Kurz-Fisher Model Research Articles

Crystal growth mechanism of directionally solidified Fe–Al–Ta eutectic composites at higher solidification rates

Fe–Al–Ta eutectic composites with solidification rates of 650 μm/s, 700 μm/s, 800 μm/s and 900 μm/s were prepared by a modified Bridgman directional solidification technique in order to study the microstructure and crystal growth mechanism. The composition, microstructure, preferential orientations of Fe–Al–Ta eutectic composites were investigated by EDX, SEM, SAED, respectively. The results show that the microstructure of Fe–Al–Ta eutectic composites presents short rods and spheres, and microstructure is gradually refined with the increase of solidification rates. It is composed of Fe (Al, Ta) matrix phase and Fe2Ta (Al) reinforcement phase. The lamellar/rod spacing is decreased with the increase of solidification rates. It was also be predicted by Kurz-Fisher model, Hunt-Lu model and Trivedi model, and the experimental results is relatively close to the Hunt-Lu model. The morphologies of solid/liquid interface at higher solidification rates were forecasted by M − S and K–F model, and the theory calculation is consistent with experimental results well. The preferential orientations of Fe–Al–Ta eutectic composites at higher solidification rates were studied by selected area electron diffraction (SAED).

Primary dendrite arm spacing and preferential orientations of the Ni–Si hypereutectic composites at different solidification rates

A hypereutectic alloy is a metallic alloy which has a composition beyond the eutectic point. As the temperature of a non-eutectic composition is lowered, the liquid mixture will precipitate one component of the mixture before the other. In the present paper, Ni–Si hypereutectic composites at the different solidification rates were prepared by a modified Bridgman directional solidification technique. Primary dendrite arm spacings of the Ni–Si hypereutectic composites were calculated at the different solidification rates according to Kurz–Fisher model, Hunt–Lu model and Trivedi model, respectively. Relation between micro-hardness and primary dendrite arm spacing was obtained. The selected area electron diffraction was adopted to confirm the preferential orientation of Ni–Si hypereutectic composites. It is found that primary dendrite arm spacing of the experimental results are very close to Kurz–Fisher model, while deviating from that predicted from Hunt–Lu model and Trivedi model. Therefore, Kurz–Fisher model is much more suitable to describe primary dendrite arm spacing of Ni–Si hypereutectic.

Role of impinging powder particles on melt pool hydrodynamics, thermal behaviour and microstructure in laser-assisted DED process: A particle-scale DEM – CFD – CA approach

High speed imaging of molten pool free-surface hydrodynamics in laser-assisted directed energy deposition process clearly revealed a highly oscillatory and dynamic melt flow due to impinging powder particles. Surprisingly, most of the reported computational work exclude the injection of powder particles and rather adopt a homogeneous mass and energy addition approach, and therefore provides less accurate predictions. In this work, we develop a coupled multi-physics particle-scale approach utilizing the discrete element method for particle trajectory prediction, the computational fluid dynamics for free-surface thermo-fluidic modelling and the cellular automata method for grain growth evolution. In the model, the governing physical phenomena, such as laser-powder interaction, in-flight particle heating, phase change (melting, vaporization and solidification), free-surface evolution, molten pool hydrodynamics and impinging particles-melt interaction have been considered. Experiments for the deposition of Inconel-625 on an Inconel-625 substrate are carried out, and the model predictions are validated with the experimental measurements. For the first time, the predicted thermo-fluidic simulation results reveal highly oscillatory, chaotic and random melt flow attributed to the impinging powder particles. During the deposition, it is found that the role of the Marangoni convection is less significant as compared to the momentum imparted by the impinging powder particles in the melt pool. Using the simulated thermal undercooling data, cellular automata-based grain growth simulation predicts elongated columnar dendrites in the melt pool that grows epitaxially from the melt pool interface and stretches towards the centre. Using the Kurz-Fisher model, the effect of local thermodynamic solidification conditions on the size of dendritic microstructure is also described. The predicted melt pool geometry, temperature field and grain structure compare well with the experimental measurements.

Benchmark Study of Thermal Behavior, Surface Topography, and Dendritic Microstructure in Selective Laser Melting of Inconel 625

In the NIST additive manufacturing benchmark (AM-Bench) experiments, melt pool geometry, cooling rates, surface topography, and dendritic microstructure in laser melted Inconel 625 were used to challenge and validate computational models of the melting and solidification process. To this end, three thermal models incorporating different physics are compared with the experimental data. It is identified that the heat convection enhanced by the thermocapillary flow inside the melt pool and heat loss caused by vaporization play pivotal roles to guarantee the accuracy of the predictions, and thus should be considered in the thermal model. Neglecting fluid flow and vaporization leads to nearly 100% difference in cooling rate during solidification, and 20% difference in cooling rate after solidification from the results. With the most accurate thermal model, surface topographies of the melt tracks are predicted and quantitatively analyzed. Using the Kurz-Fisher model, the primary dendrite arm spacing is predicted based on the thermal gradient and solidification rate predictions, while elemental segregation is predicted using the Scheil-Gulliver model and a non-equilibrium solidification model. Additionally, it is shown that increasing scan speed inhibits elemental microsegregation.

Revealing influence mechanism of a transverse static magnetic field on the refinement of primary dendrite spacing during directional solidification

The refinement mechanism of primary dendrite spacing caused by a transverse static magnetic field during directional solidification was proposed and verified experimentally in this paper. According to the Kurz-Fisher model, this magnetic field-induced refinement is related to the temperature gradient and solute redistribution in the mushy zone during directional solidification. Therefore, the effect of the magnetic field on the temperature gradient was investigated and the solute redistribution induced by the thermoelectric magnetic convection was measured by Rank sort method. The experimental results indicate that the refinement of primary dendrite spacing can be attributed to the solute redistribution rather than the change of temperature gradient.

Dendrite growth behavior in directionally solidified Fe–C–Mn–Al alloys

In this study, a series of directional solidification experiments were conducted to investigate the dendritic growth behavior in Fe–C–Mn–Al alloys with varying C contents (0.06, 0.24 and 0.68 wt%). Because of the large compositional undercooling at the front of the solid–liquid interface, dendrites developed at various growth velocities. Under the experimental conditions in the present study, the relationships between the primary dendrite arm spacing (PDAS) and growth velocity for the 0.06C, 0.24C and 0.68C alloys were λ0.06C = 11.75·V−0.30, λ0.24C = 10.38·V−0.32, and λ0.68C = 10.56·V−0.31 respectively. Comparison of the experimental data with prediction models confirmed that the PDAS of the Fe–0.68C–18.02Mn–1.35Al alloy can be predicted using the Kurz-Fisher model. The length of the mushy zone increased, and the high-temperature solidification mode changed with increasing C content, leading to complex changes in the PDAS. The results indicate that the solidification structure of Fe–C–Mn–Al alloys can be refined by increasing the growth velocity and that modifying the C content can be beneficial in avoiding the peritectic reaction.

Directional solidification of Fe-Al-Ta eutectic by electron beam floating zone melting

Fe-Al-Ta eutectic composites have been paid more attentions for high temperature application. Nevertheless, still there is a lack of research on microstructural characteristics and crystal growth mechanism of this eutectic obtained by high temperature gradient directional solidification technique. As such, Fe-Al-Ta eutectic composites were prepared by high temperature gradient electron beam floating zone melting technique in the present paper. Microstructures, solid/liquid interface morphologies and preferential orientations of the Fe-Al-Ta eutectic composites at different solidification rates were studied. Moreover, effect of interface perturbation wavelength on stability of the solid/liquid interface was calculated according to M-S theory and Kurz-Fisher model, respectively. These are consistent with the experimental results well.

Effects of the Growth Rate on Microstructures and Room Temperature Mechanical Properties of Directionally Solidified Mg-5.2Zn Alloy

Effects of the growth rate on the microstructures and room temperature mechanical properties of Mg-5.2Zn alloy were investigated using Bridgman method at a constant temperature gradient 30 K/mm with different growth rates (v = 10 ~ 100 μm/s). The microstructure of directionally solidified Mg-5.2Zn alloy is composed of dendrite primary α(Mg) phase and interdendritic α(Mg) + Mg7Zn3 eutectic, which agrees well with the predicted microstructure using Scheil model. The morphology of the primary α(Mg) phase transforms from cellular, to cellular-dendritic, and then to dendritic with the increase of growth rate from 10 μm/s to 100 μm/s. According to the Kurz–Fisher model, the approximate criterion growth rate for cellular/dendrite transition is determined to be about 12.7 μm/s, which just lies in the experimental result interval. Using non-linear fitting analysis, λ 1 (the primary dendrite arm spacing) and λ 2 (secondary dendrite arm spacing) were found to be dependent on v (growth rate) in the form of λ 1 = 8.6964 × 10−6 v −0.23983, λ 2 = 1.7703 × 10−6 v −0.34161, which is in good agreement with the calculated values by the Trivedi model and Kattamis–Flemings model, respectively. Furthermore, tensile test shows that the directional solidified experimental Mg-5.2Zn alloy shows higher strength than the non-directional solidified alloy under the same cooling rate. The dendritic structure shows higher strength than the cellular structure due to the fact that brittle interdendrite eutectic was refined in dendritic structures.

Phase-field modeling of microstructure formation during rapid solidification in Inconel 718 superalloy

The prediction of the equilibrium and metastable phase/grain morphologies during selective laser melting (SLM) of Ni-base superalloys can be accomplished using phase-field modeling (PF). In this paper, a model for binary and multi-component systems is presented and validated via the steady-state growth problem by comparison to theoretical predictions of the Green-function calculations and the Kurz–Fisher model. By means of the PF simulations, a phenomenological dependency of the growth velocity on undercooling during the rapid solidification is evaluated. It is found that the growth velocity does not achieve steady-state values for real process and material parameters. The final microstructure predicted by the PF is in good agreement with the experimental observations. Additionally, the simulations provide concentration profiles, which show a pronounced segregation of solutes to the dendrite core. The simulated microstructures and concentration fields can be used as inputs for the simulation of the precipitation of secondary phases.

Effect of withdrawal rate on microstructure and lattice misfit of a Ni3Al based single crystal superalloy

A newly developed Re-containing Ni3Al based single crystal superalloy was prepared by seeding technique. We investigated the effect of withdrawal rate (1–400μm/s) on the microstructure and the γ/γ′ lattice misfit. With increasing withdrawal rate, the as-cast microstructure changed from planar to cellular and then to dendritic, accompanied by the significant refinement of dendrite arm and γ′ phases. The morphology of γ′ phases also transformed in response to different withdrawal rates, which was ascribed to the influence of the γ/γ′ lattice misfit. In association with the evolution of the microstructures, the liquid diffusion coefficients of Ni and Ni3Al based superalloys were estimated by Kurz–Fisher model.

Characterization of microstructural length scales in directionally solidified Sn–36%Ni peritectic alloy

Sn–36%Ni peritectic alloys were directionally solidified at different growth rates under a constant temperature gradient (20 K/mm), the dependences of microstructural characteristic length scales on the growth rate were investigated. Experimental results are presented, including primary and higher order dendrite arm spacings λ1, λ2, λ3 and dendrite tip radius R of primary Ni3Sn2 phase. Comparisons between the theoretical predictions and the experimental results show that, for the primary dendrites, λ1=335.882v−0.21, which is in agreement with the Kurz–Fisher model; for the secondary dendrites, λ2=44.957v−0.277, which is consistent with the Bouchard–Kirkaldy model; for the tertiary dendrites, λ3=40.512v−0.274; for the dendrite tip radius, R=22.7v−0.36. The experimental results also show that the λ1/λ2 changes greatly with increasing growth rate while the λ1/λ3 has no significant change, indicating that tertiary dendrite arms have a more similar growth characteristics to primary dendrites compared with secondary dendrites. The λ1/R ranges from 2 to 2.3 with the increase of growth rate.

Effect of sample diameter on primary dendrite spacing of directionally solidified Al-4%Cu alloy

The relationship between primary dendrite arm spacing and sample diameter was studied during directional solidification for Al-4%Cu (mass fraction) alloy. It is shown that primary dendrite spacing is decreased with the decrease of the sample diameter at given growth rate. By regressing the relationship between primary dendrite arm spacing and the growth rate, the primary dendrite arm spacing complies with 461.76 v −0.53, 417.92 v −0.28 and 415.83 v −0.25 for the sample diameter of 1.8, 3.5 and 7.2 mm, respectively. The primary dendrite spacing, growth rate and thermal gradient for different sample diameters comply with 28.77 v −0.35 G −0.70, 23.17 v −0.35 G −0.70 and 23.84 v −0.35 G −0.70, respectively. They are all consistent with the theoretical model λ 1=k bν −a 1 G −b 1 , and b 1/ a 1=2. By analyzing the experimental results with classical models, it is shown that KURZ-FISHER model fits for the primary dendrite spacing in smaller sample diameters with weaker thermosolute convection. Whereas TRIVEDI model is suitable for describing primary dendrite arm spacing with a larger diameter ( d>2 mm) where convection should be considered.

Analytical Modeling of the Growth of Arrayed Needles during Unidirectional Solidification Process under High Temperature Gradient: Part I. Modeling of Array and Growth Theory

An approximate analytical description of the unidirectional growth of arrays of needles is proposed for the solidification under high temperature gradients. Temperature and solute distribution for a needle are described by use of functions with exponential increase/decrease and integral exponential functions. Those for arrayed needles are described by the addition of distributions. Then, a modeling of the growth of arrays of needles is developed in order to predict needle dimensions. Local equilibrium conditions are applied to determine the tip radius and unknown coefficients included in descriptions of temperature and solute distribution. Minimum undercooling of needle tip is also applied to select the primary spacing of growing needles. Predicted dimensions are studied and compared with those given by other theoretical predictions. The model predicts the growth rate of transition from planar interface to cellular, which is very close to the growth rate given by the Mullins-Sekerka theory. The predicted dependency of tip radius of curvature on growth rate is similar to the dependency given by the Kurz-Fisher model for needle growth.

The effect of temperature gradient and growth rate on spacing between primary silicon particles in rapidly solidified hypereutectic aluminium-silicon alloys

Measurements of the number N 0 of primary silicon particles per unit area in hypereutectic Al-Si alloys subjected to front velocity controlled rapid solidification by TIG weld traversing, Bridgman growth and laser surface melt traversing are shown to conform to the single relationship N 0( GV 1 2 ) 1 2 = 4.1±0.8 s 1 2 mm - 3 2 K -1, equivalent to λ ( GV 1 2 ) 1 2 = 87±11 μm 3 2 K 1 2 s - 1 4 , where λ is the mean spacing N 0 - 1 2 between particles. This result is in parametric agreement with the Hunt and Kurz-Fisher model predictions and the magnitude of λ( GV 1 2 ) 1 2 is midway between their respective predictions, as found previously for succinonitrile-acetone and Al-2 wt% Cu.