Hot Deformation Behavior and Constitutive Relationship of Monel K-500 Alloy Based on Machine Learning

ZHANG Zhen; ZHU Mingyu; FU Xukai; HE Chuan; ZHU Yuliang; WAN Yachang; ZHANG Kaiming

doi:10.3969/j.issn.1674-6457.2025.11.023

PDF(897 KB)

Journal of Netshape Forming Engineering ›› 2025, Vol. 17 ›› Issue (11) : 242-251. DOI: 10.3969/j.issn.1674-6457.2025.11.023

Superalloy Forming

Hot Deformation Behavior and Constitutive Relationship of Monel K-500 Alloy Based on Machine Learning

ZHANG Zhen¹, ZHU Mingyu¹, FU Xukai¹, HE Chuan¹, ZHU Yuliang², WAN Yachang^3,*, ZHANG Kaiming⁴

Author information +

History +

Abstract

The work aims to reasonably formulate the hot deformation process parameters of Monel K-500 alloy, explore its plastic processing ability, investigate the high temperature flow behavior of Monel K-500 alloy and establish a constitutive model based on the hot compression experiment. The hot compression experiment of 50% deformation was carried out by Gleeble-3800 hot simulation test machine at the deformation temperature of 900-1 100 ℃ and the strain rate of 0.001-1 s^‒1. The hot deformation behavior of Monel K-500 alloy was investigated. A strain-compensated Arrhenius constitutive model, an extreme Learning Machine (ELM) constitutive model, and a Support Vector Machine (SVM) constitutive model for the alloy were established. The results indicated that the stress of Monel K-500 alloy increased with the decrease of deformation temperature and the increase of strain rate. The R² and AARE of the strain-compensated Arrhenius constitutive model were 0.993 and 5.7%, respectively. For the ELM constitutive model, the R² and AARE of the test set were 0.997 and 1.8%, respectively. The R² and AARE of the SVM constitutive model's test set were 0.988 and 4.8%, respectively. The ELM constitutive model demonstrated the highest accuracy and was preferred for predicting the flow stress of Monel K-500 alloy. The application of machine learning methods could effectively replace traditional constitutive models with complex calculations, achieving high-precision predictions of flow stress.

Key words

Monel K-500 alloy / machine learning / constitutive relationship / hot deformation behavior / extreme learning machine / support vector machine

Cite this article

EndNote

Ris (Procite)

Bibtex

Download Citations

ZHANG Zhen, ZHU Mingyu, FU Xukai, HE Chuan, ZHU Yuliang, WAN Yachang, ZHANG Kaiming. Hot Deformation Behavior and Constitutive Relationship of Monel K-500 Alloy Based on Machine Learning[J]. Journal of Netshape Forming Engineering. 2025, 17(11): 242-251 https://doi.org/10.3969/j.issn.1674-6457.2025.11.023

References

[1] LIU F, ZHANG C H, HOU X H, et al.Deformation Behavior at Fatigue Crack Tip in Nickel-Based Alloy[J]. Vacuum, 2024, 228: 113491.
[2] 徐超, 吴畏, 吴勇, 等. 镍基高温合金极薄带精密轧制技术研究进展[J]. 精密成形工程, 2025, 17(7): 206-218.
XU C, WU W, WU Y, et al.Research Progress on Precision Rolling Technology of Nickel Based High-Temperature Alloy Ultra-Thin Strip[J]. Journal of Netshape Forming Engineering, 2025, 17(7): 206-218.
[3] ZHU Y H, WANG J Z, LIU H, et al.The Tribocorrosion Behavior of Monel 400 Alloy in Seawater at Different Temperatures[J]. Tribology International, 2023, 189: 108975.
[4] 王成, 巨少华, 荀淑玲, 等. 镍基耐蚀合金研究进展[J]. 材料导报, 2009, 23(3): 71-76.
WANG C, JU S H, XUN S L, et al.Progress in Research on Nickel-Based Corrosion Resistant Alloys[J]. Materials Review, 2009, 23(3): 71-76.
[5] AL-SAADI S, RAMAN R K, ANISUR M R, et al.Graphene Coating on a Nickel-Copper Alloy (Monel 400) for Microbial Corrosion Resistance: Electrochemical and Surface Characterizations[J]. Corrosion Science, 2021, 182: 109299.
[6] HE Z B, QIN Z B, GAO Z M, et al.Synergistic Effect between Cavitation Erosion and Corrosion of Monel K500 Alloy in 3.5wt% NaCl Solution[J]. Materials Characterization, 2023, 205: 113340.
[7] TÜRKMEN İ, KEDDAM M. Boronizing of Monel K500 Alloy: Microstructural Characterization and Modeling of Boron Diffusion[J]. Materials Characterization, 2024, 213: 113995.
[8] 秦明花, 郑文杰, 张雪冰, 等. Monel K-500合金的研究现状[J]. 热加工工艺, 2021, 50(11): 5-8.
QIN M H, ZHENG W J, ZHANG X B, et al.Research Status of Monel K-500 Alloy[J]. Hot Working Technology, 2021, 50(11): 5-8.
[9] CHEN Z, WANG C C, TANG C, et al.Microstructure and Mechanical Properties of a Monel K-500 Alloy Fabricated by Directed Energy Deposition[J]. Materials Science and Engineering: A, 2022, 857: 144113.
[10] 朱玉亮, 郑文杰, 宋志刚, 等. 析出相对Monel K-500合金冲击韧性的影响[J]. 钢铁研究学报, 2015, 27(10): 67-74.
ZHU Y L, ZHENG W J, SONG Z G, et al.Effect of Precipitates on Impact Toughness of Monel K-500 Alloy[J]. Journal of Iron and Steel Research, 2015, 27(10): 67-74.
[11] 杨明辉, 李星吾, 孙崇昊, 等. 定向凝固与固态相变双联协控下Monel K-500合金的组织和力学性能[J]. 金属学报, 2025, 61(4): 561-571.
YANG M H, LI X W, SUN C H, et al.Microstructure and Mechanical Properties of Monel K-500 Alloy in Synergetic Modulation of Directional Solidification and Thermal Processing[J]. Acta Metallurgica Sinica, 2025, 61(4): 561-571.
[12] 朱玉亮, 王哲, 郑文杰, 等. Monel K-500合金高温流变特性及其本构方程[J]. 钢铁研究学报, 2017, 29(11): 933-938.
ZHU Y L, WANG Z, ZHENG W J, et al.Characteristics of High Temperature Flow Behavior and Constitutive Equation of Monel K-500 Alloy[J]. Journal of Iron and Steel Research, 2017, 29(11): 933-938.
[13] 俞年年, 项金钟, 郑文杰. Monel K-500合金的热变形行为及热加工图[J]. 热加工工艺, 2018, 47(7): 172-176.
YU N N, XIANG J Z, ZHENG W J.Hot Deformation Behavior and Hot Processing Map of Monel K-500 Alloy[J]. Hot Working Technology, 2018, 47(7): 172-176.
[14] HU M W, TAN Q Y, KNIBBE R, et al.Recent Applications of Machine Learning in Alloy Design: A Review[J]. Materials Science and Engineering: R: Reports, 2023, 155: 100746.
[15] GERASHI E, POURBAGHI M, DUAN X L, et al.Machine Learning-Aided Phase and Mechanical Properties Prediction in Multi-Principal Element Alloys[J]. Computational Materials Science, 2024, 243: 113114.
[16] 杨剑锋, 乔佩蕊, 李永梅, 等. 机器学习分类问题及算法研究综述[J]. 统计与决策, 2019, 35(6): 36-40.
YANG J F, QIAO P R, LI Y M, et al.A Review of Machine-Learning Classification and Algorithms[J]. Statistics & Decision, 2019, 35(6): 36-40.
[17] 王海伟, 叶波, 冯晶, 等. 机器学习在钢铁材料研究中的应用综述[J]. 中国材料进展, 2023, 42(10): 806-813.
WANG H W, YE B, FENG J, et al.Application of Machine Learning in Steel Materials: A Survey[J]. Materials China, 2023, 42(10): 806-813.
[18] 周岳钰, 高静, 汪燕, 等. 机器学习在材料科学中的应用进展[J]. 信息记录材料, 2022, 23(6): 8-12.
ZHOU Y Y, GAO J, WANG Y, et al.Applications of Machine Learning in Material Science[J]. Information Recording Materials, 2022, 23(6): 8-12.
[19] 冯伟, 刘忠翰, 谢臻轩, 等. F316奥氏体不锈钢热变形行为与动态再结晶机制[J]. 钢铁研究学报, 2024, 36(8): 1060-1070.
FENG W, LIU Z H, XIE Z X, et al.Hot Deformation Behavior and Dynamic Recrystallization Mechanism of F316 Austenitic Stainless Steel[J]. Journal of Iron and Steel Research, 2024, 36(8): 1060-1070.
[20] 张开铭, 鲁世强, 江丰建聪, 等. Laves相NbCr₂/Nb两相合金的应变补偿物理本构关系研究[J]. 稀有金属材料与工程, 2023, 52(8): 2835-2843.
ZHANG K M, LU S Q, JIANG F J C, et al. Strain-Compensated Physical Constitutive Relation of Laves Phase NbCr₂/Nb Dual-Phase Alloy[J]. Rare Metal Materials and Engineering, 2023, 52(8): 2835-2843.
[21] 张开铭, 王克鲁, 鲁世强, 等. 基于物理参数和响应面法的S280超高强度不锈钢本构模型[J]. 塑性工程学报, 2023, 30(5): 105-115.
ZHANG K M, WANG K L, LU S Q, et al.Constitutive Model of S280 Ultra-High Strength Stainless Steel Based on Physical Parameters and Response Surface Method[J]. Journal of Plasticity Engineering, 2023, 30(5): 105-115.
[22] 张开铭. S280超高强度不锈钢动态再结晶行为及工艺参数优化研究[D]. 南昌: 南昌航空大学, 2023.
ZHANG K M.Study on Dynamic Recrystallization Behavior and Process Parameter Optimization of S280 Ultra-high Strength Stainless Steel[D]. Nanchang: Nanchang Hangkong University, 2023.
[23] YE L Y, ZHAI Y W, ZHOU L Y, et al.The Hot Deformation Behavior and 3D Processing Maps of 25Cr2Ni4MoV Steel for a Super-Large Nuclear-Power Rotor[J]. Journal of Manufacturing Processes, 2020, 59: 535-544.
[24] BABU K, PRITHIV T S, GUPTA A, et al.Modeling and Simulation of Dynamic Recrystallization in Super Austenitic Stainless Steel Employing Combined Cellular Automaton, Artificial Neural Network and Finite Element Method[J]. Computational Materials Science, 2021, 195: 110482.
[25] LU C Y, SHI J, WANG J.Physically Based Constitutive Modeling for Ti17 Alloy with Original Basketweave Microstructure in β Forging: A Comparison of Three Approaches[J]. Materials Characterization, 2021, 181: 111455.
[26] ZHAO Z W, LI J X, WANG X T, et al.Thermal Deformation Behavior of a Ni-Cr-Fe Superalloy and Its Effect on Corrosion Resistance: A Comprehensive Analysis of Strain Rate and Temperature Effects[J]. Journal of Alloys and Compounds, 2024, 1006: 176370.
[27] ZENER C, HOLLOMON J H.Effect of Strain Rate Upon Plastic Flow of Steel[J]. Journal of Applied Physics, 1944, 15(1): 22-32.
[28] HUANG G B, ZHU Q Y, SIEW C K.Extreme Learning Machine: Theory and Applications[J]. Neurocomputing, 2006, 70(1/2/3): 489-501.
[29] 陆思源, 陆志海, 王水花, 等. 极限学习机综述[J]. 测控技术, 2018, 37(10): 3-9.
LU S Y, LU Z H, WANG S H, et al.Review of Extreme Learning Machine[J]. Measurement & Control Technology, 2018, 37(10): 3-9.
[30] ELDABAH N M, SHOUKRY A, KHAIR-ELDEEN W, et al.Design and Characterization of Low Young's Modulus Ti-Zr-Nb-Based Medium Entropy Alloys Assisted by Extreme Learning Machine for Biomedical Applications[J]. Journal of Alloys and Compounds, 2023, 968: 171755.
[31] 甘露. 极限学习机的研究与应用[D]. 西安: 西安电子科技大学, 2014.
GAN L.Research and Application of Extreme Learning Machine[D]. Xi'an: Xidian University, 2014.
[32] 徐睿, 梁循, 齐金山, 等. 极限学习机前沿进展与趋势[J]. 计算机学报, 2019, 42(7): 1640-1670.
XU R, LIANG X, QI J S, et al.Advances and Trends in Extreme Learning Machine[J]. Chinese Journal of Computers, 2019, 42(7): 1640-1670.
[33] 张开铭, 温余远, 王克鲁, 等. Ti-22Al-24Nb合金热变形行为及本构关系[J]. 塑性工程学报, 2022, 29(10): 208-215.
ZHANG K M, WEN Y Y, WANG K L, et al.Hot Deformation Behavior and Constitutive Relation of Ti-22Al-24Nb Alloy[J]. Journal of Plasticity Engineering, 2022, 29(10): 208-215.
[34] ZHANG W, LI P Y, WANG L, et al.Explaining of Prediction Accuracy on Phase Selection of Amorphous Alloys and High Entropy Alloys Using Support Vector Machines in Machine Learning[J]. Materials Today Communications, 2023, 35: 105694.
[35] ALSHAIJI A, ALBINMOUSA J, PERON M, et al.Analyzing Quasi-Static Fracture of Notched Magnesium ZK60 Using Notch Fracture Toughness and Support Vector Machine[J]. Theoretical and Applied Fracture Mechanics, 2022, 121: 103463.
[36] 李海生. 支持向量机回归算法与应用研究[D]. 广州: 华南理工大学, 2005.
LI H S.Algorithm and Application Research of Support Vector Machine Regression[D]. Guangzhou: South China University of Technology, 2005.
[37] 孙德山. 支持向量机分类与回归方法研究[D]. 长沙: 中南大学, 2004.
SUN D S.The Researches on Support Vector Machine Classification and Regression Methods[D]. Changsha: Central South University, 2004.
[38] 张学工. 关于统计学习理论与支持向量机[J]. 自动化学报, 2000, 26(1): 32-42.
ZHANG X G.Introduction to Statistical Learning Theory and Support Vector Machines[J]. Acta Automatica Sinica, 2000, 26(1): 32-42.