current paper, the existing qualitative models describing the process of melting and crystallization were expanded and the experimental method was developed copying the layering of the natural ocean water–ice mixture. The experimental set‐up for studying the solidification within the intermediate zone was designed for Al–Cu alloys being the system with appropriate solidus line for creating a sufficient concentration gradient and by that temperature dependent phase fraction under isothermal conditions. The gained experimental data were used for validating a binary phase‐field model for solidification considering moving boundaries. The model includes the description of the free energy of both phases and their respective diffusion coefficients. It allows modeling a binary system at a mesoscopic spatial level by including the concentration‐driven phase transition and resolidification in the two‐phase region. The novel results will help the quantitative understanding of solidification phenomena and are highly‐evaluated from interdisciplinary point of view, including glaciology and geosciences, being ultimately significant for the understanding the global climate change landscape.

Motion Behavior of Ce‐Containing Inclusions in 8Cr4Mo4V‐Bearing Steel during Vacuum Arc Remelting

Herein, the Ce‐containing inclusions in8Cr4Mo4V‐bearing steel are taken as the research objective to develop anumerical model of inclusions motions behavior. The model is validated bycomparing it with experimental data. During the vacuum arc remelting process, inclusions move along the molten pool's surface toward the edge under theaction of resultant force, and finally become trapped within the mushy zone. Notably, the majority of inclusions are concentrated near the ingot's edge, andtheir numbers decrease as the radial distance decreases. Furthermore, thenumber of Ce‐Mg‐O‐S inclusions exceeds that of Ce‐O‐S inclusions near the ingot's center. This discrepancy arises due to lower density of Ce‐Mg‐O‐Sinclusions, which exhibits a stronger tendency to migrate toward the moltenpool's center. Additionally, as the inclusion diameter increases, buoyancy forceacting on the inclusions increases, resulting in a higher number of inclusionsnear the ingot's center. When considering the effect of gas cooling, theinclusion distribution becomes more pronounced at the ingot's edge. This isattributed to the enhanced cooling capacity of the mold resulting in the decreasing of molten pool depth and consequently a stronger ability of themushy zone to trap inclusions.

Multi-scale and multi-physics simulation of central segregation in an equiaxed dendritic mushy zone during continuous casting of steel

Centreline segregation during continuous casting of steel is highly detrimental to the end-product mechanical properties. In this study, a 3D multi-scale and multi-physics model is developed and validated that directly predicts alloy segregation occurring in peritectic steel grades having centreline equiaxed grain morphology. The model consists of four models: (1) a 1D macroscale heat transfer and solidification model, (2) a 3D mesoscale dendritic solidification model, (3) a 3D mesoscale dendritic fluid flow model, and (4) a 3D mesoscale solute transport and redistribution model. The use of a mesoscale domain where the solid and liquid phases are separately discretized allows for consideration of physical phenomena affecting segregation that are classically hidden by the averaging procedures of fully continuum approaches. Thus the new model is able to account for the multiple phenomena occurring during continuous casting while also directly considering the stochastic effects resulting from grains having randomly-placed nuclei as well as interactions between the liquid and solid phases. The results demonstrate that solute partitioning combined with intra-dendritic fluid flow leads eventually to liquid channels enriched with solute that result in centreline segregation. The predicted composition in these discrete liquid channels shows excellent agreement with a Mn centreline segregation profile experimentally-measured via microscopic X-ray fluorescence of a commercially-cast steel slab. Finally, the effects of alloy composition, and soft reduction on the degree of centreline segregation are examined.

A step-by-step thermo-elastoplastic analysis of laser beam welding

In recent years, laser beam welding has emerged as a significant contact-free fusion method due to its advantages such as high laser advance speed and minimal thermal distortion. Automation further increases its attractiveness in various industries. However, specific conditions related to temperature gradient, chemical composition, welding speed and mechanical boundary conditions can lead to solidification cracks. These cracks originate from microcracks within the weld and occur during solidification. The mushy zone is particularly prone to solidification cracking due to the dendritic morphology and entrapped liquid phases. To address this problem, this study makes a step-by-step approach using finite element simulations on the macro- and microscale. It first locates the mushy zone macroscopically using a heat source model and then analyzes the evolving dendritic microstructure at the microscopic level in a simplified manner, considering thermal and elastoplastic effects. This enables a more thorough understanding of the critical states at micro- and macroscale which may lead to solidification cracking.

Lattice Boltzmann simulation of the Prandtl number effect on the phase change heat transfer of wax in pipeline

Thermal washing is a common method of wax removal in oil fields. The law of phase change heat transfer of wax during the thermal washing process is revealed to be of great significance for improving the melting rate of wax. The lattice Boltzmann method is used to numerically simulate the process of phase change heat transfer in pipe-lines with different angles (90?, 45?, 0?, ?45?, and ?90?) of wax layers based on the enthalpy-porous medium model in the present work. The boundary condition between wax and hot water is considered as convective heat transfer boundary. The effect of the Prandtl number on the law of phase change heat transfer of the wax at various angles is investigated. The simulation results indicate a non-linear decrease in the complete melting time of the wax layer from ?90? to 90?. The heat transfer capacity is enhanced with the decrease of Prandtl number, which effectively shortens the melting time of wax. The complete melting time of the wax layer is reduced by 23.78% when the Prandtl number decreases from 79.4-59.4. The speed of convective heat transfer is increased with the decrease of Prandtl number, which means that the solid zone of wax is accelerated into the loose and porous mushy zone, and the efficiency of wax removal is improved. The research results can provide a reference for improving the efficiency of thermal washing.

Effect of static magnetic field on the molten pool dynamics during laser powder bed fusion of Inconel 718 superalloy

Recent researches show that a static magnetic field (SMF) has an impact on the molten pool dynamics and microstructure of laser powder bed fusion (L-PBF). This work is intended to the multiple effect of SMF on the molten pool dynamics during L-PBF of Inconel 718 superalloy. A three-dimensional (3D) multiphase computational fluid dynamics (CFD) model at the powder-bed scale was established by coupling the electromagnetic braking and Seebeck effect in a static vertically-distributed magnetic field. Results show that the magnetic damping force (MDF) of the order of 104 N/m3∼105 N/m3 within the whole molten pool suppresses the Marangoni convection. The thermoelectric magnetic force (TEMF) of the order of 106 N/m3∼107 N/m3 rotates in the mushy zone and further enhances the melt flow of the whole molten pool. The SMF will not transform the flow pattern and temperature distribution in the molten pool. SMFs of 0.1 T and 0.3 T will suppress the melt flow, while that of 0.5 T will enhance the melt flow. The width of molten pool first decreases and then increases when the magnetic flux density (MFD) increases from 0 T to 0.5 T. In addition, applying a SMF of 0.3 T can effectively inhibit pore defect and spatters. This work can provide insight into the control of molten pool by introducing a SMF during L-PBF.

A novel two-dimensional continuum mixture theory model for paraffin wax melting in a cavity heating from side considering volume change

Paraffin wax presents a considerable potential for thermal storage technologies, given its high latent heat. Therefore, the accurate and systematic modeling of its melting process bears significant importance. Yet, existing mathematical models fail to adequately address the velocity driven by the density change during the melting process. In this research, we introduce a novel model for paraffin wax melting within a square enclosure subject to side heating. Unlike current models, our approach posits that flow within the mushy zone is dictated by the mass equation, not Darcy’s equation, and thus excludes the usage of mushy zone constant. This assumption, premised on the idea that the density-deviation-driven flow precludes the bulk flow from penetrating the mushy zone, is confirmed through a carefully designed visual experiment. Utilizing our melting model, we construct a mathematical model anchored in the continuum mixture theory. Through a comparative analysis of results acquired by numerical methods and experimental data, we find that our innovative mathematical model effectively predicts real-world scenarios with remarkable precision. Furthermore, we explore the influence of flows within the mushy zone on the melting process. Our findings indicate a significant deviation in results when assuming zero velocity in the mushy zone, suggesting that the density-deviation-driven flow is numerically negligible. However, it is crucial to note the physical relevance of the density-deviation-driven flow in accurately predicting the melting process. The absence of this consideration allows the bulk flow in the liquid region to permeate the mushy zone, thereby introducing substantial errors.

Numerical simulation on the coupling of the elliptical particle motion and phase change

The particle sedimentation and phase change in the mushy zone are accompanied by a variety of complex transfer processes involving momentum, heat, and mass. It is very important to investigate the coupling process of particle settling and melting in the mushy zone for revealing the mechanism of the solid-liquid phase change. In this paper, the motion process and heat transfer characteristics of an elliptic particle as well as two particle interactions in the vertical channel were solved by the finite element method with the consideration of coupling of the phase change and motion. The Arbitrary Lagrangian-Euler Method (ALE) was employed to track the interface of the moving particle and fluid. Results show that the elliptical particle settles along the channel's center line vertically under gravity and undergoes phase change simultaneously. Uneven velocity and temperature fields surrounding the particle are generated by sedimentation, resulting in the particle with an irregular shape. When the initial position of the particle deviates from the center line, the particle deflects during the sedimentation and shifts both left and right in the X-direction. The different initial angles of settling also affect the sedimentation velocity and melting rate. When two particles settle simultaneously, they will lead to complex movement and heat transfer due to the interaction between each other. If the arrangement is eccentric, both particles undergo complex deflections during sedimentation, leading to different melting rates for the two particles.

Three-dimensional numerical simulation of solid-liquid phase change in the cavity of composite structures based on TPMS

Solid skeletons will play an important role in improving the thermal properties of phase change materials. For this reason, the efforts should be dedicated to studying the heat transfer characteristics of solid-liquid phase change with different structural skeletons. In this paper, the composite structures spliced with Gyroid and Diamond skeletons in the horizontal or vertical directions were established by using the Triply Periodic Minimal Surface method. A three-dimensional dimensionless lattice Boltzmann model of the phase change material (PCM) cavity with the spliced skeleton was developed by using the two-region model for solid-liquid phase change in the mushy zone. Based on the pore scale, the phase change heat transfer characteristics under the thermal conductivity ratio of the skeleton to PCM of 100 were analyzed in depth with constant temperature heating at the left wall surface. The results showed that the skeleton spliced in different directions has different effects on the temperature field and heat transfer characteristics of the phase change process. The (G + D)H spliced skeleton which was arranged by Gyroid and Diamond skeletons in the horizontal direction led to a faster melting rate of the PCM than the (D + G)H spliced skeleton which was arranged by Diamond and Gyroid skeletons. The promotion effect of a large porosity skeleton on the melting process of PCM was less than that of a small porosity skeleton. The dimensionless complete melting time for the cavity containing skeleton with porosity ε = 0.915 was increased by 35.7 % and 19.4 % compared to the cavities containing skeletons with porosity ε = 0.826 and 0.871, respectively. This study lays the foundation for the development and application of TPMS spliced skeletons in phase change heat storage and enhanced heat transfer technologies.

Numerical simulation of VAR for large-scale TC4 alloy during the solidification process

ABSTRACT A three-dimensional multi-physics model of the effect of process parameters on the evolution of the solid–liquid interface during solidification of large-scale Ti-6 wt% Al-4 wt% V (TC4) alloy by[Ballantyne, 1977 #483] (VAR) and a macroscopic model of grain nucleation and growth was established. The simulation results qualitatively reveal the evolution of solid–liquid interface and central cross-sectional solidification structure under various melting conditions, indicating that the melting zone depth increased while the mushy zone width and the number of grains decreased with the increase of melting power; the depth of the melting zone and the width of the mushy zone increase sharply with the increase in solidification velocity, the average grain radius increased, while the number of grains decreased; when the ingot diameter increased from 260 mm to 660 mm, the depth of the melting zone increased and gradually remained stable, and the width of the mushy zone gradually decreased.

Keyhole stability, arc behavior, and molten pool flow in narrow-gap oscillating laser-arc hybrid welding of titanium alloy

In the study, the keyhole stability, arc behavior and molten pool flow were investigated to clarify the welding process stability in narrow-gap oscillating laser-arc hybrid welding of titanium alloy. At an oscillating frequency of 300 Hz and amplitude of 1 mm, a concave weld with low porosity was produced. Compared with non-oscillating laser, the keyhole opening size increased about twofold, and the standard deviation of arc deflection angle differences decreased by approximately 87.6 %. Owing to the stirring effect of beam oscillation, a stable keyhole with larger opening size was formed, which facilitated the escape of bubbles from the keyhole. More excitation electrons were generated and erupted outward from the keyhole, and both plasma temperature and density increased by approximately 55.2 %. An enhanced electric channel was formed between the welding wire tip and groove center. As a result, the arc burnt stably at the groove bottom, which could melt the groove bottom synchronously, and suppress sharp corners and lack of fusion. The impact caused by droplets was cushioned as the liquid metal flowed towards the rear molten pool orderly with a circular path. Consequently, the liquid metal near the keyhole fluctuated slightly, indicating that the keyhole stability was enhanced. Besides, dendrites were fragmented and more equiaxed grains were produced due to the strong disturbance of dendrites by liquid metal in the whole mushy zone.

An operando synchrotron study on the effect of wire melting state on solidification microstructures of Inconel 718 in wire-laser directed energy deposition

Directed energy deposition (DED) with a coaxial wire-laser configuration has gained significant attention in recent years for the production of large-scale metallic components because of its low directional dependence, fast deposition rate, high feedstock efficiency, and low manufacturing costs. This work studies the coaxial wire-laser DED process of Inconel 718 alloy under a stable deposition condition with a relatively low input volumetric energy density (55.5 J/mm3). Post characterization reveals a cluster of refined grains at the center-bottom region of the as-printed track. Operando high-energy synchrotron X-ray experiments and multi-physics modeling are applied innovatively to study the fundamental mechanism responsible for the formation of this microstructure. The X-ray diffraction experiment provides direct evidence, which is supported by the simulation, that the feeding wire can reach the melt pool bottom and release solid particles (primarily carbides) near the mushy zone owing to insufficient melting. Consequently, these sub-micron sized particles suppress the growth of large columnar grains and cause the formation of unique microstructural heterogeneity. This discovery offers new opportunities for tailoring the solidification microstructure by controlling the melting state of the feedstock wire in DED process, in addition to commonly known factors such as the thermal gradient and solidification velocity.

A Fully Implicit Enthalpy-Porosity Model for Phase-Change

Abstract This article proposes a new formulation for a phase change model based on the enthalpy-porosity idea. A general one-energy equation model (1EEM) is extended to deal with the melting and solidification of pure substances and alloys. Before melting and after solidification, solid material is seen as a porous media with low porosity and very small permeability. During phase change, thermal equilibrium in the mushy zone is assumed. Viscous and form drag in the volume-averaged momentum equation are reduced as the temperature rises above the melting point. In the energy equation, latent heat is treated implicitly in the accumulation term instead of explicitly as in most works in the literature. Liquid fraction for the entire field is updated after a new temperature field is calculated. Thermophysical properties are updated with the new liquid fraction field. Governing equations are discretized according to the control-volume method. Algebraic equation sets are relaxed with the Simple Method. Inner iterations make use of the Strong Implicit Procedure. Preliminary results indicate good agreement with the literature for pure substances.

Investigation of dissimilar metal (stainless steel and copper) joining and the effect of offsetting and other welding parameters

Dissimilar metal joining without additional preparation like preheating and grooving using conventional arc welding processes. The challenges related to dissimilar joints are overcome by using proper heat distribution according to the heat requirement of different plates. In the present study, GTAW is used to join SS and Cu, mode of joining is welding-brazing mode on the SS side. The heat distribution is done by offsetting the arc towards the Cu side because of the high thermal diffusivity of Cu compared to stainless steel (SS). For the complete joining, the 2nd pass is done without offset. A “beach” of unmixed Cu metal along the Cu fusion line and “peninsula” of an unmixed SS in the weld metal is observed in the microstructure. The grain size variation is observed in the different zones of the weldment due to the segregation of SS particles in weldment. The joint integrity is analyzed with an optical microscope image of the bead, and the detailed analysis of weldment is done using FESEM images in BSD mode. From the microstructure porosity and Cu, penetration is observed in the SS side mushy zone. The microhardness of the weld bead is utilized to see the effect of grain size and amount of SS particles on the mechanical property of weldment in the different zone of the weld bead. The tensile test is conducted to study the joint property of the test coupon. The joint strength of Joint-7 is 225 MPa and percentage elongation is 17 percent, efficiency obtained is around 85 per cent of the Cu plate.

Hot Cracking Characteristics During Single-Mode Fiber and Green Laser Welding Processes in Lithium-Ion Battery Pack Manufacturing

Solidification cracking during lithium-ion battery packaging was metallurgically investigated, specifically for Cu-steel dissimilar materials. To this end, single-mode fiber and green lasers were employed under heat input conditions ranging from 1.3 to 8.0 J/mm. For both laser welds, solidification cracking was concentrated in the steel region of the fusion zone, particularly in the locally Cu-depleted region, regardless of the welding condition. Modified self-restraint tests were performed for overlapping dissimilar material combinations to elucidate the mechanism of solidification cracking. Analysis of the solidification cracking surface revealed that approximately 15?30 mass% Cu existed on the surface. Cu was highly enriched with a droplet shape, formed during solidification within the miscibility gap. By calculating the non-equilibrium weld mushy zone range based on the diffusion-controlled Scheil’s model, the solidification cracking in the Cu-depleted region was estimated at 453 K. It was strongly affected by the severe segregation of Cu (95.7 mass%) in the residual liquid at the terminal stage of the solidification path. Therefore, from a welding metallurgical perspective, homogeneous Cu distribution and minimization of Cu segregation within the fusion zone are essential for suppressing or minimizing the solidification cracking susceptibility of Cu?steel dissimilar laser welding.

Study on Mushy Zone Coefficient in Solidification Heat Transfer Mathematical Model of Thin Slab with High Casting Speed

When the casting speed of the thin slab continuous caster is increased, the ratios of the solid and liquid phases in the solidification front of the molten steel in the mold change, which affects the thickness of the solidified shell. In order to accurately calculate the thickness of the solidified shell and determine the value range of the mushy zone coefficient suitable for the mathematical model of solidification heat transfer at high casting speed, this paper established the solidification heat transfer mathematical model in thin slab funnel mold, and the influence of different mushy zone coefficients on the accuracy of solidification heat transfer mathematical model was analyzed and compared with the actual solidified shell thickness. The results showed that, when the casting speed was increased to 4~6 m/min and the coefficient of the mush zone coefficient was 3 × 108~9 × 108 kg/(m3⋅s), the thickness of solidified shell calculated by the solidification heat transfer model was in good agreement with that measured in practice. The research in this paper provides an important reference for the establishment of the solidification heat transfer mathematical model at high casting speed in the future.