On an expression for the growth of secondary dendrite arm spacing during non-equilibrium solidification of multicomponent alloys: Validation against ternary aluminum-based alloys
Ivaldo L. FerreiraAntônio Luciano Seabra MoreiraJulio A.S. AvizThiago A. CostaOtávio L. RochaAndré BarrosAmauri Garcia
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Dendrite (mathematics)
Supercooling
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In the comparison of the solidification characteristics of supercooling directional solidification (SDS) with constrained directional solidification (DS) and with the consideration of the inheritance of supercooled melt, the SDS technique established with the combination of melt supercooling and traditional DS was proposed. An exploring study on SDS techniques was also conducted using appropriate facilities, designed and manufactured by the authors’ laboratory and the deep supercooling of Cu–5.0%Ni alloy, and its DSs were implemented.
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The secondary arm spacing of undercooled Ni50Cu50 alloy did not decrease withincreasing undercooling in a simple power law, but there was a abnormal protrusion in theirrelationship in the undercooling range of 40 -- 120 K. This phenomenon was first attributedto the increase of primary dendrite tip radius occurring in the transition from solute diffusioncontrolled dendrite growth at low undercoolings to thermally controlled dendrite growth at highundercoolings. The other cause was the substantial sidebranch coarsing induced by the remeltingwhich was extremely serious in the solidification of undercooled melts.
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Arrayed growth of dendrite is studied analytically in highly supercooled melt. The proposed model takes into account the effect of interfacial shape of dendrite tip, the array of dendrite and the area of dendrite tip. Predictions are compared with experimental results in the solidification of organic alloy. A dendrite is shown to grow almost freely (unconstrained) with other dendrites in lowly supercooled melt, but constrained in highly supercooled melt.
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A novel solution approach is proposed for the numerical simulation of the solidification process of binary Al-Si hypoeutectic alloys during upward and downward solidification modes. Undercooling is always observed during solidification, but the phenomenon could not be considered in the present-day numerical solution. In this approach, the temperature distribution in the mushy zone was used to define the fraction of solid, which enabled the evaluation of the effect of dendrite tip undercooling on the characteristics of the binary alloy solidification. The present numerical algorithm was found to significantly reduce the computation time. Transient temperature distribution and solidification time from the numerical analysis, with consideration of natural convection due to temperature and concentration gradients, have been successfully simulated and validated with experiment results. Numerical results with consideration of dendrite tip undercooling have better agreement with experimental results. The effect of dendrite tip undercooling on the fluid flow (velocity profile), G, R and λ1 for both upward and downward solidification modes of Al-Si alloys have been investigated and discussed. Consideration of undercooling was found to increase G and reduce R in both solidification modes. During downward solidification, considering undercooling significantly increased flow velocity and decreased λ1. The primary dendrite arm spacing could be validated with results from uni-directional solidification experiments only when dendrite tip undercooling was considered.
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Si faceted dendrites grown from the same parallel twins under different undercooling (ΔT) were observed by in situ observation, and the dependence of faceted dendrite growth velocity (Vd) on undercooling was investigated. Vd increase linearly as the increasing ΔT. The faceted dendrite growth velocity-undercooling relationship was analyzed using a model developed on the basis of theoretical dendrite growth velocity. The results obtained using the proposed model fit the experimental results well and indicate that the twin spacing markedly affects the dendrite growth velocity-undercooling relationship.
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Rapid growth behavior of ■ has been investigated in the undercooling experiments of Cu-14%Ge, Cu-15%Ge, Cu-18.5%Ge and Cu-22%Ge alloys. Alloys of the four compositions obtain the maximum undercoolings of 202 K(0.17TL), 245 K(0.20TL), 223 K(0.20TL) and 176 K(0.17TL), respectively. As the content of Ge increases, the microstructural transition of (Cu) dendrite + ■ peritectic → ■ peritectic → ■ dendrite + (e +■ ) eutectic takes place in the alloy at small undercooling, while the microstructural transition of fragmented α (Cu) dendrite + ■ peritectic → ■peritectic →■ dendrite + e phase happens in the alloy at large undercooling. EDS analysis of the Ge content in ■ peritectic indicates that undercooling enlarges the solid solubility of α dendrite, which leads to a decrease in the Ge content in ■ as undercooling increases. In the Cu-18.5%Ge alloy composed of ■ peritectic phase, the Ge content in ■ increases when undercooling increases, which is due to the restraint of the Ge enrichment on the grain boundaries by high undercooling effect.
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