Primary Dendrite Arm Research Articles

Simulation of dendritic growth for ternary alloys based on modified cellular automaton model

Based on the binary cellular automaton method, a modified cellular automaton model for ternary alloys is developed to simulate dendrite growth controlled by solutal effects and microsegregation in the low Peclet number regime by coupling PanEngine, which is a multicomponent thermodynamic and equilibrium calculation engine. The model can be used to calculate the interfacial equilibrium composition by considering the influence of Gibbs-Thomson effect induced curvature undercooling, and multicomponents contributed constitutional undercooling. Meanwhile, the growth velocity of interface is determined by solving the solute conservation equation simultaneously with dimensionless solute supersaturation equation for each alloying element. Moreover, equilibrium liquidus temperature and equilibrium solid concentration at the interface are derived by PanEngine. Free dendrite growth of Al-7%Si-xMg ternary alloys is simulated by the present model, which shows that the increase of solute Mg can suppress the growths of both primary and secondary dendrite arms. Meanwhile, constrained columnar dendrite growth of Al-7%Si-0.5%Mg with the increases of pulling velocity and constant thermal gradient during directional solidification is calculated. The results reveal the competitive growth of columnar dendrites, and demonstrate that the primary dendrite arm spacing would decrease as the pulling velocity increases, which accords well with the Hunt model.

Prediction of Solid-liquid Interfacial Energy of Steel during Solidification and Control of Dendrite Arm Spacing

Solid–liquid interfacial energy of steel during solidification was measured predicted from the both experimental techniques of unidirectional solidification and thermal analysis applying the dendrite growth model and heterogeneous nucleation model. Solid–liquid interfacial energy changed depending on primary phase during solidification, i.e., that of primary δ phase was larger than that of γ phase. When the primary phase was the same, solid–liquid interfacial energy increased with increasing carbon content. Primary dendrite arm spacing changed depending on solid–liquid interfacial energy. A trace amount of bismuth which had the effect of a decrease in the solid–liquid interfacial energy of steel during solidification decreased primary and secondary dendrite arm spacing, significantly.

Characterization of the Microstructure Evolution and Microsegregation in a Ni-Based Superalloy under Super-High Thermal Gradient Directional Solidification

The microstructure evolution and microsegregation behavior of alloying elements in a Ni-based superalloy at a series of growth rates under super-high thermal gradient directional solidification were quantitatively characterized. Both microstructure and dendritic segregation are functions of growth rate. The high growth rate solidification leads to refinement in primary (λ1) and secondary (λ2) dendrite arm, decreased size of γ/γ′ eutectics and γ′ phase, as well as reduced microsegregation degree of alloying elements. Also with the growth rate increased, the morphology of γ′ precipitates changes from irregular shape to a cuboidal one. The electron probe microanalysis (EPMA) reveals that Cr, Mo and γ′ forming elements (Al, Ta and Nb) all partition to interdendritic region, while W and Re both preferably segregate to dendrite core. Thus at fast growth rates (or high cooling rates), finer dendrites, uniformly coherently cuboidal γ′ precipitates and decreased segregation favorable to the performance of superalloys are obtained. These quantitative results provide a basis for the establishment of cast and heat treatment process.

Silicon morphology modelling during solidification process of A356 Al alloy

In this paper, an introduction of the finite element approach to microstructure based modelling is provided, and the primary and secondary dendrite arm spacings of A356 alloy in the solidification process are simulated. The simulated results of dendrite morphology and the experimental measurements are presented and compared with the investigations of other researchers, which confirmed the accuracy of this model in its ability to predict the dendrite arm spacing. Each of the length scales, including silicon rod diameter and spacing, is discussed in detail. Analytical equations are generated for the length scales and incorporated in the Sharif University Technology academic software for the prediction of the microstructure in shape castings.

柱状デンドライトの一次枝間隔の均一化機構

In order to investigate the mechanism for equalization of primary dendrite arm spacing, in-situ observation of solutal field using succinonitrile-H2O-dye system has been carried out. The brightness, which corresponds to the concentration of dye, has been characterized by an image analyzer along the centerline of interdendritic region. When the local primary dendrite spacings were uneven, the brightness along the centerline of interdendritic region was low in case of local primary dendrite arm spacing was large. After growth with rather long distance, the local primary dendrite arm spacings became even and the brightness along the centerline of interdendritic region became uniform. The solutal profile along the interdendritic region qualitatively agreed with the calculation results of newly developed model. A dendrite trunk is prone to grow toward the wide-spacing-region because the solute concentration of this side is lower than that of the other side. This leads to equal primary spacing.

Effects of solidification parameters on microstructures of Ni3Al based single crystal

A series of Ni3Al single crystal specimens were prepared by directional solidification with seeding technique and the influence of processing parameters such as heating temperature and withdrawal rate on the microstructure and segregation tendency were investigated. In this work, dendrite structure was observed while the ranges of parameters were adopted. As the withdrawal rate or heating temperature increased, the primary dendrite arm spacing decreased gradually. The results strongly indicated that the average size of γ’ precipitates in dendrite core was larger than the one in inter-dendrite area in Ni3Al based alloys. With the increasing withdrawal rate or heating temperature, the size of γ’ precipitates in both dendrite core and inter-dendrite area decreased, while the morphology became regulated from spherality to cube. The tendency of segregation of Mo and Re in inter-dendrite area became more intense with the increasing withdrawal rate. No obvious variation of the segregation of elements was observed at different heating temperature.

成長速度変化による一次デンドライトアーム間隔の変化

成長速度変化による一次デンドライトアーム間隔の変化

Microstructures of directionally solidified Ti-46Al-5Nb alloys

Intermetallic Ti–46Al–5Nb alloys were directionally solidified at constant growth rates (V) ranging from 10 to 200μm/s under the temperature gradient of G=3.8×103K/m. Quenching was performed at the end of directional solidification (DS) experiments. Macrostructures and microstructures in the longitudinal section as well as the cross section have been investigated. Fully lamellar microstructures were observed in the above range of growth rates. At the growth rates of 10μm/s the primary phase was α while it changed to β when the growth rate was up to 20μm/s. Both the primary dendritic arm spacing (λ) and the interlamellar spacing (λs) decreased with increasing growth rate according to the relationships and, respectively. Width of columnar grain decreased with increasing growth rate, and was uneven mainly because of the peritectic transformation in interdendritic and dendritic regions. Statistical result of the volume fraction of the lamellar microstructures in different orientations shows that, the one angled 0-30°C to the growth direction has the largest volume fraction.

Growth of tertiary dendritic arms during the transient directional solidification of hypoeutectic Pb–Sb alloys

Despite the importance of a complete characterization of dendritic patterns in castings, the availability of studies on the development of tertiary dendrite arms is scarce in the literature. In the present study, the tip cooling rate, local solidification time, primary and tertiary dendrite arm spacings have been determined in Pb–Sb alloys castings directionally solidified under unsteady-state heat flow conditions. The alloys compositions experimentally examined are widely used in the as-cast condition for the manufacture of positive and negative grids of lead-acid batteries. The initial growth of tertiary dendritic arms from the secondary branches was found to occur only for a Pb–3.5 wt% Sb alloy at cooling rates in the range 0.4–0.2 K/s, with no evidence of this spacing pattern for Pb–Sb alloys having lower solute content. Tertiary dendritic branches have been observed along the entire casting lengths for alloys of the Pb–Sb hypoeutectic range having compositions higher than 4.0 wt% Sb. It is shown that a power function experimental law with a characteristic −0.55 exponent is able to characterize the tertiary spacing evolution with the solidification cooling rate for alloys compositions ≥4.0 wt% Sb. The only exception was the Pb–3.5 wt% Sb alloy for which λ 3 exhibited significant lower values when compared with the experimental values obtained for the other Pb–Sb alloys for a same solidification cooling rate.

Size-affected single-slip behavior of René N5 microcrystals

Abstract Microcompression testing was conducted on the cast single crystal nickel-base superalloy Rene N5. Microcrystals were selectively fabricated from either dendrite core or interdendritic regions. The compression axis was oriented for single-slip deformation and microcrystal diameters ranged from 2.5 to 80 μm. All microcrystals displayed several hallmarks of size-affected plastic flow, including a size-affected and stochastic flow-stress and initial strain hardening rate, as well as an intermittent flow response. The magnitude of size-affected flow-stress scaling behavior was dependent upon the plastic strain level of the flow-stress measurement, with increasing size-dependence for increasing strain levels. TEM analysis demonstrated the activation of multiple slip-systems, despite the microcrystals being oriented for single-slip deformation. Zig-zag slip was also observed in microcrystals that achieved flow stresses of ∼1300 MPa or higher. For microcrystals fabricated within interdendritic regions the flow-stress values are, on average, lower compared to dendrite core microcrystals. This difference in flow-stress is especially pronounced for microcrystals which are 5 μm in diameter. The microcrystal diameter for which bulk-like properties are estimated to be observed is approximately 350 μm, which is approaching the measured primary dendrite arm spacing for this crystal (430 μm).

Investigation of growth of single crystal SRR99 superalloy under microgravity using 50-meter-high drop tube

The SRR99 Ni-base single crystal superalloy samples were partially remelted and then solidified during free falling in a 50-meter-high drop tube. For comparison, samples solidified statically, i.e., in unit gravity, were also conducted under equivalent condition. Under the both conditions there were areas where columnar dendrites epitaxially grew from the seed crystals. The epitaxial growth of columnar dendrites in the samples solidified during free fall was subject to the influence of microgravity. It was found that the primary dendrite arm spacing of the sample solidified under microgravity was apparently larger than that of the sample solidified under gravity. The secondary arm lengths were also longer in the microgravity sample. Besides, the distributions of heavy elements such as W and Ta along the core of a primary dendrite arm were found a little bit different between the samples solidified under the two conditions. Based on the above experimental results, the effects of gravity on solidification microstructure and solute distribution were analyzed.

SOLIDIFICATION CHARACTERISTICS AND MICROSTRUCTURAL EVOLUTION OF Zn-1.26wt.% Al ALLOY

Zn–1.26 wt.% Al alloy was directionally solidified upward with a constant growth rate (V = 16.6 μm/s) in a wide range of temperature gradients (G = 1.94–5.15 K/mm) and with a constant temperature gradient (G = 5.15 K/mm) in a wide range of growth rates (V = 8.3–500 μm/s) with a Bridgman-type directional solidification furnace. Microstructure parameters, the primary dendrite arm spacing (λ1), secondary dendrite arm spacing (λ2) and dendrite tip radius (R), were measured and expressed as functions of G and V by using a linear regression analysis method. It was found that the values of λ1, λ2 and R decrease with increasing values of V and G. The experimental results were compared with the main predictive theoretical and experimental works for dendritic spacings.

INFLUENCE OF WITHDRAWAL RATE ON MICROSTRUCTURES OF BLADE SHAPED DIRECTIONALLY SOLIDIFIED DZ125 SUPERALLOY

As a precipitation hardened unidirectionally solidified Ni-based superalloy, DZ125 has been widely applied as structure materials in advanced aeroengine for gas turbine blades and vanes. In present, the paper on the influence of solidification parameters on microstructures have been largely published, but unfortunately, few of them have focused on giving a direct comparison between directional solidification characteristics in liquid metal cooling (LMC) and high rate solid- ification (HRS). In this paper, the influences of processing parameters on microstructures of blade shaped castings prepared both by LMC and HRS technique were studied. The results show that the dendrite structure and γ � precipitate in castings prepared by the same method are refined with elevated withdrawal rate; in the same solidification conditions, the LMC castings have finer dendrite structure and γ � precipitate than HRS, the larger the disparity between primary dendrite arm spacings in LMC and HRS castings, the thicker wall thickness is or the higher the withdrawal rate is. It is

Evolution of as-Cast Microstructure of Mg-Al Alloys with Solute Content and Cooling Rate

Although numerous solidification experiments have been conducted for Al, Cu and Si alloys to investigate microstructural features like primary and secondary dendrite arm spacing, solute distribution with in secondary arms and second phase fraction, no systematic solidification study on Mg alloys has been performed to understand the evolution of microstructural features as a function of cooling rate and solute content. The present study focuses on the experimental microstructural evolution of Mg-3, 6 and 9 wt. % Al alloys in the cooling rate range of 1 K/sec to 1000 K/sec. The results suggest that secondary dendrite arm spacing and amount of second phase formation are strongly dependent on both solute content and cooling rate.

Structure Refinement by a Liquid Metal Cooling Solidification Process for Single-Crystal Nickel-Base Superalloys

Single crystals of a nickel-base superalloy were directionally solidified (DS) over a range of cooling rates to evaluate the benefits of a new high thermal gradient solidification process. Solidification experiments were conducted on cylindrical bars with a liquid-metal-enhanced cooling process. This higher gradient casting process was evaluated for the degree of structure refinement, microstructural variability, and porosity distributions. Cylindrical bars of 1.6-cm diameter were solidified at rates between 8.4 and 21.2 mm/min using a tin-based, liquid metal cooling (LMC) technique and at a rate of 3.4 mm/min with a conventional Bridgman process. The LMC process produced a refined microstructure with average primary dendrite arm spacing (PDAS) and secondary dendrite arm spacing (SDAS) values as low as 164 and 25 μm, respectively, for the bar geometry evaluated. An optimum intermediate withdrawal velocity of 12.7 mm/min produced up to a 50 and 60 pct refinement in PDAS and SDAS, respectively. Further increases in withdrawal velocity produced smaller SDAS and pore sizes, but undesirable grain boundaries and excessive secondary dendrite arm growth. Voronoi tessellation methods were used to examine the extremes of the dendrite arm spacings in comparison to the average measurements, the packing of dendrites, and the correlation of porosity size and location with the dendrite structure. A simple expression for prediction of the maximum pore size is developed.

Effect of orientation on the microstructure of nickel‐based crystalline superalloys

AbstractThe effect of crystal orientation on the microstructure of a nickel‐based crystalline superalloys during directional solidification was explored. Differently oriented crystals with [001] and [011] orientations were fabricated with seeding technique. The results showed that primary dendrite arm spacings decreased simultaneously with the increase of misroientation. The primary dendrites arrange in lines in [011] single crystal. For [001] oriented crystals, the size of γ′ phase increased with the increasing of misorientation. However, it was observed that the size of γ′ decreased with large misorientation for [011] orientated growth. Meanwhile, more γ′ in [011] crystals tended to be triangular. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Microstructure evolution of directionally solidified Ti–46Al–0.5W–0.5Si alloy

Directional solidification experiments were performed on the intermetallic Ti–46Al–0.5W–0.5Si (at%) alloy using a Bridgman-type furnace. The effect of growth rate on the solidification behavior and microstructure parameters was determined. After directional solidification, the microstructure is composed of α 2/γ lamellar structures and fine Ti 5Si 3 precipitates. During the solidification process, W segregates into dendritic cores of α phase, and Si segregates into interdendritic regions. The enrichment of Si leads to the formation of Ti 5Si 3 phases. The primary dendritic arm spacings and interlamellar spacings decrease with the increasing growth rate. Because of the change of preferred growth direction (PGD), the lamellar orientation is not perpendicular to the growth direction, even if the α phase is the primary phase. The variation of lamellar orientation can be attributed to two factors. One is the history-dependence on the lamellar orientation of unmelted as-cast crystals near the initial interface of directional solidification. The other is the variation of PGD of the α phase. With the increasing growth rate, the variation of PGD of α phase is as follows: 〈0001〉→〈101̄1〉→〈2̄2̄43〉→〈101̄1〉.

Mechanical properties of directionally solidified lead-antimony alloys

The Pb-17wt% Sb alloy was directionally solidified under two solidification conditions: with different temperature gradients (G=0.93–3.67 K/mm) at a constant growth rate (V=17.50 μm/s) and with different growth rates (V=8.3–497 μm/s) at a constant temperature gradient (G=3.67 K/mm) in a Bridgman furnace. Microstructure parameters, such as primary dendrite arm spacing (λ 1), secondary dendrite arm spacing (λ 2), and dendrite tip radius (R), were measured. The microhardness (Hv) and ultimate tensile strength (σ) of the directional solidification samples were also measured. The influences of solidification and microstructure parameters on Hv and σ were investigated. The results obtained in this work were compared with similar experimental researches in literatures. It is shown that the Hv and σ values increase with the increase of G and V, but decrease with the increase of λ 1, λ 2, and R.

일방향응고시킨 Pivalic Acid-Ethanol 계에서의 Dendrite의 성장

Transparent organic materials have been frequently used as an analog of the solidifying metallic materials, because their transparency permits an in-situ observation of the microstructural development during solidification through optical microscopy. Pivalic acid (PVA)-ethanol system showing an anisotropic property in solid-liquid interfacial energy and interface kinetics was adopted in the present experiment, and the detailed experiments performed are as follows: (1) variation of dendrite tip temperature with growth velocity, (2) correlation between primary dendrite arm spacing () and the growth orientation away from the heat flow direction (tilt angle: ), (3) variation of dendrite tip radius (R) with growth velocity (V), (4) dendrite tip stability parameter () and its dependence on the concentration. Concerning the correlation between the dendrite tip temperature and growth velocity the present result is well suited to Hunt-Lu equation. As the tilt angle increases, the average primary dendrite spacing tends to increase.

Numerical modeling of crystal growth of a nickel-based superalloy with applied direct current

A cellular automaton-finite difference (CA-FD) model is developed to simulate crystal growth with applied direct current (DC) in this study. The simulated dendrite growth is controlled by the CA rules that involved the effects of the supercooling, interfacial curvature and crystal anisotropy. The electric current distribution, the temperature field and the electromagnetic flow caused by the Lorentz force are solved by the FD calculation. The directional solidification of a model nickel-based superalloy with DC field is simulated. The results show that Joule heat brought by electric current delays the dendrite growth and changes the primary dendrite arm spacing (PDAS). Excessive Joule heat will completely stop the crystal growth. The maximum allowable current intensity increases with the cooling efficiency of directional solidification. It is found that the dendrites growing with the DC field have a self-adjustment ability to achieve flat S/L interface in macroscale during directional solidification. The electromagnetic flow induced by the DC field may theoretically accelerate the dendrite growth, but usually the influence is negligible for the directional solidification of the superalloy.