Please wait a minute...
Acta Metall Sin  2021, Vol. 57 Issue (6): 822-830    DOI: 10.11900/0412.1961.2020.00289
Research paper Current Issue | Archive | Adv Search |
Precipitation Kinetics of Al3Sc in Aluminum Alloys Modeled with a New Grouping Cluster Dynamics Model
XU Kun1, WANG Haichuan1, KONG Hui1, WU Zhaoyang1(), ZHANG Zhan2
1.Key Laboratory of Metallurgical Emission Reduction & Resources Recyling, Ministry of Education, Anhui University of Technology, Ma'anshan 243032, China
2.School of Materials and Metallurgy, Wuhan University of Science and Technology, Wuhan 430081, China
Cite this article: 

XU Kun, WANG Haichuan, KONG Hui, WU Zhaoyang, ZHANG Zhan. Precipitation Kinetics of Al3Sc in Aluminum Alloys Modeled with a New Grouping Cluster Dynamics Model. Acta Metall Sin, 2021, 57(6): 822-830.

Download:  HTML  PDF(3368KB) 
Export:  BibTeX | EndNote (RIS)      
Abstract  

Cluster dynamics is a mesoscopic modeling technique describing the various kinetic stages of homogeneous precipitation by the same set of rate equations. However, when the simulated cluster size continuously increases, it easily causes an enormous computational workload, and the use of a particle-size-grouping method is often necessary to solve this problem. In this study, an ungrouped cluster dynamics model and certain existing grouping methods are reviewed. Next, a new grouping method with an assumed logarithmically-linear distribution of cluster number densities inside each group size is proposed. Comparing the results of all grouped models with the exact solution of the ungrouped model for simulating aluminum-scandium (Al3Sc) precipitation in the Al-0.18%Sc (atomic fraction) alloy at 300oC, the new grouping method was able to reduce computational costs considerably keeping enough total and local accuracies. Moreover, the reasonable agreements of the mean radii and size distributions as functions of time between experiments and simulations were obtained, demonstrating the ability of the new grouping method in modeling large-scale precipitation kinetics.

Key words:  precipitation kinetics      cluster dynamics model      particle-size-grouping method      Al-Sc alloy      homogeneous precipitation     
Received:  05 August 2020     
ZTFLH:  TG146.2  
Fund: National Natural Science Foundation of China(U1960109);Key Program for the Innovation and Entrepreneurship Support Plan for Returning Overseas Chinese Scholars in Anhui Province
About author:  WU Zhaoyang, associate professor, Tel: (0551)2311571, E-mail: ahutwzy@ahut.edu.cn

URL: 

https://www.ams.org.cn/EN/10.11900/0412.1961.2020.00289     OR     https://www.ams.org.cn/EN/Y2021/V57/I6/822

Fig.1  Comparison of Al3Sc size distributions of cluster groups calculated by 3 parlicle-size-grouping (PSG) methods with exact solution of ungrouped cluster dynamics (CD) model (rj—mean radius of cluster group, Nj—number density, t—precipitation time)
MethodStorage spaceComputational time / s
Ungrouped CD modeliM = 160008471.6
Kiritani methodGM = 200179.2
G-O methodGM = 1541798.2
New grouping methodGM = 149675.4
Table 1  Comparison of computational costs of different cluster dynamics models for a precipitation time of 1 × 107 s
Fig.2  Comparison of Al3Sc size distributions of ungrouped clusters calculated by 3 PSG methods with exact solution of ungrouped CD model
Fig.3  Comparison of calculated and measured Al3Sc precipitations for an Al-0.18%Sc alloy during isothermal aging at 300oC
Fig.4  Comparison of calculated and measured normalized precipitate size distributions of Al3Sc precipitates during isothermally ageing at 300oC and LSW distribution for 6 h (a), 72 h (b), and 350 h (c) (g(rˉ)=ΔN?/?NP/Δr?/?rP, r—radius, rˉ—normalize radius, ΔN—total number density of clusters in each size group, Δr—radius interval of clusters in each size group)
1 Mathon M H, Barbu A, Dunstetter F, et al. Experimental study and modelling of copper precipitation under electron irradiation in dilute FeCu binary alloys [J]. J. Nucl. Mater., 1997, 245: 224
2 Christien F, Barbu A. Modelling of copper precipitation in iron during thermal aging and irradiation [J]. J. Nucl. Mater., 2004, 324: 90
3 Clouet E, Barbu A, Laé L, et al. Precipitation kinetics of Al3Zr and Al3Sc in aluminum alloys modeled with cluster dynamics [J]. Acta Meter., 2005, 53: 2313
4 Lepinoux L. Modelling precipitation in binary alloys by cluster dynamics [J]. Acta Mater., 2009, 57: 1086
5 Ke H B, Wells P, Edmondson P D, et al. Thermodynamic and kinetic modeling of Mn-Ni-Si precipitates in low-Cu reactor pressure vessel steels [J]. Acta Mater., 2017, 138: 10
6 Kiritani M. Analysis of the clustering process of supersaturated lattice vacancies [J]. J. Phys. Soc. Jpn., 1973, 35: 95
7 Koiwa M. On the validity of the grouping method—Comments on “analysis of the clustering process of supersaturated lattice vacancies”–[J]. J. Phys. Soc. Jpn., 1974, 37: 1532
8 Golubov S I, Ovcharenko A M, Barashev A V, et al. Grouping method for the approximate solution of a kinetic equation describing the evolution of point-defect clusters [J]. Philos. Mag., 2001, 81A: 643
9 Ovcharenko A M, Golubov S I, Woo C H, et al. GMIC++: Grouping method in C++: An efficient method to solve large number of Master equations [J]. Comput. Phys. Commun., 2003, 152: 208
10 Liu C, He L, Zhai Y, et al. Evolution of small defect clusters in ion-irradiated 3C-SiC: Combined cluster dynamics modeling and experimental study [J]. Acta Mater., 2017, 125: 377
11 Fell M, Murphy S M. The nucleation and growth of gas bubbles in irradiated metals [J]. J. Nucl. Mater., 1990, 172: 1
12 Golubov S I, Stoller R E, Zinkle S J, et al. Kinetics of coarsening of helium bubbles during implantation and post-implantation annealing [J]. J. Nucl. Mater., 2007, 361: 149
13 Kampmann R, Wagner R. Kinetics of precipitation in metastable binary alloys—Τheory and application to Cu-1.9at % Ti and Ni-14 at % Al [A]. Decomposition of Alloys: The Early Stages [C]. Oxford: Pergamon Press, 1984: 91
14 Cahn R W, Haasen P, Kramer E J. Materials Science and Technology [M]. Weinheim: John Wiley & Sons Inc., 1991: 213
15 Svoboda J, Fischer F D, Fratzl P, et al. Modelling of kinetics in multi-component multi-phase systems with spherical precipitates: I: Theory [J]. Mater. Sci. Eng., 2004, A385: 166
16 Becker R, Döring W. Kinetische behandlung der keimbildung in übersättigten dämpfen [J]. Ann. Phys., 1935, 416: 719
17 Zhang L F, Li Y L, Ren Y. Fundamentals of non-metallic inclusions in steel: part I. Control of unsteady casting and big inclusion; nucleation, motion, removal and capture of inclusions in molten steel [J]. Iron Steel, 2013, 48(11): 1
张立峰, 李燕龙, 任 英. 钢中非金属夹杂物的相关基础研究(I)——非稳态浇铸中的大颗粒夹杂物及夹杂物的形核、长大、运动、去除和捕捉 [J]. 钢铁, 2013, 48(11): 1
18 Li Y G, Zhou W H, Huang L F, et al. Cluster dynamics modeling of accumulation and diffusion of helium in neutron irradiated tungsten [J]. J. Nucl. Mater., 2012, 431: 26
19 Gao C. Cluster dynamics simulation of defect evolution in electron-irradiated BCC Fe and Fe-Cu dilute alloys [D]. Shanghai: Shanghai University, 2015
高 超. BCC铁和铁铜合金电子辐照缺陷演化的团簇动力学模拟 [D]. 上海: 上海大学, 2015
20 Xu K, Thomas B G. Particle-size-grouping model of precipitation kinetics in microalloyed steels [J]. Metall. Mater. Trans., 2012, 43A: 1079
21 Marquis E A, Seidman D N. Nanoscale structural evolution of Al3Sc precipitates in Al(Sc) alloys [J]. Acta Mater., 2001, 49: 1909
22 Watanabe C, Kondo T, Monzen R. Coarsening of Al3Sc precipitates in an Al-0.28 wt pct Sc alloy [J]. Metall. Mater. Trans., 2004, 35A: 3003
23 Røyset J, Ryum N. Kinetics and mechanisms of precipitation in an Al-0.2 wt.% Sc alloy [J]. Mater. Sci. Eng., 2005, A396: 409
24 Fujikawa S I. Impurity diffusion of scandium in aluminium [J]. Defect Diffus. Forum., 1997, 143-147: 115
25 Novotny G M, Ardell A J. Precipitation of Al3Sc in binary Al-Sc alloys [J]. Mater. Sci. Eng., 2001, A318: 144
26 Iwamura S, Miura Y. Loss in coherency and coarsening behavior of Al3Sc precipitates [J]. Acta Mater., 2004, 52: 591
27 Robson J D, Jones M J, Prangnell P B. Extension of the N-model to predict competing homogeneous and heterogeneous precipitation in Al-Sc alloys [J]. Acta Mater., 2003, 51: 1453
28 Hyland R W. Homogeneous nucleation kinetics of Al3Sc in a dilute Al-Sc alloy [J]. Metall. Mater. Trans., 1992, 23A: 1947
29 Zener C. Theory of growth of spherical precipitates from solid solution [J]. J. Appl. Phys., 1949, 20: 950
30 Lifshitz I M, Slyozov V V. The kinetics of precipitation from supersaturated solid solutions [J]. J. Phys. Chem. Solids, 1961, 19: 35
[1] WANG Changsheng, FU Huadong, ZHANG Hongtao, XIE Jianxin. Effect of Cold-Rolling Deformation on Microstructure, Properties, and Precipitation Behavior of High-Performance Cu-Ni-Si Alloys[J]. 金属学报, 2023, 59(5): 585-598.
[2] TANG Shuai, LAN Huifang, DUAN Lei, JIN Jianfeng, LI Jianping, LIU Zhenyu, WANG Guodong. Co-Precipitation Behavior in Ferrite Region During Isothermal Process in Ti-Mo-Cu Microalloyed Steel[J]. 金属学报, 2022, 58(3): 355-364.
[3] Rui CHEN,Qingyan XU,Baicheng LIU. MODELLING INVESTIGATION OF PRECIPITATION KINETICS AND STRENGTHENING FOR NEEDLE/ROD-SHAPED PRECIPITATES INAl-Mg-Si ALLOYS[J]. 金属学报, 2016, 52(8): 987-999.
[4] Yong LI,Mingxing GUO,Ning JIANG,Xukai ZHANG,Yan ZHANG,Linzhong ZHUANG,Jishan ZHANG. PRECIPITATION BEHAVIORS AND PREPARATION OF AN ADVANCED Al-0.93Mg-0.78Si-0.20Cu-3.00Zn ALLOY FOR AUTOMOTIVE APPLICATION[J]. 金属学报, 2016, 52(2): 191-201.
[5] WANG Xiaona, HAN Lizhan, GU Jianfeng. PRECIPITATION KINETICS AND YIELD STRENGTH MODEL FOR NZ30K-Mg ALLOY[J]. 金属学报, 2014, 50(3): 355-360.
[6] SU Zhenxing WANG Yuchen WANG Shaoqing. FIRST-PRINCIPLES STUDY OF THE PHASE STRACTURES OF Al-Sc ALLOYS[J]. 金属学报, 2010, 46(5): 623-628.
[7] LIU Wenchang; CHEN Zonglin; XIAO Furen; YAO Mei; WANG Shaogang;LIU Runguang(College of Material Engineering; Yanshan University; Qinhuangdao 066004);(Shenyang Liming Engine Manufacturing Company; Shenyang 110043);(School of Materials Engineering; Harbin Institute of Technology; Harbin 150001)Correspondent:LIU Wenchang;associate professor; Tel: (0335)8057047. EFFECT OF COLD ROLLING ON THE KINETICS OF δ PHASE PRECIPITATION IN INCONEL 718[J]. 金属学报, 1998, 34(10): 1049-1054.
No Suggested Reading articles found!