Skip to main content
SpringerLink
Log in

Constitutive Equations, Processing Maps, and Microstructures of Pb-Mg-Al-B-0.4Y Alloy under Hot Compression

  • Published:
Journal of Materials Engineering and Performance Aims and scope Submit manuscript

Abstract

Hot compression behaviors of Pb-Mg-Al-B-0.4Y alloy under strain rate of 0.001-1 s−1 and temperature of 493-613 K were performed by employing hot compressing tests. According to the experimental stress–strain curves, as the strain increases, the flow stress increases firstly, then reaches the peak stress, and finally decreases to a steady state. Constitutive equations in traditional Arrhenius model and improved Arrhenius model in multi-linear regression were used to predict the flow stress of Pb-Mg-Al-B-0.4Y alloy. The values of MARE and RMSE in the traditional Arrhenius model are 11.780 and 21.169%, respectively, which are larger than 7.227 and 7.447% of the improved Arrhenius model, indicating that the predicted accuracy of the improved Arrhenius model is more accurate. The hot processing maps under the experimental conditions were established. Based on processing maps and microstructure observation, the optimum processing parameters are 0.001 s−1 ≤ \(\dot{\varepsilon }\) ≤ 0.01 s−1 and 587 K ≤ T ≤ 613 K.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

References

  1. W.R. Osório, D.M. Rosa, and A. Garcia, The Roles of Cellular and Dendritic Microstructural Morphologies on the Corrosion Resistance of Pb-Sb Alloys for Lead Acid Battery Grids, J. Power Sources, 2008, 175, p 595–603

    Google Scholar 

  2. J. Zeng, W. Chen, W. Yan, Y. Yang, and A. McLean, Effect of Permanent Magnet Stirring on Solidification of Sn-Pb Alloy, Mater. Des., 2016, 108, p 364–373

    CAS  Google Scholar 

  3. Y. Pan, Theoretical Discovery of High Capacity Hydrogen Storage Metal Tetrahydrides, Int. J. Hydrog. Energy, 2019, 44, p 18153–18158

    CAS  Google Scholar 

  4. Y. Pan, Y. Li, and Q. Zheng, Influence of Ir Concentration on the Structure, Elastic Modulus and Elastic Anisotropy of Nb-Ir Based Compounds from First-Principles Calculations, J. Alloys Compd., 2019, 789, p 860

    CAS  Google Scholar 

  5. Y. Pan, First-Principles Investigation of the New Phases and Electrochemical Properties of MoSi2 as the Electrode Materials of Lithium Ion Battery, J. Alloys Compd., 2019, 779, p 813–820

    CAS  Google Scholar 

  6. A. Iddaoudi, C. Servant, N. Selhaoui, S. Kardellass, K. Mahdouk, and L. Bouirden, Thermodynamic Modeling of the RE-Pb (RE = Sc, Dy, Gd) Systems, J. Alloys Compd., 2014, 589, p 192–199

    CAS  Google Scholar 

  7. Y.Y. Liu, G.B. Jia, and B. Yang, Molecular Dynamics Simulation on Diffusion Properties of Pb-Mg Alloy, Sci. China Ser. E Technol. Sci., 2010, 53, p 2328–2332

    CAS  Google Scholar 

  8. Z.C. Sun, H.L. Wu, J. Cao, and Z.K. Yin, Modeling of Continuous Dynamic Recrystallization of Al-Zn-Cu-Mg Alloy During Hot Deformation Based on the Internal-State-Variable (ISV) Method, Int. J. Plast., 2018, 106, p 73–87

    CAS  Google Scholar 

  9. L. Wen, K. Yu, H. Xiong, Y. Dai, S. Yang, X. Qiao, F. Teng, and S. Fan, Composition Optimization and Electrochemical Properties of Mg-Al-Pb-(Zn) Alloys as Anodes for Seawater Activated Battery, Electrochim. Acta, 2016, 194, p 40–51

    CAS  Google Scholar 

  10. B.B. Pai, U.T.S. Pillai, P. Manikandan, and A. Srinivasan, Modification of AZ91 Mg Alloys for High Temperature Applications, Trans. Indian Inst. Met., 2012, 65, p 601–606

    CAS  Google Scholar 

  11. G.H. Park, J.T. Kim, H.J. Park, Y.S. Kim, H.J. Jeong, N. Lee, Y. Seo, J.Y. Suh, H.T. Son, W.M. Wang, J.M. Park, and K.B. Kim, Development of Lightweight Mg-Li-Al Alloys with High Specific Strength, J. Alloys Compd., 2016, 680, p 116–120

    CAS  Google Scholar 

  12. N. Wang, R. Wang, C. Peng, B. Peng, Y. Feng, and C. Hu, Discharge Behaviour of Mg-Al-Pb and Mg-Al-Pb-In Alloys as Anodes for Mg-Air Battery, Electrochim. Acta, 2014, 149, p 193–205

    CAS  Google Scholar 

  13. M. Socjusz-Pedosek and L. Lityńska, Effect of Yttrium on Structure and Mechanical Properties of Mg Alloys, Mater. Chem. Phys., 2003, 80, p 472–475

    Google Scholar 

  14. C.C. Jain and C.H. Koo, Creep and Corrosion Properties of the Extruded Magnesium Alloy Containing Rare Earth, Mater. Trans., 2007, 48, p 265–272

    CAS  Google Scholar 

  15. M. Mabuehi and Y. Chino, Tensile Properties at Room Temperature to 823 K of Mg-4Y-3RE Alloy, Mater. Trans., 2002, 43(8), p 2063–2068

    Google Scholar 

  16. A. Rusinek, J.A. Rodríguez-Martínez, and A. Arias, A Thermo-Viscoplastic Constitutive Model for FCC Metals with Application to OFHC Copper, Int. J. Mech. Sci., 2010, 52, p 120–135

    Google Scholar 

  17. H. Shin and J.B. Kim, A Phenomenological Constitutive Equation to Describe Various Flow Stress Behaviors of Materials in Wide Strain Rate and Temperature Regimes, J. Eng. Mater. Technol., 2010, 132, p 021009

    Google Scholar 

  18. T. Al-Samman and G. Gottstein, Deformation Microstructures of Mg-3Al-1Zn Magnesium Alloy Compressed Over Wide Regions of Temperature and Strain Rate, Mater. Sci. Eng. A, 2008, 490, p 411–420

    Google Scholar 

  19. H.G. Jeong, Y.G. Jeong, and W.J. Kim, Micro-Forming of Zr 65 Al 10 Ni 10 Cu 15 Metallic Glasses Under Superplastic Condition, J. Alloys Compd., 2009, 483, p 279–282

    CAS  Google Scholar 

  20. J.A. del Valle and O.A. Ruano, Influence of Texture on Dynamic Recrystallization and Deformation Mechanisms in Rolled or ECAPed AZ31 Magnesium Alloy, Mater. Sci. Eng. A, 2008, 487, p 473–480

    Google Scholar 

  21. S.M. Fatemi-Varzaneh, A. Zarei-Hanzaki, and H. Beladi, Dynamic Recrystallization in AZ31 Magnesium Alloy, Mater. Sci. Eng. A, 2007, 456, p 52–57

    Google Scholar 

  22. J.G. Niu, X. Zhang, Z.M. Zhang, and B.C. Li, Influence on the Microstructure and Properties of AZ61 Magnesium Alloy at Warm Deformation, J. Mater. Process. Technol., 2007, 187–188, p 780–782

    Google Scholar 

  23. X. Zhou, M. Wang, Y. Fu, Z. Wang, Y. Li, S. Yang, H. Zhao, and H. Li, Effect of Borides on Hot Deformation Behavior and Microstructure Evolution of Powder Metallurgy High Borated Stainless Steel, Mater. Charact., 2017, 124, p 182–191

    CAS  Google Scholar 

  24. H.J. McQueen and N.D. Ryan, Constitutive Analysis in Hot Working, Mater. Sci. Eng. A, 2002, 322, p 43–63

    Google Scholar 

  25. D. Sang, R. Fu, and Y. Li, Combined Deformation Behavior and Microstructure Evolution of 7050 Aluminum Alloy During Hot Shear-Compression Deformation, Mater. Charact., 2016, 122, p 154–161

    CAS  Google Scholar 

  26. C.M. Sellars and W.J. McTegart, On the Mechanism of Hot Deformation, Acta Metall., 1966, 14, p 1136–1138

    CAS  Google Scholar 

  27. Y. Duan, P. Li, L. Ma, and R. Li, Dynamic Recrystallization and Processing Map of Pb-30Mg-9Al-1B Alloy During Hot Compression, Metall. Mater. Trans. A, 2017, 48, p 3419–3431

    CAS  Google Scholar 

  28. Y.H. Duan, Hot Deformation and Processing Map of Pb-Mg-10Al-1B Alloy, J. Mater. Eng. Perform., 2013, 22, p 3049–3054

    CAS  Google Scholar 

  29. Y.H. Duan, L.S. Ma, R.Y. Li, and P. Li, Developed Constitutive Models, Processing Maps and Microstructural Evolution of Pb-Mg-10Al-0.5 B alloy, Mater. Charact., 2017, 129, p 353–366

    CAS  Google Scholar 

  30. C. Zener and J.H. Hollomon, Effect of Strain-Rate Upon the Plastic Flow of Steel, J. Appl. Phys., 1944, 15, p 22–27

    Google Scholar 

  31. W.I. Zuzin, M.Y. Browman, and A.E.F. Melikov, Flow Resistance of Steel at Hot Forming, Metallurgy, Moscow, 1964

    Google Scholar 

  32. Y.C. Lin and X.M. Chen, A Critical Review of Experimental Results and Constitutive Descriptions for Metals and Alloys in Hot Working, Mater. Des., 2011, 32, p 1733–1759

    CAS  Google Scholar 

  33. S. Mandal, V. Rakesh, P.V. Sivaprasad, S. Venugopal, and K.V. Kasiviswanathan, Constitutive Equations to Predict High Temperature Flow Stress in a Ti-Modified Austenitic Stainless Steel, Mater. Sci. Eng. A, 2009, 500, p 114–121

    Google Scholar 

  34. W. Li, H. Li, Z.X. Wang, and Z.Q. Zheng, Constitutive Equations for High Temperature Flow Stress Prediction of Al–14Cu–7Ce Alloy, Mater. Sci. Eng. A, 2011, 528, p 4098–4103

    Google Scholar 

  35. D. Samantaray, C. Phaniraj, S. Mandal, and A.K. Bhaduri, Strain Dependent Rate Equation to Predict Elevated Temperature Flow Behavior of Modified 9Cr-1Mo (P91) Steel, Mater. Sci. Eng. A, 2011, 528, p 1071–1077

    Google Scholar 

  36. J. Zhao, H. Ding, W. Zhao, M. Huang, D. Wei, and Z. Jiang, Modelling of the Hot Deformation Behaviour of a Titanium Alloy Using Constitutive Equations and Artificial Neural Network, Comput. Mater. Sci., 2014, 92, p 47–56

    CAS  Google Scholar 

  37. P.M. Phaniraj and K.A. Lahiri, The Applicability of Neural Network Model to Predict Flow Stress for Carbon Steels, J. Mater. Proc. Tech., 2003, 141, p 219–227

    CAS  Google Scholar 

  38. Y.C. Lin and G. Liu, Effects of Strain on the Workability of a High Strength Low Alloy Steel in Hot Compression, Mater. Sci. Eng. A, 2009, 523, p 139–144

    Google Scholar 

  39. T.D. Kil, J.M. Lee, and Y.H. Moon, Quantitative Formability Estimation of Ring Rolling Process by Using Deformation Processing Map, J. Mater. Process. Technol., 2015, 220, p 224–230

    CAS  Google Scholar 

  40. Y.V.R.K. Prasad, Recent Advances in the Science of Mechanical Processing, Ind. J. Technol., 1990, 28, p 435–451

    CAS  Google Scholar 

  41. Y.V.R.K. Prasad, H.L. Gegel, S.M. Doraivelu, J.C. Malas, J.T. Morgan, K.A. Lark, and D.R. Barker, Modeling of Dynamic Material Behavior in Hot Deformation: Forging of Ti-6242, Metall. Mater. Trans. A, 1984, 15, p 1883–1892

    Google Scholar 

  42. Y.V.R.K. Prasad and T. Seshacharyulu, Modelling of Hot Deformation for Microstructural Control, Int. Mater. Rev., 1998, 43, p 243–252

    CAS  Google Scholar 

  43. Y.V.R.K. Prasad, D.H. Sastry, and S.C. Deevi, Processing Maps for Hot Working of a P/M Iron Aluminide Alloy, Intermetallics, 2000, 8, p 1067–1074

    CAS  Google Scholar 

  44. H.Z. Li, H.J. Wang, Z. Li, C.M. Liu, and H.T. Liu, Flow Behavior and Processing Map of as-cast Mg-10Gd-4.8 Y-2Zn-0.6 Zr Alloy, Mater. Sci. Eng. A, 2010, 528, p 154–160

    Google Scholar 

  45. Z.W. Cai, Z.W. Chen, F.X. Ma, F.J. Guo, and J. Qing, Dynamic Recrystallization Behavior and Hot Workability of AZ41M Magnesium Alloy During Hot Deformation, J. Alloys Compd., 2016, 670, p 55–63

    CAS  Google Scholar 

  46. S. Ramanathan, R. Karthikeyan, and G. Ganasen, Development of Processing Maps for 2124Al/SiCp Composites, Mater. Sci. Eng., A, 2006, 441, p 321–325

    Google Scholar 

  47. R. Raj, Development of a Processing Map for use in Warm-Forming and Hot-Forming Processes, Metal. Trans. A, 1981, 12, p 1089–1097

    CAS  Google Scholar 

  48. H. Wu, S.P. Wen, H. Huang, B.L. Li, X.L. Wu, K.Y. Gao, W. Wang, and Z.N. Nie, Effects of Homogenization on Precipitation of Al3(Er, Zr) Particles and Recrystallization Behavior in a New Type Al-Zn-Mg-Er-Zr Alloy, Mater. Sci. Eng., A, 2017, 698, p 313–322

    Google Scholar 

Download references

Acknowledgments

This work was supported by the Yunnan Ten Thousand Talents Plan Young & Elite Talents Project under Grant No. YNWR-QNBJ-2018-044, the Reserve Talents Project of Yunnan Province under Grant No. 2015HB019, and the National Natural Science Foundation of China under Grant No. 51761023.

Author information

Authors and Affiliations

  1. Faculty of Material Science and Engineering, Kunming University of Science and Technology, Kunming, 650093, China

    Weizong Bao, Longke Bao, Dan Liu, Deyi Qu, Zhuangzhuang Kong, Mingjun Peng & Yonghua Duan

Authors
  1. Weizong Bao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Longke Bao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Dan Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Deyi Qu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Zhuangzhuang Kong
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Mingjun Peng
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Yonghua Duan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yonghua Duan.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bao, W., Bao, L., Liu, D. et al. Constitutive Equations, Processing Maps, and Microstructures of Pb-Mg-Al-B-0.4Y Alloy under Hot Compression. J. of Materi Eng and Perform 29, 607–619 (2020). https://doi.org/10.1007/s11665-019-04544-8

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11665-019-04544-8

Keywords

Search

Navigation