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金属学报  2025, Vol. 61 Issue (9): 1425-1437    DOI: 10.11900/0412.1961.2024.00369
  研究论文 本期目录 | 过刊浏览 |
水平集法模拟GH4706合金动态再结晶过程
郑德宇, 夏玉峰(), 曾扬, 周杰
重庆大学 材料科学与工程学院 重庆 400044
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
引用本文:

郑德宇, 夏玉峰, 曾扬, 周杰. 水平集法模拟GH4706合金动态再结晶过程[J]. 金属学报, 2025, 61(9): 1425-1437.
Deyu ZHENG, Yufeng XIA, Yang ZENG, Jie ZHOU. Dynamic Recrystallization Process Simulation of GH4706 Alloy by Level-Set Method[J]. Acta Metall Sin, 2025, 61(9): 1425-1437.

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摘要: 

为了提高大型锻件的综合力学性能,必须有效预测和控制锻件整体的微观组织。对于常见的动态再结晶(DRX)经验模型,由于其不考虑形核规律和储存能差驱动的晶界迁移,因此无法预测和跟踪动态再结晶过程中的形核和微观组织形貌。针对这一问题,本工作基于水平集法和位错模型的耦合,实现了对晶粒组织形貌演化的有效模拟,对于大锻件晶粒组织均匀性控制具有重要意义。在温度950~1150 ℃和应变速率0.001~1 s-1范围内求解了基于水平集法的GH4706合金的DRX模型参数。对于无法拟合获得的参数,使用Pareto多目标优化方法,通过使实验与模拟结果偏差值达到最小从而进行逆向识别。模拟了GH4706合金在0.4~0.7应变下的动态再结晶过程,并进行实验验证。实验与模拟结果的比较表明,DRX晶粒体积分数和平均晶粒尺寸的平均偏差均在10%以下,验证了所构建模型和识别方法的有效性。

关键词 水平集法GH4706合金动态再结晶模拟优化    
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 wordslevel-set method    GH4706 alloy    dynamic recrystallization    simulation    optimization
收稿日期: 2024-11-14     
ZTFLH:  TG31  
基金资助:国家重点研发计划项目(2022YFB3705103)
通讯作者: 夏玉峰,yufengxia@cqu.edu.cn,主要从事先进材料塑性成型研究
Corresponding author: XIA Yufeng, professor, Tel: (023)65103214, E-mail: yufengxia@cqu.edu.cn
作者简介: 郑德宇,男,1983年生,博士
图1  取样位置示意图及GH4706合金初始组织的EBSD分析
图2  采用水平集函数定义晶界
图3  晶粒形核过程示意图
图4  水平集法耦合位错密度模型模拟动态再结晶(DRX)过程的流程图
图5  DIGIMU软件中的初始组织模型
图6  硬化率(θ)-流变应力(σ)以及2σθ-σ2关系曲线
Strain rate / s-1950 oC1000 oC1050 oC1100 oC1150 oC
0.001139.589.759.450.145.7
0.01197.7145.3107.583.463.5
0.1303.5217.8182.1139.7109.4
1395.7304.6272.4224.7194.1
表1  不同温度和应变速率下的饱和应力(σsat) (MPa)
Strain rate / s-1950 oC1000 oC1050 oC1100 oC1150 oC
0.00123.9124.5220.5524.4222.54
0.0123.4425.4121.9423.7224.53
0.119.2521.9120.6321.6420.43
118.3220.8319.2119.5318.94
表2  不同温度和应变速率下的软化参数(S)
Strain rate / s-1950 oC1000 oC1050 oC1100 oC1150 oC
0.001188256294331162036825746133784939
0.01283204490727316469513204424827380
0.1356900680766144362021619823855893
1583927754935219579329576843757594
表3  不同温度和应变速率下的初始软化参数(S0)
Strain rate / s-1950 oC1000 oC1050 oC1100 oC1150 oC
0.00199.508550.809517.982315.80259.64638
0.01237.0564135.655862.025641.439318.4382
0.1459.1146262.7919170.1042105.457856.3837
1553.8599389.5857295.9049184.8933103.8335
表4  不同温度和应变速率下的硬化参数(H)
Strain rate / s-1950 oC1000 oC1050 oC1100 oC1150 oC
0.0010.1840.3890.4460.2560.237
0.010.1940.1850.2690.2820.259
0.10.1610.1440.2170.2320.218
10.0830.2670.2880.1070.113
表5  不同温度和应变速率下的应变速率敏感性系数(m)
图7  基于反向传播人工神经网络(BP-ANN)和Pareto前沿方法的仿真参数识别流程
图8  多目标优化结果的Pareto前沿图
Strain rate / s-1Kg / mm3δ
950 oC1000 oC1050 oC1100 oC1150 oC
0.0015.2 × 10-63.0 × 10-62.0 × 10-66.0 × 10-72.4 × 10-71.7
0.015.0 × 10-53.0 × 10-51.7 × 10-56.0 × 10-62.2 × 10-63.1
0.18.6 × 10-45.5 × 10-43.5 × 10-46.5 × 10-51.5 × 10-55.5
13.1 × 10-22.0 × 10-27.5 × 10-31.5 × 10-31.6 × 10-47.9
表6  不同参数条件下的晶界迁移速率影响因子(δ)和形核体积(Kg)
图9  水平集模型参数与工艺参数之间的关系
图10  不同应变下的晶粒取向分布(GOS)图
图11  不同应变下的晶粒尺寸模拟图
图12  不同应变下实验及模拟的晶粒尺寸分布
图13  平均晶粒尺寸和DRX晶粒体积分数随应变演化的模拟与实验结果对比及偏差分析
StrainAverage grain size / μmΔ / %Δavg / %ξ / %
ExperimentalSimulated
0.497.199.62.57.753.16
0.569.976.89.8
0.654.460.210.6
0.739.336.18.1
表7  平均晶粒尺寸模拟结果与实验结果的相对偏差
StrainDRX fraction / %Δ / %Δavg / %ξ / %
ExperimentalSimulated
0.46.98.114.89.755.08
0.522.419.612.5
0.628.932.110.3
0.742.543.11.4
表8  DRX晶粒体积分数模拟结果与实验结果的相对偏差
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