Abstract:The cross wedge rolling technology has broad application prospects in forming axle parts. Therefore,in order to realize the cross wedge rolling forming of high-speed railway axle material LZ50 steel,it is necessary to build a constitutive model that can accurately describe its high-temperature rheological behavior. The modified Johnson Book and Zerilli Armstrong models are more accurate for predicting the metal flow stress,which can establish the constitutive equation of flow stress of LZ50 steel for these two models. At the same time,in order to accurately analyze the deformation behavior of LZ50 steel in the process of cross wedge rolling of large shaft parts,it is necessary to further analyze the average relative error EAR,correlation coefficient R and mean square error RMSE of the two models at different temperatures to judge the applicability of the model,It provides a theoretical basis for the online production of cross wedge rolling. The hot compression experiments were carried out on LZ50 steel by Gleeble-3800 thermal simulation testing machine at different compression temperatures (900,1 000,1 100 ℃) and strain rates (0.1,1,10 s-1). The true compression strain was 0.8,and 1 000 ℃ and 0.1 s-1 were used as reference temperatures and strain rates. Two high temperature rheological stress constitutive equations were constructed through the modified Johnson-Cook and Zerilli-Armstrong models,Compare the average relative error EAR,correlation coefficient R and mean square error RMSE of the two models' predicted flow stress and measured flow stress in the strain range of 0.3-0.8. The results showed that the average relative error EAR of the modified Johnson-Cook and Zerilli-Armstrong models was 3.8% and 6.9% respectively,R were 0.986 and 0.974 respectively,and RMSE was 4.979 8 MPa and 8.050 1 MPa respectively. By comparing the average relative error EAR,correlation coefficient R and mean square error RMSE of the two models under different temperature conditions,it is found that Johnson-Cook model has better prediction accuracy at 900 ℃ and 1 000 ℃,while Zerilli-Armstrong model has higher prediction accuracy at 1 100 ℃.
李诗谦, 何涛, 杜向阳, 霍元明, 贾东昇, 李汉林. 修正的J-C和Z-A模型对LZ50钢高温流变应力预测[J]. 钢铁, 2023, 58(4): 148-156.
LI Shi-qian, HE Tao, DU Xiang-yang, HUO Yuan-ming, JIA Dong-sheng, LI Han-lin. High temperature flow stress prediction of LZ50 steel based on modified J-C and Z-A models[J]. Iron and Steel, 2023, 58(4): 148-156.
[1] XU Zhi-biao,PENG Jin-fang,LIU Jian-hua,et al. Study on fretting wear and tribo-chemical behavior of LZ50 axle steel in torsional fretting fatigue[J]. Wear,2019,426/427:704. [2] LIAO Zhen,YANG Bing,QIN Ya-hang,et al. Short fatigue crack behaviour of LZ50 railway axle steel under multi-axial loading in low-cycle fatigue[J]. International Journal of Fatigue,2019,132:1. [3] 崔友久,惠卫军,张永健,等.连铸与模铸高铁车轴钢的高周疲劳破坏行为[J].中国冶金,2019,29(12):31.(CUI You-jiu,HUI Wei-jun,ZHANG Yong-jian,et al. Comparison of high-cycle fatigue properties of continuous casting and mould casting axle steels[J]. China Metallurgy,2019,29(12):31.) [4] YU Zi-ming,PENG Wen-fei,ZHANG Xiao,et al. Evolution of microstructure of aluminum alloy hollow shaft in cross wedge rolling without mandrel[J]. Journal of Central South University,2022,29(3):807. [5] XIA Ying-xiang,SHU Xue-dao,ZHU De-biao,et al. Effect of process parameters on microscopic uniformity of cross wedge rolling of GH4169 alloy shaft[J]. Journal of Manufacturing Processes,2021,66(10):145. [6] 刘鑫,周宇飞,朱春东,等. 汽车后桥主动齿轮坯的楔横轧成形工艺[J].锻压技术,2022,47(10):198.(LIU Xin,ZHOU Yu-fei,ZHU Chun-dong,et al. Cross wedge rolling process for automobile rear axle drive gear billet[J]. Forging and Stamping Technology,2022,47(10):198.) [7] 连全勇,王立新,袁峰,等. 轧制温度和轧制道次对Mg-1RE-0.5Zn-0.5Zr合金组织和性能的影响[J]. 上海金属,2020,42(5):105.(LIAN Quan-yong,WANG Li-xin,YUAN Feng,et al. Effect of rolling temperature and rolling pass on microstructure and properties of Mg-1RE-0.5Zn-0.5Zr alloy[J]. Shanghai Metals,2020,42(5):105.) [8] Razali M K,Joun M S. A new approach of predicting dynamic recrystallization using directly a flow stress model and its application to medium Mn steel[J]. Journal of Materials Research and Technology,2021,11(2):1881. [9] Razali M K,Irani M,Joun M S. General modeling of flow stress curves of alloys at elevated temperatures using bi-linearly interpolated or closed-form functions for material parameters[J]. Journal of Materials Research and Technology,2019,8(3):2710. [10] 王帅,赵阳,邵国华,等. 一种中碳高硅弹簧钢的热变形行为及流变应力模型[J].轧钢,2021,38(6):42.(WANG Shuai,ZHAO Yang,SHAO Guo-hua,et al. Hot deformation behavior and flow stress prediction model of a medium-carbon and high-silicon spring steel[J]. Steel Rolling, 2021,38(6):42.) [11] 宁广胜,蔡欣,陈卓,等. 冷作模具钢深冷处理组织和应力演变的RVE模型分析[J]. 上海金属,2021,43(3):101.(NING Guang-sheng,CAI Xin,CHENG Zhuo,et al. RVE model analysis on microstructure and stress evolution of cold work die steel during deep cryogenic treatment[J]. Shanghai Metals, 2021,43(3):101.) [12] LIN Yong-cheng,CHEN Xiao-min. A critical review of experimental results and constitutive descriptions for metals and alloys in hot working[J]. Materials and Design,2011,32(4):1733. [13] ZHU Shui-sheng,LIU Jie,DENG Xin. Modification of strain rate strengthening coefficient for Johnson-Cook constitutive model of Ti6Al4V alloy[J]. Materials Today Communications,2021,26(1):1. [14] LIU Yu,LI Ming,REN Xian-wei,et al. Flow stress prediction of Hastelloy C-276 alloy using modified ZerilliArmstrong, JohnsonCook and Arrhenius-type constitutive models[J]. Transactions of Nonferrous Metals Society of China,2020,30(11):3031. [15] Andrej Š,Jernej K. Estimating the strain-rate-dependent parameters of the Johnson-Cook material model using optimisation algorithms combined with a response surface[J]. Mathematics,2020,8(7):1. [16] LI Zhi-xin,ZHAN Mei,TIAN Jin-qiang,et al. A modified Johnson-Cook model of as-quenched AA2219 considering negative to positive strain rate sensitivities over a wide temperature range[J]. Procedia Engineering,2017,207:155. [17] NIU Li-qun,CAO Miao,LIANG Zheng-long,et al. A modified Johnson-Cook model considering strain softening of A356 alloy[J]. Materials Science and Engineering A,2020,8(9):1. [18] Shokry A,Gowid S,Kharmanda G. An improved generic Johnson-Cook model for the flow prediction of different categories of alloys at elevated temperatures and dynamic loading conditions[J]. Materials Today Communications,2021,27:1. [19] Mirzaie T,Mirzadeh H,Cabrera J. A simple Zerilli-Armstrong constitutive equation for modeling and prediction of hot deformation flow stress of steels[J]. Mechanics of Materials,2016,94:38. [20] Samantaray D,Mandal S,Bhaduri A K,et al. Analysis and mathematical modelling of elevated temperature flow behaviour of austenitic stainless steels[J]. Materials Science and Engineering A,2011,528(4):1937. [21] Ravindranadh B,Vemuri M. Physically-based constitutive model for flow behavior of a Ti-22Al-25Nb alloy at high strain rates[J]. Journal of Alloys and Compounds,2018,762:842. [22] Ahmadi H,Ashtiani H,Heidari M. A comparative study of phenomenological,physically-based and artificial neural network models to predict the hot flow behavior of API 5CT-L80 steel[J]. Materials Today Communications,2020,25:1. [23] HE An,XIE Gan-lin,ZHANG Hai-long,et al. A modified Zerilli-Armstrong constitutive model to predict hot deformation behavior of 20CrMo alloy steel[J]. Materials and Design,2013,56:122. [24] JIA Dong-sheng,HE Tao,HUO Yuan-ming,et al. Hot-compression deformation behavior and constitutive equations of LZ50 axle steel[J]. Materiali in Technologije, 2022, 56(2): 87. [25] 顾晨,郑磊,葛琛,等. TNT埋爆载荷下700 MPa高强韧钢变形行为及仿真分析[J]. 钢铁,2022,57(9):130.(GU Chen,ZHENG Lei,GE Chen,et al. Deformation behavior and simulation of 700 MPa steel subjected to TNT buried explosion load[J]. Iron and Steel,2022,57(9):130.) [26] 杨清相,蔡军,王快社,等.基于修正Johnson-Cook本构模型的BFe10-1.6-1白铜合金高温流变行为[J].塑性工程学报,2022,29(11):145.(YANG Qing-xiang,CAI Jun,WANG Kuai-she,et al. High temperature flow behavior of BFe10-1.6-1 cupronickel alloy based on modified Johnson-Cook constitutive model[J]. Journal of Plasticity Engineering, 2022,29(11):145.) [27] 陈天天,施晨琦,宁哲达,等. 金属及合金材料热变形中的本构模型与热加工图研究进展[J]. 材料导报,2022,36(增刊1):416.(CHEN Tian-tian,SHI Chen-qi,NING Zhe-da,et al. Research progress metals and alloys constitutive model and hot processing map for hot deformation[J]. Materials Reports, 2022,36(s1):416.) [28] 史鹏博,李蕊,李铭凯,等. 基于决策树和聚类算法的智能电表误差估计与故障检测[J]. 计量学报,2022,43(8):1089.(SHI Peng-bo,LI Rui,LI Ming-kai,et al. Error estimation and fault detection of smart meter based on decision tree and clustering algorithm[J]. Acta Metrologica Sinica,2022,43(8):1089.) [29] 胡德勇,高志伟,王小东,等.热轧带钢力学性能在线预测模型的开发与应用[J].轧钢,2021,38(3):9.(HU De-yong,GAO Zhi-wei,WANG Xiao-dong,et al.Development and application of otrline prediction model for mechanical properties of hot rolled strips[J].Steel Rolling,2021,38(3):9.) [30] 易振,柴琳,刘惠康,等.基于AO-ENN的LF炉C、Mn合金收得率预报模型[J].中国冶金,2022,32(5):40.(YI Zhen,CHAI Lin,LIU Hui-kang,et al.Prediction model of C and Mn alloy yield in LF based on AO-ENN[J].China Metallurgy,2022,32(5):40.)