Simulation Of Solidification Research Articles

Effects of Homogenization Conditions on the Microstructure Evolution of Aluminium Alloy EN AW 8006

The industrial production of products, such as foil and aluminium alloy strips, begins with the production of semi-finished products in the form of slabs. These are produced by the continuous casting process, which is quick and does not allow the equilibrium conditions of solidification. Non-homogeneity—such as micro and macro segregation, non-equilibrium phases and microstructural constituents, as well as stresses arising during non-equilibrium solidification—are eliminated by means of homogenization annealing. In this way, a number of technological difficulties in the further processing of semi-finished products can be avoided. The aim of this research was the optimization of the homogenization annealing of the EN AW 8006 alloy. With the Thermo-Calc software, a thermodynamic simulation of equilibrium and non-equilibrium solidification was performed. Differential scanning calorimetry (DSC) was performed on selected samples in as-cast state and after various regimes of homogenization annealing and was used for the simulation of homogenization annealing. Using an optical microscope (OM), a scanning electron microscope (SEM) and an energy dispersion spectrometer (EDS), the microstructure of the samples was examined. Based on the results, it was concluded that homogenization annealing has already taken place after 8 h at 580 °C to the extent, that the material is then suitable for further processing.

Thermodynamic evaluation and investigation of solidification microstructure in the Fe–Cr–Ni–C system

Based on a critical review on various experimentally measured phase relations and thermodynamic properties, a thermodynamic update of the Fe–Ni–C ternary system was firstly carried out by the CALPHAD (CALculation of PHAse Diagrams) method. The thermodynamic database of the Fe–Cr–Ni–C system was then established by extrapolating the description of the accepted ternary systems. No quaternary parameters were introduced in the present work. Good correspondence between calculated and experimental data has been achieved both in Fe–Ni–C and Fe–Cr–Ni–C systems. Eight as-cast alloys were studied to complement the solidification behaviors of the Fe–Cr–Ni–C system by X-ray diffraction analysis and scanning electron microscope. The solidification sequences and volume fractions of precipitated phases predicated from the modified Scheil-Gulliver solidification simulations agree reasonably with the presently measured data, which further validates the reliability of the present thermodynamic description.

Fe-C peritectic solidification of polycrystalline ferrite by phase-field method

A multi-phase-field model was applied to simulate the polycrystalline solidification of δ phase (δ-ferrite) and peritectic solidification of γ phase (γ-austenite) in Fe-C system. Four main modes of phase transformation are included in this simulation, which are solidification of δ phase L → δ, solidification of γ phase L → γ, peritectic transformation δ → γ and peritectic reaction L + δ → γ. The results reveal that the redistribution and diffusion of carbon not only controls the movement of δ-liquid, γ-liquid and γ-δ interfaces but also lead to the production of liquid channels and melting pools. In addition, the evolution of the volume fractions of each phase was analyzed, which shows the statistical law of the interaction of δ, γ and liquid phases at different stages. The present study therefore contributes to the understanding of polycrystalline simulation of Fe-C peritectic solidification and clarifies the formation mechanism of microstructure and micro-segregation.

Effects of Bi addition on solidification behavior of Mg–Al–Zn casting alloys using experiments and CALPHAD calculations

A comprehensive understanding of solidification behavior of Mg–Al–Zn–Bi alloys is necessary for designing novel casting Bi-modified AZ alloys. In this paper, 21 Mg–Al–Zn–Bi alloys were prepared to investigate the phase constituents, morphologies, grain sizes and area fractions of precipitates in as-cast microstructures, as well as their phase transition temperatures and solidification paths by using X-ray diffraction, scanning electron microscopy, optical microscopy and differential scanning calorimetric techniques. It was found that the Bi addition leads to the formation of α-Mg3Bi2 phase, which became coarse flake as Bi content increased. Besides, the Bi addition can modify the morphology of eutectic γ-Al12Mg17 phase and refine the grain size of primary phase. Moreover, the measured area fractions of precipitates increased steadily as Bi content increased, which were comparable with the model-predicated values. After that, the calculated liquidus projections in the Mg-rich corner of Mg–Al–Zn–Bi quaternary system were employed for demonstrating the effects of Bi addition on the solidification sequences. Additionally, the phase transition temperatures predicted via Scheil solidification simulations agreed well with measured values. The present work indicated that the combination of experimental investigations and thermodynamic calculations can serve as an efficient method to obtain accurate and comprehensive solidification behavior of Bi-modified Mg–Al–Zn alloys.

Permeability Tensor for Columnar Dendritic Structures: Phase-Field and Lattice Boltzmann Study

Permeability is a very important multiscale parameter providing information of dendritic structures in macroscale simulations of solidification with liquid flow during casting. In our previous study, it was demonstrated that the permeability of liquid flow normal to a columnar dendritic structure can be well approximated by the Kozeny-Carman (KC) equation with a coefficient kc = 9. In this study, the permeability of liquid flow parallel to a columnar dendritic structure is investigated using a method that combines both phase-field and lattice Boltzmann simulations. It is shown that the permeability of parallel flow can also be approximated by the KC equation with kc = 3. A permeability tensor is then proposed for a columnar dendritic structure. Validity of the permeability tensor is confirmed by simulations of liquid flow in arbitrary directions of a columnar dendritic structure.

Phase-field simulation of peritectic steels solidification with transformation-induced elastic effect

Peritectic carbon steels are more prone to surface cracking during continuous casting than other carbon steels. The main problems are the formation of longitudinal depressions and of transversal near-corner cracks. It is normally assumed that these problems are related to the δ->γ phase transformation and its associated volume contraction of 0.5%. In this work, we utilize phase-field simulations in the Fe–C and Fe–Mn to access the stress and strain fields which develop just as a consequence of the δ->γ phase transformation. We show that the deformation tends to concentrate in the vicinity of δ-γ-liquid triple junction and that the developed stresses are high enough to produce local plastic deformation of the phases. It is also demonstrated that the undercooling value set for the simulations affects the stress level in an important way.

Effect of MC carbide formation on weld solidification cracking susceptibility of austenitic stainless steel

The effect of secondary phase formation such as MC carbide during welding on solidification cracking susceptibility of fully austenitic stainless steels with various amounts of alloying elements and carbon was investigated. The solidification cracking susceptibility of Fe-24mass%Cr-26mass%Ni stainless steels with various amounts of niobium, titanium, zirconium, and carbon was evaluated by the Trans-Varestraint test.The addition of alloying elements such as niobium, titanium, and zirconium increased the brittle temperature range (BTR). The BTRs depend on the type and combination of the alloying elements and carbon content. Titanium was the most influential element on the increase in BTR compared to the other elements. The increase in carbon content tended to decrease the BTR, especially for the specimen containing titanium. The alloying elements formed phases such as the film-like MC-type carbide (MC) phase and granular Laves phase in the specimens containing 0.05% C, and a lot of the acicular MC phases in the specimens containing 0.20% C. The start temperature of the secondary phase formation differed depending on the type of the alloying element, and the temperature tended to increase with increasing carbon content. When the additions of niobium and titanium were compared, the amount of titanium segregation during solidification was smaller due to the formation of MC phases. Solidification simulation revealed that a higher amount and faster formation of the MC phase during solidification in 2Ti–20C contributed to reducing the BTR by increasing the carbon content. Thus, it is considered that the weld solidification cracking susceptibility depended on the type and amount of formation morphology, as well as start temperature during solidification corresponding to the composition of alloying elements and carbon.

Permeability tensor for columnar dendritic structures: Phase-field and lattice Boltzmann study

Permeability is a very important multiscale parameter providing information of dendritic structures in macroscale simulations of solidification with liquid flow during casting. In our previous study, it was demonstrated that the permeability of liquid flow normal to a columnar dendritic structure can be well approximated by the Kozeny–Carman (KC) equation with a coefficient kc = 9. In this study, the permeability of liquid flow parallel to a columnar dendritic structure is investigated using a method that combines both phase–field and lattice Boltzmann simulations. It is shown that the permeability of parallel flow can also be approximated by the KC equation with kc = 3. A permeability tensor is then proposed for a columnar dendritic structure. Validity of the permeability tensor is confirmed by simulations of liquid flow in arbitrary directions of a columnar dendritic structure.

Experimental phase diagram, thermodynamic modeling and solidified microstructure in the Mo–Ni–W ternary system

In this work, the isothermal section at 900 °C, a liquidus projection and invariant reaction temperatures in the Mo–Ni–W ternary system were established using X-ray diffraction (XRD), Differential Scanning calorimeter (DSC) and electron probe micro-analysis (EPMA). Based on the experimental phase diagram data from the present work and the literature, the Mo–Ni–W system was assessed by means of the CALPHAD (CALculation of PHAse Diagrams) method. The liquid, fcc-(Ni), bcc-(Mo) and bcc-(W) phases were described with a regular solution model. The sub-lattice models were used to express Gibbs energies of the intermediate phases of MoNi3, MoNi, (Mo, W)Ni4, WNi and W2Ni. The present modeling covers the entire composition and an extensive temperature ranges of the Mo–Ni–W ternary system, and a set of self-consistent thermodynamic parameters were finally obtained. Comprehensive comparisons between the calculated and measured phase diagram data show that most experimental information is satisfactorily accounted for by the present thermodynamic description. Scheil solidification simulations for a few representative as-cast alloys were performed. It was found that the solidified microstructures can be reasonably described by the Scheil simulation. The liquidus projection and reaction scheme of the Mo–Ni–W system were generated by the presented modeling.

Modeling of the alloy solidification modified by refractory nano-size particles

The authors propose a mathematical model of non-equilibrium crystallization of a binary alloy with modifying refractory nano-sized particles. The model describes heat transfer processes, as well as heterogeneous nucleation and crystallization of two components of the melt. The nucleation of the crystalline phase occurs on the surface of the nanoparticles during the supercooling of the melt. The liquidus temperature in the melt depends on the concentration of the dissolved alloying component, which is determined by the non-equilibrium lever equation. When the metal is cooled down to the eutectic temperature, the solidification of the alloy α-phase takes place, followed by solidification of β-phase if the cooling continues. The growth rate of the crystal phase is proportional to the supercooling value. The volume of the solid phase formed around the nucleus determines the size of the grain structure in the solidified alloy. The article depicts numerical simulation of aluminum melt solidification in cylindrical ingot mold, carried out by the authors. The parameters of heat exchange of the melt-mold system with the environment are available from experiments. The conditions of nucleation, crystallization rate, supercooling and solidification time prove to significantly differ within the cast. The area with the finest structure of the solidified metal is located near the wall of the mold. The calculated size of the grain structure in the casting is consistent with the experimental results. Comparing the results of numerical calculation with the data of a physical experiment on measuring the temperature during solidification of the melt and studying the properties of the cast confirm reliability of the proposed model.

3D simulations of solidification with liquid phase flow

The work discusses issues related to 3D coagulation simulations including liquid phase flow. The approach chosen by the authors is based on the numerical solution of the enthalpy solidification formula and the Navier-Stokes equation, in which the buoyancy force approximation was added. Both of these equations are discretized in space using Finite Element Method, and in both cases time integration utilizes the Theta scheme, which is a generalized form of Euler Backward approach. The presence of the Navier-Stokes equation in the model forces the use of special techniques to ensure the convergence of the solution. From a number of available methods, the method of adding stabilizing elements in the FEM formulation was chosen, i.e. the stabilization formulas PSPG/SUPG (Pressure Stabilized Petrov Galerkin/Streamline Upwind Stabilized Petrov Galerkin). The occurrence of large temperature gradients, however, made it necessary to use the so-called lumped mass matrix in the energy equation. The work presents the results obtained using a model implemented by the authors in the form of a computer program written in C++ programming language. The use of this language and appropriate libraries made it possible to obtain sufficient performance to perform 3D solidification simulations.

Failure and fracture analysis of a high-alloy Ni-Al bronze chain connector of a tube drawing machine

The investigation of a fractured Ni-Al bronze alloy connector, from a chain assembly, was performed in order to determine the potential cause of the observed failure. It is shown that the fracture occurred by fatigue due to the combined result of poor machining quality and the brittle nature of the as-cast component. This synergistic effect facilitated intergranular crack propagation through the “microstructurally sensitized” interdendritic regions. Various irregular and coarse-shaped intermetallic phases, corresponding to κ-type phases, were detected and their detrimental role on crack propagation was evaluated. Thermodynamic and kinetic simulation of solidification and phase transformation was elaborated in order to verify qualitatively and quantitatively the presence of the microscopically detected phases. Thermodynamic results were in agreement with metallographic observations. Kinetic results showed that increased cooling rate affects solidification particularly at high content of substitutional elements, such as Fe, Ni and Mn, since their diffusion is restricted and the completion of solidification is decelerated. Moreover, the high content of these elements favors the appearance of κΙ precipitates. The formation of shaped κΙ-phase cannot be eliminated, however its fraction and size can be suppressed by increasing cooling rate. The alteration of chemical composition of cast component could provide promising results as it shows a reducing tendency of κI-phase intermetallics’ formation and a higher homogeneity, even at moderate cooling rates.

Numerical Simulation of Solidification of Two Metal Droplets Impinged on Flat Plate Using Particle-based Method

Numerical Simulation of Solidification of Two Metal Droplets Impinged on Flat Plate Using Particle-based Method

Hot Cracking Susceptibility and Solidification Segregation Analysis by Computer Simulation in Duplex Stainless Steels

Solidification cracking susceptibility in arc & laser welding of DSSs (duplex stainless steels) was quantitatively evaluated and the numerical simulation of solidification cracking susceptibility has...

Thermodynamic descriptions of ternary Al–Si–Sr system supported by key experiments

Abstracts All the experimental phase equilibria and thermodynamic properties in the Si–Sr and Al–Si–Sr systems were critically reviewed. Based on the reviewed experimental data, the thermodynamic descriptions of the Si–Sr binary system were updated by using the CALculation of PHAse Diagram (CALPHAD) technique, resulting in better agreement with the experimental data, especially for the standard enthalpies of formation, than those in the previous assessment. After that, the thermodynamic assessment of the Al–Si–Sr ternary system was carried out using the CALPHAD approach. Comprehensive comparisons indicate a good agreement between the calculated phase equilibria/thermodynamic properties and the experimental/first-principles data in Al–Si–Sr ternary system. Moreover, the as-cast microstructures of 4 Sr-additional Al–Si alloys were experimentally investigated by using the scanning electron microscope and electron probe microanalysis techniques. The solidification sequence and volume fractions of precipitated phases in the 4 alloys predicated from Scheil-Gulliver solidification simulations agree reasonably with the presently measured data, which further validates the reliability of the present thermodynamic descriptions.

Accelerating phase-field modeling of solidification with a parallel adaptive computational domain approach

We developed a parallel adaptive computational domain method for accelerating the simulation of solidification in two dimensions using the phase-field model. The algorithm is paralled with the MPI library based on the domain decomposition approach. We discuss the implementation details of the parallel adaptive computational domain method and the domain decomposition based strongly implicit linear solver. We examined the performance of our algorithm by comparing with the algorithm based on the fixed computational domain and show that it greatly reduces the computational cost of solving the phase-field model. We also simulate the competitive growth process of the second and ternary dendritic arms successfully.

Phase field modeling of rapid resolidification of Al-Cu thin films

Abstract A binary alloy multi-order parameter phase field model is used to study rapid solidification in Al-Cu under conditions corresponding to recent dynamic transmission electron microscopy (DTEM) experiments. The phase field model’s sharp interface limit is set through a recent matched asymptotic analysis to follow the solute trapping and interface undercooling kinetics of the Continuous Growth Model (CGM). The phase field model convergence to the CGM sharp interface model is investigated, and based on this an optimal interface width is chosen to simulate the DTEM experimental conditions. The temperature distribution used in the phase field simulations is taken from an analytic expression extracted from experiments. Simulated solidification structures are compared to experiments, including time-resolved DTEM images and post-mortem TEM-based image quality and orientation maps. We find that the large scale morphological features of the simulated microstructures are in good agreement with the experiments, and the corresponding concentration profiles that emerge are in qualitative agreement with experiments. These results show that phase field simulations, informed with DTEM experiments, provides a promising framework to investigate rapidly solidified microstructure evolution and solute segregation, and to calibrate hard-to-determine solidification parameters.

Grain refinement in ultrasonicated binary aluminium alloys

Abstract Combined effect of solute concentration and ultrasonic treatment on the grain refinement of aluminium based alloys is studied. Silicon, copper, and nickel solutes are used. Upon ultrasonic treatment, grain refinement in Al-3 wt.%Ni alloy is more pronounced than that in Al-3 wt.%Si alloy, although the growth restriction factor of solute silicon is twice that of nickel in pure aluminium. These observations spurred this investigation about the grain refinement mechanisms operating in Al-based hypoeutectic alloys. Grain refining efficiency of different solutes is analyzed using the growth restriction factor and constitutional supercooling parameter, both calculated from Scheil-Gulliver solidification simulation. It is observed that grain refinement occurring from ultrasonic treatment in near-eutectic alloys is better explained by using the constitutional supercooling parameter rather than the growth restriction factor.

Modified embedded-atom method potential for high-temperature crystal-melt properties of Ti–Ni alloys and its application to phase field simulation of solidification

We developed new interatomic potentials, based on the second nearest-neighbor modified embedded-atom method (2NN-MEAM) formalism, for Ti, Ni, and the binary Ti–Ni system. These potentials were fit to melting points, latent heats, the binary phase diagrams for the Ti rich and Ni rich regions, and the liquid phase enthalpy of mixing for binary alloys, therefore they are particularly suited for calculations of crystal-melt (CM) interface thermodynamic and transport properties. The accuracy of the potentials for pure Ti and pure Ni were tested against both 0 K and high temperature properties by comparing various properties obtained from experiments or density functional theory calculations including structural properties, elastic constants, point-defect properties, surface energies, temperatures and enthalpies of phase transformations, and diffusivity and viscosity in the liquid phase. The fitted binary potential for Ti–Ni was also tested against various non-fitted properties at 0 K and high temperatures including lattice parameters, formation energies of different intermetallic compounds, and the temperature dependence of liquid density at various concentrations. The CM interfacial free energies obtained from simulations, based on the newly developed Ti–Ni potential, show that the bcc alloys tend to have smaller anisotropy compared with fcc alloys which is consistent with the finding from the previous studies comparing single component bcc and fcc materials. Moreover, the interfacial free energy and its anisotropy for Ti-2 atom% Ni were also used to parameterize a 2D phase field (PF) model utilized in solidification simulations. The PF simulation predictions of microstructure development during solidification are in good agreement with a geometric model for dendrite primary arm spacing.

Recent developments of dendritic solidification simulations by phase-field method

Recent developments of dendritic solidification simulations by phase-field method