Solidification Morphology Research Articles

Uncertainty Quantification in Modeling Metal Alloy Solidification

Numerical simulations of metal alloy solidification are used to gain insight into physical phenomena that cannot be observed experimentally. These models produce results that are used to draw conclusions about a process or alloy and often compared to experimental results. However, uncertainty in model inputs cause uncertainty in model results, which have the potential to significantly affect conclusions drawn from their predictions. As a step toward understanding the effect of uncertain inputs on solidification modeling, uncertainty quantification (UQ) and sensitivity analysis are performed on a transient model of solidification of Al–4.5 wt % Cu in a rectangular cavity. The binary alloy considered has columnar solidification morphology, and this model solves equations for momentum, temperature, and species conservation. UQ and sensitivity analysis are performed for the degree of macrosegregation and solidification time. A Smolyak sparse grid algorithm is used to select input values to construct a polynomial response surface fit to model outputs. This polynomial is then used as a surrogate for the complete solidification model to determine the sensitivities and probability density functions (PDFs) of the model outputs. Uncertain model inputs of interest include the secondary dendrite arm spacing (SDAS), heat transfer coefficient, and material properties. The most influential input parameter for predicting the macrosegregation level is the dendrite arm spacing, which also strongly depends on the choice of permeability model. Additionally, the degree of uncertainty required to produce accurate predictions depends on the outputs of interest from the model.

Morphology of Spherulites in Rapidly Solidified Ni3Ge Droplets

The congruently melting, single phase, L12 intermetallic β-Ni3Ge has been subject to rapid solidification via drop-tube processing. Four different cooling rates are used in this process, at very low cooling rates (≥850 μm diameter particles, ≥700 K s−1) and slightly higher cooling rates (850–500 μm diameter particles, 700–1386 K s−1) the dominant solidification morphology, revealed after etching, is that of isolated spherulites in an otherwise featureless matrix. At higher cooling rates, (500–300 μm diameter particles, 1386–2790 K s−1 and (300–212 μm diameter particles, 2790–4600 K s−1) mixed spherulite and dendritic morphologies are observed. Indeed, at the higher cooling rate dendrites with side-branches composed of numerous small spherulites are observed. Selected area diffraction analysis in the TEM indicate that the formation of spherulites is due to an order-disorder transformation. Dark-field TEM imaging has confirmed that the spherulites appear to consist of lamellae of the ordered phase, with disordered material in the space between the lamellae. The lamellar width within a given spherulite is constant, but the width is a function of cooling rate, with higher cooling rates giving finer lamellae. As such, there are many parallels with spherulite growth in polymers.

Solid-liquid interfacial free energy and its anisotropy in the Cu-Ni binary system investigated by molecular dynamics simulations

Abstract The solid-liquid interfacial free energy γ and its anisotropy in the Cu-Ni binary system were measured by using molecular dynamics simulations coupled with the capillary fluctuation method (CFM) based on an embedded atom method potential. It is found that both the interfacial energy and its anisotropy are enhanced with the increasing of the coexisting temperature, significant variations are however observed in the anisotropy parameters. Nonetheless, the anisotropy relationship is hardly modified, and the inequality γ100 > γ110 > γ111 holds for all temperatures studied. By projecting the calculated anisotropy parameter e 1 and e 2 onto the dendrite growth direction selection map, one finds that a dendrite is generally favored for the Cu-Ni alloys. Upon alloying, the preferred dendrite growth direction shifts to the vicinity of the boundary between the and hyper-branched regions, indicating the possibility of a transition of solidification morphology from a dendrite dominated to a hyper-branched one. These predictions agree well with and explain the experimental observations during the equilibrium and non-equilibrium solidifications in the Cu-Ni alloy systems.

Hydrogen-induced amorphization of Zr-Cu-Ni-Al alloy

Arc melting was utilized in this study to produce Zr55Cu30Ni5Al10 alloys under mixed atmospheres with various ratios of high-purity hydrogen to argon. The influences of hydrogen addition on the solidification structure and glass-forming ability of Zr55Cu30Ni5Al10 alloy were determined by examining microstructures in different parts of the cast ingots. The results showed that different degrees of crystallization structures were obtained in the ascast button ingots after arc melting in high-purity Ar, and the cross-sectional solidification morphology of arcmelted ingots was found to consist of crystals with varying from the bottom up. By contrast, there were completely amorphous structures in the middle and upper areas of the as-cast button ingots fabricated by adding 10% H2 to the high-purity Ar atmosphere. A clear solidification interface was found between the crystal and glass in the ascast button ingots, which indicates that hydrogen addition can enhance the Zr55Cu30Ni5Al10 alloy’s glass-forming ability. The precise mechanism responsible for this was also investigated.

Numerical analysis of fused-coating metal additive manufacturing

Limited build volumes, slow deposition rates, high feedstock costs and high machine costs significantly limit the current metal additive manufacturing market to researchers and large industrial users. In this paper, a new metal additive manufacturing (AM) process, referred to as the ‘‘metal fused-coating additive manufacturing (MFCAM),’’ was developed for high-efficiency deposition of metal parts. The new process is the combination of the metal fused-coating process and laser surface-melting process. A numerical investigation of the transient transport phenomena occurring during the fused-coating process was performed. The prevailing physical mechanisms of the fused-coating process, including the bulk liquid metal, capillarity effects at the liquid-solid interface, heat transfer, the solidification morphology of the coated layers, are identified and quantified numerically. The numerical models are validated with recent experimental results. The comparison between the numerical simulations and the experimental findings shows a good agreement. The interdependency of substrate moving speed, the height of gap between fused-coating head and substrate, the melt flow rate, and solidification morphology of the coated layers is examined in order to describe the forming process. This understanding is essential to implement effective process control in metal fused-coating additive manufacturing.

Microstructure evolution of polyvinyl alcohol aqueous solution solidated in two-dimensional direction

Porous polymers have received much attention in recent years because of their light quality,high strength,good permeability and easy-revisable.Various fabrication methods of porous polymers have been used in which ice templating is a process which can prepare porous materials with complex structures and fine microstructures.This method has been widely used to prepare porous polymers but it still has many problems,such as poor homogeneity of pore distribution and pore connectivity.To solve these problems,it is necessary to understand the morphology of ice crystal growth in the solidification process of polymer solution.In situ observation of directional solidification is adopted in this paper to study the morphology evolution during directional solidification of polyvinyl alcohol (PVA) aqueous solution with different concentrations and molecular weights under different pulling speeds.The experimental results show that the primary dendrite spacing of PVA aqueous solution decreases with the increase of pulling speed at low concentration (1 wt%,2.5 wt%).However,increasing PVA concentration does not result in significant change in primary dendrite spacing.The primary dendrite spacing varies with pulling speed whereas the dendritic primary arm tends to shrink with increasing velocity.The effects of PVA concentration and pulling speed on morphology are partly because of diffusion instability from the classical solidification theory.When the concentration of solution is 5 wt%,there is little change of primary dendrite spacing with the velocity,which is due to the suppressed diffusion instability by high concentration of the polymer solution and large viscosity.When the concentration of solution increases to 10 wt%,ice crystal morphology is seaweed-like,where the PVA molecules are enriched and crosslinked ahead the ice crystal,leading to the continuous bifurcation of the dendrites.For the solidification morphologies of the aqueous solutions with different PVA molecular weights,the primary dendrite spacing of PVA aqueous solution decreases with the increase of pulling speed at low molecular weight (Mw=24000).Increasing PVA molecular weight does not result in significant change in primary dendrite spacing.At the low PVA molecular weight,the interface shows cell morphology.With the increase of PVA molecular weight,the large chain length leads to the stronger interaction among them and suppressing their diffusion. The corresponding constitutional undercooling is strengthened,thereby promoting the interfacial instability and dendrite formation.From the classical solidification morphology formation mechanism it may be concluded that the solidification morphology of PVA aqueous solution is determined by the competition between the two different mechanisms,i.e., interface instability induced by diffusion of PVA molecule and the local phase separation from the crosslinking of PVA polymer chains.

Macroscopic elucidation of morphology of solidification by electrolytic polymerization on new development of sensor

Macroscopic elucidation of morphology of solidification by electrolytic polymerization on new development of sensor

Liquid-liquid phase separation and solidification behavior of Al-Bi-Sb immiscible alloys

Abstract In this study, the liquid-liquid phase separation of three kinds of ternary immiscible Al-Bi-Sb melts was investigated with resistivity and thermodynamics method. The resistivity-temperature curves showed the abrupt and anomalously changes with rising temperature, corresponding to the anomalous peaks of DSC curves, which confirmed the occurrence of the liquid-liquid phase separation. The effects of composition on the liquid-phase separation and final solidification morphology of Al-Bi-Sb alloys were investigated. The compositions of Al70Bi24Sb6, Al60Bi32Sb8 and Al55Bi36Sb9 all fell into liquid miscibility gap. The core-shell structure of Al-rich core covered by Bi-rich could form in three kinds of Al-Bi-Sb alloys by casting in copper mold. Unlike the core shell morphology of Al70Bi24Sb6 and Al60Bi32Sb8, the Al-rich phase distributed randomly on the Bi-rich matrix in the solidification morphology of Al55Bi36Sb9 alloy, which was attributed to the difference of Stokes effect and miscible temperature gap. This study is expected to provide a beneficial guidance and reference for preparing the monotectic alloy with core-shell structure via liquid-liquid phase separation.

Solidification morphology and segregation in continuously cast steel slab

Solidification morphology and centreline macrosegregation in continuously cast, thick steel slab samples were investigated in order to evaluate the liquid steel solidification characteristics and determine the severity of macrosegregation in cast slabs. Experimental studies were undertaken to establish the true solidification behaviour of industrial slab caster without electromagnetic stirring. Several slab samples collected from the continuous casting shop were utilized to characterize the solidification macrostructure, morphology of cast structure, and macrosegregation patterns. Macrostructural examination revealed predominantly coarse, columnar structure associated with high level of segregation which is detrimental to internal soundness of cast slabs. Liquid steels cast at high superheat (≥32°C) were generally having finer cast structures as compared to those cast at lower superheats (≤21°C). Degree of centreline segregation of Carbon (C), Phosphorus (P) and Manganese (Mn) were significantly high. Several unwanted phases (cementite, sulphide and phosphide) were also observed in the central segregated region of slab samples. An attempt was made to correlate the experimental observations with the operating parameters of the caster, and appropriate measures for improving the product quality were suggested.

Effect of Cu substitution on structural and hard magnetic properties of rapidly solidified Zr18Co82-xCux melt spun ribbons

The necessity to have rare earth free permanent magnets has driven the research efforts world over to explore the rare earth free compositions to make permanent magnets. The composition of Zr18Co82-xCux (x = 0–3) was chosen, melt spun followed by a detailed investigation on structural and magnetic properties. The melt spun ribbons obtained from these nominal compositions contained rhombohedral (R) Zr2Co11, orthorhombic (O) Zr2Co11 and fcc Co phases. The substitution of near atomic radius Cu for Co results in increase of O-Zr2Co11 phase. As a result, for an increase of Cu content from x = 0 to 3, the saturation magnetization (Ms) increases from 56 to 101emu/g, while the coercivity (Hc) decreases monotonously from 2.2 to 1.5 kOe. The easy magnetization direction lies along the plane of the ribbon. There is a significant change in the solidification morphology of the ribbons as a function of Cu content. It changes from dendritic to equiaxed and again to dendritic with increase in Cu addition.

In-situ observation of coupled peritectic growth in a binary organic model alloy

Peritectic alloys form a variety of solidification morphologies of which peritectic coupled growth (PCG) is the most peculiar. Because the conditions that lead to PCG are still under discussion, in-situ investigations of the evolution from lateral bands to PCG were carried out by using binary organic TRIS-NPG model alloys at concentrations in the peritectic region. The experiments were done vertically with relatively large rectangle glass tubings. For a hyper-peritectic alloy at growth rates below the morphological stability limits of both solid phases, we found that first the properitectic phase grew while lateral bands of the peritectic phase formed between the glass walls and the properitectic phase. Then, the peritectic phase dominated the growth until lateral bands of the now properitectic phase occurred, again close to the glass walls. Now both phases grew side-by-side as two layers at different depths in the sample. However, the properitectic phase spread locally onto the peritectic/liquid interface, so that patches of peritectic phase surrounded by a properitectic matrix developed. This resulted in creating an unstable PCG mode with cycles of increasing and decreasing phase amounts, which from a side-on view resemble tulip- and onion-like structures respectively.

Disorder-order morphologies in drop-tube processed Ni 3 Ge: Dendritic and seaweed growth

The single phase intermetallic β-Ni3Ge has been subject to rapid solidification via drop-tube processing. Droplets spanning the size range 212–38 μm, with corresponding cooling rates of 5800–54,500 K s−1, have been subject to microstructural investigation using SEM. Three dominant solidification morphologies have been identified with increasing cooling rate, namely; (i) well-defined dendrites with orthogonal side-branching, (ii) dendrites with non-orthogonal side-branching and (iii) dendritic seaweed. Selected area diffraction analysis in the TEM reveals that both types of dendrites are the disordered form of β-Ni3Ge in a matrix of the ordered, L12, form. However, the diffraction pattern from the dendritic seaweed cannot be mapped onto a cubic structure, indicating a change in the underlying crystallography coincident with the transition to the seaweed structure.

Compact seaweed growth of peritectic phase on confined, flat properitectic dendrites

Peritectic alloys form a variety of different solidification morphologies at low growth rates. An alloy with a concentration that corresponds to the hyper-peritectic limit should show a cellular/dendritic solidification of the peritectic phase for growth velocities above the corresponding constitutional undercooling limit. However, due to nucleation retardation of the peritectic phase we observed growth of properitectic dendrites before cellular growth of the peritectic could established. The transition happened via an overgrowth of dendrites with a thin layer of peritectic phase. The observations were made using a transparent, metal-like solidifying peritectic system that was solidified directionally in thin samples. In the gap between the flat dendrites and the tubing walls, the peritectic phase grew with a compact seaweed morphology, whereas in the interdendritic spacing it formed small-curved bumps. At same distance behind the tip region, more and more polycrystalline-like objects appeared at the elongated traces of the compact seaweed morphology.

Microstructural Characterisation of Glass Ceramics as a Component Part of High Pressure Discharge Lamps

Abstract The investigation presented is of part of a high pressure discharge lamp. The heart of the lamp is a ceramic burner which is sealed with a so-called glass solder, a glass ceramic comprised of a mixture of Oxides (Dysprosium Oxide, Aluminium Oxide and Silicon Oxide). Two different chemical compositions of glass solder, which are part of type of a composite material comprised of a broad spectrum of materials, are compared microscopically. The morphology of solidification, which has an effect on the operating life of the lamps is characterised using various classical methods such as optical light microscopy and Scanning Electron Microscopy.

Numerical simulation of dendritic growth in directional solidification of binary alloys using a lattice Boltzmann scheme

A lattice Boltzmann (LB) based model is utilized to simulate three dimensional dendritic growth in directional solidification of alloys. The LB–D3Q19 lattice vectors are used to describe advancement of solid–liquid interface, coupling with a conservation equation for solute transport in solidification. After model validation, the dendritic growth under several conditions of directional solidification was investigated and a solidification entropy was proposed to quantitatively characterize solidification morphologies. The results show that the present model captures tip-splitting occurring at a relative fast solidification rate. Initial thermal undercooling and solute concentration are dominant factors influencing the final microstructure. The solidification entropy reflects complexity of dendritic morphologies and it is useful to characterize dendritic growth in solidification. A design map was proposed to predict dendritic growth with and without tip-splitting, offering potential for simulating dendritic growth and microstructure evolution in solidification of alloys.

4D synchrotron X-ray tomographic quantification of the transition from cellular to dendrite growth during directional solidification

Solidification morphology directly impacts the mechanical properties of materials; hence many models of the morphological evolution of dendritic structures have been formulated. However, there is a paucity of validation data for directional solidification models, especially the direct observations of metallic alloys, both for cellular and dendritic structures. In this study, we performed 4D synchrotron X-ray tomographic imaging (three spatial directions plus time), to study the transition from cellular to a columnar dendritic morphology and the subsequent growth of columnar dendrite in a temperature gradient stage. The cellular morphology was found to be highly complex, with frequent lateral bridging. Protrusions growing out of the cellular front with the onset of morphological instabilities were captured, together with the subsequent development of these protrusions into established dendrites. Other mechanisms affecting the solidification microstructure, including dendrite fragmentation/pinch-off were also captured and the quantitative results were compared to proposed mechanisms. The results demonstrate that 4D imaging can provide new data to both inform and validate solidification models.

Rapid solidification morphologies in Ni3Ge: Spherulites, dendrites and dense-branched fractal structures

Single-phase β-Ni3Ge has been rapidly solidified via drop-tube processing. At low cooling rates (850–300 μm diameter particles, 700–2800 K s−1) the dominant solidification morphology, revealed after etching, is that of isolated spherulites in an otherwise featureless matrix. At higher cooling rates (300–75 μm diameter particles, 2800–25,000 K s−1) the dominant solidification morphology is that of dendrites, again imbedded within a featureless matrix. As the cooling rate increases towards the higher end of this range the dendrites display non-orthogonal side-branching and tip splitting. At the highest cooling rates studied (<75 μm diameter particles, >25,000 K s−1), dense-branched fractal structures are observed. Selected area diffraction analysis in the TEM reveals the spherulites and dendrites are a disordered variant of β-Ni3Ge, whilst the featureless matrix is the ordered variant of the same compound. We postulate that the spherulites and dendrites are the rapid solidification morphology and that the ordered, featureless matrix grew more slowly post-recalescence. Spherulites are most likely the result of kinetically limited growth, switching to thermal dendrites as the growth velocity increases. It is extremely uncommon to observe such a wide range of morphologies as a function of cooling rate in a single material.

Uncertainty Quantification of Modelling of Equiaxed Solidification

Numerical simulations of metal alloy solidification are used to gain insight into physical phenomena that cannot be observed experimentally. Often validation of such models has been done through comparison to sparse experimental data, to which agreement can be misinterpreted due to both model and experimental uncertainty. Uncertainty quantification (UQ) and sensitivity analysis are performed on a transient model of solidification of Al-4.5 wt.% Cu in a rectangular cavity, with equiaxed (grain refined) solidification morphology. This model solves equations for momentum, temperature, and species conservation; UQ and sensitivity analysis are performed for the degree of macrosegregation. A Smolyak sparse grid algorithm is used to select input values to construct a response surface fit to model outputs. The response surface is then used as a surrogate for the solidification model to determine the sensitivities and probability density functions of the model outputs. Uncertain model inputs of interest include the secondary dendrite arm spacing, equiaxed particle size, and fraction solid at which the rigid mushy zone forms. Similar analysis was also performed on a transient model of direct chill casting of the same alloy.

Numerical analysis of heat transfer during multi-layer selective laser melting of AlSi10Mg

A three-dimensional finite element model is developed to simulate multi-layer deposition of AlSi10Mg in selective laser melting (SLM) by using commercial ANSYS software. The temperature distribution, thermal history, molten pool depth, remelting depth, cooling rate and solidification morphology parameter in multi-layer buildup process are investigated. Furthermore, the effect of laser energy input on the melting and solidification process is evaluated. The results show that the temperature and molten pool depth gradually increases with new layers and energy input. The cooling rate increases progressively while the solidification morphology parameter decreases with the increase of energy input. It leads to obtain fine grains with low energy input. To verify the accuracy of simulated results, experiments are performed. Compared simulated results with experimental ones, good agreement is obtained.

Evaluation of three kinds of MCrAlY coatings produced by electrospark deposition

Three kinds of MCrAlY coatings with different aluminum contents (5%, 8%, 12%) were prepared by electrospark deposition (ESD), their microstructure and oxidation behavior were studied by SEM and XRD. The results showed that the phase composition of the coatings changed from single γ-Ni to γ-Ni+β-NiAl hypoeutectic to γ-Ni+β-NiAl hypereutectic with increasing aluminum content, and their solidification morphologies changed from cluster of cellular structure to cellular dendrites to coarse dendrites with secondary arms. When exposed at 1000 °C, the coatings with higher Al content had a stronger tendency to form θ-Al2O3 in the initial several hours. After 100 h of oxidation, a dense and adherent α-Al2O3 scale formed on all of the three coatings but the thickness of α-Al2O3 scale and the amount of remaining θ-Al2O3 increased with increasing Al content. These results revealed different characteristics of ESD MCrAlY coatings which could provide scientific guidance for industrial application.