Solidification Microstructure Formation Research Articles

Enhanced conservative phase field method for moving contact line problems

AbstractThe traditional Allen–Cahn phase field model doesn't conserve mass and is mostly used in solidification microstructure formation. However, a recently modified Allen–Cahn phase field model has riveted the attention of the academic community. It was obtained by subtracting the curvature‐driven flow term from the advective Allen–Cahn phase field model, and thus improves the boundedness of the phase field. More recently, the model has been further refined with the recovered signed distance function to compute interface normal vectors. This paper develops a three dimensional phase field model, based on the abovementioned Allen–Cahn phase field model. The model was discretized using a finite difference method on a half‐staggered grid. More important, interfacial tension was expressed in a potential form. The model was tested against a number of cases and was applied to impacts in various conditions. Besides, the model was parallelized using the shared memory parallelism, OpenMP, to facilitate computation.

Influence of Mo and W on Solidification Microstructure Formation for Ni-hard Type Cast Iron

Influence of Mo and W on Solidification Microstructure Formation for Ni-hard Type Cast Iron

Keyhole mode wobble laser welding of a nickel base superalloy - Modeling, experiments, and process maps

Keyhole mode wobble laser welding is gaining increasing acceptance due to its ability to bridge gaps, refine microstructure, and enhance the mechanical properties of welds. However, the impact of amplitude, frequency, welding speed, laser beam power, and beam radius on the heat flux distribution, melting pattern, and three-dimensional temperature field is not well understood. To address this need, here we report a combined experimental and computational study to investigate the effects of the key wobble welding parameters on the energy distribution impinging on the welding track, keyhole formation, three-dimensional fluid flow and heat transfer during wobble laser welding of Inconel 740H. The modeling results were rigorously tested using experiments in which the welding speed, laser power, and wobble amplitude and frequency were varied. A bimodal power density distribution with higher power density near the edge than in the middle of the track occurred when the wobble amplitude significantly exceeded the laser beam diameter. A high wobble amplitude resulted in a wide and shallow pool while the wobble frequency used in this work did not significantly impact the fusion zone geometry. A set of process maps were constructed to understand the role of wobble laser parameters in achieving a desirable fusion zone geometry during keyhole mode wobble laser welding. Finally, wobble laser welding with a high amplitude was found to favor rapid solidification and the formation of finer solidification microstructure.

Influence of Cu and Cr contents on the solidification path and microstructure formation of hypoeutectic as-cast Al–Cu–Cr alloys

Influence of Cu and Cr contents on the solidification path and microstructure formation of hypoeutectic as-cast Al–Cu–Cr alloys

Multi-Phase-Field Simulation of Non-Equilibrium Solidification in 316L Stainless Steel under Rapid Cooling Condition

Additive manufacturing has attracted much attention as a new technology for producing lightweight and high-strength materials. The multi-phase-field method has been used in powerful numerical simulations to predict solidification microstructure formation in additive manufacturing. To verify the non-equilibrium multi-phase-field (NEMPF) model that can consider strong out-of-equilibrium solid/liquid interfacial conditions, the NEMPF model coupled with the CALPHAD-based thermodynamic database was used to simulate the solidification process in 316L stainless steel (SS) under a rapid cooling condition. The results show that interstitial carbon atoms tend to segregate at the solid/liquid interface, whereas no concentration gradient is observed at the grain boundary between the solid phases. Conversely, substitutional Cr, Mo, and Mn atoms were segregated in the solid grain boundaries. The effects of interfacial mobility and interfacial permeability on the solidification behavior were investigated. The results show that these parameters strongly influence the solidification rate and distribution of the solute concentration at the solid/liquid interface.

Solidification microstructure variations in additively manufactured Ti-6Al-4V using laser powder bed fusion

Laser powder bed fusion (LPBF) offers unique opportunities to produce metallic components without conventional design and manufacturing constraints. During additive manufacturing process, titanium alloys like Ti-6Al-4V undergo solid-state transformation that conceals initial solidification microstructure from room-temperature observations. Revealing the as-solidified microstructure can be critical to understanding the early stages of solidification. Using orientation relationships between parent (α) and child (β) phases, the as-solidified microstructures across the LPBF build volume has been reconstructed. Based on the as-solidified parent phase information, variations of the thermal and solidification conditions that occur during the LPBF of Ti-6Al-4V are revealed. The results show that how high cooling rates in the initially solidified lower layers contributed to orientation distribution during parent phase solidification, compared to upper layers in the build volume. Furthermore, the approach demonstrates the potential to further explore solidification microstructure and defect formation in titanium alloys during additive manufacturing.

Microstructure refinement mechanisms in undercooled solidification of binary and ternary nickel based alloys

Molten glass purification and cycle superheating technologies were used to make Ni65Cu35, Ni65Cu33Co2 and Ni65Cu31Co4 alloys obtain maximum undercoolings of 320 K, 292 K and 300 K respectively. In order to analyze the relationship between morphological characteristics of solidification front and undercooling change during migration of solid–liquid interface, a high-speed camera was used to capture pictures of the recalescence process. Observing the microstructure of the undercooled alloys using metallographic microscope, the characteristics and evolution of microstructure during rapid solidification process of undercooled liquids were analyzed. It was found that grain refinement mechanisms of highly undercooled Ni–Cu–Co alloys was the same as those of the Ni–Cu alloys. Dendrite remelting leads to the grain refinement at low undercooling, while the dominant factor of grain refinement at high undercooling is recrystallization process induced by stress. The internal driving force can be divided into two parts: one is the thermal stress generated by the releasing of solidification latent heat during recalescence process, and the other is the stress and strain accumulated by interaction of liquid flow and primary dendrite during rapid solidification. We also found that addition of third element Co not only played an important role in solidification rate and recalescence effect, but also significantly improved the average hardness of grain refined microstructure, which was about 80% higher than that of as cast alloy. The addition of trace Co was also conducive to the formation of non-segregation solidification microstructure.

Phase Field Modeling of Air Entrapment in Binary Droplet Impact with Solidification Microstructure Formation

A novel numerical model was developed to investigate air entrapment in binary droplet impact with solidification microstructure formation under practical plasma spraying conditions. The evolving liquid–gas interface was tracked by the explicit finite difference solution to the Cahn–Hilliard equation, coupled with the Navier–Stokes equations. Another diffuse interface model was invoked to trace solid–liquid and grain–grain boundaries. The model was discretized using an explicit finite difference method on a half-staggered grid. The velocity pressure coupling was decoupled with the projection method. The in-house code was written in Fortran and was run with the aid of the shared memory parallelism, OpenMP. The time duration over which gas compressibility matters was estimated. Typical cases with air entrapment were studied with the model. The effect of droplet porosity on air entrapment was probed into as well: the larger the porosity of a droplet, the bigger the trapped air bubble. The grain growth near the air bubble is skewed. Moreover, a case without air entrapment was also shown herein to stress that air bubbles could be suppressed or even eliminated in plasma spraying by adjusting the landing positions of successive droplets.

Influence of growth velocity on fragmentation during directional solidification of Al – 14 wt.% Sn alloy studied by in-situ synchrotron X-radiography

Directional solidification of Al – 14 wt.% Sn alloy was investigated by means of synchrotron X-radiography at the European Synchrotron Radiation Facility (ESRF). The dynamics of the solidification microstructure formation was studied in-situ and in real-time. In the present manuscript, a special attention is given to the influence of increasing growth velocity on the fragmentation phenomenon of dendrite arms, which has an important role and impact on the final grain structure. Fragmentations of both secondary dendrite arms and more strikingly part of primary trunks have been observed. The experiments show that the number of fragments increases concomitantly with the solidification growth rate until it reaches a limit value after which fewer or no more fragments are observed. The possible origins of the fragmentation are discussed in detail and the likelihood of each of these potential mechanisms is estimated to understand the reason of both primary and secondary arm detachment. It is shown that the fragmentation in a transient regime is correlated to the variations of the solute accumulation, latent heat rejection and the curvature of the attachment neck during solidification. Moreover, during these experiments, Columnar-to-Equiaxed Transition (CET) induced by the fragmentation phenomenon is observed. The velocity of the dendrite fragments due to the buoyancy force is a major parameter to control the CET and our results show that a reverse Equiaxed-to- Columnar Transition can even be observed. Once the growth velocity is of the same order or higher than the fragment flotation velocity, the fragments are trapped within the columnar dendritic microstructure, and CET cannot take place or the equiaxed regime cannot be sustained.

Deterministic modeling of solidification microstructure formation in directed energy deposition fabricated Ti6Al4V

Metal additive manufacturing (MAM) technology is now widely applied in the manufacturing and remanufacturing industry, among which microstructure simulation gradually shows its importance. Traditional solidification microstructure simulation methods all have their merits as well as drawbacks when applied in MAM cases. In this work, a deterministic solidification microstructure model, named “invasion model”, is established to avoid the essential defects of traditional methods. This model focuses on the interaction between the neighboring bi-crystals instead of simulating the growth kinetics of each columnar grain or deriving the field form of variables. Within a bi-crystal system, the grain boundary tilt from thermal gradient direction is understood as a transient invasion behavior of one grain to another, and the competitive grain growth behavior along the buildup process of MAM is a summary of all the invasions in bi-crystal systems. To fill the gaps in the rapid solidification theory, a database recording the anisotropic growth effect under a rapid directional solidification condition was established with the help of an artificial neural network (ANN). Wire feed directed energy deposition (DED) fabricated Ti6Al4V thin-wall samples with full dendritic columnar grains (prior beta) are used as a benchmark to test the validation of the novel simulation model. The grain geometrical structure of reconstructed prior β grains along the build-up direction has a good agreement with the simulation result. The model can also be applied to other cases of MAM or combine with various models to achieve real-time as-solidified crystallographic feature prediction when it meets the scope of application. • Traditional solidification microstructure simulation methods all have their merits and drawbacks when applied in MAM cases. • Invasion model is established to investigate the transient competitive grain growth behavior within bi-crystal systems. • Wire DED Ti6Al4V thin-wall samples are used as a benchmark to test the validation of the novel simulation model.

An enhanced phase field model for micron-scale droplet impact with solidification microstructure formation

In this work, a novel diffuse interface model combining droplet impact with solidification microstructure formation was developed. A number of numerical models simulating droplet impact with solidification have been invented, but few are capable of unveiling the nucleation and growth of polycrystalline crystals on a micro scale. This paper thus aims to propose a diffuse interface model to simulate droplet impact, and moreover, solidification microstructure formation. To implicitly track the evolving liquid-gas interface, the Cahn-Hilliard equation is coupled with the Navier-Stokes equation. A phase field model involving polycrystalline growth is responsible for the capturing of solid-liquid interface and grain-grain boundaries. The current model is discretized explicitly such that it lends itself to shared-memory parallelism like OpenMP. A parallel SOR scheme based on Red/Black ordering is used to solve the pressure velocity coupling. The model was applied to various impact conditions in plasma spraying, including both single and multiple droplet impact, to show its robustness. Besides, with the model being modified slightly, non-equilibrium effect induced by rapid solidification was investigated as well.

Solidification microstructure and residual stress correlations in direct energy deposited type 316L stainless steel

Localised fluctuation in residual stress distribution for direct energy deposited 316L stainless steel thin plate was revealed through high-energy synchrotron X-ray diffraction. The macroscopic residual stress levels are changed steadily across the article according to the characteristic cooling rates, as implied by the measured dendrite arm lengths. Localised fluctuations of residual stress in the length scale, between 500 and 600 µm, coincides well with the morphological variations of the solidification microstructure that formed during direct energy deposition. Computations indicate a greater propensity for related mesoscopic thermal gradient fluctuations along the solidification front of the moving melt pool. Novel perspectives on residual stress across multiple length-scales and its relevance to the formation of solidification microstructure in metal additive manufacturing is analysed by considering the experimental results.

Ablation Casting: Solidification Characteristics, Microstructure Formation, and Mechanical Properties

Ablation casting is an emerging sand casting technology that achieves high cooling rates in a casting during its solidification, especially its eutectic solidification of the metal, resulting in an extremely fine eutectic microstructure, reduced levels of defect, and enhanced mechanical properties of the casting. The technology is creating extensive interest in the industry for its capability in producing castings with high mechanical properties and internal integrity. However, scientific research lags behind the industrial applications of this new technology. There is a lack of scientific understanding on the solidification features of the castings made using ablation casting. Experimental data on the microstructural length scales seem inconsistent. This article aims at interpreting the experimental data available in the literature by considering the solidification characteristics of ablation casting. The paper also discusses certain research needs to further exploring the potential of the ablation casting process.

Thermodynamics and solidification kinetics of Ag–Ni–Co immiscible alloys

Phase equilibria in the Ag–Co and Ag–Ni–Co systems were experimentally determined. Thermodynamic assessments for these two systems were performed by applying the Calculation of Phase Diagrams method on the basis of the present and previous experimental results. The optimized thermodynamic parameters bring about a good agreement between the calculated results and experimental data in these two systems. Solidification experiments were conducted for Ag–Ni–Co alloys, and samples with composite microstructure were obtained, in which the (Ni, Co)-rich dispersed-phase particles (DPPs) distribute uniformly in the Ag matrix. The microhardness of the Ag–Ni–Co alloys increases with the content of nickel and cobalt and the cooling rate of the alloys during solidification. A model was developed to analyze the solidification microstructure formation of Ag–Ni–Co alloys by coupling the thermodynamic and kinetic calculations. The microstructure evolution was simulated and discussed in details. The numerical results are consistent with the experimental ones. They demonstrate that the cooling rate during the nucleation of the (Ni, Co)-rich dispersed-phase droplets (DPDs)/DPPs has a dominant influence on the solidification microstructure. The effect of Ostwald ripening of the DPDs/DPPs during solidification is very weak under the present cooling conditions.

Modeling Microstructure Formation in Yttria-Stabilized Zirconia (YSZ) Droplet with High Impact Velocity in Supersonic Plasma Spray

In plasma spraying, copious heterogeneous nucleation starts when a molten ceramic droplet spreads on a cold surface under rapid cooling. Some nuclei will survive and grow, eventually forming a splat of grains of distinct crystalline orientations. This paper aims to predict the dynamic process of yttria-stabilized zirconia (YSZ) droplet impact with solidification microstructure formation under various plasma spray conditions. A diffuse interface model was developed to track the evolving liquid–gas and solid–liquid interfaces. Continuously dense YSZ droplet impacts with different impacting angles were conducted, along with a hollow droplet impact. Results reveal that competitive growth among crystals is limited in the planar solidification, and that columnar structure dominates all the tests performed owing to a large thermodynamic driving force, and that given the rapid spreading of YSZ droplets along a solid surface, solidification may be safely assumed to take place mostly after spreading. Besides, typical crystal growth velocities are around 1 m/s, and local equilibrium can be assumed in the bulk.

Numerical investigation of solidification microstructure formation in sequential YSZ droplet impact under supersonic plasma spraying

A coupled CFD and diffuse interface model was developed to predict the dynamic process of solidification microstructure formation of sequential yttria-stabilized zirconia (YSZ) droplet impact under supersonic plasma spraying. The numerical model relies on the explicit finite difference solution of the Navier-Stokes and energy balance equations, coupled with the Cahn-Hilliard equation, to track liquid-gas interface, and of a phase field model for solidification microstructure formation involving polycrystalline growth to trace solid-liquid interface. Extensive simulations, differing in the status of the first droplet and the impacting parameters of the second one, were carried out. The results reveal that solidification microstructure still follows a columnar pattern if the second droplet lands on the first that is just starting spreading, and that the growth direction around the contact region in the second splat will be obviously skewed by fluid flow if the first has been solidified, owing to earlier and easier nucleation on the top surface of the first splat, thus confirming the epitaxial growth across the splat-splat interface. Computed results are also compared with thermal spray experiments, with gratifying agreement obtained.

The effects of Cr addition on microstructure, hardness and tensile properties of as-cast Al–3.8wt.%Cu–(Cr) alloys

An investigation is made on the effects of Cr addition (0.25 and 0.50wt%) on the solidification evolution, microstructure formation, hardness and tensile properties of Al–3.8Cu–(Cr) alloys. Solidification experiments were carried out in a vertical furnace using a metallic mold cooled from the bottom, thus permitting solidified ingots under transient heat flow conditions to be obtained. The solidification system was instrumented with thermocouples at positions along the length of the ingot to permit the solidification cooling rate to be determined from bottom to top of the ingots. The ingots were transversally and longitudinally sectioned to extract specimens for metallographic analyze, hardness and tensile tests. The macrostructures are shown to be entirely columnar along the length of the Al–3.8Cu and Al–3.8Cu–0.25Cr alloys ingots, whereas the Al–3.8Cu–0.50Cr alloy is shown to have a columnar-to-equiaxed transition close to the top. For any alloy ingot examined, the Al-rich matrix is characterized by a cellular morphology for high cooling rates followed by cellular/dendritic transitions with the decrease in cooling rate. The addition of Cr to the Al–3.8Cu alloy promoted the formation of Al23CuFe and Al7CuCrFe phases precipitated in the matrix and eutectic mixture, preventing formation of isolated Al–Fe intermetallic compounds. Hardness and tensile strength increased with increasing alloy Cr content, with highest values of both properties associated with the Al–3.8Cu–0.50Cr alloy ingot. Experimental equations correlating hardness/tensile strength and cellular spacing are proposed. These equations were coupled to the theoretical Hunt–Lu model to estimate hardness and ultimate tensile strength as a function of the cellular spacing.

Cooling curve thermal analysis, phase constitution, and solidification characteristics of cast Mg–5Gd–2Y–xNd–Zr alloys

Mg–RE alloys are high-strength magnesium alloys with great application potential. The solidification pathways and microstructure formation of most Mg–RE alloys are still under discussion. In the present research, phase constitution and solidification characteristics of Mg–5Gd–2Y–xNd–Zr (x = 0, 2, 4, 6) alloys were investigated using a Computer-Aided Cooling Curve Analysis (CA-CCA) system, together with microstructure observation and phase identification methods including SEM, EDS, and XRD. The results show that the solidification microstructure of Mg–5Gd–2Y–Zr alloy was composed of α-Mg and Mg24RE5 phase. And the addition of Nd leads to the formation of β phase through a eutectic reaction, L → Mg24RE5 + α-Mg + β. Combining the CA-CCA and microstructure observation results, the non-equilibrium solidification route and solid fraction–time relationship of Mg–5Gd–2Y–xNd–Zr (x = 0, 2, 4, 6) alloys was summarized. Besides, hot tearing susceptibility of the investigated alloys was evaluated according to their solid fraction–time relationship using Clyne–Davies’ criterion.

Numerical modeling of YSZ droplet impact/spreading with solidification microstructure formation in plasma spraying

A comprehensive numerical model has been developed, which is capable of representing the impact and spreading of a high-velocity yttria-stabilized zirconia (YSZ) molten droplet with microstructure formation in plasma thermal spraying processes. The numerical model entails the explicit finite difference solution of the Navier-Stokes equations and the energy balance equations, coupled with the Cahn-Hilliard equation to track the liquid-gas two phase interface and with a phase field model for solidification microstructure formation involving the polycrystalline growth. Numerical model procedures are given. The model, after being checked for mesh-independence, was applied to study the spreading and solidification of a high-temperature high-velocity YSZ droplet impinging upon a preheated substrate surface under the conditions typical of supersonic plasma thermal spraying processes. Extensive numerical simulations were carried out and results reveal that the solidification microstructure formed in the spreading droplet consists primarily of columnar grains. Computed results are also compared with thermal spray experiments, and gratifying agreement is obtained.

Effect of ultrasonic excitation on the process of L-PBFAM

Abstract Laser-Powder bed fusion additive manufacturing (L-PBFAM) is a layer-by-layer metal manufacturing technique that allows unlimited freedom of design with no increase in manufacturing complexity. Currently, parts made through L-PBFAM need to be heat treated and annealed to prevent residual stress, anisotropy, low ductility, and low fatigue life inherent to the process. This paper demonstrates that the adoption ultrasonic excitation to the L-PBFAM process is able to alleviate some of the aforementioned problems. To determine the effects of ultrasonic excitation on the solidification process and microstructure formation, a phase field simulation model incorporating the effect of ultrasonic cavitation in the melt pool was created. Finite Element Method simulation in ANSYS was used to determine the initial macro thermal condition of the melt pool, while the phase field was used to simulate the nucleation and grain growth within the melt pool under ultrasonic excitation based on thermodynamic theory. Robust Design of Experiment (DOE), guided by insights on the L-PBFAM process, was conducted to determine the contributions of different process parameters on the grain size and configuration. The simulated grain structure showed close correlation to optical micrographs of fabricated 304 L Stainless Steel L-PBFAM samples. The ultrasonic excitation is shown to have a significant effect on the microstructure and the cooling rate of the melt pool is found to be the key process optimization parameter affecting the grain morphology.