Isothermal constant strain rate compression experiments were conducted on 34CrNi3MoV steel using a thermal simulation experimental machine to study its thermal deformation behavior, with deformation temperatures ranging from 800 - 1 200 °C and strain rates ranging from 0,01 - 10 s-1 , and the corresponding stress-strain curves were obtained for 60 % compression. According to the results, through regression analysis of the 1stOpt software, parameter values of three constitutive models were obtained, and then the precision of prediction was compared by different models of flow stress

Guo, L. X.

Ju, D. Y.

Wang, Y. Q.

Xu, D.

Zhao, H. Y.

Zheng, B.

English

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71METALURGIJA 62 (2023) 1, 71-73B. ZHENG, D. XU, Y.Q. WANG, L.X. GUO, H.Y. ZHAO, D.Y. JUSTUDY ON CONSTITUTIVE MODELS OF HOT DEFORMATION FOR 34CrNi3MoV STEELReceived – Primljeno: 2022-06-06Accepted – Prihvaćeno: 2022-08-20Original Scientific Paper – Izvorni znanstveni radIsothermal constant strain rate compression experiments were conducted on 34CrNi3MoV steel using a thermal simulation experimental machine to study its thermal deformation behavior, with deformation temperatures rang-ing from 800 - 1 200 °C and strain rates ranging from 0,01 - 10 s-1 , and the corresponding stress-strain curves were obtained for 60 % compression. According to the results, through regression analysis of the 1stOpt software, param-eter values of three constitutive models were obtained, and then the precision of prediction was compared by dif-ferent models of flow stress.Key words: 34CrNi3MoV steel, hot deformation, flow stress, constitutive modelISSN 0543-5846METABK 62(1) 71-73 (2023)UDC – UDK 669.15.26.24.28.292:539.324:536.45:620.16:621.72=111INTRODUCTIONThe thermal deformation behavior of metal materi-als is quite complex, involving work hardening effect and softening effect, and the deformation resistance is affected by coupling factors such as strain rate, strain value and experimental temperature of deformation [1-4]. Based on the fundamental role of constitutive model, many scholars have worked to develop constitutive models with higher fitting accuracy. For example, re-searchers[4-6] such as Bin Yao, Dong Xu, et al. used the hyperbolic sinusoidal form of coupled polynomials to express the thermal constitutive equation of different materials, which is more accurately calculated but less easy to use in finite element simulations; Zhicheng Cheng et al [7] used a neural network model training function and parameters to obtain a predictive stress model for 42CrMo steel; Zhihui Cai et al [8] studied the Johnson-Cook constitutive model and proposed a modi-fied model of Johnson-Cook equation, which was shown to be a better fit for the quasi-static and dynamic deformation of medium Mn steel. In this study, 34CrN-i3MoV steel with the addition of trace alloy is studied , this steel grade is mainly used in the production of mili-tary components, so there is less information available to study the thermal constitutive relationship of this steel grade.B. Zheng, D. Xu(corresponding author Email: xudong_xyz@163.com), H.Y. Zhao, D.Y. Ju: School of Materials and Metallurgy, University of Science and Technology Liaoning, Anshan, ChinaB. Zheng, D. Xu: Technology Innovation Center for High Quality Cold Heading Steel of Hebei Province, Hebei University of Engineering, Handan, China Y.Q. Wang: Technology center, Zhongyuan Special Steel Equipment Manufacturing Corp. Ltd, Jiyuan, ChinaL.X. Guo: Technology Innovation Center for Wear Resistant Steel Plate of High plasticity and High Toughness of Hebei Province, Hebei Puy-ang Iron and Steel Corp. Ltd, Handan, ChinaIn this paper, the thermal deformation behavior of 34CrNi3MoV steel under different thermal deformation conditions was studied by using a thermal simulation ex-periment machine, and different high-temperature consti-tutive equations of 34CrNi3MoV steel were established. The coefficients of the equations were determined by fit-ting, and the prediction accuracy of different constitutive models was compared. The aim is to provide accurate flow stress model for finite element simulation of metal plastic forming, and to provide necessary theoretical guidance for practical production process.THERMAL DEFORMATION EXPERIMENTThe experimental steel was taken from a forging stock of 34CrNi3MoV steel from a special steel plant, and the main chemical compositions (mass fraction) were as follows: C 0,31 % - 0,35 %, Ni 3,0 % - 3,3 %, Cr 1,2 % - 1,5 %, Mn 0,5 % - 0,8 %, Mo 0,35 % - 0,45 %, Si 0,15 % - 0,4 %, V 0,1 % - 0,2 %. The samples were processed into φ 8 mm × 12 mm by wire cutting, so that the thermal compression experiments at differ-ent thermal deformation conditions could be carried out through hot simulation experiments.The thermal deformation behavior was tested by thermal compression experiments, and the specific ex-perimental process was as follows: The samples were heated at the rate of 20 °C/s, held for 5 min to complete austenitizing at 1 200 °C, and then cooled at the rate of 10 °C/s to the experimental temperature of 800, 900, 1 000, 1 100, and 1 200 °C, respectively. After holding for 10 s, isothermal-constant strain rate compression was performed at different strain rates (0,01 s-1, 0,1 s-1, 1 s-1 and 10 s-1). The maximum of hot compression was 60 %. Displacement-load data were got during the hot 72  METALURGIJA 62 (2023) 1, 71-73B. ZHENG et al.: STUDY ON CONSTITUTIVE MODELS OF HOT DEFORMATION FOR 34CrNi3MoV STEELcompression process. After compression, the samples were immediately water-cooled and quenched.EXPERIMENTAL RESULTSAccording to the test results of the thermal simula-tion test, the data points were collected and then were transformed into true strain-true stress curve, which is evaluated between 0 and 0,5 of true strain, and the curves of different thermal deformation conditions were shown in Figure 1, and the strain rates during the ex-periment of (a), (b), (c) and (d) are 0.01 s-1, 0.1 s-1, 1 s-1 and 10 s-1, respectively.According to Figure 1, in general: the deformation temperature and strain rate have great influence on the stress. Like most metal materials, the stress decreases when the temperature increases, and the stress increases when the strain rate increases; At the same strain rate, the stress peak moves to the left when increase of deformation temperature; When the deformation temperature is the same, the higher the strain rate is, the higher the stress peak is, and the corresponding strain variable is also larger.RESULTS AND DISCUSSIONConstruction of the constitutive model  and determination of parametersThe accurate expression of the constitutive equation contributed significantly to the study of thermal defor-mation, and different models were proposed by differ-ent researchers according to the research objects and experimental approaches. In this paper, three commonly used constitutive relationship models [4-8], namely norton-Hoff Law, Zerili-Armstrong, Generalized John-son & Cook model, were fitted by 1stOpt software to determine the model parameters.The Norton-Hoff Law model was shown in Equa-tion (1):  (1)where  denotes the strain rate, s-1; σ denotes the flow stress / MPa; T denotes the thermodynamic temperature / K; ε denotes the strain; a1, a2, a3, n1 and n2 are the pa-rameters of Eq. (1).After transforming in a mathematical way, the pa-rameters of the Norton-Hoff Law model calculated by 1stOpt software were: a1 = 3,6769, a2 = -0,008694, a3 = 4856,0912, n1 = 0,1237, and n2 = 0,09685.The Zerilli-Armstrong model was shown in Equa-tion (2).  (2)where b1, b2, b3, b4, b5, and h are the parameters of Eq. (2).The parameters of the Zerilli-Armstrong model cal-culated by 1stOpt software were: b1 = 35,9, b2 = 4528,2642, b3 = 0,002512, b4 = 6,6324×10-5, b5 = -52,2455, and h = -0,2182.The generalized Johnson & Cook model as shown in equation (3).  (3)where c1, c2, c3, c4, c5, m1, m2 and m3 are the parameters of Eq. (3); where , T is the thermody-namic temperature, K; Troom and Tmelt are the room tem-perature and the melting temperature of the steel grade, 298,15 K and 1 714,15 K, respectively.The parameters of the Generalized Johnson & Cook model calculated by 1stOpt software were: c1 = 0,5989, Figure 1  The stress-strain curves under different experimental conditions(a) 0,01 s-1; (b) 0,1 s-1; (c) 1 s-1; (d) 10 s-173B. ZHENG et al.: STUDY ON CONSTITUTIVE MODELS OF HOT DEFORMATION FOR 34CrNi3MoV STEELMETALURGIJA 62 (2023) 1, 71-73c2 = -26,8689, c3 = 6,5171 × 10-8 , c4 = 2,4039, c5 = 3,1369, m1 = 0,1365, m2 = 0,09703, and m3 = -2,0309.Comparison of the prediction accuracy  of three constitutive modelsIn order to more accurately describe the efficiency of establishing three constitutive relationships, the va-lidity of the above models was verified by introducing the correlation coefficient (R) and the average absolute relative error (AARE).  (4)  (5)where and are the test of flow stress values and calcu-lated values, respectively; is the average value of E, P; is the total numbers of results obtained experimentally.The magnitude of was usually used to analyze the de-gree of correlation of linear relationship between the ex-perimental and calculated values, but it did not necessar-ily represent the degree of agreement, because the pre-dicted data might all be over or under. On the other hand, AARE was the average relative error of the calculated value and the experimental value, so it could better repre-sent the consistency between the overall calculated value and the experimental value. In this paper, and were com-bined to evaluate the accuracy of flow stress prediction.Table 1 showed the accuracy assessment values under different constitutive models. As could be seen from Ta-ble 1 that the R-value of both Norton-hoff model and Johnson & Cook model was 0,985; the R-value of Nor-ton-Hoff Law model was slightly lower at 0,983. How-ever, compared with 12 % of the Norton-Hoff model and Johnson & Cook model, the AARE value of the Norton-Hoff Law model was a little higher, which was 13,2 %.Figure 2 showed correlation of flow stress data be-tween the experimental and calculated values. For this steel grade, the R and AARE values were almost the same for the Norton-hoff model and the Johnson & Cook model, but from Figure 2, it can be seen that the Norton-hoff model deviated more at low and medium stress (high temperature, small strain, or low strain rate) compared to the Johnson & Cook model, and the high stress (low temperature, large strain, or high strain rate) were fitted somewhat better.CONCLUSION(1) After transforming in a mathematical way, the constant coefficients of the three commonly used con-stitutive equations were calculated by 1stOpt software, and the predictive accuracy of the above constitutive equations was verified by the coefficient and AARE, and the correlation coefficient of all three constitutive models could reach above 0,98.(2) The Johnson & Cook model fits better when the 34CrNi3MoV steel is at low to medium stress level, i.e., high temperature, small strain or low strain rate.(3) The stress results are higher for low tempera-ture, large strain or high strain rate experiments, and the Norton-hoff model is a better fit in these cases.AcknowledgmentsThis article was financed by the Special Projects for Military-Civilian Collaborative Innovation in Science and Technology of Hebei Province (22351001D), and the Key project of Handan Scientific Research Pro-gram(21122015004).REFERENCES[1] H. Song, J. Yoo, S. S. Sohn, M. Koo, S. Lee. Achievement of high yield strength and strain hardening rate by forming fine ferrite and dislocation substructures in duplex lightw eight steel, Mat. Sci. Eng. A 704 (2017), 287-291.[2] S. Yadav, S. Singhal, Y. Jasra, R. K. Saxena. Determination of Johnson-Cook material model for weldment of mild ste-el, Materials Today: Proceedings 28 (2020), 1801-1808.[3] H. Ji, H. Duan, Y. Li, W. Li, Y. Lu. Optimization the wor-king parameters of as-forged 42CrMo steel by constitutive equation-dynamic recrystallization equation and proces-sing maps, J. Mater. Res. Technol. 9 (2020) 4, 7210-7224.[4] T. Blades. Hot Deformation Behavior of 2Cr11Mo1VNbN Steel Used for Steam, Special Steel Technology 27 (2021) 3, 26-29.[5] D. Xu, M. Y. Zhu, Z. Y. Tang, C. Ji. The Flow Stress Beha-vior of SCM435 Steel under Hot Compression, Metal. Int. 18 (2013) 3, 106-114.[6] P. Y. Liu, Z. J. Meng, Z. J. Liu, Y. K. Du, L. Zhao, H. X. Ma, L. D. Ma. Constitutive equation of Q460NH high-strength weathering steel based on strain compensation and modification, Forging & Stamping Technology 47 (2022) 3, 219-226.[7] Z. C. Cheng, H. Q. Liu, W. Yu, Q. W. Cai. Deformation Behavior and Constitutive Equation of 42CrMo Steel at High Temperature, Proceedings of Chinese Materials Con-ference (2021), 234-244.[8] Z. H. Cai, D. L. Zhang, G. Q. Wen, and Y. J. Zhou. Dynamic Deformation Behavior and Its Constitutive Model of Fe-11Mn-4Al-0.2C Medium-Mn Steel, Journal of Northeastern University (Natural Science) 42 (2021) 9, 1275-1281.Note:  Dong Xu is the responsible translator and the corresponding author, Handan, Hebei, China.Figure 2  Correlation of data between the calculated and experimental valuesTable 1  R, R2 and AARE values under different constitutive modelsParameter Norton-Ho Law Norton-ho Johnson & CookR 0,983 0,985 0,985R2 0,966 0,970 0,970AARE 13,2 % 11,96 % 12,0 %

Study on constitutive models of hot deformation for 34CrNi3MoV steel

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