Dendrite Tip Temperature Research Articles

Thermal and solute diffusion in [formula omitted]-Mg dendrite growth of Mg-5wt.%Zn alloy: A phase-field study

Thermal and solute diffusion plays an important role in α-Mg dendrite growth, the diffusion mechanism of which is still unclear. Here, thermal and solute diffusion in α-Mg dendrite growth of Mg-5wt.%Zn alloy under non-isothermal solidification were studied using the phase-field method. Results show that solidification latent heat will be concentrated at the dendrite intersection, which makes thermal field distribution non-uniform, and it is similar to the profile formed by connecting primary dendrite tips. The increase in temperature will shorten primary dendrite arms, reduce side-branching development, increase dendrite tip temperature, and decrease dendrite tip concentration stability. Moreover, solidification latent heat will first diffuse to undercooled melt, then diffuse to other areas, finally, system temperature tends to be unified. The variation range of concentration difference is very small in the solidification process, and solute field distribution is uniform all the time. The local high-concentration areas will be formed after the superposition of the solute enrichment layer, and solute atoms will first diffuse to undercooled melt through the solid-liquid interface, and then concentrate between side-branching and dendrites.

Sensitivity analysis of dendritic growth kinetics in a Bridgman furnace front tracking model

A directional solidification experiment of a Ti-Al-Nb-B-C alloy by power down method is simulated using a Bridgman furnace front tracking model. The effect of varying the dendritic growth parameters; C, the columnar dendrite growth coefficient, and n, the undercooling exponent, is investigated. A matrix of growth coefficients and undercooling exponents - at three levels each, based around a growth law for Ti-46wt.%Al - is applied in simulations, and the effect on columnar dendrite tip temperature, tip velocity, and tip temperature gradient is observed. The simulation results show that the dendrite tip velocity and temperature gradient at the tip are practically unaffected by the use of different growth parameters. However, the predicted columnar dendrite tip undercooling did vary to give the required dendrite tip velocity. This finding has implications for the analysis of microstructural transitions, such as the Columnar to Equiaxed Transition (CET). In conclusion, it is suggested that, for transient solidification conditions, a CET prediction criterion based on tip undercooling is preferable to one that uses growth velocity.

Prediction of solidification cracking in laser welds of type 310 stainless steels

The occurrence of solidification cracks in laser welds of type 310 stainless steels was predicted by numerical analyses of the solidification brittle range (ductility curve for cracking) and thermal strain in the weld metal. The solidification brittle range in laser welding was estimated from that in arc welding based on the numerical analyses of supercooling (for calculating dendrite tip temperature) and segregation (for calculating completely solidified temperature) during rapid solidification. The calculated solidification brittle range was reduced with an increase in the welding speed because of the enhanced supercooling and the inhibited solidification segregation. The thermal strain analysis by FEM suggested that solidification cracks would occur in SUS310S welds at laser travelling velocity of 60 mm/s applying the initial strain of 1.5%, while no solidification cracks in SUS310EHP welds at any laser travelling velocities applying the higher initial strain of 2.2%. The cantilever type cracking test in laser welding revealed that the predicted results of occurrence of solidification cracks were consistent with experimental ones.

Effect of thermodynamic interactions on the rapid solidification kinetics of Ni-Cu-Co alloys

Most theoretical work on solidification focuses on dilute binary alloys, while those commonly used in industry are multi-component with high solute concentrations. In concentrated alloys, the diffusion of one component will be inevitably influenced by the others, which will further affect the rapid solidification kinetics. Assuming local non-equilibrium at the solid/liquid (S/L) interface and in the bulk liquid, the kinetics of planar interface migration and dendrite growth in strongly non-equilibrium solidification of Ni-Cu-Co alloys is comparatively studied. It is found that, for planar interface kinetics, the thermodynamic interactions lead to a non-monotonic tendency of the partition coefficient of Co with a slightly lowered interface temperature. Meanwhile, for dendrite growth (i.e. curved interface), the curvature effect and the thermodynamic interactions together result in the non-monotonic variation of partition coefficients. Due to the lowered dendrite tip temperature as a result of the thermodynamic interactions, larger undercooling is needed for interface migration and the dendrite growth is slowed down.

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.

Modeling on Dendrite Growth of Medium Carbon Steel during Continuous Casting

AbstractDendrite growth is an important phenomenon during steel solidification. In the current paper, a numerical method was used to analyse and calculate the dendrite tip radius, dendrite growth velocity, liquid concentration, temperature gradient, cooling rate, secondary dendrite arm spacing, and the dendrite tip temperature in front of the solid/liquid (S/L) interface for the solidification process of medium carbon steels during continuous casting. The current model was well validated by published models and measurement data. The results show that in the continuous casting process, the dendrite growth rate is dominated by the casting speed. Dendrite growth rate, liquid concentration at the S/L interface, temperature gradient and cooling rate decrease with proceeding solidification and solid shell thickness growth, while other parameters such as dendrite tip radius, secondary dendrite arm spacing, and dendrite tip temperature in front of the S/L interface become larger with solidification progress and solid shell thickness growth. Parametric investigations were carried out. The effects of the stability coefficient, temperature gradient and casting speed on the micro‐structural parameters were discussed. Under the same conditions, higher casting speed promotes coarser secondary dendrite arm spacing and enlarges the dendrite tip radius, while decreasing temperature gradient, reducing the dendrite growth rate and making the solute distribute more uniform.

Microstructures in rapidly solidified AISI 304 interpreted according to phase selection theory

The objective of this work is to use laboratory rapid solidification techniques to predict microstructures in AISI 304 produced during industrial processes. Two quenching methods have been employed to obtain a wide range of undercooling and microstructures: single roller melt spinning onto a copper wheel and casting into a conic mould. The experimental results are compared with theoretical predictions by using appropriate thermophysical parameters for the melt calculated with Thermocalc software while the dendrite tip temperature for ferrite and austenite phases is computed within the phase selection theory by means of a code written in MATLAB language.

Study of microstructure and solute partitioning in a cast Ti-48Al-2Cr-2Nb alloy by quenching during directional solidification technique

One major hindrance to effective implementation of cast gamma TiAl-based intermetallic alloys in aircraft engines lies in the variability of their mechanical properties resulting from chemical and microstructural heterogeneities. In the present work, the buildup of microsegregation in a cast Ti-48Al-2Cr-2Nb alloy is investigated through experiments of quenching during directional solidification (QDS). The solidification process, as well as the partitioning of alloying elements, between the solid and liquid phases, is investigated. Considering experimental conditions, the α-hcp phase is found to be the primary solidifying phase. A low dendrite tip temperature of 1475 °C was estimated from thermal recordings. These observations could be explained considering the value of the thermal gradient (around 4 °C/mm). Quantitative values of partition coefficients are proposed for Al, Cr, and Nb. In addition to Al, Cr is found to segregate in interdendritic regions, whereas Nb tends to be retained in the Ti-rich inner dendrites. Considering experimental cumulative solute distributions, the buildup of microsegregation can be satisfactorily represented on the basis of Gulliver-Scheil assumptions. Due to high-temperature quenching, the QDS experiments are also found to be appropriate to the study of high-temperature phase transformations and microstructural development of TiAl-based alloys. The results of QDS experiments are discussed with regard to the range of microstructural and chemical heterogeneities determined within Ti-48Al-2Cr-2Nb investment castings. Finally, regarding solid-state phase transformations subsequent to solidification, the study attempts to explain the formation of B2 phase particles stabilized by the ternary additions.

Numerical modeling of columnar to equiaxed transition with consideration of molten steel flow

The numerical model of columnar to equiaxed transition (CET) was constructed with consideration of molten steel flow. Solid shell growth was analyzed by using macroscopic heat flow model in addition to heat transfer due to the fluid flow at the solidification front, which was calculated by fluid flow model. At the same time, the dendrite tip temperature and the growth of equiaxed crystal in the undercooled liquid region was estimated and the CET position was diagnosed. By the application of electromagnetic stirrer (EMS), the superheat in the pool diminished and undercooled region was enlarged by heat transfer due to fluid flow at the solidification front. In addition, the ratio of equiaxed zone increased with the increase of grain density by EMS. Therefore, it has been estimated that solidification structure change by application of EMS was caused by superimposition of these two effects. Moreover the size of equiaxed crystal estimated by this model could show good agreements with experimental ones.

The Effect of Solidification Rates and Thermal Gradients on Directionally Solidified Microsturucture in the Ni-Base Superally GTD111M

Morphological evolution and growth mechanism at the solid/liquid interface during solidification were investigated in the Ni-base superalloy GTD111M by directional soldification and quenching(DSQ) technique. The experiments were conducted by changing solidification rate(V) and thermal gradient(G) which are major solidification process variables. High thermal gradient condition could be obtained by increasing the furnace temperature and closely attaching the heating and cooling zones in the Bridgeman type furnace. The dendritic/equiaxed transition was found in the G/V value lower than <TEX>$0.05<TEX>$\times$</TEX>10{^3}^{\circ}C$</TEX>s/<TEX>$\textrm{mm}^2$</TEX>, and the planar interface of the MC-<TEX>${\gamma}$</TEX> eutectic was found under <TEX>$17 <TEX>$\times$</TEX> 10{^3}^{\circ}C$</TEX> s/<TEX>$\textrm{mm}^2$</TEX>. It was confirmed that the dendrite spacing depended on the cooling rate(GV), and the primary spacing was affected by the thermal gradient more than solidification rate. The dendrite lengths were decreased as increasing the thermal graditne, and the dendrite tip temperature was close to the liquidus temperature at <TEX>$50 \mu\textrm{m}$</TEX>/s.

Kinetic undercooling in solidification of a hypereutectic Al–Si alloy; effect of solidifying within a ceramic preform composite

Dendrite tip temperature measurements are reported for the hypereutectic alloy Al–30% Si, directionally solidified as a bulk (non-composite) alloy, and also as the matrix of a fibrous metal matrix composite. Over the range of tip velocities studied (10–1000μms) the primary Si tip undercooling in the directionally solidified bulk alloy increases slightly with increasing tip velocity, and indicates, by its large value, the presence of significant kinetic undercooling. This is in contrast with solidification of the composite, in which the primary Si tip undercooling decreases markedly with increasing tip velocity and is in quantitative agreement with theory for cellular solidification with no kinetic undercooling. These results, supported by metallographic observations, indicate that “wetting” of the alumina fibers by the growing silicon phase in the composite essentially eliminates the kinetic barrier to growth of primary Si crystals. The underlying mechanism is rationalized on the basis of macroscopic capillaric analysis at the solid/fiber/liquid juncture. This juncture is shown to be significantly more efficient in nucleating new facet planes than is a re-entrant twin plane corner.

The Impurity Effect in the Space Shuttle Dendritic Growth Experiments with Succinonitrile

The high purity succinonitrile (SCN) used in the recent space shuttle dendritic growth experiments of Glicksman and co-workers was reported to be 99.999% pure. This material is treated as a very dilute alloy with a composition C o = 0.001%. The dendrite tip temperature ( T t) is determined from both heat flow and interfacial equilibrium considerations. Only the latter is affected by the presence of impurities. For the experimentally measured values of the tip growth rate ( R) and tip radius ( r t), the values of T t estimated on the basis of the Ivantsov heat flow solution are in excess of the equilibrium melting point of succinonitrile. A consideration of the impurity effect suggests that the microgravity experiments correspond to what is considered to be the rapid solidification regime. The chemical Peclet number, p = Rr t/2 D L, where D L is the diffusivity of the impurity, is greater than one-half (p > 0.50) in a large number of experiments and greater than one ( p > 1) in some experiments.

Calculation of Dendrite Tip Temperature during Constrained Growth

Calculation of Dendrite Tip Temperature during Constrained Growth

Optimum stability conjecture for the role of interface kinetics in selection of the dendrite operating state

We develop a model that allows interface kinetics to be incorporated in a simple way in the determination of the dendrite operating state. The model is based on an optimum stability conjecture, according to which the dendrite tip radius is related to the wavelength of the fastest growing Fourier component in a linear stability analysis that includes consideration of interface kinetics. The basic idea is similar to that of the marginal stability hypothesis but leads to a value of the selection parameter σ = 2κ d 0/( Vϱ 2) that decreases as the Peclet number Pe = Vϱ/(2κ) is increased ( V = dendrite growth velocity, ϱ = dendrite tip radius, κ = thermal diffusivity and d 0 = capillary length). This results in 1/σ being a linear function of 1/ϱ. The Ivantsov equation for the dimensionless supercooling S in terms of Pe is modified to account for capillarity and kinetics by using the dendrite tip temperature instead of the melting temperature in the original Ivantsov equation. This yields a complete parametric solution to the problem, and the resulting “scaling laws” are exhibited for the case of two spatial dimensions. We also reexamine the data of Rubinstein and Glicksman for dendritic growth in pivalic acid for which σ varies by about 100% over the measured range of supercooling. The value of 1/σ is nearly linear in 1/ϱ, in agreement with the optimum stability conjecture. Comparison with the present theory results in a kinetic coefficient of μ = 0.218cm/s·K. The resulting calculated values of V and ϱ are found to be in better agreement with experiment than for constant σ, but still show considerable discrepancy at small supercoolings, probably due to convection. This stability theory is based on a planar geometry rather than on a parabolic geometry, the modification of the Ivantsov relation is crude, and the theory completely neglects treatment of anisotropy of either capillarity or interface kinetics, which are known to be important from microscopic solvability theory. Nevertheless, we identify a dimensionless group m = μ/ T Mγ(κ L V) which must be small for interface kinetics to be important ( T M = absolute melting temperature, γ = crystal-melt surface free energy, and L V = latent heat per unit volume).

Columnar dendritic solidification in a metal- matrix composite

Results are presented of a study on columnar dendritic solidification of the matrix of a fibrous metal-matrix composite, the fibers of which are aligned SiC fibers 140 m in diameter and the matrix of which is Al-4.5 wt pct Cu. Samples were produced by pressure infiltration of the metal-matrix into a preform of the fibers. The matrix was subsequently remelted and resolidified under controlled thermal gradient and growth rate. Dendrite growth begins in the center of the interstices left between the fibers. The dendrite tip temperature is not significantly influenced by the fibers, but the usual linear dependency of dendrite arm spacing ont 1/3 (wheret is time during solidification) is altered significantly in the narrower interstices at long solidification times. The underlying mechanism is dendrite arm coalescence which takes place at a sufficiently rapid rate in the composite that the microstructure gradually becomes nondendritic. The solid/liquid interface then is parallel to the matrix/fiber interface. A model is presented for the kinetics of dendrite arm coalescence and compared with experimental results. The amount of microsegregation that was found in the matrix within interstices is significantly less than that found in the usual cast alloy, especially at long solidification times (low cooling rates). The mechanism responsible for the observed reduction in microsegregation is solid-state diffusion which is enhanced in the composite by the fact that the fibers place an upper limit on the dendrite arm spacing, and hence on the required diffusion distance.

A critical examination of the dendrite growth models: Comparison of theory with experimental data

Dendrite tip temperature, dendrite tip radius and primary arm spacing data, and their variation with the growth speed and temperature gradient for directionally solidified succinonitrile-acetone, succinonitrile-salol, aluminum-copper, and lead-paladium alloys have been examined against their qualititative and quantitative fit with predictions from several dendrite growth models. The Burden and Hunt analysis while predicting the proper quantitative behavior, does not in general, yield a good quantitative agreement with experimental data. Models due to Trivedi, and more recently, Laxmanan (minimum dendrite tip undercooling approach as well as the tip stability approach) show a very good quantitative fit with the experimental data. Predictions of dendrite tip temperature and tip composition in the liquid have been shown to be inadequate to distinguish between the models within the experimentally feasible directional solidification conditions. Therefore, in order to determine which model is most appropriate, additional directional solidification experiments involving simultaneous measurements of dendrite tip radius, tip temperature, tip composition, and primary arm spacing in the low growth velocity regime are suggested.

Dendrite characteristics in directionally solidified Pb-8 Pct Au and Pb-3 Pct Pd alloys

Pb-8 pct Au and Pb-3 pct Pd alloy specimens partially directionally solidified and then quenched have been examined in order to characterize their dendritic microstructural details and solute composition profiles. Dendrite tip radii have been measured by a controlled sectioning technique. Dendrite tip radius, solute content of quenched liquid at the dendrite tip, solute profile within the interdendritic region and ahead of the dendrite tip, cell length, and the primary arm spacing values obtained experimentally have been compared with the theoretical predictions. Two groups of models, one based on the minimum undercooled dendrite tip criterion and the other based on the marginal stability at the dendrite tip, have been examined. The Burden and Hunt model, based on the “minimum undercooling” approach, does not predict the observed behavior. However, a modification of the Burden and Hunt's model recently proposed by Laxmanan shows a good fit to the experimentally observed parameters. The models based on the marginal stability approach also predict most of the observed behavior well. It is concluded that quantitative comparison of the primary arm spacing measurements can not form the basis of distinguishing among the various dendrite growth models in a positive temperature gradient. There is a critical need to carry out carefully controlled directional solidification experiments in a well characterized metallic alloy system to help distinguish between the minium dendrite tip undercooling and the marginal stability approaches. New experiments based on simultaneous measurements of (a) dendrite tip radius, (b) dendrite tip temperature, and (c) the solute profile ahead of the dendrite tip—all in a convection free atmosphere—are required.

Deformation behavior of an omega hardened alpha-beta titanium alloy : Ernest Levine, Steven Hayden & Harold Margolin

We develop a model that allows interface kinetics to be incorporated in a simple way in the determination of the dendrite operating state. The model is based on an optimum stability conjecture, according to which the dendrite tip radius is related to the wavelength of the fastest growing Fourier component in a linear stability analysis that includes consideration of interface kinetics. The basic idea is similar to that of the marginal stability hypothesis but leads to a value of the selection parameter σ = 2κd0/(Vϱ2) that decreases as the Peclet number Pe = Vϱ/(2κ) is increased (V = dendrite growth velocity, ϱ = dendrite tip radius, κ = thermal diffusivity and d0 = capillary length). This results in 1/σ being a linear function of 1/ϱ. The Ivantsov equation for the dimensionless supercooling S in terms of Pe is modified to account for capillarity and kinetics by using the dendrite tip temperature instead of the melting temperature in the original Ivantsov equation. This yields a complete parametric solution to the problem, and the resulting “scaling laws” are exhibited for the case of two spatial dimensions. We also reexamine the data of Rubinstein and Glicksman for dendritic growth in pivalic acid for which σ varies by about 100% over the measured range of supercooling. The value of 1/σ is nearly linear in 1/ϱ, in agreement with the optimum stability conjecture. Comparison with the present theory results in a kinetic coefficient of μ = 0.218cm/s·K. The resulting calculated values of V and ϱ are found to be in better agreement with experiment than for constant σ, but still show considerable discrepancy at small supercoolings, probably due to convection. This stability theory is based on a planar geometry rather than on a parabolic geometry, the modification of the Ivantsov relation is crude, and the theory completely neglects treatment of anisotropy of either capillarity or interface kinetics, which are known to be important from microscopic solvability theory. Nevertheless, we identify a dimensionless group m = μ/TMγ(κLV) which must be small for interface kinetics to be important (TM = absolute melting temperature, γ = crystal-melt surface free energy, and LV = latent heat per unit volume).