Equiaxed Dendrite Growth Research Articles

Structures in grain-refined directionally solidified hypoeutectic Al-Cu alloys: Benchmark experiments under microgravity on-board the International Space Station

Benchmark solidification experiments were successfully performed under microgravity conditions on-board the International Space Station (ISS) within the ESAprogramme CETSOL (Columnar-to-Equiaxed Transition in SOLidification Processing). Cylindrical samples of grain-refined Al-4wt.%Cu, Al-10wt.%Cu and Al-20wt.%Cu alloys were directionally solidified in a gradient furnace to investigate columnar and equiaxed dendritic growth structures as well as the columnar to equiaxed transition under diffusive conditions. The determination of temperature gradients; interface velocities; and cooling rates at liquidus, solidus, and eutectic front positions provides well-defined thermal experimental characterization. The evaluation of the flight samples demonstrates that no significant macrosegregation along the sample axis occurred and no radial effects were observed. Therefore, purely diffusive solidification behaviour without any residual melt convection can be assumed for these microgravity experiments. The analyses of the microstructure in longitudinal cross-sections show dendritic structures without any pore formation and the averaged eutectic fraction is largely constant along the sample. The samples of refined Al-4wt.%Cu alloy show a sharp CET from columnar dendrites to a fine equiaxed steady-state grain structure whereas in the samples of refined Al-10wt.%Cu and Al-20wt.%Cu alloy, only equiaxed dendritic grain growth is observed. A quantitative analysis of the equiaxed grain morphology shows, that the shapes of the equiaxed dendrites depend on the applied temperature gradient, but the grain sizes in radial and longitudinal directions are identical. Therefore, a fully equiaxed dendritic growth structure without dendrite elongation was obtained. Compared to experiments in microgravity with non-refined Al-Cu alloys the average equiaxed grain size is about three times smaller.

Elucidating the promoting mechanism of nitrogen in the columnar-to-equiaxed transition of steel ingot

Based on the behavior of heat and mass transfer ahead of the advancing columnar front, combined with the nucleation and growth of dendrites, as well as the blocking mechanism of columnar-to-equiaxed transition (CET), the promoting mechanism of nitrogen in the CET of steel ingot was elucidated. It was found that the CET moves from the center to the edge of the ingot as the nitrogen content increases, resulting in a decrease in the columnar dendrite zone and an increase in the equiaxed dendrite zone. The occurrence of this phenomenon can be attributed to two factors. On the one hand, an increase in nitrogen content leads to an increase in critical nucleation supercooling and incubation time of dendrites, causing a decrease in the number of dendrites nucleation. Additionally, the higher nitrogen content reduces the restriction effect of solute on the growth of columnar dendrites, leading to an increase in dendrite size. On the other hand, within the constitutional supercooling (CS) zone ahead of the advancing columnar front, both the CS and temperature gradient decrease with increasing nitrogen content, while the CS increases and the temperature gradient decreases with the distance from the advancing columnar front. Consequently, the nitrogen solute primarily influences the nucleation and growth of columnar and equiaxed dendrites, as well as the length, temperature gradient, and growth restriction factor Qc of the CS zone, resulting in changes in the heat and mass transfer behavior ahead of the advancing columnar front, thereby promoting CET.

Scaling law for growth of misoriented equiaxed Al-Cu dendrites: A phase-field study with in situ experiment validation

We consider the effect of a mutual misorientation between two interacting equiaxed dendrites in polycrystalline materials on the scaling law of growth from undercooled melt. This effect is investigated by three-dimensional quantitative phase-field simulations of Al-Cu alloy solidification in thin samples. It has been found that the equiaxed dendritic growth kinetics changes due to the reduced solute interaction when considering mutual grain misorientation, and both the characteristic growth rate and primary dendritic arm length can be approximately correlated linearly to the misorientation of two dendrites. The scaling law, which originally uses the solute composition and the distance between two nuclei as physical parameters to describe the dynamics of primary dendritic arms, is then adapted with consideration of the misorientation. Compared with the previous scaling law that only concerns face-to-face growth of two dendrites, the predictions of the newly proposed scaling law taking the grain orientation in account are in better agreement with the experimental data.

Application of a meshless space-time adaptive approach to phase-field modelling of polycrystalline solidification

We have developed a 2-D numerical meshless adaptive approach for phase-field modelling of dendritic solidification. The quadtree-based approach decomposes the computational domain into quadtree sub-domains of different sizes. The algorithm generates uniformly-distributed computational nodes in each quadtree sub-domain. We apply the meshless radial basis function generated finite difference method and the forward Euler scheme to discretise governing equations in each computational node. The fixed ratio between the characteristic size and the node spacing of a quadtree sub-domain ensures space adaptivity. The adaptive time-stepping accelerates the calculations further. In the framework of previous research studies, we used the approach to solve quantitative phase-field models for single dendrite growth in pure melts and dilute binary alloys. In the present study, we upgrade the solution procedure for the modelling growth of multiple differently oriented dendrites. Along with the space-time adaptive approach, we apply non-linear preconditioning of the phase-field equation to increase computational efficiency. We investigate a novel numerical approach’s accuracy and computational efficiency by simulating the equiaxed dendrite growth from a dilute binary alloy.

Multiple-relaxation-time lattice Boltzmann model for anisotropic liquid–solid phase change

An extended lattice Boltzmann model is proposed for the anisotropic solidification process based on the quantitative phase-field equation. To include the anisotropy, we derive an equivalent diffusion matrix and design an off-diagonal relaxation-time matrix to recover it within the framework of the lattice Boltzmann method. Different from the standard collision-streaming algorithm, a correction step after the streaming step is introduced, which improves the model’s locality. Numerical tests are conducted for the equiaxed dendrite growth in both two and three dimensions. Results obtained by the present lattice Boltzmann model have a good agreement with analytical solution and numerical prediction in literature. Furthermore, the present model shows superiority in efficiency especially for the large-scale modeling in the parallel machines.

Numerical Analysis of Nucleation and Growth of Stray Grain Formation during Laser Welding Nickel-Based Single-Crystal Superalloy Part II: Solidification Cracking Diminution through Single-Crystallinity Control

The effect of thermo-metallurgical factors, such as heat input and welding configuration, on solidification cracking driving forces nearby dendrite tip, such as solidification temperature range and columnar/equiaxed transition (CET) was thermodynamically and kinetically discussed with aid of comprehensive numerical analysis for multicomponent melt-pool solidification during laser processing under non-equilibrium solidification conditions to better understand problematical solidification cracking phenomena. By using (001)/[100] welding configuration, axisymmetrical distributions of columnar/equiaxed transition and solidification temperature range alongside solidification interface are homogeneously produced on both sides of weld pool. By using (001)/[110] welding configuration, nonaxisymmetrical distributions are heterogeneously produced, and are able to bring about infelicitous microstructure degradation. Unidirectional region of [001] columnar dendrite is more prone to epitaxial growth without morphology transition to conservatively better crystallography-assisted single-crystal growth. Unidirectional epitaxial growth is collapsed, and onset of stray grain nucleation and solidification cracking eventuates in [100] region of equiaxed dendrite growth. Low heat input relatively broadens portion of unidirectional columnar dendrite, where stray grain is infrequently nucleated and grown, and thus morphology transition seldom happens, as long as undercooling and solidification temperature range alongside dendrite tip are sufficient low to challengingly develop crackless dendrite growth and high-quality weld by thermometallurgy-aided single-crystallinity control. Auspicious (001)/[100] welding configuration simultaneously abates overall stray grain nucleation and constricts solidification temperature range nearby fusion boundary to wane microstructure heterogeneity. Conversely, plenteous stray grain formation is kinetically attained and extensive solidification temperature range nearby fusion boundary is thermodynamically obtained by problematical (001)/[110] welding configuration to metallurgically induce pernicious equiaxed dendrite and disintegrate dendrite growth. Moreover, the mechanism of solidification cracking diminution as consequence of appropriate optimization of thermo-metallurgical determinants during multicomponent nickel-based single-crystal superalloy melt-pool non-equilibrium solidification is also proposed. The potent consistency between the predicted and experimented results is exceedingly tenable.

Numerical Analysis of Nucleation and Growth of Stray Grain Formation during Laser Welding Nickel-Based Single-Crystal Superalloy Part I: Morphology and Size of Dendrite Growth

The dependency of morphology development and dendrite growth on welding conditions (laser power, welding speed and welding configuration) is numerically analyzed to decrease nucleation and growth of stray grain formation during laser processing aerospace component surface of ternary Ni-Cr-Al single-crystal superalloy. Proper (001)/[100] welding configuration crystallographically initiates three axisymmetrical distributions of microstructure development, i.e. stray grain formation, morphology development and dendrite trunk spacing, alongside the advancing solid/liquid interface of molten pool, whereby metallurgical properties are increased. Unpromising (001)/[110] welding configuration tends to crystallographically possesses unaxisymmetrical microstructure development to favor substantial crack-vulnerable dendrite size and morphology. Epitaxial [001] columnar dendrite growth region is favored for single-crystal dendrite growth, while vulnerable [100] equiaxed dendrite growth region is more susceptible to solidification cracking. The lower heat input is used, the smaller stray grain formation, negligible columnar/equiaxed transition (CET) and finer dendrite trunk spacing are consistently promoted by narrower constitutional undercooling ahead of solid/liquid interface to improve crack-resistant microstructure development and weld integrity. When comparing between [100] dendrite growth region on the right side and [010] dendrite growth region on the left side, (001)/[110] welding configuration spontaneously engenders severer stray grain formation, insidious columnar/equiaxed transition and coarser dendrite trunk spacing on the right side to deteriorate microstructure development with restriction of the same heat input on both sides of weld pool. The mechanism of asymmetrical solidification cracking as result of crystallography-induced microstructure degradation is therefore proposed. The theoretical predictions of asymmetrical solidification cracking susceptibility are comparable with experiments.

Time invariance of three-dimensional morphology of equiaxed dendrite: A phase-field study

Dendrite morphology has a significant effect on solute segregation and fluid flow in bulk metallic materials. Therefore, the detailed morphological evolution of dendrites is important to better understand these processes. Recently, three-dimensional (3D) dendrite morphology has been analyzed using interface shape distribution (ISD) maps that are spanned by the curvedness and shape factor of the local solid−liquid interface in an Al−Cu alloy. Data were collected through in-situ observations using synchrotron radiation imaging techniques [J.W. Gibbs et al.: Sci. Rep., 5 (2015) 11824]. This methodology is quite effective for describing 3D dendrites. In this study, we thoroughly investigated the morphological evolution and the related ISD map of free-growing equiaxed dendrites in an Al−3mass%Cu alloy using a quantitative phase-field model. The ISD was found to differ depending on the degree of undercooling. Importantly, the results indicate the presence of a time-invariant feature after sufficient branching and growth of secondary arms, when the degree of undercooling is substantial enough to produce a bunch of branching. The time invariance is considered a universal feature of equiaxed dendrite growth.

The Morphology and Solute Segregation of Dendrite Growth in Ti-4.5% Al Alloy: A Phase-Field Study

Ti-Al alloys have excellent high-temperature performance and are often used in the manufacture of high-pressure compressors and low-pressure turbine blades for military aircraft engines. However, solute segregation is easy to occur in the solidification process of Ti-Al alloys, which will affect their properties. In this study, we used the quantitative phase-field model developed by Karma to study the equiaxed dendrite growth of Ti-4.5% Al alloy. The effects of supersaturation, undercooling and thermal disturbance on the dendrite morphology and solute segregation were studied. The results showed that the increase of supersaturation and undercooling will promote the growth of secondary dendrite arms and aggravate the solute segregation. When the undercooling is large, the solute in the root of the primary dendrite arms is seriously enriched, and when the supersaturation is large, the time for the dendrite tips to reach a steady-state will be shortened. The thermal disturbance mainly affects the morphology and distribution of the secondary dendrite arms but has almost no effect on the steady-state of the primary dendrite tips. This is helpful to understand the cause of solute segregation in Ti-Al alloy theoretically.

Mesoscopic modeling of equiaxed and columnar solidification microstructures under forced flow and buoyancy-driven flow in hypergravity: Envelope versus phase-field model

Quantitative modeling of solidification microstructures growing under the influence of convection is a challenging multiscale problem. It is of particular interest in processes where strong flow is present, such as centrifugal casting of Ti–Al alloys, where hypergravity strongly reinforces the buoyancy-driven flow. We present the coupling of the mesoscopic envelope model for dendritic solidification with fluid flow. We use the model to investigate columnar and equiaxed dendritic growth of the β-solidifying Ti–45 at.%Al under the influence of flow. The calculations are compared to phase-field results in 2D. For equiaxed growth the case of forced flow is treated. For columnar growth, the influence of buoyancy-driven flow on the growing structure and on the primary dendrite arm spacing is characterized for gravity levels ranging from 0 to ± 15 g. The computational cost of the mesoscopic simulations is around two orders of magnitude lower than that of phase field. We show that the mesoscopic model can accurately reproduce the microstructure characteristics, such as grain shape and primary arm spacing (PDAS), as long as the dendrite tip remains parabolic. When flow effects in columnar growth are strong enough to change the tip shape and induce tip splitting events, the mesoscopic envelope model does not reproduce the resulting branched microstructures. It does however predict the corresponding PDAS reduction at the correct gravity level.

Effect of Diffusion Length in Modeling of Equiaxed Dendritic Solidification under Buoyancy Flow in a Configuration of Hebditch–Hunt Experiment

Modeling of equiaxed solidification is vital for understanding the solidification process of metallic alloys. In this work, an extended literature review is given for the models currently used for equiaxed solidification simulations. Based on this analysis, we present a three-phase multiscale equiaxed solidification model in which some approximations regarding solute transport at microscopic scale are put together in a new way and incorporated into macroscopic transport equations. For the latter, a term relating to the momentum exchange between the two phases is revised, and a modification for the grain packing algorithm is proposed. A modernized model for equiaxed dendrite growth is tested using a case of solidification of Sn-5 wt pct Pb alloy in a parallelepiped cavity that mimics the Hebditch–Hunt experiment. The results obtained using two approaches to calculate diffusion length are presented and compared both with each other and with numerical results from elsewhere. It is demonstrated that diffusion length has a crucial effect on the final segregation pattern.

Effect of time–modulated magnetic fields on the solidification structure and extrusion properties of wrought aluminum alloys

Wrought aluminum alloys and in particular extruded products have a large economic importance worldwide. The opportunities to increase the quality or to reduce the production cost have great a strong finance and ecologic incentive. AC magnetic fields provide the possibility to influence the melt flow in a contactless way to influence the temperature and solute distribution in front of the solidification front. Many studies have shown the beneficial effects like a distinct grain refinement or the promotion of a transition from a columnar to an equiaxed dendritic growth (CET). The use of time-modulated magnetic fields are able to avoid segregation effects, just like known from privies studies they work with permanent rotating magnetic fields, for example.This present study examines the directional solidification of commercial wrought aluminum alloys from a water-cooled copper chill. Rotating time-modulated magnetic fields were used to agitate the melt. Our results demonstrate the potential of time-modulated magnetic fields to control the grain size, the formation of intermetallic phases and extrusion properties.

Cellular Automaton Study of Hydrogen Porosity Evolution Coupled with Dendrite Growth During Solidification in the Molten Pool of Al-Cu Alloys

Welding porosity defects significantly reduce the mechanical properties of welded joints. In this paper, the hydrogen porosity evolution coupled with dendrite growth during solidification in the molten pool of Al-4.0 wt pct Cu alloy was modeled and simulated. Three phases, including a liquid phase, a solid phase, and a gas phase, were considered in this model. The growth of dendrites and hydrogen gas pores was reproduced using a cellular automaton (CA) approach. The diffusion of solute and hydrogen was calculated using the finite difference method (FDM). Columnar and equiaxed dendrite growth with porosity evolution were simulated. Competitive growth between different dendrites and porosities was observed. Dendrite morphology was influenced by porosity formation near dendrites. After solidification, when the porosities were surrounded by dendrites, they could not escape from the liquid, and they made pores that existed in the welded joints. With the increase in the cooling rate, the average diameter of porosities decreased, and the average number of porosities increased. The average diameter of porosities and the number of porosities in the simulation results had the same trend as the experimental results.

Near-isothermal furnace for in situ and real time X-ray radiography solidification experiments.

In this paper, we present a newly developed near-isothermal X-ray transparent furnace for in situ imaging of solidification processes in thin metallic samples. We show that the furnace is ideally suited to study equiaxed microstructure evolution and grain interaction. To observe the growth dynamics of equiaxed dendritic structures, a minimal temperature gradient across the sample is required. A uniform thermal profile inside a circular sample is achieved by positioning the sample in the center of a cylindrical furnace body surrounded by a circular heater arrangement. Performance tests with the hypo-eutectic Al-15wt.%Cu and the near-eutectic Al-33wt.%Cu alloys validate the near-isothermal character of the sample environment. Controlled cooling rates of less than 0.5 K min(-1) up to 10 K min(-1) can be achieved in a temperature range of 720 K-1220 K. Integrated in our rotatable laboratory X-ray facility, X-RISE, the furnace provides a large field of view of 10.5 mm in diameter and a high spatial resolution of ∼4 μm. With the here presented furnace, equiaxed dendrite growth models can be rigorously tested against experiments on metal alloys by, e.g., enabling dendrite growth velocities to be determined as a function of undercooling or solutal fields in front of the growing dendrite to be measured.

Benchmark experiments and numerical modelling of the columnar-equiaxed dendritic growth in the transparent alloy Neopentylglycol-(d)Camphor

Solidification benchmark experiments on columnar and equiaxed dendritic growth, as well as the columnar-equiaxed transition have been carried out under diffusion-dominated conditions for heat and mass transfer in a low-gravity environment. The system under investigation is the transparent organic alloy system Neopentylglycol-37.5wt.-%(d)Camphor, processed aboard a TEXUS sounding rocket flight. Solidifications was observed by standard optical methods in addition to measurements of the thermal fields within the sheet like experimental cells of 1 mm thickness. The dendrite tip kinetic, primary dendrite arm spacing, temporal and spatial temperature evolution, columnar tip velocity and the critical parameters at the CET have been analysed. Here we focus on a detailed comparison of the experiment “TRACE” with a 5-phase volume averaging model to validate the numerical model and to give insight into the corresponding physical mechanisms and parameters leading to CET. The results are discussed in terms of sensitivity versus numerical parameters.

Equiaxed and columnar dendrite growth simulation in Al-7Si- Mg ternary alloys using cellular automaton method

In this paper, a modified cellular automaton (MCA) model allowing for the prediction of dendrite growth of Al-Si-Mg ternary alloys in two and three dimensions is presented. The growth kinetic of S/L interface is calculated based on the solute equilibrium approach. In order to describe the dendrite growth with arbitrarily crystallographic orientations, this model introduces a modified decentered octahedron algorithm for neighborhood tracking to eliminate the effect of mesh dependency on dendrite growth. The thermody namic and kinetic data needed for dendrite growth is obtained through coupling with Pandat software package in combination with thermodynamic/kinetic/equilibrium phase diagram calculation databases. The effect of interactions between various alloying elements on solute diffusion coefficient is considered in the model. This model has first been used to simulate Al-7Si (weight percent) binary dendrite growth followed by a validation using theoretical predictions. For ternary alloy, Al-7Si-0.5Mg dendrite simulation has been carried out and the effects of solute interactions on diffusion matrix as well as the differences of Si and Mg in solute distribution have been analyzed. For actual application, this model has been applied to simulate the equiaxed dendrite growth with various crystallographic orientations of Al-7Si-0.36Mg ternary alloy, and the predicted secondary dendrite arm spacing (SDAS) shows a reasonable agreement with the experimental ones. Furthermore, the columnar dendrite growth in directional solidification has also been simulated and the predicted primary dendrite arm spacing (PDAS) is in good agreement with experiments. The simulated results effectively demonstrate the abilities of the model in prediction of dendritic microstructure of Al-Si-Mg ternary alloy.

Modelling the creation and destruction of columnar and equiaxed zones during solidification and melting in multi-pass welding of steel

The authors present a novel meso-scale (mm–cm) numerical model of multi-pass welding of stainless steel based on the front tracking formulation. During a typical multi-pass notched butt weld, multiple cycles of melting and solidification occur throughout the weld pool, where previously solidified equiaxed zones are destroyed by melting and subsequently resolidify in columnar form. These thermal cycles result from the thermal effects of the current deposition of liquid filler metal being superimposed onto those of the previous pass. The advancement of the liquidus isotherm is employed to characterize melting, while both columnar and equiaxed dendritic growth in the undercooled melt are considered in the model of solidification. Columnar solidification is simulated using a front tracking method where computational markers are employed to explicitly define the advancing columnar front. Competing equiaxed solidification is modelled using a volume averaging approach. During the first and second welding passes of a case study, the weld pool solidifies as purely columnar. This is due to the high thermal gradient present in the weld pool, which results in a very small region of undercooled liquid ahead of the columnar front and subsequently low levels of equiaxed grain nucleation/growth. Towards the end of the third and final pass the equiaxed grains have sufficient dwell time in the undercooled liquid to form a coherent network and present a physical barrier to the advancing columnar front. A Columnar to Equiaxed Transition (CET) occurs and the remainder of the weld pool solidifies in a fully equiaxed microstructure. The results are compared with Hunt’s analytical model of CET and the agreement is reasonably good. The occurrence of CET throughout the weld pool is directly predicted via this front tracking model without the need to rely on estimated thermal gradients and solidification rates. Further simulations indicate that CET can be promoted, even in early passes, by increasing the grain refiner level and/or by pre-heating the parent metal.

A Modified Cellular Automaton Model for the Quantitative Prediction of Equiaxed and Columnar Dendritic Growth

Since the characteristic of dendrite is an important factor determining the performance of castings, a two-dimensional cellular automaton model with decentered square algorithm is developed for quantitatively predicting the dendritic growth during solidification process. The growth kinetics of solid/liquid interface are determined by the local equilibrium composition and local actual liquid composition, and the calculation of the solid fraction increment is based on these two compositions to avoid the solution of growth velocity. In order to validate the developed model, quantitative simulations of steady-state dendritic features over a range of undercooling was performed and the results exhibited good agreement with the predictions of LGK (Lipton–Glicksman–Kurz) model. Meanwhile, it is demonstrated that the proposed model can be applied to simulate multiple equiaxed dendritic growth, as well as columnar dendritic growth with or without equiaxed grain formation in directional solidification of Al–Cu alloys. It has been shown that the model is able to simulate the growth process of multi-dendrites with various preferential orientations and can reproduce a wide range of complex dendritic growth phenomena such as nucleation, coarsening of dendrite arms, side branching in dendritic morphologies, competitive growth as well as the interaction among surrounding dendrites.

Simulation of Grain Growth during Solidification of Twin-Roll Continuously Cast Pure Aluminum with a Modified CA Model

Abstract A new mathematic model for the nucleation and the dendrite growth of twin-roll-continuously cast pure aluminum thin strip during solidification process was developed based on cellular automaton(CA)-finite element(FE) method and the classical transfer equations during dendrite growth. The model coupled the temperature field calculation and microstructure simulation. The solute diffusion, the curvature undercooling and the latent heat releasing were also considered in the model, all of which have significant influence on the dendrite evolution. So the dendrite growth morphology can be modeled. The applications of the model in equiaxed dendrite growth, multiple equiaxed dendrite growth, columnar grain growth, and columnar dendrite transformation to equiaxed dendrite in twin-roll-continuously cast aluminum thin strip solidification were presented. The microstructure simulation results were compared with the experimental results and they were in good agreement in dendrite morphology.

Numerical Simulation of Binary Alloy Crystal Growth of Multiple Dendrites and Direcitonal Solidification Using Phase-Field Method

Phase field method (PFM) offers the prospect of carrying out realistic numerical calculation on dendrite growth in metallic systems. The dendritic growth process of multiple dendrites and direcitonal solidification during isothermal solidifications in a Fe-0.5mole%C binary alloy were simulated using phase field model. Competitive growth of multiple equiaxed dendrites were simulated, and the effect of anisotropy on the solute segregation and microstructural dedritic growth pattern in directional solidification process was studied in the paper. The simulation results showed the impingement of arbitrarily oriented grains, and the grains began to impinge and coalesce the adjacent grains with time going on, which made the dendrite growth inhibited obviously. In the directional solidification, the maximum concentration gradient showed in the dendrite tip, and highest solute concentration existed at the bottom of the dendrites. With the increasing of the anisotropy, dendrite tip radius became smaller, and the crystal structure is more uniform and dense.