2024
DOI: 10.3390/ma17040865
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Prediction of the Secondary Arms Spacing Based on Dendrite Tip Kinetics and Cooling Rate

Ibrahim Sari,
Mahmoud Ahmadein,
Sabbah Ataya
et al.

Abstract: Secondary dendrite arm spacing (SDAS) is one of the most important factors affecting macrosegregation and mechanical properties in solidification processes. Predicting SDAS is one of the major parameters in foundry technology. In order to predict the evolution of microstructures during the solidification process, we proposed a simple model which predicted the secondary dendrite arm spacing based solely on the tip velocity (related to the tip supersaturation) and cooling rate. The model consisted of a growing c… Show more

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Cited by 3 publications
(4 citation statements)
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“…Also, S 1 = 2πr 1 and S 2 = 2πr 2 are the surface areas per unit length of cylinders 1 and 2, respectively, and V total = πR 2 f is the total volume of the envelope per unit length. Furthermore, the mixture concentration of the coarsening phenomenon is defined as per Equation (9). Equations ( 3)-( 9) were solved in MATLAB R2022b Software simultaneously through an iterative calculation to obtain the growth of the arms and their corresponding average solid concentration during the coarsening phenomenon.…”
Section: The Growth Modelmentioning
confidence: 99%
See 1 more Smart Citation
“…Also, S 1 = 2πr 1 and S 2 = 2πr 2 are the surface areas per unit length of cylinders 1 and 2, respectively, and V total = πR 2 f is the total volume of the envelope per unit length. Furthermore, the mixture concentration of the coarsening phenomenon is defined as per Equation (9). Equations ( 3)-( 9) were solved in MATLAB R2022b Software simultaneously through an iterative calculation to obtain the growth of the arms and their corresponding average solid concentration during the coarsening phenomenon.…”
Section: The Growth Modelmentioning
confidence: 99%
“…At this stage, the number of side-arms is Materials 2024, 17, 912 2 of 12 reduced (retraction of small side branches towards their parent stem) and, consequently, the average microstructural length scale increases. I. Sari et al [9] proposed a novel model that accurately predicts the secondary dendrite arm spacing (SDAS) based solely on the tip velocity and cooling rate during the directional solidification of different Pb-Sn alloys. The model involved a growing cylinder inside a liquid cylindrical envelope.…”
Section: Introductionmentioning
confidence: 99%
“…Kurz [ 27 ] suggested an approximation for calculating the tip Peclet number (Pe) by inversing the Ivantsov solution. However, Sari et al [ 28 ] reported that the accuracy of the Kurz approximation for estimating Pe, with respect to the Ivantsov function, showed a relatively high error of approximately 20% when estimating Pe at low supersaturation values, which is significant and cannot be negligible. Therefore, Sari et al [ 28 ] proposed a refined approximation specifically tailored to compute the Peclet number for a given supersaturation, building upon the Kurz approach.…”
Section: Introductionmentioning
confidence: 99%
“…However, Sari et al [ 28 ] reported that the accuracy of the Kurz approximation for estimating Pe, with respect to the Ivantsov function, showed a relatively high error of approximately 20% when estimating Pe at low supersaturation values, which is significant and cannot be negligible. Therefore, Sari et al [ 28 ] proposed a refined approximation specifically tailored to compute the Peclet number for a given supersaturation, building upon the Kurz approach. This new approximation was in good agreement with the Ivantsov function for a wide range of supersaturation values.…”
Section: Introductionmentioning
confidence: 99%