Solidification Velocity Research Articles

Uncertainty analysis of microsegregation during laser powder bed fusion

Quality control in additive manufacturing can be achieved through variation control of the quantity of interest (QoI). We choose in this work the microstructural microsegregation to be our QoI. Microsegregation results from the spatial redistribution of a solute element across the solid–liquid interface that forms during solidification of an alloy melt pool during the laser powder bed fusion process. Since the process as well as the alloy parameters contribute to the statistical variation in microstructural features, uncertainty analysis of the QoI is essential. High-throughput phase-field simulations estimate the solid–liquid interfaces that grow for the melt pool solidification conditions that were estimated from finite element simulations. Microsegregation was determined from the simulated interfaces for different process and alloy parameters. Correlation, regression, and surrogate model analyses were used to quantify the contribution of different sources of uncertainty to the QoI variability. We found negligible contributions of thermal gradient and Gibbs–Thomson coefficient and considerable contributions of solidification velocity, liquid diffusivity, and segregation coefficient on the QoI. Cumulative distribution functions and probability density functions were used to analyze the distribution of the QoI during solidification. Our approach, for the first time, identifies the uncertainty sources and frequency densities of the QoI in the solidification regime relevant to additive manufacturing.

Microstructure Evolution of Binary and Multicomponent Manganese Steels During Selective Laser Melting: Phase-Field Modeling and Experimental Validation

In additive manufacturing processes, solidification velocities are extremely high in comparison to ordinary directional solidification. Therefore, the dependencies of the primary dendrite arm spacing (PDAS) on the process parameters deviate from the dependencies predicted by standard analytical methods. In this work, we investigate the microstructure evolution and element distribution in Fe-18.9Mn and Fe-18.5Mn-Al-C alloys solidified during the selective laser melting process. A quantitative multicomponent phase-field model verified by Green-function calculations (Karma, Rappel: Phys. Rev. E, 1998, 57, 4323) and the convergence analysis is used. The resulting non-standard dependencies of the PDAS on the process parameters in a wide range of solidification velocities are compared with analytical calculations. It is shown that the numerical values of the PDAS are similar to the values predicted by the Kurz–Fisher method for the low and intermediate solidification velocities and are smaller for the solidification velocities higher than 0.03 m/s. The PDAS and the Mn distribution in a Fe-18.5Mn-Al-C alloy are compared to the experimental results and a very good agreement is found.

Formation Mechanism and Nucleation Effect of Ti2O3–TiN Complex Nucleus at Solidification Front of 18Cr Ferritic Stainless Steel

Formation mechanism of Ti2O3–TiN complex nucleus and its nucleation effect on δ-Fe at solidification front of Fe-18Cr ferritic stainless steel was investigated through experimental and theoretical methods. According to the equilibrium calculation, Ti2O3 will crystallize in the molten steel before solidification and TiN will not form until the solid phases appear. However, complex nucleus and equiaxed grains exist in the edge of Ti-bearing ingot, where the solidification velocity and temperature gradient are high. Therefore, complex nucleus is indicated to be formed at solidification front and a non-equilibrium solidification model for multi-component alloy was established to investigate the dendrite tip interface phenomenon. The calculation results exhibit an element enrichment at solidification front and explain well with the formation of complex nucleus before solidification. It is also found that there is approximate lattice matching between TiN, and Ti2O3, δ-Fe on the basis of disregistry theory. These results are consistent with the observed complex nucleus and the increased equiaxed zone ratio (EZR) of Ti-bearing ferritic stainless steel.

Transition of solid-liquid interface and tensile properties of CoCrFeNi high-entropy alloys during directional solidification

In order to understand effect of solidification velocity on microstructure evolution and mechanical properties of high entropy alloys (HEAs), CoCrFeNi HEA samples were directionally solidified at different solidification velocities (5–50 μm/s). The results show that all samples were directionally solidified, but the solid-liquid interface and columnar grains are different. Microstructure of them is only composed of FCC solid solution phase. Morphology of solid-liquid interface transforms from cellular, to cellular-dendritic, and then to dendritic with increasing of solidification rate. The criterion of solidification rate for cellular/dendrite transition is calculated as about 26.1 μm/s based on experimental results. The width of columnar grains decreases from 200 μm to 100 μm with solidification rate increasing from 5 μm/s to 50μm/s. Meanwhile, secondary dendrite spacing decreases from 200 μm to 30 μm for dendritic solidified samples (v = 10–50 μm/s). Tensile testing show that the yield strength improves from 233 MPa to 383 MPa, and the ultimate tensile strength improves from 431 MPa to 596 MPa with increasing of solidification rate. Meanwhile, the elongation of all samples is more than 34.3%, but rupture morphology analysis shows that the rupture changes from quasi-cleavage fracture to ductility fracture. The improvement of tensile properties is resulted from grain boundary strengthening of the columnar grain and second dendrite.

Development of an Anti-Trapping Current for Phase Field Models Using Arbitrary CALPHAD Thermodynamics

Unless corrected by so called anti-trapping currents, phase field models of solidification display a dependence upon the diffuse interface width, δ, used in the simulation. This is most commonly manifest as a reduction in solute partitioning, which is both growth velocity and interface width dependent, resulting in a serious impediment to quantitative simulation. However, such anti-trapping currents are often restricted to very simple materials thermodynamics, appropriate only to dilute ideal solutions. Here we propose a form of the anti-trapping current which can be implemented for arbitrary thermodynamics, including both Redlich-Kister solution phases and sub-lattice models for intermetallic growth. The effect of the new anti-trapping current is illustrated with respect to Pb dendrites growing from a Pb-Sn melt containing either 25% or 30% Sn. The new anti-trapping current is shown to render the solutions independent of the diffuse interface width both with regard to solute partitioning and other growth metrics such as solidification velocity and dendrite tip radius.

Multi-scale simulation of dendrite growth for direct energy deposition of nickel-based superalloys

In this study, a multi-scale model that integrates a macro-scale transient three-dimensional mass and heat transfer model and a micro-scale thin-interface phase-field model is developed to simulate the solidification behavior of the molten pool and the dendritic growth behavior for direct energy deposition process. Both the longitudinal molten pool morphology and the primary dendritic arm spacing (PDAS, Λ) of the columnar dendrites are validated by experiments. As revealed from the macro-scale simulation, the solidification velocity Vs and the temperature gradient G are coupled with an opposite trend, and the cooling rate R decreases along the solid/liquid interface from the top to the bottom of the molten pool. The micro-scale simulation shows that a power-law function (Λ ∝ R−1.31) with a scaling factor much larger than a traditional directional solidification (Λ ∝ R−0.5). Moreover, contrary to Hunt's and Kurz-Fisher's linear models, a circuitous relationship between Λ and G−0.5Vs−0.25 is found to be clustered within a narrow region. The coupled solidification parameters along the solidification interface with an asymptotic increase of G near the bottom of the molten pool contribute to the above PDAS observations.

Microstructure characteristics and its formation mechanism of selective laser melting SiC reinforced Al-based composites

SiC ceramic reinforced Al-based composites were successfully synthetized by selective laser melting (SLM) of 8.5 vol % SiC/AlSi10 Mg powder mixtures. The mechanism of microstructure evolution in an individual molten pool of the SLM processing was investigated. Three characteristic zones were well distinguished, including center and boundary areas of the molten pool as well as the heat-affected zone. The results revealed that the microstructure changing from columnar dendrite growth to cellular growth along the building direction could be attributed to the change of G/R (G is temperature gradient and R is solidification velocity). Phase identification of the SLM-fabricated parts was performed by X-Ray Diffraction (XRD) and Energy Dispersive Spectroscopy (EDS) analysis, further demonstrating the in-situ formed phases in the molten pool. Al4SiC4 crystals were formed in situ around the partially melted SiC ceramic particles. The nanoindentation tests conducted on different areas of the SLM-fabricated Al-based composites exhibited the high nanohardness (2.27 GPa and 2.15 GPa) and the elastic modulus (78.94 GPa and 75.46 GPa) in the center and boundary of molten pool, respectively, which were much higher than the reported value of conventional materials.

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The response dynamics of AlSi eutectic microstructures on accelerated and decelerated directional solidification conditions is investigated with optical in-situ techniques during processing. In contrast to regular eutectics the microstructure in eutectic and off eutectic AlSi alloys is independent of the processing history. The spacing between the Si lamellae is completely determined by the locally achieved solidification velocity and can be calculated using well-known theories for stationary growth of irregular eutectics. The observation is important to industrial casting processes which are typically non-stationary, because the theory of stationary growth can be used to predict the eutectic morphology also under instationary conditions.

Microstructure simulations of Inconel 718 during selective laser melting using a phase field model

In this study, the microstructure evolution of the Inconel 718 alloy fabricated by selective laser melting (SLM) was investigated by a phase field model. The temperature gradient and the solidification velocity were first calculated from a finite element thermal model of SLM and then used as the input of the phase field model to simulate the microstructure growth with time. The influences of the build height and laser beam scanning speed on the microstructure evolution were studied and evaluated. The results show that the columnar dendritic arm spacing values estimated from the phase field simulations are comparable to experimental and analytical results. With the increase of the build height, the dominated values of thermal gradient and cooling rate decreased first and then slightly increased at the top end of the manufacturing process. The microstructural evolution along the build height agreed well with the experimental test. In addition, with the increase of the laser beam scanning speed, the dominant temperature gradient increased to a certain value and then decreased, and the direction of the maximum temperature gradient tended to be parallel to the part build direction. Moreover, the temperature gradient affects the dendrite growth significantly, a greater temperature gradient resulting in a higher growth speed.

Specifically designed concentration profiles created by sudden velocity changes during directional solidification

We investigate how macrosegregation formation during directional solidification can be purposefully influenced to form sequences of concentration gradients along rod shaped samples. The effects of sudden changes of the solidification velocity on solute segregation are systematically characterized for conditions with reduced and enhanced melt convection, respectively. We present a solidification routine that is capable of creating alloy samples with specifically designed concentration profiles that are comprised of areas with low solute concentration and peaks of steeply increasing and decreasing solute concentration. The peaks can be adjusted with respect to the concentration interval, width and individual position along the sample. These multiple graded materials are useful for the characterization of (multicomponent) diffusion processes.

Microstructural Evolution with Solidification Rate and Heat-Treatment of Single Crystal Superalloy CMSX-4 Grown using Seed

The CMSX-4 superalloy including refractory elements was directionally solidified using the seed of a [001] single crystal to control the growth direction to [001], where solidification velocity was changed from 25 to 160 μm/s. In the log-log plot between spacing and solidification velocity, the primary dendrite arm spacing and secondary dendrite arm spacing linearly decreased with slopes of -0.288 and -0.318, respectively, as solidification velocity increased. A γ/γ′ eutectic structure was observed in the interdendritic region and the size linearly decreased with increasing solidification velocity. However, the volume fraction of the γ/γ′ eutectic structure did not change significantly with solidification velocity. Micro-segregation of the refractory elements was found in the primary dendrite arm region. These elements were not uniformly distributed even after solid-solution heat treatment, and an irregularly coarse γ′ -phase was observed in the interdendritic region after heat-treatment. Key words: superalloy, directional solidification, seed, single crystal

Dynamic instability of the steady state of a planar front during non-equilibrium solidification of binary alloys

The dynamic stability of the steady state arising during rapid solidification of a binary alloy with a planar front is examined. Earlier work (Galenko and Danilov, 2000) that was derived under the assumption of dilute solutions and linearized phase diagrams is extended and generalized to the case of non-linear phase diagrams and concentrated alloys. The present treatment confirms the validity of the earlier derived criteria for the stability of a steady state of a planar front independently of any thermodynamic model describing non-equilibrium solidification of binary alloys.It is found that in temperature and concentration ranges where the solidus concentration increases with increasing solidification velocity, the steady state of the planar front is dynamically unstable. It is discussed how such a dynamic instability of the steady state of a solidifying planar front has an effect on its morphological stability. This is a possible explanation for the discrepancy between morphological stability theory and published experimental data (Hoglund et al., 1998) obtained from rapidly solidified Si-Sn melts.

Fabrication, Properties and Applications of Porous Metals with Directional Pores

Porous metals with long cylindrical pores aligned in one direction are fabricated by unidirectional solidification through pressurized gas method (PGM) and thermal decomposition method of gas compounds (TDM). The pores are evolved from insoluble gas when the molten metal dissolving the gas is solidified in the dissolving gas (PGM) or inert gas (TDM). Three fabrication techniques, mold casting, continuous zone melting and continuous casting techniques, are adopted. The latter two techniques can control the solidification velocity and the last one possesses a merit for mass production of lotus metals. The porosity, pore diameter and its length are able to be controlled by the solidification velocity and ambient gas pressure, while the pore direction can be controlled by the solidification direction. Anisotropy in the elastic and mechanical properties is resulted from anisotropic pore morphology. The anisotropic behaviors of tensile, compressive and fatigue strength are explained in terms of the dependence of stress concentration on the pore orientation. The anisotropic properties of thermal, electrical conduction and magnetization are also found, which are attributed to the scattering of heat flux, electric current and magnetic flux with anisotropic pores, respectively. Several applications of the porous metals to manufacturing products are investigated. The unidirectional pores can be utilized for high performance of heat sinks for electronic devices of cars and computers. Thus, the porous metals are expected to be used for various manufacturing products.

Simulation of temperature, stress and microstructure fields during laser deposition of Ti–6Al–4V

We study the evolution of prior columnar β phase, interface L phase, and α phase during directional solidification of a Ti–6Al–4V melt pool. Finite element simulations estimate the solidification temperature and velocity fields in the melt pool and analyze the stress field and thermal distortions in the solidified part during the laser powder bed fusion process. A phase-field model uses the temperature and velocity fields to predict the formation of columnar prior-β(Ti) phase. During the solidification of the β phase from an undercooled liquid, the residual liquid below the solidus temperature within the β columns results in the α phase. The finite element simulated stress and strain fields are correlated with the length scales and volume fractions of the microstructure fields. Finally, the coalescence behavior of the β(Ti) cells during solidification is illustrated. The above analyses are important as they can be used for proactive control of the subsequent modeling of the heat treatment processes.

Growth velocity-undercooling relationship and structure refinement mechanism of undercooled Ni-Cu alloys

The growth velocity-undercooling relationship as a function of bulk undercoolings was systematically measured using high speed thermal imaging of highly undercooled Ni-Cu alloy samples. It was found that the growth velocity of Ni80Cu20 alloy was almost coincident with that of Ni95Cu5 alloy and the growth velocity of Ni85Cu15 alloy was almost coincident with that of Ni90Cu10 alloy, which was a new result that was unreported previously for concentrated solid solution alloys. It was also found that the solidification velocity increased smoothly with undercooling up to the maximum value. Growth velocity can be adequately represented by the current dendritic growth model. A clear discontinuity in the growth velocity-undercooling curve was observed at a critical undercooling. This discontinuity in the velocity-undercooling curve can be attributed to the finite speed of solute diffusion in the bulk liquid ahead of the growing dendrite. Microstructural evidences in these samples indicative the occurrence of dendritic fragmentation. Microstructural analysis using light microscopy and EBSD analysis reveals that recrystallization accompanies the grain refinement at high undercoolings. Furthermore, at high undercoolings, a high density of annealing twins in the as solidified samples indicates the occurrence of recrystallization in the solidification microstructure and a high density of subgrains in the quenched samples are observed within the microstructure, which indicates the occurrence of extensive recovery, a result previously unreported in samples solidified from highly undercooled melts.

Prediction of Primary Dendrite Arm Spacing with Solidification Velocity and Temperature Gradient during Directional Solidification in CMSX-4 Superalloy

Directional solidification experiments were carried out to estimate the effect of solidification velocity and temperature gradient on primary dendrite arm spacing (PDAS) in the Ni-based superalloy, CMSX-4 alloy. The specimens were solidified at velocities of 1, 5, 25, 50 and 100 mm/s under given temperature gradients of 12.5, 18, 23 K/mm. The models for predicting PDAS with solidification conditions had the form of λ ∝ V−1/4G−1/2, but the experimental results exhibited a discrepancy with the exponents of −1/4 and −1/2 in V and G, respectively. Therefore, a phenomenological formula based on the experimental results was proposed to predict PDAS, and it was found that the predicted PDAS under the experimental conditions was in good agreement with the experimental results. Key words: directional solidification, dendrite arm spacing, temperature gradient, Ni base superalloy

Do rotating magnetic fields unconditionally lead to grain refinement? A case study for directionally solidified Al-10wt%Cu alloys

The effect of solidification velocity and electromagnetic stirring on grain refining was investigated experimentally during the directional solidification of rod-like Al-10wt%Cu alloy samples. Applying low solidification velocities leads to a dendritic microstructure consisting of elongated equiaxed crystals, which result from fragmented dendrite arms forming new grains. This grain-refining effect vanishes for higher solidification velocities, leading to a microstructure dominated by a lower number of larger columnar grains. Moderate electromagnetic stirring under laminar flow conditions does not promote grain refinement. By contrast, a sufficiently strong forced melt flow induced by a rotating magnetic field significantly increases the number of grains in the range of solidification velocities investigated within this study. It is assumed that a turbulent melt flow supports the fragmentation of dendrite arms and thus the formation of new grains, which finally leads to grain refinement.

Entrapment of Inclusions by Solidified Hooks at the Subsurface of Ultra-Low-Carbon Steel Slab

To understand the mechanism for the entrapment of non-metallic inclusions by curved hooks beneath the surface of continuous casting slabs, the etching of the slab, the observation of hooks and the detection of inclusions on sections vertical and parallel to the slab surface were performed. The location of inclusions and hooks was revealed, and forces acting on the inclusion below a hook were analyzed. Inclusions gathered more below the curved hook than in the overflow zone above the hook. From the observation of hooks and inclusions on sections vertical to the slab surface, the number density of 3 to 5 μm inclusions in the hook zone and no-hook zone was very close, while the number density of > 10 μm inclusions in the hook zone was larger than that in the no-hook zone. From the observation on sections parallel to the slab surface, > 20 μm inclusions were located near the hook line more than in other regions, and the number density of inclusions in the hook zone was more than that in the no-hook zone. The apparent friction coefficient dominated the critical capturing size of inclusions from the solidification front, and the deflection angle, flow velocity, sulfur content and solidification velocity had influences on the size range.

Effect of the Pulling Velocity of Directional Solidification on Thermal Conductivity of Mg-Ag-Zn Alloys

Specimens of as-cast Mg-1Ag-Zn, Mg-3Ag-Zn and Mg-5Ag-Zn alloys were fabricated, and then the specimens' thermal conductivity was calculated. With the increase of Ag content, the thermal conductivity of as-cast alloys decreases significantly. After that, directionally solidified specimens of the above mentioned as-cast Mg-Ag-Zn alloys were made at three different pulling velocities: V=25 μm/s, V=50 μm/s, V=75 μm/s, and then their thermal conductivity was calculated again. The results show that with the increase of the pulling velocity, the thermal conductivity of alloys decreases significantly. Variations in the solute content and the pulling velocities are believed to play important roles in the thermal conductivity of Mg-Ag-Zn alloys. Since these two factors can strengthen the electron's scattering process, reduce their free path, and thereby reduce the alloys' thermal conductivity.

Effect of Nb Addition on Dendrite Growth and Equiaxed Grain Ratio of Fe-20 Pct Cr High-Purity Ferritic Stainless Steel

The acquisition of a high equiaxed zone ratio (EZR) is crucial for ferritic stainless steel (FSS). The main method of achieving this is to use effective particles to promote heterogeneous nucleation. In this study, an increased EZR was obtained owing to dendritic growth kinetics influenced by Nb addition. The EZR increased from 12 to 44 pct when 0.7 wt pct Nb was added to the FSS. The mechanism of increase of the EZR was analyzed by modified dendritic growth kinetics using the Kurz–Giovanola–Trivedi model coupled with thermodynamic data from ThermoCalc. The dendritic growth kinetics for Fe-20 pct Cr and Fe-20 pct Cr-0.7 pct Nb can be expressed as $$ V = 2.258 \times 10^{ - 5} \cdot \Delta T^{3.617} $$ and $$ V = 5.755 \times 10^{ - 7} \cdot \Delta T^{3.248} $$ , respectively, which means that undercooling (ΔT) of Fe-20 pct Cr-0.7 pct Nb was larger than that of Fe-20 pct Cr under the same solidification velocity (V). The undercooling enlarged at the dendrite tip then provided favorable nucleation conditions for FSS and increased the EZR. The as-cast structure, simulated by the cellular automaton–finite element model combined with modified dendritic growth kinetics, compared well with an actual ingot.