Constitutive analysis of Cu-DHP alloy during hot compression
Keywords:
Cu-DHP alloy, Hot working, Constitutive modeling, Power law breakdown, Strain rate sensitivity index
Abstract
The hot deformation behavior of the deoxidized high-phosphorus copper (Cu-DHP) was investigated during compressive deformation at a wide deformation temperature range of 200 to 1000 °C and strain rates ranging from 0.0005 to 0.4 s-1. The flow curves related to the hot working regime (500 to 1000 °C) generally showed distinct peak stresses with the fall of flow stress after the peak point, revealing the occurrence of dynamic recrystallization (DRX). By increasing the Zener-Hollomon parameter, the cyclic flow curves were replaced by the single-peak ones, and finally by the characteristic dynamic recovery (DRV) curves. At temperatures lower than half of the melting point, only DRV-type curves were observed. Based on the constitutive analysis, the apparent activation energy of 274.1 kJ/mol, hyperbolic sine power of 4.88, and power law stress exponent of 5.27 were obtained, resulting in the flow stress equations to describe material flow in the hot working regime. The power law breakdown and the importance of deformation temperature were also critically discussed based on mathematical fitting, strain rate sensitivity index, and microstructural analysis.
References
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[2] Ban, Y., Zhang, Y., Jia, Y., Tian, B., Volinsky, A.A., Zhang, X., Zhang, Q., Geng, Y., Liu, Y. and Li, X., 2020. Effects of Cr addition on the constitutive equation and precipitated phases of copper alloy during hot deformation. Materials & Design, 191, p.108613.
[3] Liu, Y., Liu, D., Du, Y., Liu, S., Kuang, D., Deng, P., Zhang, J., Du, C., Zheng, Z. and He, X., 2017. Calculated interdiffusivities resulting from different fitting functions applied to measured concentration profiles in Cu-rich fcc Cu–Ni–Sn alloys at 1073 K. Journal of Mining and Metallurgy, Section B: Metallurgy, 53(3), pp.255-255.
[4] Angela, I., Basori, I. and Sofyan, B.T., 2020. Effect of cold rolling and annealing temperature to the characteristics of α+ β'phases in Cu-29.5 Zn-2.5 Al alloy produced by gravity casting. Journal of Mining and Metallurgy, Section B: Metallurgy, 56(1), pp.89-97.
[5] Ghasemi, S., Vaghar, S., Pourzafar, M., Dehghani, H. and Heidarpour, A., 2020. A novel predictive model for estimation of cell voltage in electrochemical recovery of copper from brass: application of gene expression programming. Journal of Mining and Metallurgy, Section B: Metallurgy, 56(2), pp.237-245.
[6] Jiménez-Ruiz, E., Lostado-Lorza, R. and Berlanga-Labari, C., 2024. A Comprehensive Review of Fatigue Strength in Pure Copper Metals (DHP, OF, ETP). Metals, 14(4), p.464.
[7] Taylor, S., Masters, I., Li, Z. and Kotadia, H.R., 2020. Direct observation via in situ heated stage EBSD analysis of recrystallization of phosphorous deoxidised copper in unstrained and strained conditions. Metals and Materials International, 26, pp.1030-1035.
[8] He, D., Chen, X.Y. and Lin, Y.C., 2024. The improved physically-mechanism constitutive model for a Ni-Mo-Cr-based superalloy with the pre-precipitation of μ phase in hot forming. Journal of Alloys and Compounds, p.174934.
[9] Babu, K.A. and Mandal, S., 2017. Regression based novel constitutive analyses to predict high temperature flow behavior in super austenitic stainless steel. Materials Science and Engineering: A, 703, pp.187-195.
[10] Kareem, S.A., Anaele, J.U., Olanrewaju, O.F., Adewale, E.D., Osondu-Okoro, N.C., Aikulola, E.O., Falana, S.O., Gwalani, B., Bodunrin, M.O. and Alaneme, K.K., 2024. Insights into hot deformation of medium entropy alloys: Softening mechanisms, microstructural evolution, and constitutive modelling—a comprehensive review. Journal of Materials Research and Technology.
[11] Martin, P., Muñoz, J.A., Ferrari, B., Sanchez-Herencia, A.J., Aguilar, C. and Cabrera, J.M., 2024. Microstructure and constitutive modeling of an ultrafine-grained refractory high-entropy alloy fabricated by powder metallurgy. Journal of Materials Research and Technology, 30, pp.7910-7926.
[12] Lin, Y.C., Huang, J., Li, H.B. and Chen, D.D., 2018. Phase transformation and constitutive models of a hot compressed TC18 titanium alloy in the α+ β regime. Vacuum, 157, pp.83-91.
[13] Savaedi, Z., Motallebi, R. and Mirzadeh, H., 2022. A review of hot deformation behavior and constitutive models to predict flow stress of high-entropy alloys. Journal of Alloys and Compounds, 903, p.163964.
[14] Belyakov, A., Miura, H. and Sakai, T., 1998. Dynamic recrystallization under warm deformation of polycrystalline copper. ISIJ international, 38(6), pp.595-601.
[15] Zhang, Y., Volinsky, A.A., Xu, Q.Q., Chai, Z., Tian, B., Liu, P. and Tran, H.T., 2015. Deformation behavior and microstructure evolution of the Cu-2Ni-0.5 Si-0.15 Ag alloy during hot compression. Metallurgical and Materials Transactions A, 46, pp.5871-5876.
[16] Alaneme, K.K., Kareem, S.A. and Bodunrin, M.O., 2023. Hyperbolic–sine constitutive model determined hot deformation mechanisms and workability response of Al–Zn/Cu and Al–Zn/SiC based composites. Results in Engineering, 19, p.101255.
[17] Prasad, Y.V.R.K. and Rao, K.P., 2021. Kinetics and dynamics of hot deformation of OFHC copper in extended temperature and strain rate ranges. International Journal of Materials Research, 96(1), pp.71-77.
[18] Prasad, Y.V.R.K. and Rao, K.P., 2005. Processing maps and rate controlling mechanisms of hot deformation of electrolytic tough pitch copper in the temperature range 300–950 C. Materials Science and Engineering: A, 391(1-2), pp.141-150.
[19] Liu, Y., Xiong, W., Yang, Q., Zeng, J.W., Zhu, W. and Sunkulp, G., 2018. Constitutive behavior and processing map of T2 pure copper deformed from 293 to 1073 K. Journal of Materials Engineering and Performance, 27, pp.1812-1824.
[20] Yang, J.Y. and Kim, W.J., 2020. Examination of high-temperature mechanisms and behavior under compression and processing maps of pure copper. Journal of Materials Research and Technology, 9(1), pp.960-968.
[21] Mirzadeh, H., 2015. Physically based constitutive description of OFHC copper at hot working conditions. Kovove Mater., 53, pp.105-111.
[22] Huang, S.H., Chai, S.X., Xia, X.S., Chen, Q. and Shu, D.Y., 2016. Compression deformation behavior and processing map of pure copper. Strength of Materials, 48(1), pp.98-106.
[23] Chen, G., Jin, Y., Wang, J., Zhang, C., Chen, Q., Zhang, H., Zhao, X., Li, Z., Xie, C. and Du, Z., 2022. Dislocation density-based constitutive model and processing map for T2 copper during isothermal and time-variant deformation. Metals and Materials International, 28(9), pp.2134-2145.
[24] Galvao, I., Loureiro, A. and Rodrigues, D.M.E., 2012. Influence of process parameters on the mechanical enhancement of copper-DHP by FSP. Advanced Materials Research, 445, pp.631-636.
[25] Leal, R.M., Almeida Leitão, C.M., Loureiro, A., Rodrigues, D.M.E. and Vilaça, P., 2010, March. Microstructure and hardness of friction stir welds in pure copper. In Materials Science Forum (Vol. 636, pp. 637-642). Trans Tech Publications Ltd.
[26] Iordache, D.M., Oprescu, E.R., Malea, C.I., Niţu, E.L., Crăcănel, M.O. and Bădulescu, C., 2021, October. Determination of Johnson-Cook material constants for Copper using traction tests and inverse identification. In IOP Conference Series: Materials Science and Engineering (Vol. 1182, No. 1, p. 012032). IOP Publishing.
[27] Kumar, A. and Brar, G.S., 2021. Numerical investigation of friction crush welding aluminium and copper sheet metals with flanged edges. In E3S Web of Conferences (Vol. 309, p. 01015). EDP Sciences.
[28] Zhao, G., Tian, Y., Li, H., Ma, L., Li, Y. and Li, J., 2024. Microstructure evolution and dynamic recrystallization mechanisms of 316L stainless steel during hot deformation. Archives of Civil and Mechanical Engineering, 24(1), p.35.
[29] Phaniraj, C., Samantaray, D., Mandal, S. and Bhaduri, A.K., 2011. A new relationship between the stress multipliers of Garofalo equation for constitutive analysis of hot deformation in modified 9Cr–1Mo (P91) steel. Materials Science and Engineering: A, 528(18), pp.6066-6071.
[30] McQueen, H.J. and Ryan, N.D., 2002. Constitutive analysis in hot working. Materials Science and Engineering: A, 322(1-2), pp.43-63.
[31] Motallebi, R., Savaedi, Z. and Mirzadeh, H., 2022. Additive manufacturing–A review of hot deformation behavior and constitutive modeling of flow stress. Current Opinion in Solid State and Materials Science, 26(3), p.100992.
[32] Blaz, L., Sakai, T. and Jonas, J.J., 1983. Effect of initial grain size on dynamic recrystallization of copper. Metal Science, 17(12), pp.609-616.
[33] Langdon, T.G., 2022. Identifying creep mechanisms in plastic flow. International Journal of Materials Research, 96(6), pp.522-531.
[34] Mukherjee, A.K., 2002. An examination of the constitutive equation for elevated temperature plasticity. Materials Science and Engineering: A, 322(1-2), pp.1-22.
[35] Mirzadeh, H., Cabrera, J.M. and Najafizadeh, A., 2011. Constitutive relationships for hot deformation of austenite. Acta materialia, 59(16), pp.6441-6448.
[36] Hosford, W.F., 2010. Mechanical behavior of materials. Cambridge university press.
[37] Rösler, J., Harders, H. and Bäker, M., 2007. Mechanical behaviour of engineering materials: metals, ceramics, polymers, and composites. Springer Science & Business Media.
[38] Belyakov, A., Gao, W., Miura, H. and Sakai, T., 1998. Strain-induced grain evolution in polycrystalline copper during warm deformation. Metallurgical and Materials Transactions A, 29, pp.2957-2965.
[39] Wusatowska-Sarnek, A.M., 2005. The new grain formation during warm and hot deformation of copper. Journal of Engineering Materials and Technology, 127, pp.295-300.
Published
2025/12/19
How to Cite
Kalhor, A., Rodak, K., Maleki, M., Sohrabi, M. J., Mobasheri, M., Mirzadeh, H., & Habibi Parsa, M. (2025). Constitutive analysis of Cu-DHP alloy during hot compression. Journal of Mining and Metallurgy, Section B: Metallurgy, 61(2), 221-231. Retrieved from https://aseestant.ceon.rs/index.php/jmm/article/view/55770
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