A numerical analysis of dendritic and cellular array growth: the spacing adjustment mechanisms

Lu, Shu-Zu; Hunt, J. D.

doi:10.1016/0022-0248(92)90006-5

Cited by 168 publications

(127 citation statements)

References 47 publications

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“…The eutectic microstructure for composition C O~ will be present below the eutectic temperature Ti, whereas a dendritic structure will be present above the interface temperature of Ti. These results can now be represented either in the velocity-composition or the interface temperaturecomposition plots, as shown in Figure 32 For this Al-Si alloy, the eutectic growth belongs to irregular eutectic, thus: (11) v(a)2 = $ 2~, K,=cOnstanti…”

Section: CDmentioning

confidence: 99%

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Microstructural development of rapid solidification in Al-Si powder

Jin

1995

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Section: CDmentioning

confidence: 99%

“…These parameters were substituted into equations (6,7) to get constants Kr and KC. Then Kr and Kc were substituted into equations (11,12,13) to obtain constantl=6.89x10-7 mm3/s, constant2=8.9x10-3 mmK.…”

Section: CDmentioning

confidence: 99%

Microstructural development of rapid solidification in Al-Si powder

Jin

1995

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“…A related set of calculations on dendrite arrays has been performed by Lu and Hunt [17]. Our work should be viewed as complementary to their model in the sense that our work is relevant to the description of slender morphologies at moderate to large dendrite spacings which their calculations would have diculty describing.…”

Section: Introductionmentioning

confidence: 83%

“…The scaled tip radius for the dendrite is then given by (24). From q(z) we ®nd the inner solution R in from (18) and (17). Knowing R in and P, we can then calculate a composite solution for the dendrite shape from equations (10)±(15).…”

Section: An Integral Equation For the Directional Solidification Of Smentioning

confidence: 99%

On the solidification of dendritic arrays: selection of the tip characteristics of slender needle crystals by array interactions

Spencer

Huppert

1998

Acta Materialia

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AbstractÐWe obtain a unique solution to the well known indeterminacy for Ivantsov dendrites [Dokl. Akad. Nauk. SSSR, 58, 567 (1947)] by considering the directional solidi®cation of a binary alloy as an array of interacting needle crystal dendrites. From the results of an asymptotic theory for the steady-state solidi®cation of slender needle crystal arrays, the shape of the dendrite can be obtained from the solution of a non-linear integral equation. Here we solve this integral equation numerically to determine the characteristics of the solutions and compare the results to dendrite morphologies observed in experiments. The integral equation has a solvability condition that selects a distinct tip radius and tip undercooling for a given set of experimental conditions and dendrite spacings. This selection criteria is fundamentally dierent from traditional tip selection theories based on surface energy, and is linked to the interactions of dendrites in the array. Predictions of the tip radius are in good agreement with experimental measurements for conditions where the asymptotic theory is expected to be valid. Our results suggest that the tip radius increases with array spacing in the experimentally relevant parameter range. This relationship is consistent with the existence of a range of stable array spacings during directional solidi®cation: the lower bound on array spacings is set by the stability criteria for array overgrowth, and an upper bound may be determined by the condition for tip splitting. In the asymptotic limit of small dendrite spacings, our integral equation interestingly has a degenerate set of solutions, indicating a transition from selection to degeneracy in the limit of small spacings. The explanation of this transition is beyond the scope of our theory and remains to be addressed. # 1998 Acta Metallurgica Inc.

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“…The primary dendrite model for A356 alloy developed at ORNL is based on a recently successful model reported by Hunt and co-workers (Hunt, 1991;Lu and Hunt, 1992;Lu, Hunt, Gilgien and Kurz, 1994;Hunt and Lu, 1996) for dendrite array growth in binary alloys. Although the model describes the physics of dendritic array growth under directional solidification conditions, it is likely that the prediction can be extended to treat primary dendrite size during equiaxed grain growth.…”

Section: Prediction Of Primary Dendrite Spacing (Size)mentioning

confidence: 99%

Design and Product Optimization for Cast Light Metals

Viswanathan¹

2001

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A numerical analysis of dendritic and cellular array growth: the spacing adjustment mechanisms

Cited by 168 publications

References 47 publications

Microstructural development of rapid solidification in Al-Si powder

Microstructural development of rapid solidification in Al-Si powder

On the solidification of dendritic arrays: selection of the tip characteristics of slender needle crystals by array interactions

Design and Product Optimization for Cast Light Metals

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