The deformation behavior of 6005A aluminum alloy at a strain rate of 0,01-10s-1, a deformation temperature of 673- 773K and a total strain of 0,8 was studied. Using the stress-strain data of 6005A aluminum alloy with a strain of 0,05-0,8, an Arrhenius-type constitutive model was established. And verified the accuracy of the model. The results show that: the flow stress of 6005A aluminum alloy increases with the increase of strain rate, and decreases with the increase of deformation temperature; Under different strains, the correlation coefficient (R) between the experimental value and the predicted value is as high as 98 %, and the average relative error (AARE) is less than 10 %, indicating that the established model has high predictability

H. C. Ji

H. Q. Zhang

W. C. Pei

Y. G. Li

English

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261METALURGIJA 60 (2021) 3-4, 261-264H. Q. ZHANG, H. C. JI, W. C. PEI, Y. G. LI RESEARCH ON MODEL OF 6005A ALUMINUM ALLOYReceived – Primljeno: 2021-02-14Accepted – Prihvaćeno: 2021-04-10Original Scientific Paper – Izvorni znanstveni radH. Q. Zhang, H. C. Ji, (E-mail: jihongchao@ncst.edu.cn), W. C. Pei, Y. G. Li, College of Mechanical Engineering, North China University of Science and Technology, Hebei, Tangshan, ChinaThe deformation behavior of 6005A aluminum alloy at a strain rate of 0,01-10s-1, a deformation temperature of 673-773K and a total strain of 0,8 was studied. Using the stress-strain data of 6005A aluminum alloy with a strain of 0,05-0,8, an Arrhenius-type constitutive model was established. And verified the accuracy of the model. The results show that: the flow stress of 6005A aluminum alloy increases with the increase of strain rate, and decreases with the in-crease of deformation temperature; Under different strains, the correlation coefficient (R) between the experimental value and the predicted value is as high as 98 %, and the average relative error (AARE) is less than 10 %, indicating that the established model has high predictability. Keywords: 6005A aluminum alloy, extrusion, temperature, true stress-true strain curves, Arrhenius constitutive modelINTRODUCTION6005A aluminum alloy is a medium-strength, low-density alloy. It is one of the most widely used alloys in the aviation and railway industries [1,2]. For the ma-chining parameters related to the microstructure and mechanical properties of the product, it is very impor-tant to comprehensively study the hot deformation be-havior of the alloy.In recent years, many scholars have used various constitutive models to predict the constitutive behavior of different metals [3-4]. Among them, the Arrhenius constitutive model proposed by Sellers and Tegart [5] is suitable for different temperature ranges and is one of the widely used constitutive models under thermal working conditions. Cai et al. [6] established the Arrhe-nius constitutive equation of 3Cr23Ni8Mn3N strain compensation, and verified the accuracy of the constitu-tive model by calculating the correlation coefficient and relative error. Samantaray et al. [7] established the Ar-rhenius constitutive model of 9Cr-1Mo steel and used it to predict high temperature flow stress, and finally ob-tained good prediction results. However, the plastic compression deformation behavior of 6005A aluminum alloy under heat is still poorly understood and far from optimized.In this paper, the effects of deformation temperature, strain rate and strain on the flow stress of 6005A alu-minum alloy extrusions under isothermal compression are studied. The parameters of the 6005A aluminum al-loy Arrhenius constitutive model were calculated with a strain of 0,05 – 0,8, and the Arrhenius constitutive mod-el under different strain conditions was established to simulate the plastic flow behavior of 6005A aluminum ISSN 0543-5846METABK 60(3-4) 261-264 (2021)UDC – UDK 669.715:620.172:536.5:620.16-539.373/513.6.086.5=111alloy in a specific temperature range and strain rate. And verify its accuracy.EXPERIMENTAL MATERIALS AND PROCESSESThe experimental material is 6005A aluminum al-loy, and its chemical composition (in wt.%) is 0,8 Si; 0,35 Fe; 0,1 Cu; 0,1 Mn; 0,6 Mg; 0,1 Cr; 0,1 Zn; 0,1 Ti; 97,75 Al; (bal.) Fe. The experiment was carried out on the Gleeble-1500D thermal simulation test machine, and the deformation temperature was set to 673, 723, 773 K respectively. The strain rate is 0,01, 0,1, 1, 10 s-1. The total strain is set to 0,8. Before isothermal compres-sion, the sample is preheated and kept at the deforma-tion temperature for 5,0 min to achieve temperature equilibrium. According to the experimental results, the stress-strain curve of 6005 aluminum alloy is estab-lished, as shown in Figure 1.ESTABLISHMENT OF ARRHENIUS MODLEThere are three expressions commonly used in the Arrhenius constitutive model, as follows:  (ασ<0,8) (1)  (ασ>1,2) (2)  (For all σ)  (3)Where α, β and m satisfy:  (4)In the equation,  is the strain rate (s-1); A, B, C rep-resent material constant;σ is the true stress(MPa); R is the gas friction constant 8,3145 mol-1·K-1; Q is deforma-tion activation energy (J. mol-1); T is absolute tempera-ture (K); m, n is the stress index; α, β are stress level parameters independent of temperature .262H. Q. ZHANG et al.: RESEARCH ON MODEL OF 6005A ALUMINUM ALLOY METALURGIJA 60 (2021) 3-4, 261-264The parameter Z can be introduced, which indicates the relationship between deformation activation energy (Q), strain rate and deformation temperature during metal deformation.   (5)Combining equation (5):  (6)Take the stress under different deformation condi-tions when the strain is 0,4 as an example to calculate the material constant, Take the logarithm of equation (1) and equation (2):  (7)  (8)Substitute the stress values of different strain rates (0,01, 0,1, 1, 10 s-1) and different deformation tempera-tures (773 K, 723 K, 673 K) into equation (7) and equa-tion (8). And equation (7) and equation (8) are fitted and calculated to obtain m = 8,826, β = 0,167.therefore, the value of α can be obtained by equation (4), that is, α = 0,0189.Take the logarithm of equation (3):  (9)As shown in equation (9). When the deformation temperature and strain rate are determined, the follow-ing results can be obtained:   (10)  (11)Substitute the above value α into equation (10) and equation (11), and fit equations (10) and (11) under dif-ferent deformation conditions. The method of linear fit-ting calculation can get n = 6,590 and Q / (Rn) = 3521,437. Usually the R value is 8,3145 mol-1·K-1. By calculation, when the strain is 0,4 and Q = 243,4401kJ/mol.The deformation activation energy of 6005A alu-minum alloy can be obtained. Substitute Q into equa-tion (5), and when the strain is 0,4, the parameters Z of different strain rates and deformation temperatures can be obtained. Convert equation (3) to equation (5), and take the logarithm of both sides of the equation:  (12)Due to lnZ and ln[sinh(ασ)] are linear relationships, lnC is the intersection of the curve. lnZ and ln[sinh(ασ)] linear fitting calculations in different deformation con-ditions can be obtained by lnC = 38,014, C = 3,232×1016.Substituting A, C, n, and Q into equation (6), the Ar-rhenius constitutive model of 6005A aluminum alloy at 0,4 strain can be obtained. Figure 1 True stress – strain curves of 6005A aluminum alloy.263H. Q. ZHANG et al.: RESEARCH ON MODEL OF 6005A ALUMINUM ALLOYMETALURGIJA 60 (2021) 3-4, 261-264  (13)Similarly, the values of m, β, α, n, Q and strain 0,05-0,8 can be calculated by the same method, as shown in Table 1.VERIFY THE ACCURACY OF THE MODELThe Arrhenius constitutive model is used to predict the flow stress of 6005A aluminum alloy, and the pre-dicted results are compared with experimental data. The result obtained is shown in Figure 5 In order to more accurately illustrate the accuracy of the equation predic-tion, according to equation (14) and equation (15), the standard statistical parameter (R) and the average abso-lute relative error AARE (%) are used.   (14)   (15)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 2 shows the comparison be-tween experimental and predicted values under the Ar-Table 1 Values of m, β, α, n, Q and lnCp Strain0,05 0,1 0,2m 10,925 10,353 9,375β 0,2042 0,1917 0,1714α 0,01869 0,01852 0,01828n 8,184 7,752 7,004Q 219972,13 229013,74 238334,51lnC 33,6897 35,2725 37,0204p 0,3 0,4 0,5m 9,135 8,826 8,647β 0,1707 0,1670 0,1668α 0,01869 0,01892 0,01929n 6,821 6.590 6,459Q 242560,79 243440,15 242334,22lnC 37,7512 38,0144 37,9198p 0,6 0,7 0,8m 8,677 8,758 9,426β 0,1705 0,1764 0,2010α 0,01965 0,02014 0,02132n 6,487 6,543 7,079Q 240114,36 240174,26 244736,79lnC 37,5353 37,4450 37,8006Figure 2  Comparison of predicted and experimental values of flow stress 264H. Q. ZHANG et al.: RESEARCH ON MODEL OF 6005A ALUMINUM ALLOY METALURGIJA 60 (2021) 3-4, 261-264rhenius constitutive model. As can be seen from the figure, the predicted values of each point are almost consistent with the experimental values. This shows that the Arrhenius constitutive model has a higher pre-diction accuracy for the prediction of the flow stress of 6005A aluminum alloy. Figure 3 shows the correlation between experimen-tal values and predicted data. As can be seen from the figure, the prediction results are usually highly corre-lated. The correlation coefficient is R = 0,992, AARE (%) = 4,828 % and less than 10 %. CONCLUSIONThe true stress-true strain curve under the same con-ditions is consistent. It increases suddenly, then slowly decreases after reaching a peak, and finally becomes stable. Deformation temperature and strain rate have a significant effect on the stress and strain curve of 6005A aluminum alloy. The value of flow stress increases with the increase of strain rate, and decreases with the in-crease of deformation temperature. The Arrhenius constitutive model of 6005A alu-minum alloy was obtained at a strain of 0,05 to 0,8. Af-ter calculation, the correlation coefficient is R = 0,992, AARE (%) = 4,828 % is less than 10 %. The forecast meets the expected accuracy.AcknowledgmentsThis work is support by the Tangshan talent founda-tion innovation team (20130204D) and funded by S&P Program of Hebei (Grant No.19012204Z), Tangshan science and technology major special project (19140203F).REFERENCES[1] 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)5, 524-531.[2] Cornacchia G., Cecchel S., Panvini A. A comparative stu-dy of mechanical properties of metal inert gas (MIG)-cold metal transfer (CMT) and fiber laser-MIG hybrid welds for 6005A T6 extruded sheet[J]. International Journal of Advanced Manufacturing Technology 94(2018)5, 2017-2030.[3] Lin Y. C., Chen M. S., Zhang J. Modeling of flow stress of 42CrMo steel under hot compression[J]. Materials Science & Engineering:A 499(2009)1-2,88-92.[4] Cao J., Li F. G., Ma W. F., et al. Constitutive equation for describing true stress–strain curves over a large range of strains[J]. Philosophical Magazine Letters 100 (2020) 10, 476-485.[5] Sellars C. M., Mctegart W.J.. On the mechanism of hot deformation[J]. Acta Metallurgica 14(1966)9,1136-1138.[6] Cai Z. M., Ji. H. C., Pei W. C., et al. Constitutive model of 3Cr23Ni8Mn3N heat-resistant steel based on back propa-gation (BP) neural network (NN) [J]. Metalurgija 58(2019)3-4, 191-195.[7] Samantaray D, Mandal S, Bhaduri A K. A comparative stu-dy on Johnson Cook, modified Zerilli–Armstrong and Arrhenius-type constitutive models to predict elevated temperature flow behavior in modified 9Cr–1Mo steel[J]. Computational Materials Science 47(2009)2, 568-576.Note:  The responsible translator for English language is Z S Peng-North China University of Science and Technology, ChinaFigure 3  Correlation between experimental flow stress and predicted flow stress of 6005A aluminum alloy

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