Authors’ reply

Combeau, Hervé; Drezet, Jean‐Marie; Mo, Asbjørn; Rappaz, M.

doi:10.1007/s11661-998-0121-2

Cited by 5 publications

(17 citation statements)

References 5 publications

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“…in the fitting of approximate microsegregation models to numerical or exact solutions [5,19] indicate 2 Ͻ m Ͻ 2.5. where the second term on the right-hand side represents the With values of m ϭ 2.333 and n ϭ 1/3, Eq. [18] gives contribution from the coarsening of the domain.…”

Section: The Concept Of a Back-diffusionmentioning

confidence: 99%

“…[16] through [19]) suggests that the dilution effect of coarsening alone can be described using a Fourier number of ␣ ϭ ␣ c ϭ 0.1 in a basic microsegregation model. This is tested on comparing predictions from a basic model, with the Fourier number set at ␣ ϭ 0.1, with predictions from the exact solutions of microsegregation due to coarsening alone (Eqs.…”

Section: B Limiting Case: No Solid Diffusionmentioning

confidence: 99%

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A unified model of microsegregation and coarsening

Voller

Beckermann

1999

Metall Mater Trans A

100

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Using a coordinate transform in a standard microsegregation model it is shown that the effect of coarsening on the dilution of the liquid phase can be accounted for by adding a dimensionless parameter ␣ c to the back-diffusion Fourier number. Through theory, for the case of parabolic growth, and numerical experiments for the constant cooling rate, it is shown that a constant value of ␣ c ϭ 0.1 is a sound choice across a wide range of casting and alloy conditions. This finding allows for the development of a unified model for microsegregation and coarsening. In particular, previous approximate microsegregation models can be readily modified to account for coarsening.

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Section: The Concept Of a Back-diffusionmentioning

confidence: 99%

Section: B Limiting Case: No Solid Diffusionmentioning

confidence: 99%

A unified model of microsegregation and coarsening

Voller

Beckermann

1999

Metall Mater Trans A

100

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“…As stated by Combeau et al, [8] who have investigated remelting due to temporary increasing temperatures during solidification, the departure from the interface equilibrium, which is observed in rapid solidification (e.g., Reference 9), should occur at much lower cooling rates during remelting as a result of the low diffusivity in the solid. As stated by Combeau et al, [8] who have investigated remelting due to temporary increasing temperatures during solidification, the departure from the interface equilibrium, which is observed in rapid solidification (e.g., Reference 9), should occur at much lower cooling rates during remelting as a result of the low diffusivity in the solid.…”

Section: Experimental Procedures and Resultsmentioning

confidence: 89%

“…[1,2,3] In the most advanced models, [4][5][6][7][8][9][10] various effects such as solid-state diffusion, dendrite arm coarsening, and undercooling are considered. Recent reviews of analytical and numerical solutions are available.…”

Section: Introductionmentioning

confidence: 99%

The influence of temperature gradient zone melting on microsegregation

Kraft

Pompe

Exner

1998

Metall Mater Trans A

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Adding an algorithm for considering temperature gradient zone melting (TGZM) to an existing numerical model for predicting microstructure and microsegregation allows the prediction of migration distances of dendrite arms and asymmetric concentration distributions in the arms. Provided that detailed information on the time dependence of the temperature gradient as well as the cooling rate is available from heat flow calculations, accurate predictions of the type and amount of secondary phases or dendrite arm spacings are possible for cooling conditions at which TGZM is active. Parameter studies are performed to investigate the influence of TGZM for typical temperature gradients (0.01 to 10 K/mm). Sawtoothlike concentration distributions are predicted for high-temperature gradients. A binary Al-6.8 wt pct Cu alloy is solidified unidirectionally and asymmetrical concentration profiles are measured. Considering TGZM in the simulation results in good agreement of model predictions with experimental measurements in the position of the minimum concentration and the asymmetric shape of the concentration profile as well as dendrite arm spacings and amount of second phase.

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“…Likewise, microsegregation models based on the assumption of a parabolic solute profile in the solid [6] are available, because the formulation of the back-diffusion term is in this case very simple. Combeau et al [7] suggested generalizing this approach by approximating the solute profile in solid by a power-law or a polynomial function. However, for some multicomponent and multiphase alloys, it might be necessary to completely solve the diffusion equation or to determine the precise thermodynamic quantities by means of a thermodynamic software, which requires a fully numerical approach.…”

Section: Introductionmentioning

confidence: 99%

Quantification of Microsegregation in Cast Al-Si-Cu Alloys

Ganesan

Thuinet

Dye

et al. 2007

Metall Mater Trans B

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The random sampling approach offers an elegant yet accurate way of validating microsegregation models. However, both instrumental errors and interference from secondary phases complicate the treatment of randomly sampled microprobe data. This study demonstrates that the normal procedure of sorting the data for each element independently can lead to inaccurate estimation of segregation profiles within multicomponent, multiphase, aluminum alloys. A recently proposed alloy-independent approach is shown to more reliably isolate these interferences, allowing more accurate validation of microsegregation models. Application of this approach to examine solidification segregation of a 319-type alloy demonstrated that, for these slowly cooled castings, neither Sr or TiB 2 additions significantly affected coring of Cu within the primary a-Al dendrites. Comparison against predictions of CALPHAD-type Gulliver-Scheil models was less satisfactory. Consideration of back-diffusion and morphology effects through a one-dimensional (1-D) numerical model do not improve the agreement. Possible reasons for the lack of agreement are hypothesized.

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Authors’ reply

Cited by 5 publications

References 5 publications

A unified model of microsegregation and coarsening

A unified model of microsegregation and coarsening

The influence of temperature gradient zone melting on microsegregation

Quantification of Microsegregation in Cast Al-Si-Cu Alloys

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