Dynamic Recrystallization Process Simulation of GH4706 Alloy by Level-Set Method

doi:10.11900/0412.1961.2024.00369

Acta Metall Sin

2025, Vol. 61

Issue (9): 1425-1437 DOI: 10.11900/0412.1961.2024.00369

Research paper

Current Issue | Archive | Adv Search

Dynamic Recrystallization Process Simulation of GH4706 Alloy by Level-Set Method

ZHENG Deyu, XIA Yufeng(

), ZENG Yang, ZHOU Jie

School of Materials Science and Engineering, Chongqing University, Chongqing 400044, China

Cite this article:

ZHENG Deyu, XIA Yufeng, ZENG Yang, ZHOU Jie. Dynamic Recrystallization Process Simulation of GH4706 Alloy by Level-Set Method. Acta Metall Sin, 2025, 61(9): 1425-1437.

Download:

HTML

PDF(3073KB)
Export: BibTeX | EndNote (RIS)

Abstract

It is crucial to accurately predict and control the overall microstructure uniformity of large forgings to enhance their comprehensive mechanical properties. Common empirical models of dynamic recrystallization (DRX) do not consider the nucleation mechanisms and grain boundary migration driven by stored energy differences, thereby limiting their ability to predict and track nucleation events and microstructure morphology during the DRX process. To address this limitation, this study proposes an effective simulation approach for microstructure morphology evolution by integrating the level-set method with a dislocation model. The level set function, implemented on a fixed grid within the Eulerian framework, enables the numerical tracking of evolving curves or surfaces on Cartesian grids. Further, it also facilitates topological evolution handling, thereby eliminating the need for complex curve or surface parameterization. Parameters of the DRX model based on the level set method were determined using stress-strain experimental data of the GH4706 alloy within the temperature range of 950-1150 ^oC and strain rate range of 0.001-1 s^-1. Although certain model parameters were obtained through fitting, the two critical parameters of nucleation volume per unit time at the grain boundary surface and factor affecting grain boundary migration rate could not be determined in this way. These were instead identified using a Pareto multi-objective optimization method, which iteratively minimized the discrepancy between experimental data and simulated results through reverse analysis. The DRX fraction and the average grain size were selected as the optimization objectives. The average deviation percentages between the experimental data and simulated results of the two optimization objectives under varying strain conditions were used as evaluation functions. Through continuous multi-objective iterative optimization, an optimal parameter set was derived. Simulation results for the GH4706 alloy under different parameter combinations revealed a linear relationship between the DRX model parameters with the process variables. The DRX behavior of the GH4706 alloy under strains of 0.4-0.7 was simulated and experimentally validated. A comparison between the experimental data and simulation results showed that the average deviation of both the DRX grain volume fraction fraction and grain size was less than 10%. This confirmed the validity of the model and parameter identification approach. Thus, this study provides a robust theoretical framework for simulating the microstructure uniformity of GH4706 alloy during large forgings and offers valuable insights for predicting and regulating the microstructural uniformity.

Key words: level-set method GH4706 alloy dynamic recrystallization simulation optimization

Received: 14 November 2024

ZTFLH:

TG31

Fund: National Key Research and Development Program of China(2022YFB3705103)

Corresponding Authors: XIA Yufeng, professor, Tel: (023)65103214, E-mail: yufengxia@cqu.edu.cn

	Service

	E-mail this article
	Add to citation manager
	E-mail Alert
	RSS
	（）
	Articles by authors
	ZHENG Deyu
	XIA Yufeng
	ZENG Yang
	ZHOU Jie

URL:

https://www.ams.org.cn/EN/10.11900/0412.1961.2024.00369 OR https://www.ams.org.cn/EN/Y2025/V61/I9/1425

Fig.1 Schematic of sampling position (a) and inverse pole figure (IPF) (b) and grain size distribution (c) of initial microstructure of GH4706 superalloy (ND—normal direction, TD—transverse direction, CD—compression direction)

Fig.2 Definition of grain boundaries using level-set functions (Ψ represents level-set function; Ψ₁, Ψ₂, and Ψ₃ represent level set functions for Grain 1, Grain 2, and Grain 3, respectively)

Fig.3 Schematic of grain nucleation process (ρ—dislocation density, ρ_cr—critical dislocation density, L—critical nucleation distance)

Fig.4 Flowchart of dynamic recrystallization (DRX) simulation using level-set method coupled with dislocation density model (L-J represents Laarsaoui-Jonas, LS represents level-set; Ψ_i —the ith level-set function, Δt—time step, M—migration rate of grain boundaries, γ—grain boundary energy, ΔΨ_i —the ith level-set function per unit, α—Taylor factor, µ—material shear modulus, b—Burgers vector, ρ_m—dislocation density of deformed grains, ρ_i —dislocation density of the ith equiaxed grain, $Ψ i 0$ —interfaces of the ith level set function per unit; M₀—pre exponential factor, Q_m—activation energy for grain boundary migration, R—gas constant, T—thermodynamic temperature, V—growth rate of grains, $δ ε ˙$ —factors affecting grain boundary migration rate, $E —$ jump for energy storage of grains; $ε ˙$ —strain rate, τ—dislocation line energy, H—hardening parameter, S—softening parameter; ε—strain, H₀—initial hardening parameter, S₀—initial softening parameter, $ε ˙ 0$ —calibration constant for strain rate, Q—activation energy, m—strain rate sensitivity coefficient)

Fig.5 Initial microstructure model in DIGIMU software

Fig.6 Relationship curves of σ-θ (a) and 2σθ-σ² (b) (θ—hardening rate, σ—flow stress, σ_sat—saturated stress)

Table 1 σ_sat under different temperatures and strain rates

Table 2 S under different temperatures and strain rates

Table 3 S₀ under different temperatures and strain rates

Table 4 H under different temperatures and strain rates

Table 5 m under different temperatures and strain rates

Fig.7 Simulation parameter identification process based on back propogation artificial neural network (BP-ANN) and Paretn-optimization method (f—objective function, f₁—average grain size objective function, f₂—DRX fraction objective function)

Fig.8 Pareto sketch map of multi-object optimization results (δ—factors affecting grain boundary migration rate, K_g— nucleation volume)

Table 6 δ and K_g under different parameters

Fig.9 Relationships between level-set parameters and process parameters (Z—Zener-Hollomon parameter)
(a) lnK_g-lnZ (b) δ-ln

ε ˙

Fig.10 Grain orientation spread (GOS) maps at different strains of 0.4 (a), 0.5 (b), 0.6 (c), and 0.7 (d)

Fig.11 Simulation maps of grain sizes at different strains of 0.4 (a), 0.5 (b), 0.6 (c), and 0.7 (d)

Fig.12 Experimental and simulated grain size distributions at different strains of 0.4 (a), 0.5 (b), 0.6 (c), and 0.7 (d)

Fig.13 Comparisons of average grain size (a) and DRX grain volume fraction (c) with different strains acquired from experiment and simulation; and relative deviation (Δ) and standard deviation (ξ) of average grain size (b) and DRX grain volume fraction (d) (Δ_avg—average deviation)

Table 7 Relative deviations between simulated and experimental results of average grain size

Table 8 Relative deviations between simulated and experimental results of DRX grain volume fraction

[1]	Zhang S, Zeng L R, Zhao D Q, et al. Comparison study of microstructure and mechanical properties of standard and direct-aging heat treated superalloy Inconel 706 [J]. Mater. Sci. Eng., 2022, A839: 142836
[2]	Du J H, Lv X D, Dong J X, et al. Research progress of wrought superalloys in China [J]. Acta Metall. Sin., 2019, 55: 1115 doi: 10.11900/0412.1961.2019.00142
	杜金辉, 吕旭东, 董建新等. 国内变形高温合金研制进展 [J]. 金属学报, 2019, 55: 1115 doi: 10.11900/0412.1961.2019.00142
[3]	Huang S. Microstructure control and mechanical properties optimization of GH4706 wrought superalloy [D]. Shenyang: Northeastern University, 2014
	黄烁. 变形高温合金GH4706组织控制与力学性能优化 [D]. 沈阳: 东北大学, 2014
[4]	Yang W H, deBarbadillo J J, Morita K, et al. A freckle criterion for the solidification of superalloys with a tilted solidification front [J]. JOM, 2004, 56(9): 56
[5]	Fesland J P, Petit P. Manufacturing alloy 706 forgings [A]. Loria E A. Superalloys 718, 625, 706 and Various Derivatives [M]. Warrendale: TMS, 1994: 229
[6]	Sun Y F, Xiang C, Zhang T, et al. Microstructures and mechanical properties of GH4169 superalloy manufactured by selective laser melting [J]. Acta Metall. Sin., 2024, DOI: 10.11900/0412.1961.2024.00075
	孙勇飞, 向超, 张涛等. 选区激光熔化GH4169高温合金的微观组织和力学性能 [J]. 金属学报, 2024, DOI: 10.11900/0412.1961.2024.00075
[7]	Li L, Wang Y, Li H, et al. Effect of the Zener-Hollomon parameter on the dynamic recrystallization kinetics of Mg-Zn-Zr-Yb magnesium alloy [J]. Comput. Mater. Sci., 2019, 166: 221
[8]	Meng Y, Sugiyama S, Yanagimoto J. Microstructure of Cr-V-Mo steel processed by recrystallization and partial melting and its effect on mechanical properties [J]. Mater. Trans., 2014, 55: 921
[9]	Li F L, Fu R, Bai Y R, et al. Effects of initial grain size and strengthening phase on thermal deformation and recrystallization behavior of GH4096 superalloy [J]. Acta Metall. Sin., 2023, 59: 855 doi: 10.11900/0412.1961.2021.00532
	李福林, 付锐, 白云瑞等. 初始晶粒尺寸和强化相对GH4096高温合金热变形行为和再结晶的影响 [J]. 金属学报, 2023, 59: 855 doi: 10.11900/0412.1961.2021.00532
[10]	Avrami M. Kinetics of phase change. II Transformation-time relations for random distribution of nuclei [J]. J. Chem. Phys., 1940, 8: 212
[11]	Sellars C M. The physical metallurgy of hot working [A]. Hot Working and Forming Processes: Proceedings of an International Conference on Hot Working and Forming Processes [M]. London: The Metals Society, 1980
[12]	Jonas J J, Quelennec X, Jiang L, et al. The Avrami kinetics of dynamic recrystallization [J]. Acta Mater., 2009, 57: 2748
[13]	Rollett A D, Raabe D. A hybrid model for mesoscopic simulation of recrystallization [J]. Comput. Mater. Sci., 2001, 21: 69
[14]	Zhu H J, Chen F, Zhang H M, et al. Review on modeling and simulation of microstructure evolution during dynamic recrystallization using cellular automaton method [J]. Sci. China Technol. Sci., 2020, 63: 357
[15]	Xu Q H, Zhang C, Zhang L W, et al. Cellular automaton modeling of dynamic recrystallization of nimonic 80A superalloy based on inhomogeneous distribution of dislocations inside grains [J]. J. Mater. Eng. Perform., 2018, 27: 4955
[16]	Han Z Q. Simulation of dynamic recrystallization based on Monte Carlo method [D]. Ji'nan: Shandong University, 2007
	韩振强. 基于Monte Carlo方法的金属动态再结晶组织模拟 [D]. 济南: 山东大学, 2007
[17]	Zhou G W, Li Z H, Li D Y, et al. A polycrystal plasticity based discontinuous dynamic recrystallization simulation method and its application to copper [J]. Int. J. Plast., 2017, 91: 48
[18]	Hallberg H. Approaches to modeling of recrystallization [J]. Metals, 2011, 1: 16
[19]	Bernacki M, Logé R E, Coupez T. Level set framework for the finite-element modelling of recrystallization and grain growth in polycrystalline materials [J]. Scr. Mater., 2011, 64: 525
[20]	Scholtes B, Boulais-Sinou R, Settefrati A, et al. 3D level set modeling of static recrystallization considering stored energy fields [J]. Comput. Mater. Sci., 2016, 122: 57
[21]	Cruz-Fabiano A L, Logé R, Bernacki M. Assessment of simplified 2D grain growth models from numerical experiments based on a level set framework [J]. Comput. Mater. Sci., 2014, 92: 305
[22]	Jin Y, Bozzolo N, Rollett A D, et al. 2D finite element modeling of misorientation dependent anisotropic grain growth in polycrystalline materials: Level set versus multi-phase-field method [J]. Comput. Mater. Sci., 2015, 104: 108
[23]	Bernacki M. Kinetic equations and level-set approach for simulating solid-state microstructure evolutions at the mesoscopic scale: State of the art, imitations, and prospects [J]. Prog. Mater. Sci., 2024, 142: 101224
[24]	Agnoli A, Bernacki M, Logé R, et al. Selective Growth of low stored energy grains during δ sub-solvus annealing in the inconel 718 nickel-based superalloy [J]. Metall. Mater. Trans., 2015, 46A: 4405
[25]	Gao J. Research on topology optimization for multiscale design of structure-material based on parametric level set [D]. Wuhan: Huazhong University of Science and Technology, 2019
	高杰. 基于参数化水平集的结构/材料多尺度拓扑优化设计研究 [D]. 武汉: 华中科技大学, 2019
[26]	Peczak P, Luton M J. The effect of nucleation models on dynamic recrystallization I. Homogeneous stored energy distribution [J]. Philos. Mag., 1993, 68B: 115
[27]	Cram D G, Zurob H S, Brechet Y J M, et al. Modelling discontinuous dynamic recrystallization using a physically based model for nucleation [J]. Acta Mater., 2009, 57: 5218
[28]	Guo Q M, Li D F, Peng H J, et al. Nucleation mechanisms of dynamic recrystallization in Inconel 625 superalloy deformed with different strain rates [J]. Rare Met., 2012, 31: 215
[29]	Rios P R, Siciliano Jr F S, Sandim H R Z, et al. Nucleation and growth during recrystallization [J]. Mater. Res., 2005, 8: 225
[30]	Beltran O, Huang K, Logé R E. A mean field model of dynamic and post-dynamic recrystallization predicting kinetics, grain size and flow stress [J]. Comput. Mater. Sci., 2015, 102: 293
[31]	Li J C, Wu X D, Liao B, et al. Simulation of low proportion of dynamic recrystallization in 7055 aluminum alloy [J]. Trans. Nonferrous Met. Soc. China, 2021, 31: 1902
[32]	Quan G Z, Zhang K K, An C, et al. Analysis of dynamic recrystallization behaviors in resistance heating compressions of heat-resistant alloy by multi-field and multi-scale coupling method [J]. Comput. Mater. Sci., 2018, 149: 73
[33]	Reyes L A, Garza C, Delgado M, et al. Cellular automata modeling for rotary friction welding of Inconel 718 [J]. Mater. Manuf. Processes, 2022, 37: 877
[34]	Hu W Z. Research on the modeling and optimization algorithms for the slab design and the hot rolling production planning of steel plate [D]. Chongqing: Chongqing University, 2019
	呼万哲. 中厚板坯料设计及其热轧生产计划建模与优化算法研究 [D]. 重庆: 重庆大学, 2019
[35]	Quan G Z, Zhang Y, Lei S, et al. Characterization of flow behaviors by a PSO-BP integrated model for a medium carbon alloy steel [J]. Materials, 2023, 16: 2982

[1]	ZHANG Mingchuan, XU Qinsi, LIU Yi, CAI Yusheng, MU Yiqiang, REN Dechun, JI Haibin, LEI Jiafeng. Effect of Hot-Pressing Temperature on the Microstructure and Properties of the Diffusion-Bonded Region of TC4 Alloy[J]. 金属学报, 2025, 61(8): 1183-1192.
[2]	BAO Chengli, LI Hao, HU Li, ZHOU Tao, TANG Ming, HE Qubo, LIU Xiangguo. Construction of Hot Processing Map of Solutionized Mg-10Gd-6Y-1.5Zn-0.5Zr Alloy and Microstructure Evolution[J]. 金属学报, 2025, 61(4): 632-642.
[3]	ZOU Jianxin, ZHANG Jiaqi, ZHAO Yingyan, LIN Xi, DING Wenjiang. Progress in the Research and Application of High-Capacity Mg-Based Hydrogen Storage Alloy Materials[J]. 金属学报, 2025, 61(3): 420-436.
[4]	LI Junjie, LI Panyue, HUANG Liqing, GUO Jie, WU Jingyang, FAN Kai, WANG Jincheng. Progress in Multiscale Simulation of Solidification Behavior in Vacuum Arc Remelted Ingot[J]. 金属学报, 2025, 61(1): 12-28.
[5]	WANG Lin, WEI Chen, WANG Lei, WANG Jun, LI Jinshan. Simulation of Core-Shell Structure Evolution of Cu-Co Immiscible Alloys[J]. 金属学报, 2024, 60(9): 1239-1249.
[6]	HUANG Zengxin, JIANG Yihang, LAI Chunming, WU Qingjie, LIU Dahai, YANG Liang. Analysis of the Correlation Between the Energy and Crystallographic Orientation of Grain Boundaries in Fe Based on Atomistic Simulations[J]. 金属学报, 2024, 60(9): 1289-1298.
[7]	LIU Guanghui, WANG Weiguo, Rohrer Gregory S, CHEN Song, LIN Yan, TONG Fang, FENG Xiaozheng, ZHOU Bangxin. {111}/{111} Near Singular Boundaries in a Dynamically Recrystallized Al-Zn-Mg-Cu Alloy Compressed at Elevated Temperature[J]. 金属学报, 2024, 60(9): 1165-1178.
[8]	YANG Ruize, ZHAI Ruzong, REN Shaofei, SUN Mingyue, XU Bin, QIAO Yanxin, YANG Lanlan. Evolution and Healing Mechanism of 1Cr22Mn16N High Nitrogen Austenitic Stainless Steel Interface Microstructure During Plastic Deformation Bonding[J]. 金属学报, 2024, 60(7): 915-925.
[9]	ZHOU Li, ZHANG Mingyuan, YANG Xinsheng, LIU Zhenyu, WANG Quanzhao, XIAO Bolv, MA Zongyi. Simulation of Thermal Expansion Coefficient of Configurational GNPs/2009Al Composites[J]. 金属学报, 2024, 60(7): 977-989.
[10]	CHEN Shenghu, WANG Qiyu, JIANG Haichang, RONG Lijian. Effect of δ-Ferrite on Hot Deformation and Recrystallization of 316KD Austenitic Stainless Steel for Sodium-Cooled Fast Reactor Application[J]. 金属学报, 2024, 60(3): 367-376.
[11]	REN Song, WU Jiazhu, ZHANG Yi, ZHANG Dabin, CAO Yang, YIN Cunhong. Numerical Simulation on Effects of Spatial Laser Beam Profiles on Heat Transport During Laser Directed Energy Deposition of 316L Stainless Steel[J]. 金属学报, 2024, 60(12): 1678-1690.
[12]	DING Kuankuan, DING Jianxiang, ZHANG Kaige, BAI Zhongchen, ZHANG Peigen, SUN Zhengming. Micro/Nano-Mechanical Behavior and Microstructure Evolution of Eco-Friendly Ag/Ti₂SnC Composite Electrical Contacts Under Multi-Field Coupled Erosion[J]. 金属学报, 2024, 60(12): 1731-1745.
[13]	GUO Songyuan, LIU Wenbo, YANG Qingcheng, QI Xiaoyong, YUN Di. Phase Field Simulation of Viscous Sintering[J]. 金属学报, 2024, 60(12): 1691-1700.
[14]	LI Yanqiang, ZHAO Jiuzhou, JIANG Hongxiang, ZHANG Lili, HE Jie. Liquid-Solid Phase Separation Process of Pb-Al Alloy Under the Effect of Electric Current Pulses[J]. 金属学报, 2024, 60(12): 1710-1720.
[15]	GUO Jie, HUANG Liqing, WU Jingyang, LI Junjie, WANG Jincheng, FAN Kai. Evolution of Macrosegregation During Three-Stage Vacuum Arc Remelting of Titanium Alloys[J]. 金属学报, 2024, 60(11): 1531-1544.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Shared

Discussed