Use Gleeble-3800 thermal simulation test machine to conduct thermal tensile test on 6005A aluminum alloy at 623~723 K and 0,01~1 s-1 strain rate. Using the obtained true stress-strain curve, the modified Zerilli-Armstrong (m- Z-A) model considering strain compensation was used to construct the constitutive model of the alloy. The results show that the correlation coefficient and average absolute error of the m-Z-A model are 0,97311 and 4,1779 %, respectively. The experimental data is in good agreement with the predicted curve obtained by calculating the model, which verifies the feasibility of the model

H. C. Ji

H. Y. Long

J. F. Jin

R. Yao

X. Y. Shao

English

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265METALURGIJA 60 (2021) 3-4, 265-268R. YAO, H. C. JI, J. F. JIN, X. Y. SHAO, H. Y. LONGHIGH TEMPERATURE CONSTITUTIVE MODEL OF 6005A ALUMINUM ALLOYReceived – Primljeno: 2021-01-15Accepted – Prihvaćeno: 2021-04-10Original Scientific Paper – Izvorni znanstveni radR. Yao, H.C. Ji (E-mail: jihongchao@ncst.edu.cn), X.Y. Shao, H. Y. Long, College of Mechanical Engineering, North China University of Science and Technology, Hebei, Tangshan, China; J.F. Jin, CRRC TANGSHAN CO., LTD., Hebei Tangshan, China.Use Gleeble-3800 thermal simulation test machine to conduct thermal tensile test on 6005A aluminum alloy at 623~723 K and 0,01~1 s-1 strain rate. Using the obtained true stress-strain curve, the modified Zerilli-Armstrong (m-Z-A) model considering strain compensation was used to construct the constitutive model of the alloy. The results show that the correlation coefficient and average absolute error of the m-Z-A model are 0,97311 and 4,1779 %, re-spectively. The experimental data is in good agreement with the predicted curve obtained by calculating the mod-el, which verifies the feasibility of the model. Keywords: aluminum alloy 6005A, constitutive model, tensile test, flow stress, Zerilli-Armstrong (Z-A) modelINTRODUCTION6005A aluminum alloy has good formability, corro-sion resistance, weldability, strong fatigue strength and medium static strength, so it is widely used in panel components in the aerospace industry and railway ap-plications [1,2]. In order to accurately design the ther-mal mechanical processing parameters directly related to the microstructure and mechanical properties of the final product, it is very important to comprehensively study the thermal deformation behavior of the alloy. Most reports published so far have focused on the influ-ence of friction, stirring and welding parameters on the flow behavior of 6005A aluminum alloy at different temperatures [3]. However, the plastic tensile deforma-tion behavior of 6005A aluminum alloy under heat is still poorly understood and far from being optimized.At present, scholars from various countries have carried out a lot of research on the constitutive model of materials during thermal deformation. For example, Li et al. [4] established peak constitutive equation of 21-4N heat-resistant steel, Ji et al. [5] established peak con-stitutive equation of TA15 titanium alloy, Cai et al. [6] established constitutive equation of 33Cr23Ni8Mn3N heat-resistant steel.In this paper, based on the high temperature tensile test, the modified Z-A model of 6005A aluminum alloy is established using stress and strain data. Finally veri-fied its accuracy.ISSN 0543-5846METABK 60(3-4) 265-268 (2021)UDC – UDK 669.715:620.17:62.001.57:536.5.45:620.16-539.374=111EXPERIMENTAL MATERIALS AND PROCESSESThe experimental material in this study is 6005A aluminum alloy, and its composition is:0,0~0,9 % Si,0,4~0,6 % Mg,0,0~3,5 % Fe,0,0~0,1 % Cu, 0,0~0,1 % Mn, 0,0~0,1 % Cr, 0,0~0,1 % Ti,0,15 Al.The experiment was carried out on the Gleeble-3800 thermal simulation test machine, and the deformation temperature was set to 623, 673 and 723 K. The strain rate is 0,01, 0,1, 1 s-1, and the sample is heated to the deformation temperature at a rate of 10 K/s and kept for 2 minutes. Then perform isothermal stretching.RESULTS AND DISCUSSIONFigure 1 shows the true stress-true strain curve of 6005A aluminum alloy. It can be seen from Figure 1: The flow stress of the alloy is greatly affected by the deforma-tion temperature and strain rate. At the same strain rate, as the temperature increases, the true stress decreases sig-nificantly. At the same deformation temperature, as the deformation rate increases, the stress level increases.Samantaray D et al. [7] proposed a modified Zerilli-Armstrong model based on the physical concept of the Zerilli-Armstrong model. This model is widely used in the study of the constitutive relationship of alloys with FCC lattice structure., Its expression is shown in equa-tion (1):  (1)In the equation: T* = T - Tr, Tr is the reference tem-perature; * =  / r,  is the experimental strain rate, r is the reference strain rate; C1, C2, C3, C4, C5, C6, n is a material parameter, characterize the hardening rate of a material with strain.266R. YAO et al.: HIGH TEMPERATURE CONSTITUTIVE MODEL OF 6005A ALUMINUM ALLOY METALURGIJA 60 (2021) 3-4, 265-268Select the reference temperature as 623 K, the refer-ence strain rate is 0,01 s-1, under the reference tempera-ture and reference strain rate, equation (1) can be re-written as:  (2)Taking the natural logarithm on both sides of the equal sign of equation (3), get:  (3)Make ; .Rewrite the formula equationas :  (4)At a reference strain rate of 0,01 s-1, Take e as 0,06, 0,08, 0,1, 0,12, 0,14, 0,16, 0,18, 0,2, 0,22, 0,24, 0,26, respectively, Make the relationship diagram under dif-ferent temperature conditions, as shown in Figure 2, fit the points in the graph, to get the intercept and slope values at different values of e, It corresponds to I and S respectively.Take the value of Rp0.2 corresponding to the 0,2 % residual strain in and as the value of C1, which is C1 = 49,86 MPa. According to the obtained I and S1 values, make ln(expI-C1) and S1-ε diagrams, as shown in Figure (3a) and Figure (3b), it can be found that there is a rela-tively good linear relationship between the two. Fit the points in the graph, according to the intercept and slope values obtained by fitting, according to the intercept and slope values obtained by fitting, C2 = 22,32395 and n = 0,44413, C3 = 0,00428 and C4 = 0,00422.Make S2 = C5 + C6T*, equation (1) can be written in the form of equation (5) under specified strain condi-tions, S2 can be obtained by linear fitting of a polyno-mial of lns-lnė, the relationship diagram is shown in Figure  (4a), C5, C6 can be obtained by calculating the linear relationship of S2 - T*, as shown in Figure (4b). Find C5 = 0,09266 and C6 = 7,82×10-5.  (5)Through the above steps, the relevant material pa-rameters of the Modified Zerilli-Armstrong (Z-A) mod-el are shown in Table 1.MODEL ACCURACY ANALYSISIn order to verify the selected constitutive model’s ability to predict flow stress of 6005A aluminum alloy, bring different temperature and strain values into the Figure 1  True stress-true strain curves at different temperatures: (a)623 K; (b)673 K; (c)723 KFigure 2  Relationship diagram: (a)fitting; (b) local amplification267R. YAO et al.: HIGH TEMPERATURE CONSTITUTIVE MODEL OF 6005A ALUMINUM ALLOYMETALURGIJA 60 (2021) 3-4, 265-268above constitutive model, and compare the experimental value of flow stress with the predicted value, as shown in Figure 5. It can be seen that when the deformation tem-perature is the same, the calculation results are more con-sistent with the test results in the uniform deformation stage and different strain rates. In summary, the constitu-tive model constructed in this paper has high accuracy Figure 3  Fitting relationship between deformation parameters: (a) ; (b) S1-eFigure 4  Fitting relationship between deformation parameters: (a) ; (b) S2-T*Figure 5  Comparison of predicted values and experimental values of different models: (a)623 K; (b)673 K; (c)723 KTable 1 Parameters for the modified Z-A modelConstants n C1 C2Value 0,44413 49,86 22,32395Constants C3 C4 C5Value 0,00428 0,00422 0,09266Constants C6Value 7,82×10-5268R. YAO et al.: HIGH TEMPERATURE CONSTITUTIVE MODEL OF 6005A ALUMINUM ALLOY METALURGIJA 60 (2021) 3-4, 265-268and can be used to predict the rheological behavior of 6005A aluminum alloy during warm forming.In order to more accurately quantify and compare the prediction accuracy of the two constitutive equa-tions established, it is necessary to perform statistical error analysis on the prediction data and experimental data, Introduce two statistical parameters, the correla-tion coefficient (R) and the average absolute error (δAARE), to further evaluate the predictive ability of the model, as can be seen from Figure 6. A good correlation (R = 0,97311) between the experimental and the pre-dicted data is obtained, while the mean regular residual was found to be 4,1779 %.  (7)  (8)In the equation, E is the experimental stress, P is the predicted stress, ,  is the average of the experimental and predicted values, and N is the total number of ex-perimental data.Figure 6  Correlation test between predicted value and experimental valueCONCLUSIONThe flow stress of 6005A aluminum alloy during hot deformation is more sensitive to deformation tempera-ture and strain rate, and increases with the decrease of deformation temperature and the increase of strain rate.The established constitutive model of 6005A alu-minum alloy has high accuracy. The modified (Z-A) model can be used to predict the rheological behavior of 6005A aluminum alloy during warm forming.AcknowledgmentsThis work is supported by the Tangshan talent foun-dation innovation team (20130204D) and funded by S&P Program of Hebei (Grant No.19012204Z).REFERENCES[1] Simar A., Nielsen K. L., Meester B. D., et al. Micro-mecha-nical modelling of ductile failure in 6005A aluminium using a physics based strain hardening law including stage IV[J]. Engineering Fracture Mechanics 13(2010)77,2491-2503.[2] Dong P., Li H., Sun D., et al. Effects of welding speed on the microstructure and hardness in friction stir welding joints of 6005A-T6 aluminum alloy[J]. Materials & De-sign 45(2013),524-531.[3] Simar A., Y. Bréchet, Meester B. D., et al. Integrated mo-deling of friction stir welding of 6xxx series Al alloys: Pro-cess, microstructure and properties[J]. Progress in Mate-rials Science 57(2012)1,95-183. [4] Li Y., Ji H., Li W., et al. Hot Deformation Characteristics-Constitutive Equation and Processing Maps-of 21-4N He-at-Resistant Steel.[J]. Materials 12(2018)1, 89.[5] Ji H., Peng Z., Pei W., et al. Constitutive equation and hot processing map of TA15 titanium alloy[J]. Materials Rese-arch Express 7(2020)4,045608.[6] Cai Z., Ji H., Pei W., et al. An Investigation into the Dyna-mic Recrystallization (DRX) Behavior and Processing Map of 33Cr23Ni8Mn3N Based on an Artificial Neural Network (ANN)[J]. Materials 13(2020)6,1282.[7] Samantaray D., Mandal S., Borah U., et al. A thermo - vi-scoplastic constitutive model to predict elevated - tempera-ture flow behaviour in a titanium-modified austenitic stainless steel[J]. Materials Science & Engineering A 526(2009)1-2,1-6.Note:  The responsible translator for English language is Z. Ma-North China University of Science and Technology, China

High temperature constitutive model of 6005A aluminum alloy

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