Please wait a minute...
Acta Metall Sin  2019, Vol. 55 Issue (12): 1569-1580    DOI: 10.11900/0412.1961.2019.00082
Research paper Current Issue | Archive | Adv Search |
Modelling of Q&P Steel Heat Treatment Process Based on Finite Element Method
ZHANG Qingdong,LIN Xiao,LIU Jiyang(),HU Shushan
School of Mechanical and Engineering, University of Science and Technology Beijing, Beijing 100083, China
Download:  HTML  PDF(12134KB) 
Export:  BibTeX | EndNote (RIS)      

Quenching and partitioning (Q&P) steel is a kind of high strength and toughness steels which has a majority of martensite at room temperature and a certain amount of retained austenite through the quenching and carbon distribution heat treatment process of cold-rolled carbon-silicon-manganese steel. In this work, the typical Q&P high-strength steel, QP980 steel, is taken as an example to carry out the physical simulation study of the whole process of heat treatment. A creep-like strain equation coupled with temperature and time is proposed to describe the volume change of materials during Q&P heat treatment. The phase transformation kinetics equation, phase transformation strain and phase transformation plasticity equation of Q&P heat treatment with the influence of quenching temperature were established, and the thermal expansion coefficient of each phase of Q&P steel was obtained. According to the coupling principles of temperature, microstructure and stress-strain field, a numerical simulation model for the whole process of Q&P heat treatment was developed. In this model, the physical simulation of QP980 steel thermal-elastoplastic incremental constitutive equations are implemented to commercial finite element software ABAQUS as the user subroutines. The model was validated by Q&P heat treatment experiment on Gleeble thermal-mechanical simulator. The calculated values of the models are both in good agreement with the experimental values.

Key words:  Q&P steel      heat treatment      numerical simulation      experimental research     
Received:  26 March 2019     
ZTFLH:  TG156.34  
Fund: National Science and Technology Support Project(No.2011BAE13B05);National Natural Science Foundation of China(No.51075031)
Corresponding Authors:  Jiyang LIU     E-mail:

Cite this article: 

ZHANG Qingdong, LIN Xiao, LIU Jiyang, HU Shushan. Modelling of Q&P Steel Heat Treatment Process Based on Finite Element Method. Acta Metall Sin, 2019, 55(12): 1569-1580.

URL:     OR

Fig.1  Experimental scheme (a) and continuous cooling transformation (CCT) curves (b) of continuous cooling of quenching and partitioning (Q&P) QP980 steel (A—austenite, B—bainite, F—ferrite, M—martensite)
Fig.2  Normal temperature structures after quenching at the cooling rates of 1 ℃/s (a), 2 ℃/s (b), 5 ℃/s (c), 10 ℃/s (d), 30 ℃/s (e) and 50 ℃/s (f)
Fig.3  Schemes of thermal expansion experiment (a) and phase change kinetics experiment (b) (Tq—quenching temperature)
Fig.4  Experimental scheme of phase change plasticity
Fig.5  Experimental heating and cooling system of Q&P heat treatment with different distribution temperatures
Fig.6  Relationships between axial strain and temperature during stress-free quenching and tempering (Ms—martensite transformation start temperature)(a) the first quenching process (b) the second quenching process
Fig.7  The relationship between martensite volume fraction (ξM1) and quenching temperature in the first quenching process
Fig.8  Microstructure changes before and after the second quenching process with different quenching temperatures
Fig.9  Phase change kinetics curves of the second quenching process with different quenching temperature Q&P heat treatment
Fig.10  Wide-direction strain of martensite transformation process under external loading
Fig.11  The measured value of phase change plasticity coefficient (k) and linear fitting (σ—stress in the same direction as phase transformation plastic strain)
Fig.12  Axial strain during Q&P heat treatment with different distribution temperatures

Time / s

Coefficient of primary temperature termCoefficient of quadratic temperature termCoefficient of cubic temperature term


Table 1  The results of cubic polynomial fitting of reduced temperature coefficient
Coefficient of equation

Coefficient value

Coefficient of equation

Coefficient value

Coefficient of equation

Coefficient value

Table 2  Creep strain equation coefficients of QP980 high strength steel
Fig.13  Comparison of the calculated and measured values of creep-like strain
Fig.14  Loading system of heating and cooling for Q&P heat treatment experiments on gleeble
Fig.15  Model validation finite element model of heat distribution of test samples
Fig.16  Comparisons between simulated and measured deformations of samples in different stages of Q&P heat treatment process(a) first quenching process (b) partitioned heating process(c) partitioned holding process (d) second quenching process
Fig.17  Variations of phase volume fraction with time in Q&P heat treatment stages(a) first quenching process (b) distribution process (c) second quenching process
[1] Speer J G, Edmonds D V, Rizzo F C, et al. Partitioning of carbon from supersaturated plates of ferrite, with application to steel processing and fundamentals of the bainite transformation [J]. Curr. Opin. Solid State Mater. Sci., 2004, 8: 219
[2] Speer J G, Assun??o F C R, Matlock D K, et al. The "quenching and partitioning" process: Background and recent progress [J]. Mater. Res., 2005, 8: 417
[3] Xu Z Y. New Processes for Steel Heat Treatment [J]. Heat Treatment, 2007(01): 1
[3] (徐祖耀.钢热处理的新工艺 [J]. 热处理, 2007(01): 1)
[4] Khan S A, Bhadeshia H K D. Kinetics of Martensitic transformation in partially bainitic 300M steel [J]. Mater. Sci. Eng., 1990, A129: 257
[5] Bhadeshia H K D H. Carbon content of retained austenite in quenched steels [J]. Met. Sci., 1983, 17: 151
[6] Yamanaka S, Sakanoue T, Yoshii T, et al. Influence of transformation plasticity on the distortion of carburized quenching process of Cr-Mo steel ring [J]. J. Soc. Mater. Sci. Jpn., 1999, 48: 733
[7] Ju D Y, Narazaki M. Simulation and experimental verification of residual stress and distortion during quenching of steel [A]. Proceeding of the 20th ASM Heat Treating Society Conference [C]. St. Louis, MO, USA: ASM International, 2000: 441
[8] Arimoto K, Horino T, Ikuta F, et al. Explanation of the origin of distortion and residual stress in water quenched cylinders using computer simulation [J]. J. ASTM Int., 2006, 3: 253
[9] Inoue T, Yamaguchi T, Wang Z G. Stresses and phase transformations occurring in quenching of carburized steel gear wheel [J]. Mater. Sci. Technol., 1984, 1: 872
[10] Mukai R, Ju D Y. Simulation of carburizing-quenching of a gear. Effect of carbon content on residual stresses and distortion [J]. J. Phys. IV France, 2004, 120: 489
[11] Imatani S, Okuno Y, Inoue T. Experiment and simulation for thick-plate bending by high frequency inductor [J]. Acta Metall. Sin. (Engl. Lett.), 1998, 11: 449
[12] Inoue T, Arimoto K, Ju D Y. Development of heat treatment simulation program "HEARTS"—Theory, strategy, function and some examples [A]. Residual Stresses III: Science and Technology [C], London and New York: Elsevier Applied Science,1992, 1: 226
[13] Inoue T, Arimoto K. Development and implementation of CAE system “HEARTS” for heat treatment simulation based on metallo-thermo-mechanics [J]. J. Mater. Eng. Perform, 1997, 6: 51
[14] Ju D Y, Inoue T. On the material process simulation code COSMAP-simulated examples and its experimental verification for heat treatment process [J]. Key Eng. Mater., 2007, 345-346: 955
[15] Inoue T, Tanaka T, Ju D Y, et al. Transformation plasticity and the effect on quenching process simulation [J]. Key Eng. Mater., 2007, 345-346: 915
[16] Inoue T. On phenomenological mechanism of transformation plasticity and inelastic behavior of a steel subjected to varying temperature and stress- application of unified transformation-thermo plasticity theory [J]. J. Soc. Mater. Sci. Jpn., 2008, 57: 225
[17] Inoue T. Phenomenological mechanism of transformation plasticity and the constitutive law coupled with thermo-mechanical plasticity [J]. Adv. Mater. Res., 2008, 33-37: 1351
[18] Inoue T. Transformation plasticity-the mechanism and some applications [J]. Mater. Sci. Forum, 2009, 614: 11
[19] Inoue T. Mechanism of transformation plasticity and the unified constitutive equation for transformation-thermo-mechanical plasticity with some applications [J]. Int. J. Microstruct. Mater. Prop., 2010, 5: 319
[20] Inoue T. Mechanics and characteristics of transformation plasticity and metallo-thermo-mechanical process simulation [J]. Proc. Eng., 2011, 10: 3793
[21] Inoue T. Macro-, meso-, and nanoscopic metallo thermo mechanics [J]. J. Phys. IV France, 2004, 120: 3
[22] Denis S. Considering stress-phase transformation interactions in the calculation of heat treatment residual stresses [J]. J. Phys. IV France, 1996, 6: C1-159
[23] Denis S, Archambault P, Aubry C, et al. Modelling of phase transformation kinetics in steels and coupling with heat treatment residual stress predictions [J]. J. Phys. IV France, 1999, 9: Pr9-323
[24] Lee S J, Lee Y K. Finite element simulation of quench distortion in a low-alloy steel incorporating transformation kinetics [J]. Acta Mater., 2008, 56: 1482
[25] Leblond J B, Devaux J, Devaux J C. Mathematical modelling of transformation plasticity in steels I: Case of ideal-plastic phases [J]. Int. J. Plast., 1989, 5: 551
[26] Leblond J B, Devaux J. A new kinetic model for anisothermal metallurgical transformations in steels including effect of austenite grain size [J]. Acta Metall., 1984, 32: 137
[27] Liu Y, Qin S W, Hao Q G, et al. Finite element simulation and experimental verification of internal stress of quenched AISI 4140 cylinders [J]. Metall. Mater. Trans., 2017, 48A: 1
[28] De Oliveira W P, Savi M A, Pacheco P M C L. Finite element method applied to the quenching of steel cylinders using a multi-phase constitutive model [J]. Arch. Appl. Mech., 2013, 83: 1013
[29] De Oliveira W P, Savi M A, Pacheco P M C L, et al. Thermomechanical analysis of steel cylinders quenching using a constitutive model with diffusional and non-diffusional phase transformations [J]. Mech. Mater., 2010, 42: 31
[30] Carlone P, Palazzo G S, Pasquino R. Finite element analysis of the steel quenching process: Temperature field and solid-solid phase change [J]. Comput. Math. Appl., 2010, 59: 585
[31] Smoljan B. Prediction of mechanical properties and microstructure distribution of quenched and tempered steel shaft [J]. J. Mater. Process. Technol., 2006, 175: 393
[32] Bok H H, Choi J W, Suh D W, et al. Stress development and shape change during press-hardening process using phase-transformation-based finite element analysis [J]. Int. J. Plast., 2015, 73: 142
[33] Song G S, Liu X H, Wang G D, et al. Numerical Simulation on Carburizing and Quenching of Gear Ring [J]. J. Iron Steel Res., 2007, 14: 47
[34] Chen B, Peng X H, Nong S N, et al. An incremental constitutive relationship incorporating phase transformation with the application to stress analysis for the quenching process [J]. J. Mater. Process. Technol., 2002, 122: 208
[35] Han Q L, Liu G Q, Dong L, et al. FEM simulation of quenching process for dissimilar material welded using steel and titanium alloy [J]. Trans. Mater. Heat Treat., 2007, 28(4): 139
[35] (韩庆礼, 刘国权, 董 雷等. 异种材料淬火过程的有限元模拟 [J]. 材料热处理学报, 2007, 28(4): 139)
[36] Ginzburg V B, translated by Jiang M D, Wang G Z. High-Quality Steel Rolling [M]. Beijing: Metallurgical Industry Press, 2000: 1
[36] (金兹伯格 V B著, 姜明东, 王国栋译. 高精度板带材轧制理论与实践 [M]. 北京: 冶金工业出版社, 2000: 1)
[37] Coret M, Combescure A. A mesomodel for the numerical simulation of the multiphasic behavior of materials under anisothermal loading (application to two low-carbon steels) [J]. Int. J. Mech. Sci., 2002, 44: 1947
[38] Jiang Y, Zeng P, Lou L L. Numerical simulation of quenching process of steel 26Cr2Ni4MoV with thermo-mechano-metallurgical coupling [J]. J. Harbin Inst. Technol., 2002, 34: 302
[38] (蒋 昱, 曾 攀, 娄路亮. 26Cr2Ni4MoV钢淬火过程的三场耦合数值模拟 [J]. 哈尔滨工业大学学报, 2002, 34: 302)
[39] Koistinen D P, Marburger R E. A general equation prescribing the extent of the austenite-martensite transformation in pure iron-carbon alloys and plain carbon steels [J]. Acta Metall., 1959, 7: 59
[40] Videau J C, Cailletaud G, Pineau A. Experimental study of the transformation-induced plasticity in a Cr-Ni-Mo-Al-Ti steel [J]. J. Phys. IV France, 1996, 6: C1-465
[41] Coret M, Calloch S, Combescure A. Experimental study of the phase transformation plasticity of 16MND5 low carbon steel induced by proportional and nonproportional biaxial loading paths [J]. Eur. J. Mech., 2004, 23: 823
[42] Greenwood G W, Johnson R H. The deformation of metals under small stresses during phase transformations [J]. Proc. Royal Soc. London, 1965, 283A: 403
[43] Atkins E. Elements of X-ray Diffraction [J]. Phys. Today, 1978, 10: 50
[44] Sun C Y, Zeng P, Lei L P, et al. Experimental extract of transformation plastic strain during phase transformation [J]. J. Plast. Eng., 2007, 14(6): 161
[44] (孙朝阳, 曾 攀, 雷丽萍等. 基于物理模拟的相变塑性应变分离方法 [J]. 塑性工程学报, 2007, 14(6): 161)
[45] Liu Z. Numerical simulation of heat treatment process [M]. Beijing: Science Press, 1996: 119
[45] (刘 庄. 热处理过程的数值模拟 [M]. 北京: 科学出版社, 1996: 119)
[46] Xu X J, Chen G X, Liu C C, et al. Numerical simulation of the stresses evolution during tempering of steel [J]. Heat Treat.Met., 1997, (3): 12
[46] (许学军, 陈国学, 刘春成等. 钢的回火过程中应力演化的数值模拟 [J]. 金属热处理, 1997, (3): 12)
[47] Wang M M. Study on tempering of Mn-Mo-Ni steel for large forgings of nuclear power [D]. Shanghai: Shanghai Jiao Tong University, 2013
[47] (王明敏. 核电大锻件用Mn-Mo-Ni钢的回火研究 [D]. 上海: 上海交通大学, 2013)
[48] Liu G Y, Li M W, Zhang S J. Thermal numerical simulation and experiment in quenching process of medium and heavy plate [J]. J. Iron Steel Res., 2007, 19(8): 51
[48] (刘国勇, 李谋渭, 张少军. 中厚板淬火过程的热力学数值模拟及实验 [J]. 钢铁研究学报, 2007, 19(8): 51)
[49] Fang G, Zeng P. Finite element simulation of metal quenching [J]. Tsinghua Sci. Technol., 2004, 9: 555
[1] HAO Zhibo, GE Changchun, LI Xinggang, TIAN Tian, JIA Chonglin. Effect of Heat Treatment on Microstructure and Mechanical Properties of Nickel-Based Powder Metallurgy Superalloy Processed by Selective Laser Melting[J]. 金属学报, 2020, 56(8): 1133-1143.
[2] WANG Fuqiang, LIU Wei, WANG Zhaowen. Effect of Local Cathode Current Increasing on Bath-Metal Two-Phase Flow Field in Aluminum Reduction Cells[J]. 金属学报, 2020, 56(7): 1047-1056.
[3] LIU Jizhao, HUANG Hefei, ZHU Zhenbo, LIU Awen, LI Yan. Numerical Simulation of Nanohardness in Hastelloy N Alloy After Xenon Ion Irradiation[J]. 金属学报, 2020, 56(5): 753-759.
[4] WANG Cunyu,CHANG Ying,ZHOU Fengluan,CAO Wenquan,DONG Han,WENG Yuqing. M3 Microstructure Control Theory and Technology of the Third-Generation Automotive Steels with HighStrength and High Ductility[J]. 金属学报, 2020, 56(4): 400-410.
[5] WANG Bo,SHEN Shiyi,RUAN Yanwei,CHENG Shuyong,PENG Wangjun,ZHANG Jieyu. Simulation of Gas-Liquid Two-Phase Flow in Metallurgical Process[J]. 金属学报, 2020, 56(4): 619-632.
[6] WANG Tao,WAN Zhipeng,LI Zhao,LI Peihuan,LI Xinxu,WEI Kang,ZHANG Yong. Effect of Heat Treatment Parameters on Microstructure and Hot Workability of As-Cast Fine Grain Ingot of GH4720Li Alloy[J]. 金属学报, 2020, 56(2): 182-192.
[7] WU Jing,LIU Yongchang,LI Chong,WU Yuting,XIA Xingchuan,LI Huijun. Recent Progress of Microstructure Evolution and Performance of Multiphase Ni3Al-Based Intermetallic Alloy with High Fe and Cr Contents[J]. 金属学报, 2020, 56(1): 21-35.
[8] XU Qingyan,YANG Cong,YAN Xuewei,LIU Baicheng. Development of Numerical Simulation in Nickel-Based Superalloy Turbine Blade Directional Solidification[J]. 金属学报, 2019, 55(9): 1175-1184.
[9] Peiyuan DAI,Xing HU,Shijie LU,Yifeng WANG,Dean DENG. Influence of Size Factor on Calculation Accuracy of Welding Residual Stress of Stainless Steel Pipe by 2D Axisymmetric Model[J]. 金属学报, 2019, 55(8): 1058-1066.
[10] WAN Xiangliang, HU Feng, CHENG Lin, HUANG Gang, ZHANG Guohong, WU Kaiming. Influence of Two-Step Bainite Transformation on Toughness in Medium-Carbon Micro/Nano-Structured Steel[J]. 金属学报, 2019, 55(12): 1503-1511.
[11] LU Shijie, WANG Hu, DAI Peiyuan, DENG Dean. Effect of Creep on Prediction Accuracy and Calculating Efficiency of Residual Stress in Post Weld Heat Treatment[J]. 金属学报, 2019, 55(12): 1581-1592.
[12] TIAN Tian, HAO Zhibo, JIA Chonglin, GE Changchun. Microstructure and Properties of a New Third Generation Powder Metallurgy Superalloy FGH100L[J]. 金属学报, 2019, 55(10): 1260-1272.
[13] HE Bo, XING Meng, YANG Guang, XING Fei, LIU Xiangyu. Effect of Composition Gradient on Microstructure and Properties of Laser Deposition TC4/TC11 Interface[J]. 金属学报, 2019, 55(10): 1251-1259.
[14] Yuping QIU, Hao DAI, Hongbin DAI, Ping WANG. Tuning Surface Composition of Ni-Pt/CeO2 Catalyst for Hydrogen Generation from Hydrous Hydrazine Decomposition[J]. 金属学报, 2018, 54(9): 1289-1296.
[15] Jun LI, Mingxu XIA, Qiaodan HU, Jianguo LI. Solutions in Improving Homogeneities of Heavy Ingots[J]. 金属学报, 2018, 54(5): 773-788.
No Suggested Reading articles found!