A finite element formulation for macrosegregation during alloy solidification using a fractional step method and equal-order elements

Chen, Qipeng; Shen, Houfa

doi:10.1016/j.commatsci.2018.08.009

Cited by 6 publications

(8 citation statements)

References 35 publications

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“…The macroscopic equations are solved according to the literature [23]. Once the variations of the master variables, such as the average enthalpy, ∆H n , composition, ∆w n , and liquid velocity, ∆v v , over one macro time step ∆t at the FE nodes are available, the corresponding variations of the average enthalpy, δH n , composition, δw n , and liquid velocity, δv n , over one micro time step δt are firstly interpolated in time by:…”

Section: Coupling Strategymentioning

confidence: 99%

“…Various solidification experiments [20][21][22] were performed based on the tin-lead (Sn-Pb) alloys due to their strong segregation tendency and operability in the laboratory, giving better experimental benchmarks for numerical validation. This contribution is devoted to achieving a direct macroscopic modeling with a 2D cellular automaton-finite element (CAFE) model, which is an extension of a newly developed FE model by the authors [23] for the prediction of macrosegregation during the solidification of binary alloys. The CAFE model is applied to the solidification benchmark experiment of a Sn-3wt.%Pb alloy [22], in which a fully developed fluid flow is initiated and a columnar-to-equiaxed transition (CET) occurs.…”

Section: Introductionmentioning

confidence: 99%

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Direct Macroscopic Modeling of Grain Structure and Macrosegregation with a Cellular Automaton–Finite Element Model

Chen

Shen

2019

Metals

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Grain structure and macrosegregation are two main factors determining mechanical properties of components and are strongly coupled during alloy solidification. A two-dimensional (2D) cellular automaton (CA)–finite element (FE) model is developed to achieve a direct macroscopic modeling of grain structure and macrosegregation during the solidification of binary alloys. With the conservation equations of mass, momentum, energy, and solute solved by a macroscopic FE model and the grain structure described by a microscopic CA model, a two-way coupling between the CA and FE models is applied. Furthermore, the effect of the fluid flow on the dendrite tip growth velocity is considered by modified dendrite tip growth kinetics. The CAFE model is applied to a quasi-2D benchmark solidification experiment of a Sn–3.0wt.%Pb alloy, and the grain structure and macrosegregation are predicted simultaneously. It is demonstrated that the model has a capacity to describe the undercooling ahead of the growth front. The growth directions of columnar grains, grain sizes, and columnar-to-equiaxed transition (CET) position are obviously modified by the fluid flow, and obvious segregated channels almost aligned with the orientations of the columnar grains are found. Qualitatively good agreement is obtained between the predicted segregation profiles and experimental measurements.

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Section: Coupling Strategymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Direct Macroscopic Modeling of Grain Structure and Macrosegregation with a Cellular Automaton–Finite Element Model

Chen

Shen

2019

Metals

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“…A fractional step method is applied to Equations (1) and (2) to decouple the velocity and pressure, by which linear equal-order elements are allowed to interpolate the velocity and pressure. Details of the finite element formulations and numerical algorithms are available in reference [27]. The grain structure are tracked based on the CA lattice.…”

Section: Solution Algorithmmentioning

confidence: 99%

“…This section is dedicated to clarify the effects of the casting speed and casting temperature on the grain structure and macrosegregation in the non-grain-refined billet, in which a CET was suspected. Case 2 corresponds to the non-grain-refined billet DC cast experimentally [27]. With identical configurations to case 2, only the casting speed or the casting temperature is modified in cases 3-6.…”

Section: Effects Of the Casting Speed And Casting Temperaturementioning

confidence: 99%

Transient Modeling of Grain Structure and Macrosegregation during Direct Chill Casting of Al-Cu Alloy

Chen

Shen

2019

Processes

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Grain structure and macrosegregation are two important aspects to assess the quality of direct chill (DC) cast billets, and the phenomena responsible for their formation are strongly interacted. Transient modeling of grain structure and macrosegregation during DC casting is achieved with a cellular automaton (CA)–finite element (FE) model, by which the macroscopic transport is coupled with microscopic relations for grain growth. In the CAFE model, a two-dimensional (2D) axisymmetric description is used for cylindrical geometry, and a Lagrangian representation is employed for both FE and CA calculations. This model is applied to the DC casting of two industrial scale Al-6.0 wt % Cu round billets with and without grain refiner. The grain structure and macrosegregation under thermal and solutal convection are studied. It is shown that the grain structure is fully equiaxed in the grain-refined billet, while a fine columnar grain region and a coarse columnar grain region are formed in the non-grain-refined billet. With the increasing casting speed, grains become finer and grow in a direction more perpendicular to the axis, and the positive segregation near the centerline becomes more pronounced. The increasing casting temperature makes grains coarser and the negative segregation near the surface more pronounced.

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“…Several attempts have already been made to understand the solidification characteristics of heavy ingots through numerical simulations of ingot casting processes using the finite element method (FEM) [ 16 , 30 , 31 , 32 , 33 , 34 ]. Hence, to investigate the effects of the reduced hot-top height on the casting qualities of ingots, the ingot casting operations were simulated by the THERCAST ® 3D finite-element code.…”

Section: Introductionmentioning

confidence: 99%

Feasibility of Reduced Ingot Hot-Top Height for the Cost-Effective Forging of Heavy Steel Ingots

Kim

et al. 2020

Materials

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Feasibility studies have been performed on ingots with reduced hot-top heights for the cost-effective hot forging of heavy ingots. The quality of the heavy ingots is generally affected by internal voids, which have been known to be accompanied by inclusions and segregation. To guarantee the expected mechanical performance of the forged products, these voids should be closed and eliminated during the hot open die forging process. Hence, to effectively control the internal voids, the optimum hot-top height and forging schedules need to be determined. In order to improve the utilization ratio of ingots, the ingot hot-top height needs to be minimized. To investigate the effect of the reduced hot-top height on the forged products, shaft and bar products have been manufactured via hot forging of ingots having various hot-top heights. From the operational results, the present work suggests effective forging processes to produce acceptable shaft and bar products using ingots having reduced hot tops. The mechanical properties of shop-floor products manufactured from ingots with reduced hot tops have also been measured and compared with those of conventional ingot products.

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A finite element formulation for macrosegregation during alloy solidification using a fractional step method and equal-order elements

Cited by 6 publications

References 35 publications

Direct Macroscopic Modeling of Grain Structure and Macrosegregation with a Cellular Automaton–Finite Element Model

Direct Macroscopic Modeling of Grain Structure and Macrosegregation with a Cellular Automaton–Finite Element Model

Transient Modeling of Grain Structure and Macrosegregation during Direct Chill Casting of Al-Cu Alloy

Feasibility of Reduced Ingot Hot-Top Height for the Cost-Effective Forging of Heavy Steel Ingots

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