Establishment and Accuracy Analysis of Hansel-Spittel Constitutive Model for 15CrMoG Alloy Steel

FU Wentao; WANG Wei; MA Shibo; MU Zhenkai; WANG Baoyu; LIU Hongwei

doi:10.3969/j.issn.1674-6457.2025.06.022

PDF(1542 KB)

Journal of Netshape Forming Engineering ›› 2025, Vol. 17 ›› Issue (6) : 206-214. DOI: 10.3969/j.issn.1674-6457.2025.06.022

Iron and Steel Forming

Establishment and Accuracy Analysis of Hansel-Spittel Constitutive Model for 15CrMoG Alloy Steel

FU Wentao^1a, WANG Wei^1a,1b*, MA Shibo^1a,1b, MU Zhenkai^1a,1b, WANG Baoyu², LIU Hongwei^1a

Author information +

History +

Abstract

The work aims to grasp the high-temperature rheological law of the material under different conditions and provide a reference for the hot working process. An isothermal compression test of 15GrMoG heat-resistant steel was conducted at deformation temperature of 900-1 200 ℃ and a strain rate of 5-20 s^-1 with a Gleeble thermal simulation testing machine. Based on the experimental data, the material parameters of the Hansel-Spittel (H-S) constitutive model were solved by linear fitting and custom nonlinear fitting methods. Due to the high sensitivity of parameter A in the H-S constitutive model, the polynomial fitting method of strain was used instead of the conventional numerical average method to correct parameter A, so as to improve the accuracy of the H-S model. The result showed that the real stress-strain curve of 15CrMoG alloy steel shifted to the high stress zone with the decrease of deformation temperature or increase of strain rate, indicating that the flow stress of the alloy steel conformed to the thermal deformation behavior of typical alloy steel. The correlation coefficient R and the average absolute relative error of the predicted stress value and the experimental stress value of isothermal compression of the constructed constitutive model were 0.997 45 and 2.324 3%, respectively. After correction, the correlation coefficient R reached 0.998 13, and the average absolute relative error was reduced to 1.812 3%. The conclusion indicates that the high-temperature deformation behavior of 15CrMoG can be more accurately described by the Hansel-Spittel correction, and the H-S constitutive model after correction of parameter A has good accuracy and prediction performance.

Key words

15CrMoG steel / isothermal compression test / high temperature deformation behavior / Hansel-Spittel constitutive model / model modification

Cite this article

EndNote

Ris (Procite)

Bibtex

Download Citations

FU Wentao, WANG Wei, MA Shibo, MU Zhenkai, WANG Baoyu, LIU Hongwei. Establishment and Accuracy Analysis of Hansel-Spittel Constitutive Model for 15CrMoG Alloy Steel[J]. Journal of Netshape Forming Engineering. 2025, 17(6): 206-214 https://doi.org/10.3969/j.issn.1674-6457.2025.06.022

References

[1] 李群, 金淼, 邹宗园, 等. 基于循环拉-压试验的混合硬化模型参数确定及模型应用[J]. 机械工程学报, 2020, 56(2): 63-68.
LI Q, JIN M, ZOU Z Y, et al.Parameter Determination and Application Research of Mixed Hardening Model Based on Cyclic Tension-Compression Test[J]. Journal of Mechanical Engineering, 2020, 56(2): 63-68.
[2] 邬宇轩, 李静媛, 侯艳阳. Johnson-Cook、修正的Zerilli-Armstrong及Arrhenius本构模型对奥氏体不锈钢流变应力的预测[J/OL]. 热加工工艺, 2024: 1-8. (2024-08-29). http://kns.cnki.net/KCMS/detail/detail.aspx?filename=SJGY20250306005&dbname=CJFD&dbcode=CJFQ.
WU Y X, LI J Y, HOU Y Y. Prediction of Flow Stress of Austenitic Stainless Steel by Johnson-Cook, Modified Zerilli-Armstrong and Arrhenius Constitutive Models[J/OL]. China Industrial Economics, 2024: 1-8. (2024-08-29). http://kns.cnki.net/KCMS/detail/detail.aspx?filename=SJGY20250306005&dbname=CJFD&dbcode=CJFQ.
[3] 孙岑花, 施文鹏, 王津, 等. 基于Arrhenius与机器学习的TC21钛合金本构模型研究[J]. 精密成形工程, 2024, 16(8): 102-110.
SUN C H, SHI W P, WANG J, et al.Constitutive Model of TC21 Titanium Alloy Based on Arrhenius Equation and Machine Learning[J]. Journal of Netshape Forming Engineering, 2024, 16(8): 102-110.
[4] 王旻曦, 刘建涛, 张义文. 基于Arrhenius和神经网络模型对镍基合金热变形行为的研究[J]. 粉末冶金工业, 2024, 34(3): 46-53.
WANG M X, LIU J T, ZHANG Y W.Research on Hot Deformation Behavior of a Nickel-based Alloys Based on Arrhenius and Artificial Neural Network Model[J]. Powder Metallurgy Industry, 2024, 34(3): 46-53.
[5] 苏志毅, 陈学文, 杨圳, 等. δ相时效态GH4169合金Zerilli-Armstrong本构模型及其参数反求方法[J]. 塑性工程学报, 2024, 31(8): 133-139.
SU Z Y, CHEN X W, YANG Z, et al.Zerilli-Armstrong Constitutive Model of δ Phase-Aged GH4169 Alloy and Its Parameters Inversion Method[J]. Journal of Plasticity Engineering, 2024, 31(8): 133-139.
[6] 郭自洋, 王伟, 马世博, 等. 18CrNiMo7-6合金钢Zerilli-Armstrong本构模型的建立及修正[J]. 锻压技术, 2024, 49(4): 235-241.
GUO Z Y, WANG W, MA S B, et al.Establishment and Modification on Zerilli-Armstrong Constitutive Model for 18CrNiMo7-6 Alloy Steel[J]. Forging & Stamping Technology, 2024, 49(4): 235-241.
[7] SU S J, WU Y J, WANG G H, et al.Optimal Calibration of Q235B Steel Johnson-Cook Model Parameters Based on Global Response Surface Algorithm[J]. Journal of Marine Science and Application, 2024, 23(2): 470-478.
[8] 尹小燕, 骆静, 朱杰. 基于Hansel-Spittel模型的齿环用HAl61-4-3-1合金本构模型构建[J]. 重庆理工大学学报(自然科学), 2021, 35(1): 111-117.
YIN X Y, LUO J, ZHU J.Construction of High-Temperature Constitutive Model of HAl61-4-3-1 Alloy for Synchronizer Ring Based on Hansel-Spittel Mode[J]. Journal of Chongqing University of Technology (Natural Science), 2021, 35(1): 111-117.
[9] 李露, 周旭东, 陈学文, 等. PCrNi₃MoV钢Hansel-Spittel 流变应力模型[J]. 河南科技大学学报(自然科学版), 2020, 41(6): 1-5.
LI L, ZHOU X D, CHEN X W, et al.Hansel-Spittel Flow Stress Model of PCrNi₃MoV Steel[J]. Journal of Henan University of Science and Technology (Natural Science), 2020, 41(6): 1-5.
[10] 马斌, 李平, 梁强. HNi55-7-4-2合金高温本构模型构建及应用[J]. 兵器材料科学与工程, 2020, 43(4): 108-113.
MA B, LI P, LIANG Q.Construction and Application of High-Temperature Constitutive Model of HNi55-7-4-2 Alloy[J]. Ordnance Material Science and Engineering, 2020, 43(4): 108-113.
[11] 陈学文, 杨喜晴, 王纳纳. GCr₁₅SiMn钢的温变形行为及Hansel-Spittel流变应力模型[J]. 金属热处理, 2018, 43(5): 34-38.
CHEN X W, YANG X Q, WANG N N.Warm Deformation Behavior and Hansel-Spittel of Constitutive Model of GCr₁₅SiMn Steel[J]. Heat Treatment of Metals, 2018, 43(5): 34-38.
[12] PAN P J, TU H S, ZHU W X, et al.High-temperature Creep Behaviour of 15CrMoG Heat-resistant Steel[J]. IOP Conference Series: Materials Science and Engineering, 2019, 504(1): 012032.
[13] 杨玉先, 向昌武, 石国光, 等. 15CrMoG高压锅炉管在线热处理混晶的产生原因分析与工艺改进[J]. 钢管, 2012, 41(6): 14-17.
YANG Y X, XIANG C W, SHI G G, et al.Analysis of the Causes and Process Improvement of On-line Heat Treatment of 15CrMoG High-pressure Boiler Tube Mixed Crystallization[J]. Steel Pipe, 2012, 41(6): 14-17.
[14] 陈香. 15CrMoG钢屈服强度偏低的原因及改进措施[J]. 热处理技术与装备, 2022, 43(3): 11-13.
CHEN X.Reasons for Low Yield Strength of 15CrMoG Steel and Improvement Measures[J]. Heat Treatment Technology and Equipment, 2022, 43(3): 11-13.
[15] 杨京, 王伟, 张双杰, 等. 15CrMoG耐高温合金钢Johnson-Cook本构模型建立与精度分析[J]. 精密成形工程, 2023, 15(9): 159-167.
YANG J, WANG W, ZHANG S J, et al.Establishment and Accuracy Analysis of Johnson-Cook Constitutive Model for 15CrMoG High-Temperature Resistant Alloy Steel[J]. Journal of Netshape Forming Engineering, 2023, 15(9): 159-167.
[16] 杨京, 王伟, 张双杰, 等. 15CrMoG耐热钢高温变形行为及Arrhenius本构模型[J]. 塑性工程学报, 2024, 31(2): 137-145.
YANG J, WANG W, ZHANG S J, et al.High-Temperature Deformation Behavior of 15CrMoG Heat-Resistant Steel and Arrhenius Constitutive Model[J]. Journal of Plasticity Engineering, 2024, 31(2): 137-145.
[17] 刘贵彬, 解小琴, 王平, 等. 15CrMoG钢管弯曲回弹的改进PSO-BP评估[J]. 机械设计与制造, 2023(10): 130-133.
LIU G B, XIE X Q, WANG P, et al.Improved PSO-BP Evaluation of 15CrMoG Steel Pipe Bending[J]. Machinery Design & Manufacture, 2023(10): 130-133.
[18] BILBAO O, LOIZAGA I, ALONSO J, et al.42CrMo₄ Steel Flow Behavior Characterization for High Temperature Closed Dies Hot Forging in Automotive Components Applications[J]. Heliyon, 2023, 9(11): e22256.
[19] 杨怡思, 陈学文, 张博, 等. 基于粒子群算法的GCr15钢温热成形Hansel-Spittel本构模型参数反求优化方法[J]. 材料热处理学报, 2022, 43(7): 147-156.
YANG Y S, CHEN X W, ZHANG B, et al.Reverse Optimization Method of Hansel-Spittel Constitutive Model Parameters for Warm Forming of GCr15 Steel Based on Particle Swarm Optimization[J]. Transactions of Materials and Heat Treatment, 2022, 43(7): 147-156.
[20] 郭乐乐, 陈学文, 周旭东, 等. 基于原位观测的Cr5合金钢Hansel-Spittel高温本构模型修正方法及试验验证[J]. 塑性工程学报, 2021, 28(6): 88-95.
GUO L L, CHEN X W, ZHOU X D, et al.Correction Method and Experimental Verification of Hansel-Spittel Constitutive Model of Cr5 Alloy Steel at High Temperature Based on In-Situ Observation[J]. Journal of Plasticity Engineering, 2021, 28(6): 88-95.
[21] 李亚强, 刘建华, 邓振强, 等. 15CrMoG钢包晶凝固特征与机制[J]. 金属学报, 2020, 56(10): 1335-1342.
LI Y Q, LIU J H, DENG Z Q, et al.Peritectic Solidification Characteristics and Mechanism of 15CrMoG Steel[J]. Acta Metallurgica Sinica, 2020, 56(10): 1335-1342.
[22] 李亚强, 刘建华, 何杨, 等. 15CrMoG钢棒材表面缺陷机理分析和工艺改进[J]. 特殊钢, 2019, 40(6): 1-6.
LI Y Q, LIU J H, HE Y, et al.Surface Defects Analysis and Mechanism Research of 15CrMoG Steel Bars and Process Improvement[J]. Special Steel, 2019, 40(6): 1-6.
[23] 陈飞, 周琦杰, 董凯, 等. 带内法兰的超大型阶梯筒体仿形锻造理论与方法[J]. 锻压技术, 2024, 49(7): 147-159.
CHEN F, ZHOU Q J, DONG K, et al.Profiling Forging Theory and Method of Ultra-Large Stepped Cylinder with Inner Flange[J]. Forging & Stamping Technology, 2024, 49(7): 147-159.
[24] 林鹏, 张洪才, 左辉, 等. 包晶钢15CrMoG方坯表面缺陷分析与改进[J]. 连铸, 2023, 48(1): 61-65.
LIN P, ZHANG H C, ZUO H, et al.Analysis and Improvement of Surface Defects of Peritectic Steel 15CrMoG Billet[J]. Continuous Casting, 2023, 48(1): 61-65.
[25] PAN J P, TU S H, ZHU X W, et al.Creep Behavior and Cavitation Evolution of 15CrMoG Steel at High Temperatures[J]. Advances in Mechanical Engineering, 2019, 11(8): 1-7.
[26] NIU L Q, ZHANG Q, WANG B, et al.A Modified Hansel-Spittel Constitutive Equation of Ti-6Al-4V during Cogging Process[J]. Journal of Alloys and Compounds, 2022, 894: 162387.
[27] CHEN X W, WANG N N, MA X, et al.Hot Deformation Behaviour and Hansel-Spittel Constitutive Model of Cr5 Alloy for Heavy Backup Roll[J]. International Journal of Computational Materials Science and Surface Engineering, 2018, 7(3/4): 205.
[28] YANG H, CHEN X Y, HE C W, et al.Constitutive Model of Metal Rubber Based on Modified Iwan Model under Quasi-Static Compression and Random Vibration[J]. Mechanical Systems and Signal Processing, 2024, 215: 111427.
[29] WU G L, WANG H.Nonlinear Correction of Elastic Section in HJC Constitutive Model[J]. International Journal of Impact Engineering, 2024, 189: 104955.