Solid Phase Region Research Articles

Development of an analytical model to investigate temperature distribution and melt geometry in the laser powder bed fusion process under different operating parameters

Laser powder bed fusion (L-PBF) fabricates components by melting layers of metal powder. Consequently, it has the potential to induce interparticle air gaps or generate unpredictable stresses. As such, understanding temperature distribution and predicting the melt pool based on process parameters are essential. While numerous numerical studies in the literature aim to determine these parameters, these numerical estimation methods often demand extensive computational time and powerful processors. This study introduces a new analytical model and a solution method, offering a significantly faster and more precise solution compared to numerical approaches. Furthermore, the developed model allows the identification of liquid and solid phase regions within the part during production, along with insights into the phase region changes over time. Eigenfunction expansion, separation of variables, and variable transformation methods were employed in the analytical solution of the model equations. Results obtained from this method have been validated by experimental studies available in the literature. By utilizing the derived solution function, the L-PBF process was parametrically investigated, revealing temperature distributions and melt pool geometries. The parametric study focused on the laser power, spot size, and powder layer thicknesses as variable parameters. The study determined that a 50 W increase in laser power raises the maximum melt pool temperature by an average of 800 K, and laser power has been identified as the most influential parameter affecting temperature distribution and melt pool geometry.

A semi-analytical method based on the Green's function for the laser melting process of the metal materials

Thermal responses of the metal materials subjected to intense laser irradiation are complicated due to the phase change in the melting process. In order to simplify this problem, previous studies usually ignored the liquid phase or took the usage of finite element method, which limited the achievement of theoretical breakthroughs. In the present study, a one-dimensional heat transfer model with consideration of phase change was established to describe the melting process of the metal materials caused by a constant intense laser beam. The governing equations with three domains were constructed in the piecewise form: the liquid phase region (melted already), the solid phase region (unmelted yet) and the melting region. The limited discretization method was employed to describe the moving of the soli-liquid interface and the energy exchange. The piecewise governing equations in liquid and solid region were solved separately and analytically by means of the Green's function method, and the calculation result was verified by the finite element simulation. The results of the analytical model were in good agreement with those of the finite element simulation, and the maximal prediction errors of the temperature field prediction between the theoretical model and FE simulation is limited to 2.8 %. In addition, the influences of heat source intensity, material heat conductivity, latent heat on the melting process were discussed in detail. The analytical and simulation results reveal that the semi-analytical solution in piecewise for 1-D laser melting process can be successfully used to reflect the dynamic temperature response of the metal materials and the movement of the solid-liquid interface. This work is of guiding significance for the analytical solution of the multi-dimensional melting process of the metal materials under the fixed and continuous laser beams.

Saturated phase change threshold of plume flow gas species under low temperature and rarefied environment

Gas species in high altitude plume flow are all exposed to low temperature, thus making possible phase change processes on those other than H2O vapor. In order to obtain saturated threshold of gas species, which is normally abundant in plume flow, this study establishes Gibbs phase calculation method for CO2, CO, H2, and N2. The non-continuum effect caused by rarefied gas environment is quantitatively calculated by ratio between molecular free path scale and characteristic length of investigated object. Validation on Gibbs method is guaranteed by comparison between calculated results and data from American National Standards Institute (ANSI), while non-continuum effect method is verified by revealing essential reason for gas-solid phase change processes resembling droplet condensation phenomenon observed in high altitude environment. According to the results, non-continuum effect only influences gas-solid boundary. Phase change for rarefied gas species can only occur under low temperature. Saturated threshold deflects toward solid phase region below specific molecules number density, thus decreasing gas to solid phase change trend. Both increasing on characteristic length and existence of other gas components contamination decreases non-continuum effect. Variation on non-continuum effect shows biggest influence on CO2 saturated phase change threshold, while shows smallest influence on that of N2.

Effect of T-shaped fin arrangements on the temperature control performance of a phase change material heat sink

The control of operating temperature in phase change material (PCM) heat sinks is restricted by their low thermal conductivity. The present study proposes a novel T-shaped fin strategy, targeting to improve the thermal management capability of PCM heat sinks in the field of electronic devices, i.e., the originality behind is that heat flux from the heated surface can be transported to the solid phase region by T-shaped fins over a longer distance. Based on the background of photovoltaic cell thermal management, a numerical calculation was conducted to investigate the temperature control performance of PCM heat sinks with different T-shaped fin layouts, which was compared with heat sinks without fins and with rectangular fins. The key discoveries indicate that the melting front in the heat sink cavity was severely influenced by the fins, which first suppressed and then enhanced natural convection in the melting process and improved the PCM temperature uniformity. Compared to the unfinned and rectangular fin systems, the employment of T-shaped fins could reduce melting time respectively by up to 25.5% and 14.5% (achieved by case 8), and lower wall temperature respectively by maximum values of 18.9 °C and 4.9 °C (obtained by case 12).

Dielectric constant of disordered phases of the smallest monoalcohols: Evidence for the hindered plastic crystal phase

With gradual temperature increase in premelting regions of solid phase of methanol and high pressure phase of ethanol, and using novel procedure of separation of electrode polarization effects, we are able to register the contribution of relaxation process to low-frequency dielectric constant. This contribution is about half the liquid’s dielectric constant near temperature of solidification, and is almost an order of magnitude higher than reported earlier for ambient pressure phase of methanol. As opposed to dielectric constant of water at ambient pressure, which does not change much during crystallization, our finding indicates the hindrance of molecule rotation in orientationally disordered phases of monoalcohols. Similar dielectric responses of ambient pressure methanol and high-pressure phase of ethanol imply existence of hindered plastic crystal phase of ethanol (not observed at low pressures). We also have found some dynamic disorder in nominally fully ordered phase of these monoalcohols.

Phase and microstructure selection in peritectic alloys under high G-V ratio

Abstract A new model for the case of a superposition of a phase transformation and a microstructure transition from columnar plane front to equiaxed dendritic growth for peritectic alloys is presented. This model is applied to Fe–Ni alloys where a phase transition from γ to δ takes place when the solute content decreases. The results of the model are compared with predictions of the nucleation constitutional undercooling model. They show that the peritectic two-(solid) phase region is restricted and may completely disappear depending on nucleation undercooling and dendrite growth kinetics.

Amorphization, mechano-crystallization, and crystallization kinetics of mechanically alloyed AlFeCuZnTi high-entropy alloys

Equiatomic and non-equiatomic AlFeCuZnTi high-entropy alloys (HEAs) were prepared by high energy ball milling of elemental powders. For the equiatomic HEA with chemical composition at the boundary of solid solution and amorphous phase regions, an amorphous phase was obtained at moderate milling times, which was mechano-crystallized into a BCC solid solution by continued milling. For the non-equiatomic HEA with chemical composition well within the solid solution region, the same BCC solid solution was obtained during mechanical alloying. The crystallization kinetics of the amorphous HEA was studied by differential scanning calorimetry (DSC) thermal analysis. The crystallization activation energy (calculated based on the Kissinger equation) was correlated to the mean self-diffusion activation energy of the constituting elements, which was related to the multi-component nature of HEAs.

Interactions of l-arginine with Langmuir monolayers of common phospholipids at the air-water interface

The interactions of l-arginine (l-arg) with Langmuir monolayers of three most common phospholipids, which are sodium salt of dipalmitoylphosphatidylglycerol (DPPG), dipalmitoylphosphatidylcholine (DPPC) and dipalmitoylphosphatidylethanolamine (DPPE), have been investigated at the air-water interface. The surface pressure-area (π-A) isotherms of these monolayers have been measured with a film balance and monolayer morphology has been observed by a Brewster angle microscopy (BAM). The DPPG monolayers on pure water do not show any phase transition but show irregular shaped condensed phases formed just after evaporation of the solvent at 20 °C. However, this monolayer on l-arg solution subphase indicates a first-order phase transition from liquid expanded to liquid condensed (LE-LC) phases and forms LC domains at the same temperature. With an increase in the l-arg concentration in the subphase up to 5.0 × 10−4 M, the π-A shows an overall increasingly greater expansion in the molecular area. All of the π-A isotherms recorded on ≥5.0 × 10−4 M l-arg solution subphases almost coincide with each other. These changes in the phase behavior have been explained by the fact that l-arg having guanidinium cationic group undergoes strong hydrogen bonding interaction with the anionic phosphatidylglycerol (PG-) head group. The bonding between two molecules is further strengthened by electrostatic attraction between cationic l-arg and anionic PG- ions. The BAM observation of the monolayer morphology supports this explanation. On the other hand, a very negligible interaction has been observed between l-arg and DPPC or DPPE monolayers. The π-A isotherms in the presence of l-arg for both the amphiphiles show a very little expansion only in the LE phase region, but coincide in the so called solid phase region. The monolayer morphology of both the monolayers also supports these results. This little effect of expansion in the LE region may be explained by the ion-pair formation between cationic l-arg and anionic head groups in the monolayers at lower pressures. However, due to compression at high pressure, the l-arg molecules are squeezed out from the amphiphile head groups.

Experiment and Calculation of Solid Liquid Phase Equilibria in the Ternary System KCl−KBr−H2O at T = 273 K

In this work, the solid-liquid phase equilibrium in the ternary system KCl−KBr−H2O at T = 273 K has been investigated by using the isothermal dissolution equilibrium method. Based on determined solubility data of saturated liquid phase and corresponding humid residue composition, the experimental phase diagram has been constructed. The result shows that the type of the system is classified as completely solid solution type due to the existence of solid solution K(Cl, Br). The phase diagram of the ternary system KCl−KBr−H2O at 273 K is divided into an unsaturated liquid phase filed and one solid crystalline phase region corresponding to K(Cl, Br) by an univariant solubility curve on which there is without any invariant point. The function which described the relationship between the composition of solid solution and the solubility of two salts in saturated liquid phase was constructed by multiple regression. The Pitzer equation has been selected to calculate the solubility data in the ternary system KCl−KBr−H2O at T = 273 K. The solubility modelling approach agrees with experimental solubility data.

Solubility measurement and prediction of phase equilibria in the quaternary system LiCl + NaCl + KCl + H2O and ternary subsystem LiCl + NaCl + H2O at 288.15 K

Using isothermal dissolution method, the phase equilibrium relationship in quaternary system LiCl + NaCl + KCl + H2O and the ternary subsystem LiCl + NaCl + H2O at 288.15 K were investigated. Each phase diagram of two systems was drawn. The phase diagram of LiCl + NaCl + H2O system contains two solid phase regions of crystallization LiCl·2H2O and NaCl. In the phase diagram of LiCl + NaCl + KCl + H2O system, there are three crystallization regions: LiCl·2H2O, NaCl and KCl respectively. In this paper, the solubilities of phase equilibria in two systems were calculated by Pitzer's model at 288.15 K. The predicted phase diagrams generally agree with the experimental phase diagrams.

Solid Liquid Phase Equilibria in the Ternary Systems KCl–ZnCl2–H2O and MgCl2–ZnCl2–H2O at 278 K

This paper presents the solid–liquid equilibria phase diagrams of two ternary systems KCl–ZnCl2–H2O and MgCl2–ZnCl2–H2O at 278 K using the method of isothermal dissolution equilibrium. Integrated with the determined equilibrated liquid phase and humid residue composition, the phase diagrams of the two systems were generated. At the same time, the invariant points, the univariant solubility curves and the solid crystalline phase regions are displayed and discussed. The results of the experiment show that the two ternary systems are classified as complex owing to the formation of double salt. The phase diagram of the ternary system KCl–ZnCl2–H2O at 278 K is comprised of two invariant points, three univariant solubility curves and three solid crystalline phase regions corresponding to KCl, ZnCl2·2H2O and 2KCl·ZnCl2·2H2O. The phase diagram of the ternary system MgCl2–ZnCl2–H2O at 278 K includes two invariant points, three univariant solubility curves and three solid crystalline phase regions corresponding to MgCl2·6H2O, MgCl2·ZnCl2·6H2O and ZnCl2·2H2O. The densities of ternary mixtures at 278 K were measured. The possibility of Laliberte model to predict densities of investigated ternary saturated solution was checked. The results show that this model is allowed to offer fundamental description for densities of ternary mixtures and calculated results are in good agreement with the experimental values.

A Model for FGM/SMA Bilayer Beams Accounting for Asymmetric SMA Behavior

A new model is proposed for bilayer cantilever beams consisting of shape memory alloy (SMA) and functionally graded material (FGM) layers and subjected to loading at the tip. The model accounts for tensile-compressive SMA behavior through the use of an appropriate set of constitutive relations and considers the deformation of the beam within the frame of the Timoshenko beam theory. The derivation of the model proceeds by first determining the correct sequence in which different solid phase structures develop within the SMA layer as the load is applied, resulting in the formation of distinct solid phase regions. The boundaries separating these regions are then located and used in deriving appropriate moment and shear force equations throughout a complete loading-unloading cycle. The model is capable of tracking the deviation of the neutral surface with respect to the mid-plane and the distribution of martensite in the beam as the load varies. The nonlinear variation of stress and strain in a cross section of the beam is also considered. Results of beam deflection and neutral surface deviation are presented and validated against finite element simulations of a 3D model of a beam consisting of a Nitinol and CNT-reinforced layers.

Experimental study and theoretical simulation of fluid phase equilibrium in the subsystems of quinary system NaBr–KBr–MgBr2–SrBr2–H2O at 298 K

Abstract Underground brine known as one of special fluids existing in nature has been regarded as a kind of comprehensive mineral resource. After multi-step separation mining, it can realize the effective extraction and recovery of various mineral resources. Conducting a series of further studies on this kind of natural fluid, especially on the study of fluid phase equilibrium, will be of great significance to explore the rules of its geochemical evolution and formation, and to guide the follow-up fluid mineralization simulation. Based on the above considerations, stable phase equilibria and solubility data of unreported subsystems for quinary system NaBr–KBr–MgBr2–SrBr2–H2O at 298 K were determined by the method of isothermal dissolution equilibrium aiming at the compositions of the underground brine in western Sichuan Basin. The research contents in this work include two ternary systems (NaBr–SrBr2–H2O, KBr–SrBr2–H2O) and three quaternary systems (NaBr–KBr–SrBr2–H2O, NaBr–MgBr2–SrBr2–H2O, and KBr–MgBr2–SrBr2–H2O). The phase diagrams of listed above systems were all drawn by experimental data. The experimental results show that there are no solid solutions as well as any complex salts in the three ternary systems. These phase diagrams all contain two solid phase regions of crystallization, two isothermal dissolution curves and only one isothermal-isobaric invariant point. At 298 K, quaternary systems NaBr–KBr–SrBr2–H2O belongs to a simple type, and the phase diagram consists of only one isothermal-isobaric invariant point, three isothermal dissolution curves and three crystallization regions. In the phase diagram of quaternary system NaBr–MgBr2–SrBr2–H2O at 298 K, there are two isothermal-isobaric invariant points, five isothermal dissolution curves, and four crystallization regions. In the quaternary systems KBr–MgBr2–SrBr2–H2O at 298 K, it was found that one complex salt (KBr·MgBr2·6H2O) formed and the phase diagram has two isothermal-isobaric invariant points, five isothermal dissolution curves, and four crystallization regions. The solubilities of the above subsystems at 298 K were predicted accurately by referring to Pitzer's electrolyte solution theory. It was found that the predicted results were coincided basically with the experimental data.

A phase field method for the numerical simulation of rigid particulate in two-phase flows

In this paper, we propose a phase field method for the numerical simulations of a moving solid object in two-phase flows. A three-phase Cahn–Hilliard and Navier–Stokes model is employed for this problem. The solid region is represented by a single phase in the three-phase system. The rigidity constraint of the solid phase and the no-slip boundary condition on the solid-fluid interface is imposed by attributing a high viscosity to the solid phase. The solid velocity is then averaged over the solid phase region by the momentum conservation of solid phase. In the aspect of numerics, we design an efficient adaptive finite element method to solve the problem. Several numerical simulation results are given to show the capacity and efficiency of our model and numerical method.

A model for shape memory alloy beams accounting for tensile compressive asymmetry

A new analytical model is derived for cantilever beams made from superelastic shape memory alloy and subjected to tip load. The deformation of the beam is described based on Timoshenko beam theory using constitutive relations that account for asymmetric shape memory alloy response in tension and compression. Analytical moment and shear force equations are developed and the position of the neutral axis and the different solid phase regions in the beam are tracked throughout a full loading–unloading cycle. Validation of the proposed model is carried out against data from the literature and from the finite element analysis considering tensile–compressive asymmetry in shape memory alloy behavior.

A New Approach for Calculating Cohesive Energy of Solid Neon Based on the First Principles

Based on the first principles and quantum mechanics, a new approach is put forward to calculate the cohesive energy of face-centered cubic solid neon, in which both the two-body and the total many-body interaction potentials are reasonably emphasized by a new combination formula. It shows that the new scheme is a simple and accurate tool to understand the high-pressure behaviors of solid neon, and it will be applied to calculate the compression curves of dense Helium, Argon, Krypton and Xenon at very high pressures. It is expected that this method can be applicable to all rare gas, including the gas, solid, and liquid phase regions, even of molecular systems, ionic systems.

Mushy-zone microstructure and concentration variation of Co-93wt.%Sb hyperperitectic alloy under TGZM effect

Skutterudite thermoelectric material, CoSb3 is a peritectic compound, and the traditional preparation method needs several days to obtain single-phase CoSb3 by annealing treatment. In this work, we employed temperature gradient zone melting (TGZM) to investigate the microstructure evolution of Co-93wt.%Sb alloy in mushy zone under different thermal stabilization time. Due to the existence of temperature gradient, two mushy zones between complete liquid phase region and solid phase region were observed. There exists a solute gradient across the mushy zone and the solute diffuses from the cold side to the hot side, inducing that the liquid droplet migrates up the temperature gradient. As the thermal stabilization time increases, the volume fraction of the liquid in mushy zone decreases, and the initial solid/liquid interface moves downwards paralleling to the temperature gradient. After 4h thermal stabilization time, the solute concentration is higher in liquid zone than the nominal alloy concentration, and lower in the mushy zone measured by Energy Dispersive Spectroscopy (EDS). By means of TGZM effect, the preparation time for the CoSb3 thermoelectric materials was shortened remarkably.

Measurement of Mineral Solubilities in the Ternary Systems NaCl–PbCl2–H2O and MgCl2–PbCl2–H2O at 373 K

In this paper, isothermal solubility equilibrium method was used to study the mineral solubilities of two ternary systems sodium chloride-lead chloride-water and magnesium chloride-lead chloride-water at 373 K. The solubilities of the salt minerals and the densities of saturated solution in these systems were measured at 373 K. Based on the determined equilibrium solubility data and the corresponding equilibrium solid phase, the isothermal solubility diagrams of the ternary systems were shown, respectively. The results show that both the two ternary systems are simple total saturated at 373 K that neither double salt nor solid solution produced under the condition. Besides, the isothermal solubility diagrams of the two ternary systems at 373 K are both constituted of a eutectic point, two isothermal solubility curves and two solid crystalline phase regions. The two equilibrium solid phases corresponding to the eutectic point of the sodium chloride-lead chloride-water ternary system are NaCl and PbCl2. The two equilibrium solid phases corresponding to the eutectic point of the magnesium chloride-lead chloride−water ternary system are MgCl2 · 6H2O and PbCl2. The experimental result of density was simply discussed.

Analytical model for a superelastic Timoshenko shape memory alloy beam subjected to a loading–unloading cycle

We propose a new analytical model for a superelastic shape memory alloy prismatic cantilever beam subjected to a concentrated force at the tip. The force is gradually increased and then removed and the corresponding distribution of phase transformation fields in the beam is determined, analytically, in both the transverse and longitudinal directions. Analytical moment–curvature and shear force–shear strain relations are also derived during loading and unloading of the beam. The proposed model is validated against an exact numerical beam model as well as a three-dimensional finite element analysis model for the same beam, with very good agreement in each case. Moreover, an experiment is proposed and carried out to characterize the load–deflection response of a shape memory alloy beam under the same boundary conditions as those considered in deriving the model. The obtained response is in good agreement with the analytical model as well as three-dimensional finite element analysis simulations. The analytical method provides a direct mathematical way for describing the material and structural properties of the beam and the distribution of the different solid phase regions as they change under the influence of an applied load and allows the determination of details such as the boundaries of solid phase regions immediately and accurately using equations. The same would require postprocessing at possibly significant computational cost and personal effort if finite element analysis or similar numerical methods are used.

Enthalpy-based multiple-relaxation-time lattice Boltzmann method for solid-liquid phase-change heat transfer in metal foams.

In this paper, an enthalpy-based multiple-relaxation-time (MRT) lattice Boltzmann (LB) method is developed for solid-liquid phase-change heat transfer in metal foams under the local thermal nonequilibrium (LTNE) condition. The enthalpy-based MRT-LB method consists of three different MRT-LB models: one for flow field based on the generalized non-Darcy model, and the other two for phase-change material (PCM) and metal-foam temperature fields described by the LTNE model. The moving solid-liquid phase interface is implicitly tracked through the liquid fraction, which is simultaneously obtained when the energy equations of PCM and metal foam are solved. The present method has several distinctive features. First, as compared with previous studies, the present method avoids the iteration procedure; thus it retains the inherent merits of the standard LB method and is superior to the iteration method in terms of accuracy and computational efficiency. Second, a volumetric LB scheme instead of the bounce-back scheme is employed to realize the no-slip velocity condition in the interface and solid phase regions, which is consistent with the actual situation. Last but not least, the MRT collision model is employed, and with additional degrees of freedom, it has the ability to reduce the numerical diffusion across the phase interface induced by solid-liquid phase change. Numerical tests demonstrate that the present method can serve as an accurate and efficient numerical tool for studying metal-foam enhanced solid-liquid phase-change heat transfer in latent heat storage. Finally, comparisons and discussions are made to offer useful information for practical applications of the present method.