Skip to main content
Log in

Zr–Nb Alloys and Its Hot Deformation Analysis Approaches

  • Published:
Metals and Materials International Aims and scope Submit manuscript

Abstract

Zr and its alloys are considered as strategic materials for nuclear industry. In nuclear industries, zirconium and its alloys are mostly used to manufacture the tubes for reactors. The properties of the end component i.e. tube is fully dependent on the material processing route and the final microstructure. Therefore, in the present review paper, brief description of zirconium and its alloys is provided, bringing in the effect of various phase stabilizers and the microstructures after processing. Additionally, the processing route of Zr and Zr–Nb alloys are explained in terms of primary and secondary processing. In primary processing, the production of usable shapes is obtained through ingot melting followed by secondary operations such hot rolling or forging. Further, optimization of mechanical properties can be done by controlling the microstructure using various thermo-mechanical processes. The secondary processing such as cold working and/or annealing also helps to control the final microstructure to large extent. The microstructure control is fully dependent on the dominant deformation mechanism during the hot deformation. The dominant deformation mechanism depends on relative ease with which following processes occur; dislocation generation and glide, cross slip and climb and, diffusion. The possible restoration mechanisms for different Zr-alloys are discontinuous dynamic recrystallization (DDRX), continuous dynamic recrystallization (CDRX), rotational recrystallization (RRX), geometric dynamic recrystallization (GDX), dynamic recovery (DRV) accompanied by grain growth (GG). There are various techniques which helps to understand the hot deformation behaviour of any material. These techniques are; analysis of stress–strain data, development of processing maps, development of constitute equation. At the end, present paper summarises the work related to processing map, findings of processing map in terms of safe processing parameter, dominant deformation mechanism, role of activation energies during deformation of Zr–Nb alloys and their different phases (i.e. single α or β phase, or two phase α + β).

Graphic Abstract

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

Access this article

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
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25

Similar content being viewed by others

References

  1. W.W. Stephens, Extractive metallurgy of zirconium—1945 to the present, in Zirconium in the Nuclear IndustrySixth International Symposium, American Society for Testing and Materials-ASTM Vancouver, Canada, ed. by Franklin/Adamson (1984)

  2. Thermophysical properties of material for nuclear engineering: a tutorial and collection of data. (report) Nuclear Power Technology Development Section, International Atomic Energy Agency, Vienna, Austria: 2008, ISBN 978–92–0–106508–7.

  3. R.W.L. Fong, R. Miller, H.J. Saari, S.C. Vogel, Crystallographic texture and volume fraction of α and β phases in Zr-2.5Nb pressure tube material during heating and cooling. Metall. Mater. Trans. A Phys. Metall. Mater. Sci. 43, 806–821 (2012). https://doi.org/10.1007/s11661-011-0914-6

    Article  CAS  Google Scholar 

  4. Waterside corrosion of zirconium alloys in nuclear power plants, (Report), International Atomic Energy Agency, VIENNA, 1998 IAEA-TECDOC-996, ISSN 1011–4289

  5. J.K. Mackenzie, J.S. Bowles, The crystallography of martensite transformations-IV body-centred cubic to orthorhombic transformations. Acta Metall. 5, 137–149 (1957). https://doi.org/10.1016/0001-6160(57)90018-4

    Article  Google Scholar 

  6. C. Lemaignan, A.T. Motta, Zirconium alloys in nuclear applications. Mater. Sci. Technol. (2006). https://doi.org/10.1002/9783527603978.mst0111

    Article  Google Scholar 

  7. V. Krett, J. Cleveland, N.P.T.D. Section, Thermophysical Properties of Materials for Water Cooled Reactors, Div. Nucl. Power Fuel Cycle, IAEA-TECDOC-949 1–280 (1997)

  8. J.B. Vander Sande, A.L. Bement, An investigation of second phase particles in Zircaloy-4 alloys. J. Nucl. Mater. 52, 115–118 (1974). https://doi.org/10.1016/0022-3115(74)90032-4

    Article  CAS  Google Scholar 

  9. T. Grover, A. Pandey, S.T. Kumari, A. Awasthi, B. Singh, P. Dixit, P. Singhal, K.K. Saxena, Role of titanium in bio implants and additive manufacturing: an overview. Mater. Today Proc. (2020). https://doi.org/10.1016/j.matpr.2020.02.636

    Article  Google Scholar 

  10. E. Vitikainen, P. Nenonen, Transmission electron microscopy studies on intermetallics in some zirconium alloys. J. Nucl. Mater. 78, 362–373 (1978). https://doi.org/10.1016/0022-3115(78)90458-0

    Article  CAS  Google Scholar 

  11. R. Krishnan, M.K. Asundi, Zirconium alloys in nuclear technology. Proc. Indian Acad. Sci. Sect. C Eng. Sci. 4, 41–56 (1981). https://doi.org/10.1007/BF02843474

    Article  CAS  Google Scholar 

  12. S.A. Aldridge, B.A. Cheadle, Age hardening of Zr–2.5 wt% Nb slowly cooled from the (α + β) phase field. J. Nucl. Mater. 42, 32–42 (1972). https://doi.org/10.1016/0022-3115(72)90004-9

    Article  CAS  Google Scholar 

  13. C.D. Williams, R.W. Gilbert, Tempered structures of a Zr–2.5 wt% Nb alloy. J. Nucl. Mater. 18, 161–166 (1966). https://doi.org/10.1016/0022-3115(66)90078-X

    Article  CAS  Google Scholar 

  14. T.R.G. Kutty, K. Ravi, C. Ganguly, Studies on hot hardness of Zr and its alloys for nuclear reactors. J. Nucl. Mater. 265, 91–99 (1999). https://doi.org/10.1016/S0022-3115(98)00610-2

    Article  CAS  Google Scholar 

  15. M. Christensen, W. Wolf, C.M. Freeman, E. Wimmer, R.B. Adamson, L. Hallstadius, P.E. Cantonwine, E.V. Mader, Effect of alloying elements on the properties of Zr and the Zr–H system. J. Nucl. Mater. 445, 241–250 (2014). https://doi.org/10.1016/j.jnucmat.2013.10.040

    Article  CAS  Google Scholar 

  16. G.C. Weatherly, The precipitation of γ-hydride plates in zirconium. Acta Metall. 29, 501–512 (1981). https://doi.org/10.1016/0001-6160(81)90074-2

    Article  CAS  Google Scholar 

  17. J.J. Kearns, C.R. Woods, Effect of texture, grain size, and cold work on the precipitation of oriented hydrides in Zircaloy tubing and plate. J. Nucl. Mater. 20, 241–261 (1966). https://doi.org/10.1016/0022-3115(66)90036-5

    Article  CAS  Google Scholar 

  18. J.S. Bradbrook, G.W. Lorimer, N. Ridley, The precipitation of zirconium hydride in zirconium and zircaloy-2. J. Nucl. Mater. 42, 142–160 (1972). https://doi.org/10.1016/0022-3115(72)90021-9

    Article  CAS  Google Scholar 

  19. A. Miquet, D. Charquet, C. Michaut, C.H. Allibert, Effect of Cr, Sn and O contents on the solid state phase boundary temperatures of Zircaloy-4. J. Nucl. Mater. 105, 142–148 (1982). https://doi.org/10.1016/0022-3115(82)90368-3

    Article  CAS  Google Scholar 

  20. D. Arias, J.P. Abriata, The Cr − Zr (Chromium–Zirconium) system. Bull. Alloy Phase Diagr. 7, 237–244 (1986). https://doi.org/10.1007/BF02868997

    Article  CAS  Google Scholar 

  21. R.W.L. Fong, Anisotropic deformation of Zr–2. 5Nb pressure tube material at high temperatures. J. Nucl. Mater. 440, 467–476 (2013). https://doi.org/10.1016/j.jnucmat.2013.01.308

    Article  CAS  Google Scholar 

  22. H.H. Klepfer, Zirconium–niobium binary alloys for boiling water reactor service part I—corrosion resistance. J. Nucl. Mater. 9, 65–76 (1963). https://doi.org/10.1016/0022-3115(63)90169-7

    Article  CAS  Google Scholar 

  23. H.H. Klepfer, Zirconium–niobium binary alloys for boiling water reactor service part II—corrosion hydrogen embrittlement. J. Nucl. Mater. 9, 77–84 (1963). https://doi.org/10.1016/0022-3115(63)90170-3

    Article  Google Scholar 

  24. J. Park, B. Choi, S.J. Yoo, Y.H. Jeong, Corrosion behavior and oxide properties of Zr–1. 1 wt% Nb–0. 05 wt% Cu alloy. J. Nucl. Mater. 359, 59–68 (2006). https://doi.org/10.1016/j.jnucmat.2006.07.017

    Article  CAS  Google Scholar 

  25. J.K. Chakravartty, G.K. Dey, S. Banerjee, Y.V.R.K. Prasad, Characterization of hot deformation behaviour of Zr–2.5Nb–0.5Cu using processing maps. J. Nucl. Mater. 218, 247–255 (1995). https://doi.org/10.1016/0022-3115(94)00379-3

    Article  CAS  Google Scholar 

  26. N. Saibaba, S. Jha, S. Tonpe, K. Vaibhaw, V. Deshmukh, S. Ramana Rao, K. Mani Krishna, S. Neogy, D. Srivastava, G. Dey, R. Kulkarni, B. Rath, E. Ramadasan, S. Anantharaman, Microstructural studies of heat treated Zr-2.5Nb alloy for pressure tube applications. J. ASTM Int. 8(6), 1–15 (2011). https://doi.org/10.1520/JAI103213

  27. B. Hutchinson, B. Lehtinen, M. Limbäck, M. Dahlbäck, A study of the structure and chemistry in Zircaloy-2 and the resulting oxide after high temperature corrosion. J. ASTM Int. 4(10), 1–13 (2007). https://doi.org/10.1520/JAI101106

  28. A.R. Massih, T. Andersson, P. Witt, M. Dahlbäck, M. Limbäck, Effect of quenching rate on the β-to-α phase transformation structure in zirconium alloy. J. Nucl. Mater. 322, 138–151 (2003). https://doi.org/10.1016/S0022-3115(03)00323-4

    Article  CAS  Google Scholar 

  29. S. Banerjee, R. Krishnan, Martensitic transformation in zirconium–niobium alloys. Acta Metall. 19, 1317–1326 (1971). https://doi.org/10.1016/0001-6160(71)90068-X

    Article  CAS  Google Scholar 

  30. S. Neogy, D. Srivastava, G.K. Dey, J.K. Chakraborty, P.K. De, S. Banerjee, A study on metallurgical properties of two zirconium alloys for high burn-up fuel tube applications, Mumbai (2003). Report BARC--2003/E/027, 35(10). https://doi.org/BARC/2003/E/027

  31. R.E. Logé, Y.B. Chastel, M.Y. Perrin, J.W. Signorelli, R. a. Lebensohn, Hot extrusion of zircaloy-4 tubes: induced crystallographic textures and influence of the initial microstructure, Math. Model. Met. Process. Manuf. The Metallurgical Society of CIM, 35(19), 35038137–35038148 (2000)

  32. S.D. Cramer, J. Bernard, S. Covino (eds.), Corrosion: Environments and Industries (ASM International, Russell Township, 2006)

    Google Scholar 

  33. G. Maussner, E. Steinberg, E. Tenckhoff, Nucleation and growth of intermetallic precipitates in Zircaloy-2 and Zircaloy-4 and correlation to nodular corrosion behavior, in Zirconium in the Nuclear Industry (2008). https://doi.org/10.1520/stp28130s

  34. R.V. Kulkarni, K.V. Mani Krishna, S. Neogy, D. Srivastava, E. Ramadasan, R.S. Shriwastaw, B.N. Rath, N. Saibaba, S.K. Jha, G.K. Dey, Mechanical properties of Zr–2.5%Nb pressure tube material subjected to heat treatments in α + β phase field. J. Nucl. Mater. 451, 300–312 (2014). https://doi.org/10.1016/j.jnucmat.2014.04.005

    Article  CAS  Google Scholar 

  35. W. Peng, W. Zeng, Q. Wang, H. Yu, Characterization of high-temperature deformation behavior of as-cast Ti60 titanium alloy using processing map. Mater. Sci. Eng. A (2013). https://doi.org/10.1016/j.msea.2013.01.008

    Article  Google Scholar 

  36.  F. Humphreys, M. Hatherly, Recrystallization and related annealing phenomena: second edition. J. Chem. Inf. Model. (2004). https://doi.org/10.1016/B978-0-08-044164-1.X5000-2

  37. A. Saboori, M. Dadkhah, M. Pavese, D. Manfredi, S. Biamino, P. Fino, Hot deformation behavior of Zr–1%Nb alloy: flow curve analysis and microstructure observations. Mater. Sci. Eng. A 696, 366–373 (2017). https://doi.org/10.1016/J.MSEA.2017.04.049

    Article  CAS  Google Scholar 

  38. H. Shi, J. Li, J. Mao, W. Lu, The elimination of the yield point phenomenon in a new zirconium alloy: influence of degree of recrystallization on the tensile properties. Scr. Mater. (2019). https://doi.org/10.1016/j.scriptamat.2019.05.008

    Article  Google Scholar 

  39. N. Saibaba, N. Keskar, K. V. Mani Krishna, V. Raizada, K. Vaibhaw, S.K. Jha, D. Srivastava, G.K. Dey, A numerical study of the effect of extrusion parameters on the temperature distribution in Zr–2.5Nb, in: Zirconium in the Nuclear Industry, 17th Vol. (2015) https://doi.org/10.1520/stp154320130023

  40. F.J. Humphreys, M. Hatherly, Recrystallization of Two-Phase Alloys, in Recrystallization and Related Annealing Phenomena (2004). https://doi.org/10.1016/b978-008044164-1/50013-x

  41. R.D. Doherty, D.A. Hughes, F.J. Humphreys, J.J. Jonas, D. Juul Jensen, M.E. Kassner, W.E. King, T.R. McNelley, H.J. McQueen, A.D. Rollett, Current issues in recrystallization: a review. Mater. Sci. Eng. A 238, 219–274 (1997). https://doi.org/10.1016/S0921-5093(97)00424-3

    Article  Google Scholar 

  42. S.E. Ion, F.J. Humphreys, S.H. White, Dynamic recrystallisation and the development of microstructure during the high temperature deformation of magnesium. Acta Metall. (1982). https://doi.org/10.1016/0001-6160(82)90031-1

    Article  Google Scholar 

  43. R.E. Logé, J.W. Signorelli, Y.B. Chastel, M.Y. Perrin, R.A. Lebensohn, Sensitivity of α-ZY4 high-temperature deformation textures to the β-quenched precipitate structure and to recrystallization: application to hot extrusion. Acta Mater. (2000). https://doi.org/10.1016/S1359-6454(00)00179-8

    Article  Google Scholar 

  44. S. Banerjee, S.J. Vijayakar, R. Krishnan, Precipitation in zirconium–niobium martensites. J. Nucl. Mater. 62, 229–239 (1976). https://doi.org/10.1016/0022-3115(76)90019-2

    Article  CAS  Google Scholar 

  45. M.P. Himbeault, D.D. Chow, C.K. Puls, Deformation behavior of irradiated Zr–2.5Nb pressure tube material. Metall. Mater. Trans. A 25, 135–145 (1994)

    Article  Google Scholar 

  46. J.Y. Kim, K.S. Na, Y.D. Kim, J.H. Kim, K.Y. Lee, K.N. Kim, S.J. Kim, Creep behavior of Zr–1.5Nb–0.4Sn–0.1Fe–0.1Cu alloy. Acta Mech. Solida Sin. 21, 308–311 (2008). https://doi.org/10.1007/s10338-008-0835-0

    Article  Google Scholar 

  47. J.K. Chakravartty, R. Kapoor, A. Sarkar, S. Banerjee, Dynamic recrystallization in zirconium alloys. J. ASTM Int. (2010). https://doi.org/10.1520/JAI103003

    Article  Google Scholar 

  48. J. Chakravartty, R. Kapoor, A. Sarkar, S. Banerjee, Dynamic recrystallization in zirconium alloys. J. ASTM Int, 7(8), 1–17 (2010). https://doi.org/10.1520/JAI103003

  49. K. Huang, R.E. Logé, A review of dynamic recrystallization phenomena in metallic materials. Mater. Des. 111, 548–574 (2016). https://doi.org/10.1016/j.matdes.2016.09.012

    Article  CAS  Google Scholar 

  50. J.K. Chakravartty, G.K. Dey, S. Banerjee, Y.V.R.K. Prasad, Dynamic recrystallisation during hot working of Zr–2–5Nb: characterisation using processing maps. Mater. Sci. Technol. 12, 705–716 (1996). https://doi.org/10.1179/mst.1996.12.9.705

    Article  CAS  Google Scholar 

  51. J.K. Chakravartty, Y.V.R.K. Prasad, M.K. Asundi, Processing map for hot working of alpha-zirconium. Metall. Trans. A 22, 829–836 (1991). https://doi.org/10.1007/BF02658992

    Article  Google Scholar 

  52. J.K. Chakravartty, S. Banerjee, Y.V.R.K. Prasad, M.K. Asundi, Hot-working characteristics of Zircaloy-2 in the temperature range of 650–950 °C. J. Nucl. Mater. 187, 260–271 (1992). https://doi.org/10.1016/0022-3115(92)90506-G

    Article  CAS  Google Scholar 

  53. O. Bocharov, S. Zavodchikov, V. Belov, A. Kabanov, V. Kotrekhov, V. Rozhdestvenski, V. Filippov, A. Losistskiy, A. Shikov, Temperature and strain rate effects on Zr–1%Nb alloy deformation. J. ASTM Int. 2, 207–221 (2005). https://doi.org/10.1520/JAI12335

    Article  Google Scholar 

  54. J.K. Chakravartty, S. Banerjee, Y.V.R.K. Prasad, Superplasticity in β-zirconium: a study using a processing map. Scr. Metall. Mater. 26, 75–78 (1992). https://doi.org/10.1016/0956-716X(92)90372-L

    Article  CAS  Google Scholar 

  55. D.L. Douglass, The relative contributions of dispersion and solution strengthening in Zr–Sn–Nb alloys. J. Nucl. Mater. 9, 252–260 (1963). https://doi.org/10.1016/0022-3115(63)90143-0

    Article  CAS  Google Scholar 

  56. Y. Tan, L. Ji, W. Liu, S. Xiang, F. Zhao, Y. Liang, Effect of hot deformation on α → β phase transformation in 47Zr–45Ti–5Al–3 V alloy. Trans. Nonferrous Met. Soc. China 28, 1947–1957 (2018). https://doi.org/10.1016/S1003-6326(18)64840-X

    Article  CAS  Google Scholar 

  57. S. Banerjee, G.K. Dey, D. Srivastava, S. Ranganathan, Plate-shaped transformation products in zirconium-base alloys. Metall. Mater. Trans. A Phys. Metall. Mater. Sci. 28, 2201–2216 (1997). https://doi.org/10.1007/s11661-997-0178-3

    Article  Google Scholar 

  58. P. Gaunt, J.W. Christian, The crystallography of the β–α transformation in zirconium and in two titanium–molybdenum alloys. Acta Metall. 7, 534–543 (1959). https://doi.org/10.1016/0001-6160(59)90189-0

    Article  CAS  Google Scholar 

  59. J.S. Bowles, J.K. Mackenzie, The crystallography of martensite transformations I. Acta Metall. 2, 129–137 (1954). https://doi.org/10.1016/0001-6160(54)90102-9

    Article  CAS  Google Scholar 

  60. A. Sarkar, J.K. Chakravartty, Hot deformation behavior of Zr–1Nb alloy: characterization by processing map. J. Nucl. Mater. 440, 136–142 (2013). https://doi.org/10.1016/j.jnucmat.2013.04.080

    Article  CAS  Google Scholar 

  61. R. Kapoor, J.K. Chakravartty, C.C. Gupta, S.L. Wadekar, Characterization of superplastic behaviour in the (α + β) phase field of Zr–2.5 wt%Nb alloy. Mater. Sci. Eng. A (2005). https://doi.org/10.1016/j.msea.2004.09.023

    Article  Google Scholar 

  62. R. Kapoor, J.K. Chakravartty, Characterization of hot deformation behaviour of Zr–2.5Nb in β phase. J. Nucl. Mater. (2002). https://doi.org/10.1016/S0022-3115(02)01290-4

    Article  Google Scholar 

  63. H.K. Khandelwal, R.N. Singh, A.K. Bind, S. Sunil, B.N. Rath, J.B. Singh, S. Kumar, J.K. Chakravartty, Influence of soaking temperature and time on microstructure and mechanical properties of water quenched Zr–2.5Nb alloy. Mater. Perform. Charact. 3, 51 (2014). https://doi.org/10.1520/mpc20130051

    Article  Google Scholar 

  64. S. Neogy, D. Srivastava, G.K. Dey, J.K. Chakravartty, S. Banerjee, Annealing studies on Zr–1Nb and Zr–1Nb–1Sn–0.1Fe alloys. Trans. Indian Inst. Met. 57, 509–519 (2004)

    CAS  Google Scholar 

  65. K.K. Saxena, V. Pancholi, S.K. Jha, G.P. Chaudhari, D. Srivastava, G.K. Dey, A novel approach to understand the deformation behavior in two phase region using processing map. J. Alloys Compd. 706, 511–519 (2017). https://doi.org/10.1016/j.jallcom.2017.02.177

    Article  CAS  Google Scholar 

  66. Y.V.R.K. Prasad, T. Seshacharyulu, Modelling of hot deformation for microstructural control. Int. Mater. Rev. 43, 243–258 (1998). https://doi.org/10.1179/imr.1998.43.6.243

    Article  CAS  Google Scholar 

  67. S.V.S.N. Murty, B.N. Rao, B.P. Kashyap, Development and validation of a processing map for zirconium alloys. Model. Simul. Mater. Sci. Eng. (2002). https://doi.org/10.1088/0965-0393/10/5/303

    Article  Google Scholar 

  68. D. Halici, C. Poletti, Flow localization modelling in Ti alloys and Ti matrix composites. Key Eng. Mater. 651–653, 3–8 (2015). https://doi.org/10.4028/www.scientific.net/KEM.651-653.3

    Article  Google Scholar 

  69. M. Dikovits, C. Poletti, F. Warchomicka, Deformation mechanisms in the near-β titanium alloy Ti–55531. Metall. Mater. Trans. A Phys. Metall. Mater. Sci. 45, 1586–1596 (2014). https://doi.org/10.1007/s11661-013-2073-4

    Article  CAS  Google Scholar 

  70. B. Kumar, K.K. Saxena, S.R. Dey, V. Pancholi, A. Bhattacharjee, Processing map-microstructure evolution correlation of hot compressed near alpha titanium alloy (TiHy 600). J. Alloys Compd. 691, 906–913 (2017). https://doi.org/10.1016/j.jallcom.2016.08.301

    Article  CAS  Google Scholar 

  71. Y. Xu, L. Hu, Y. Sun, Processing map and kinetic analysis for hot deformation of an as-cast AZ91D magnesium alloy. Mater. Sci. Eng. A 578, 402–407 (2013). https://doi.org/10.1016/j.msea.2013.04.110

    Article  CAS  Google Scholar 

  72. Y.V.R.K. Prasad, K.P. Rao, S. Sasidhara, Hot working guide a compendium of processing maps. ASM Int. (2015). https://doi.org/10.1016/B978-0-08-033454-7.50019-X

    Article  Google Scholar 

  73. S.K. Rajput, M. Dikovits, G.P. Chaudhari, C. Poletti, F. Warchomicka, V. Pancholi, S.K. Nath, Physical simulation of hot deformation and microstructural evolution of AISI 1016 steel using processing maps. Mater. Sci. Eng. A 587, 291–300 (2013). https://doi.org/10.1016/j.msea.2013.08.057

    Article  CAS  Google Scholar 

  74. M.F. Ashby, A first report on deformation-mechanism maps. Acta Metall. 20, 887–897 (1972). https://doi.org/10.1016/0001-6160(72)90082-X

    Article  CAS  Google Scholar 

  75. R. Raj, Development of a processing map for use in warm-forming and hot-forming processes. Metall. Trans. APhys. Metall. Mater. Sci. 12 A, 1089–1097 (1981). https://doi.org/10.1007/BF02643490

    Article  Google Scholar 

  76. Y.V.R.K. Prasad, H.L. Gegel, S.M. Doraivelu, J.C. Malas, J.T. Morgan, K.A. Lark, D.R. Barker, Modeling of dynamic material behavior in hot deformation: forging of Ti–6242. Metall. Trans. A (1984). https://doi.org/10.1007/BF02664902

    Article  Google Scholar 

  77. F. Montheillet, J.J. Jonas, K.W. Neale, Modeling of dynamic material behavior: a critical evaluation of the dissipator power co-content approach. Metall. Mater. Trans. A Phys. Metall. Mater. Sci. 27 A, 232–235 (1996). https://doi.org/10.1007/BF02647764

    Article  Google Scholar 

  78. S.V.S.N. Murty, B.N. Rao, Ziegler’s criterion on the instability regions in processing maps. J. Mater. Sci. Lett. 17, 1203–1205 (1998). https://doi.org/10.1023/A:1006541710533

    Article  Google Scholar 

  79. S.V.S.N. Murty, B.N. Rao, B.P. Kashyap, On the hot working characteristics of 2014 Al–20 vol% Al2O3 metal matrix composite. J. Mater. Process. Technol. 166(2005), 279–285 (2014). https://doi.org/10.1016/j.jmatprotec.2004.09.088

    Article  CAS  Google Scholar 

  80. B.K. Kodli, R. Karre, K.K. Saxena, V. Pancholi, S.R. Dey, A. Bhattacharjee, Flow behaviour of TiHy 600 alloy under hot deformation using gleeble 3800. Adv. Mater. Process. Technol. (2017). https://doi.org/10.1080/2374068X.2017.1342065

    Article  Google Scholar 

  81. B.K. Kodli, K.K. Saxena, S.R. Dey, V. Pancholi, A. Bhattacharjee, Texture studies of hot compressed near alpha titanium alloy (IMI 834) at 1000°C with different strain rates, in IOP Conference Series: Materials Science and Engineering (2015). https://doi.org/10.1088/1757-899X/82/1/012032

  82. P. Yadav, K. Saxena, Effect of heat-treatment on microstructure and mechanical properties of Ti alloys: an overview. Mater. Today Proc. (2020). https://doi.org/10.1016/j.matpr.2020.02.541

    Article  Google Scholar 

  83. K.K. Saxena, K.S. Suresh, R.V. Kulkarni, K.V. Mani Krishna, V. Pancholi, D. Srivastava, Hot deformation behavior of Zr–1Nb alloy in two-phase region—microstructure and mechanical properties. J. Alloys Compd. 741, 281–292 (2018). https://doi.org/10.1016/j.jallcom.2018.01.008

    Article  CAS  Google Scholar 

  84. K.K. Saxena, S.D. Yadav, S. Sonkar, V. Pancholi, G.P. Chaudhari, D. Srivastava, G.K. Dey, S.K. Jha, N. Saibaba, Effect of temperature and strain rate on deformation behavior of zirconium alloy: Zr–2.5Nb. Procedia Mater. Sci. 6, 278–283 (2014). https://doi.org/10.1016/j.mspro.2014.07.035

    Article  CAS  Google Scholar 

  85. K.K. Saxena, S.D. Yadav, S. Sonkar, V. Pancholi, G.P. Chaudhari, D. Srivastava, G.K. Dey, S.K. Jha, N. Saibaba, Effect of temperature and strain rate on deformation behavior of zirconium alloy: Zr–2.5Nb. Procedia Mater. Sci. (2014). https://doi.org/10.1016/j.mspro.2014.07.035

    Article  Google Scholar 

  86. K. Saxena, S. Sonkar, R. Kumar, V. Pancholi, G. Chaudhari, D. Srivastava, G. Dey, S. Jha, N. Saibaba, Effect of temperature and strain rate on deformation behavior of zirconium alloy: Zr–2.5Nb–0.5Cu. Procedia Mater. Sci. 6, 188–193 (2014). https://doi.org/10.1016/j.mspro.2014.07.023

    Article  CAS  Google Scholar 

  87. Y. Sun, W.D. Zeng, Y.Q. Zhao, X.M. Zhang, X. Ma, Y.F. Han, Constructing processing map of Ti40 alloy using artificial neural network. Trans. Nonferrous Met. Soc. China (English Ed.) 21, 159–165 (2011). https://doi.org/10.1016/S1003-6326(11)60693-6

    Article  CAS  Google Scholar 

  88. Y.V.R.K. Prasad, T. Seshacharyulu, Processing maps for hot working of titanium alloys. Mater. Sci. Eng. A 243, 82–88 (1998). https://doi.org/10.1016/s0921-5093(97)00782-x

    Article  Google Scholar 

  89. S.V.S.N. Murty, B.N. Rao, Hot working characteristics of Zr–2–5Nb using processing maps. Mater. Sci. Technol. 14, 835–837 (1998)

    Article  CAS  Google Scholar 

  90. I. Kartika, Y. Li, H. Matsumoto, A. Chiba, Constructing processing maps for hot working of Co–Ni–Cr–Mo superalloy. Mater. Trans. 50, 2277–2284 (2009). https://doi.org/10.2320/matertrans.M2009103

    Article  CAS  Google Scholar 

  91. J.J. Jonas, R.A. Holt, C.E. Coleman, Plastic stability in tension and compression. Acta Metall. 24, 911–918 (1976). https://doi.org/10.1016/0001-6160(76)90039-0

    Article  Google Scholar 

  92. S.V.S.N. Murty, B.N. Rao, On the development of instability criteria during hotworking with reference to IN 718. Mater. Sci. Eng. A 254, 76–82 (1998)

    Article  Google Scholar 

  93. S.V.S.N. Murty, B.N. Rao, On the flow localization concepts in the processing maps of IN718. Mater. Sci. Eng. A 267, 159–161 (1999). https://doi.org/10.1016/S0921-5093(99)00122-7

    Article  Google Scholar 

  94. S.V.S.N. Murty, B.N. Rao, B.P. Kashyap, Identification of flow instabilities in the processing maps of AISI 304 stainless steel. J. Mater. Process. Technol. 166, 268–278 (2005). https://doi.org/10.1016/j.jmatprotec.2004.09.089

    Article  CAS  Google Scholar 

  95. K.K. Saxena, S. Sonkar, V. Pancholi, G.P. Chaudhari, D. Srivastava, G.K. Dey, S.K. Jha, N. Saibaba, Hot deformation behavior of Zr–2.5Nb alloy: a comparative study using different materials models. J. Alloys Compd. 662, 94–101 (2016). https://doi.org/10.1016/j.jallcom.2015.11.183

    Article  CAS  Google Scholar 

  96. E.W. Hart, Theory of the tensile test. Acta Metall. 15, 351–355 (1967). https://doi.org/10.1016/0001-6160(67)90211-8

    Article  CAS  Google Scholar 

  97. S.V.S.N. Murty, B.N. Rao, B.P. Kashyap, Instability criteria for hot deformation of materials. Int. Mater. Rev. 45, 15–26 (2000). https://doi.org/10.1179/095066000771048782

    Article  CAS  Google Scholar 

  98. K.K. Saxena, V. Pancholi, G.P. Chaudhari, D. Srivastava, G.K. Dey, S.K. Jha, N. Saibaba, Hot deformation behaviour and microstructural evaluation of Zr-1Nb alloy, in Materials Science Forum (2017). https://doi.org/10.4028/www.scientific.net/MSF.890.319

  99. J.K. Chakravartty, R. Kapoor, A. Sarkar, V. Kumar, S.K. Jha, N. Saibaba, S. Banerjee, Identification of safe hot-working conditions in cast Zr-2.5Nb, in Zirconium in the Nuclear Industry 17th Vol. (2015) https://doi.org/10.1520/stp154320120197

  100. Y.C. Lin, Y.C. Xia, X.M. Chen, M.S. Chen, Constitutive descriptions for hot compressed 2124–T851 aluminum alloy over a wide range of temperature and strain rate. Comput. Mater. Sci. 50, 227–233 (2010). https://doi.org/10.1016/j.commatsci.2010.08.003

    Article  CAS  Google Scholar 

  101. K.K. Saxena, S.K. Jha, V. Pancholi, G.P. Chaudhari, D. Srivastava, G.K. Dey, N. Saibaba, Role of activation energies of individual phases in two-phase range on constitutive equation of Zr–2.5Nb–0.5Cu alloy. Trans. Nonferrous Met. Soc. China (English Ed.) 27, 172–183 (2017). https://doi.org/10.1016/S1003-6326(17)60020-7

    Article  CAS  Google Scholar 

  102. K.K. Saxena, V. Pancholi, D. Srivastava, G.K. Dey, S.K. Jha, N. Saibaba, Determination of instability in Zr-2.5Nb-0.5Cu using Lyapunov function, in Material Science Forum (2015). https://doi.org/10.4028/www.scientific.net/MSF.830-831.329

  103. S.R. Bodner, Y. Partom, Constitutive equations for elastic-viscoplastic strain-hardening materials. J. Appl. Mech. Trans. ASME (1975). https://doi.org/10.1115/1.3423586

    Article  Google Scholar 

  104. A. Rusinek, J.R. Klepaczko, Shear testing of a sheet steel at wide range of strain rates and a constitutive relation with strain-rate and temperature dependence of the flow stress. Int. J. Plast 17, 87–115 (2001). https://doi.org/10.1016/S0749-6419(00)00020-6

    Article  CAS  Google Scholar 

  105. F.J. Zerilli, R.W. Armstrong, Dislocation-mechanics-based constitutive relations for material dynamics calculations. J. Appl. Phys. 61, 1816–1825 (1987). https://doi.org/10.1063/1.338024

    Article  CAS  Google Scholar 

  106. T. Mirzaie, H. Mirzadeh, J.M. Cabrera, A simple Zerilli–Armstrong constitutive equation for modeling and prediction of hot deformation flow stress of steels. Mech. Mater. 94, 38–45 (2016). https://doi.org/10.1016/j.mechmat.2015.11.013

    Article  Google Scholar 

  107. H. Zhang, W. Wen, H. Cui, Y. Xu, A modified Zerilli–Armstrong model for alloy IC10 over a wide range of temperatures and strain rates. Mater. Sci. Eng. A 527, 328–333 (2009). https://doi.org/10.1016/j.msea.2009.08.008

    Article  CAS  Google Scholar 

  108. D.L. Preston, D.L. Tonks, D.C. Wallace, Model of plastic deformation for extreme loading conditions. J. Appl. Phys. 93, 211–220 (2003). https://doi.org/10.1063/1.1524706

    Article  CAS  Google Scholar 

  109. G.Z. Voyiadjis, A.H. Almasri, A physically based constitutive model for fcc metals with applications to dynamic hardness. Mech. Mater. 40, 549–563 (2008). https://doi.org/10.1016/j.mechmat.2007.11.008

    Article  Google Scholar 

  110. R.L. Goetz, V. Seetharaman, Modeling dynamic recrystallization using cellular automata. Scr. Mater. 38, 405–413 (1998). https://doi.org/10.1016/S1359-6462(97)00500-9

    Article  CAS  Google Scholar 

  111. Z. Jin, J. Liu, Z. Cui, D. Wei, Identification of nucleation parameter for cellular automaton model of dynamic recrystallization. Trans. Nonferrous Met. Soc. China 20, 458–464 (2010). https://doi.org/10.1016/S1003-6326(09)60162-X

    Article  CAS  Google Scholar 

  112. U.F. Kocks, Laws for work-hardening and low-temperature creep. J. Eng. Mater. Technol. Trans. ASME (1976). https://doi.org/10.1115/1.3443340

    Article  Google Scholar 

  113. G.R. Johnson, W.H. Cook, A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures.pdf, in International symposium on ballistic, 541–547 (1983)

  114. A.S. Khan, H. Zhang, L. Takacs, Mechanical response and modeling of fully compacted nanocrystalline iron and copper. Int. J. Plast 16, 1459–1476 (2000). https://doi.org/10.1016/S0749-6419(00)00023-1

    Article  CAS  Google Scholar 

  115. B. Farrokh, A.S. Khan, Grain size, strain rate, and temperature dependence of flow stress in ultra-fine grained and nanocrystalline Cu and Al: synthesis, experiment, and constitutive modeling. Int. J. Plast 25, 715–732 (2009). https://doi.org/10.1016/j.ijplas.2008.08.001

    Article  CAS  Google Scholar 

  116. A. Molinari, G. Ravichandran, Constitutive modeling of high-strain-rate deformation in metals based on the evolution of an effective microstructural length. Mech. Mater. 37, 737–752 (2005). https://doi.org/10.1016/j.mechmat.2004.07.005

    Article  Google Scholar 

  117. A. Marchattiwar, A. Sarkar, J.K. Chakravartty, B.P. Kashyap, Dynamic recrystallization during hot deformation of 304 austenitic stainless steel. J. Mater. Eng. Perform. 22, 2168–2175 (2013). https://doi.org/10.1007/s11665-013-0496-0

    Article  CAS  Google Scholar 

  118. J. Li, X. Xia, Modeling high temperature deformation behavior of large-scaled Mg–Al–Zn magnesium alloy fabricated by semi-continuous casting. J. Mater. Eng. Perform. 24, 3539–3548 (2015). https://doi.org/10.1007/s11665-015-1640-9

    Article  CAS  Google Scholar 

  119. H. Mirzadeh, A simplified approach for developing constitutive equations for modeling and prediction of hot deformation flow stress. Metall. Mater. Trans. A Phys. Metall. Mater. Sci. 46, 4027–4037 (2015). https://doi.org/10.1007/s11661-015-3006-1

    Article  CAS  Google Scholar 

  120. N. Kotkunde, H.N. Krishnamurthy, P. Puranik, A.K. Gupta, S.K. Singh, Microstructure study and constitutive modeling of Ti–6Al–4 V alloy at elevated temperatures. Mater. Des. 54, 96–103 (2014). https://doi.org/10.1016/j.matdes.2013.08.006

    Article  CAS  Google Scholar 

  121. C.M. Sellars, W.J. McTegart, On the mechanism of hot deformation. Acta Metall. (1966). https://doi.org/10.1016/0001-6160(66)90207-0

    Article  Google Scholar 

  122. J.J. Jonas, M. Sellars, Strength and structure hot-working conditions. Int. Mater. Rev. 14, 24 (1969)

    Article  Google Scholar 

  123. H. Mirzadeh, Constitutive description of 7075 aluminum alloy during hot deformation by apparent and physically-based approaches. J. Mater. Eng. Perform. 24, 1095–1099 (2015). https://doi.org/10.1007/s11665-015-1389-1

    Article  CAS  Google Scholar 

  124. H. Mirzadeh, J.M. Cabrera, A. Najafizadeh, Constitutive relationships for hot deformation of austenite. Acta Mater. 59, 6441–6448 (2011). https://doi.org/10.1016/j.actamat.2011.07.008

    Article  CAS  Google Scholar 

  125. C. Phaniraj, M. Nandagopal, S.L. Mannan, P. Rodriguez, The relationship between transient and steady state creep in AISI 304 stainless steel. Acta Metall. Mater. 39, 1651–1656 (1991). https://doi.org/10.1016/0956-7151(91)90253-W

    Article  CAS  Google Scholar 

  126. D. Samantaray, C. Phaniraj, S. Mandal, A.K. Bhaduri, Strain dependent rate equation to predict elevated temperature flow behavior of modified 9Cr–1Mo (P91) steel. Mater. Sci. Eng. A 528, 1071–1077 (2011). https://doi.org/10.1016/j.msea.2010.10.036

    Article  CAS  Google Scholar 

  127. D. Samantaray, S. Mandal, A.K. Bhaduri, P.V. Sivaprasad, An overview on constitutive modelling to predict elevated temperature flow behaviour of fast reactor structural materials. Trans. Indian Inst. Met. 63, 823–831 (2010). https://doi.org/10.1007/s12666-010-0126-6

    Article  CAS  Google Scholar 

  128. Z.H.A. Kassam, Z. Wang, E.T.C. Ho, Constitutive equations for a modified Zr–2.5wt.%Nb pressure tube material. Mater. Sci. Eng. A (1992). https://doi.org/10.1016/0921-5093(92)90007-N

    Article  Google Scholar 

  129. Y.C. Lin, X.M. Chen, A critical review of experimental results and constitutive descriptions for metals and alloys in hot working. Mater. Des. 32, 1733–1759 (2011). https://doi.org/10.1016/j.matdes.2010.11.048

    Article  CAS  Google Scholar 

  130. A. Cingara, H.J. McQueen, New formula for calculating flow curves from high temperature constitutive data for 300 austenitic steels. J. Mater. Process. Technol. 36, 31–42 (1992). https://doi.org/10.1016/0924-0136(92)90236-L

    Article  Google Scholar 

  131. C. Zener, J.H. Hollomon, Effect of strain rate upon plastic flow of steel. J. Appl. Phys. 15, 22–32 (1944). https://doi.org/10.1063/1.1707363

    Article  Google Scholar 

  132. J.H. Kim, S.L. Semiatin, C.S. Lee, Constitutive analysis of the high-temperature deformation of Ti–6Al–4 V with a transformed microstructure. Acta Mater. 51, 5613–5626 (2003). https://doi.org/10.1016/S1359-6454(03)00426-9

    Article  CAS  Google Scholar 

  133. N. Kotkunde, A.D. Deole, A.K. Gupta, S.K. Singh, Comparative study of constitutive modeling for Ti–6Al–4 V alloy at low strain rates and elevated temperatures. Mater. Des. 55, 999–1005 (2014). https://doi.org/10.1016/j.matdes.2013.10.089

    Article  CAS  Google Scholar 

  134. Z. Yuan, F. Li, H. Qiao, M. Xiao, J. Cai, J. Li, A modified constitutive equation for elevated temperature flow behavior of Ti–6Al–4 V alloy based on double multiple nonlinear regression. Mater. Sci. Eng. A 578, 260–270 (2013). https://doi.org/10.1016/j.msea.2013.04.091

    Article  CAS  Google Scholar 

  135. C. Zhang, X.Q. Li, D.S. Li, C.H. Jin, J.J. Xiao, Modelization and comparison of Norton-Hoff and Arrhenius constitutive laws to predict hot tensile behavior of Ti–6Al–4 V alloy. Trans. Nonferrous Met. Soc. China (English Ed.) 22, s457–s464 (2012). https://doi.org/10.1016/S1003-6326(12)61746-4

    Article  CAS  Google Scholar 

  136. G. Chen, C. Ren, X. Qin, J. Li, Temperature dependent work hardening in Ti–6Al–4 V alloy over large temperature and strain rate ranges: experiments and constitutive modeling. Mater. Des. 83, 598–610 (2015). https://doi.org/10.1016/j.matdes.2015.06.048

    Article  CAS  Google Scholar 

  137. G.B. Wei, X.D. Peng, F.P. Hu, A. Hadadzadeh, Y. Yang, W.D. Xie, M.A. Wells, Deformation behavior and constitutive model for dual-phase Mg–Li alloy at elevated temperatures. Trans. Nonferrous Met. Soc. China (English Ed.) 26, 508–518 (2016). https://doi.org/10.1016/S1003-6326(16)64139-0

    Article  CAS  Google Scholar 

  138. C. Qin, Z.K. Yao, Y.Q. Ning, Z.F. Shi, H.Z. Guo, Hot deformation behavior of TC11/Ti–22Al–25Nb dual-alloy in isothermal compression. Trans. Nonferrous Met. Soc. China 25, 2195–2205 (2015). https://doi.org/10.1016/S1003-6326(15)63832-8

    Article  CAS  Google Scholar 

  139. I. Balasundar, T. Raghu, B.P. Kashyap, Modeling the hot working behavior of near-α titanium alloy IMI 834. Prog. Nat. Sci. Mater. Int. 23, 598–607 (2013). https://doi.org/10.1016/j.pnsc.2013.11.004

    Article  Google Scholar 

  140. P. Wanjara, M. Jahazi, H. Monajati, S. Yue, J.P. Immarigeon, Hot working behavior of near-α alloy IMI834. Mater. Sci. Eng. A 396, 50–60 (2005). https://doi.org/10.1016/j.msea.2004.12.005

    Article  CAS  Google Scholar 

  141. J. Porntadawit, V. Uthaisangsuk, P. Choungthong, Modeling of flow behavior of Ti–6Al–4 V alloy at elevated temperatures. Mater. Sci. Eng. A 599, 212–222 (2014). https://doi.org/10.1016/j.msea.2014.01.064

    Article  CAS  Google Scholar 

  142. T. Seshacharyulu, S.C. Medeiros, W.G. Frazier, Y.V.R.K. Prasad, Hot working of commercial Ti–6Al–4 V with an equiaxed α–β microstructure: materials modeling considerations. Mater. Sci. Eng. A 284, 184–194 (2000). https://doi.org/10.1016/s0921-5093(00)00741-3

    Article  Google Scholar 

  143. K.K. Saxena, S.K. Jha, V. Pancholi, G.P. Chaudhari, D. Srivastava, G.K. Dey, N. Saibaba, Role of activation energies of individual phases in two-phase range on constitutive equation of Zr–2.5Nb–0.5Cu alloy. Trans. Nonferrous Met. Soc. China (English Ed.) (2017). https://doi.org/10.1016/S1003-6326(17)60020-7

    Article  Google Scholar 

  144. S. Upadhyay, K.K. Saxena, Effect of Cu and Mo addition on mechanical properties and microstructure of grey cast iron: an overview. Mater. Today Proc. (2020). https://doi.org/10.1016/j.matpr.2020.02.524

    Article  Google Scholar 

  145. N. Kumar, A. Bharti, K.K. Saxena, A re-analysis of effect of various process parameters on the mechanical properties of Mg based MMCs fabricated by powder metallurgy technique. Mater. Today Proc. (2020). https://doi.org/10.1016/j.matpr.2020.02.427

    Article  Google Scholar 

  146. R. Srivastava, B. Singh, K.K. Saxena, Influence of S and Mn on mechanical properties and microstructure of grey cast iron: an overview. Mater. Today Proc. (2020). https://doi.org/10.1016/j.matpr.2020.02.577

    Article  Google Scholar 

  147. G. Lütjering, Influence of processing on microstructure and mechanical properties of (α + β) titanium alloys. Mater. Sci. Eng. A 243, 32–45 (1998). https://doi.org/10.1016/s0921-5093(97)00778-8

    Article  Google Scholar 

  148. R.V. Kulkarni, S. Neogy, B.N. Rath, K. Manikrishna, D. Srivastava, N. Saibaba, I. Samajdar, E. Ramadasan, G.K. Dey, S. Anatharaman, Microstructural and textural evolution in heat treated Zr–2.5% Nb pressure tube material subjected to dilatometric studies. Trans. Indian Inst. Met. 64, 395–399 (2011). https://doi.org/10.1007/s12666-011-0104-7

    Article  CAS  Google Scholar 

  149. R.V. Kulkarni, K.V.M. Krishna, S. Neogy, D. Srivastava, E. Ramadasan, G.K. Dey, N. Saibaba, S.K. Jha, R.S. Shriwastaw, S. Anantharaman, Determination of correlation parameters for evaluation of mechanical properties by small punch test and automated ball indentation test for Zr–2. 5% Nb pressure tube material. Nucl. Eng. Des. 265, 1101–1112 (2013). https://doi.org/10.1016/j.nucengdes.2013.10.009

    Article  CAS  Google Scholar 

  150. W.J. Evans, Optimising mechanical properties in alpha + beta titanium alloys. Mater. Sci. Eng. A 243, 89–96 (1998). https://doi.org/10.1016/s0921-5093(97)00784-3

    Article  Google Scholar 

  151. R.A. Holt, In-reactor deformation of cold-worked Zr–2.5Nb pressure tubes. J. Nucl. Mater. 372, 182–214 (2008). https://doi.org/10.1016/j.jnucmat.2007.02.017

    Article  CAS  Google Scholar 

  152. A.K. Dureja, S.K. Sinha, A. Srivastava, R.K. Sinha, J.K. Chakravartty, P. Seshu, D.N. Pawaskar, Flow behaviour of autoclaved, 20% cold worked, Zr–2.5Nb alloy pressure tube material in the temperature range of room temperature to 800°c. J. Nucl. Mater. 412, 22–29 (2011). https://doi.org/10.1016/j.jnucmat.2011.01.023

    Article  CAS  Google Scholar 

  153. S. Neogy, D. Srivastava, J.K. Chakravartty, G.K. Dey, S. Banerjee, Microstructural evolution in Zr–1Nb and Zr–1Nb–1Sn–0.1Fe alloys. Metall. Mater. Trans. A Phys. Metall. Mater. Sci. 38, 485–498 (2007). https://doi.org/10.1007/s11661-006-9026-0

    Article  CAS  Google Scholar 

  154. R. Kondo, N. Nomura, Y. Suyalatu, H. Tsutsumi, T.Hanawa Doi, Microstructure and mechanical properties of as-cast Zr–Nb alloys. Acta Biomater. 7, 4278–4284 (2011). https://doi.org/10.1016/j.actbio.2011.07.020

    Article  CAS  Google Scholar 

  155. S.X. Liang, M.Z. Ma, R. Jing, Y.K. Zhou, Q. Jing, R.P. Liu, Preparation of the ZrTiAlV alloy with ultra-high strength and good ductility. Mater. Sci. Eng. A 539, 42–47 (2012). https://doi.org/10.1016/j.msea.2012.01.022

    Article  CAS  Google Scholar 

  156. R. Filip, K. Kubiak, W. Ziaja, J. Sieniawski, The effect of microstructure on the mechanical properties of two-phase titanium alloys. J. Mater. Process. Technol. 133, 84–89 (2003). https://doi.org/10.1016/S0924-0136(02)00248-0

    Article  CAS  Google Scholar 

  157. Z.F. Shi, H.Z. Guo, R. Liu, X.C. Wang, Z.K. Yao, Microstructure and mechanical properties of TC21 titanium alloy by near-isothermal forging. Trans. Nonferrous Met. Soc. China (English Ed.) (2015). https://doi.org/10.1016/S1003-6326(15)63580-4

    Article  Google Scholar 

  158. Y.H. Jeong, K.S. Rheem, C.S. Choi, Y.S. Kim, Effect of beta heat treatment on microstructure and nodular corrosion of zircaloy-4. J. Nucl. Sci. Technol. (1993). https://doi.org/10.1080/18811248.1993.9734463

    Article  Google Scholar 

  159. S.X. Liang, L.X. Yin, X.Y. Liu, R. Jing, Y.K. Zhou, M.Z. Ma, R.P. Liu, Effects of annealing treatments on microstructure and mechanical properties of the Zr–45Ti–5Al–3 V alloy. Mater. Sci. Eng. A 582, 374–378 (2013). https://doi.org/10.1016/j.msea.2013.06.007

    Article  CAS  Google Scholar 

  160. J.S. Yoo, I.S. Kim, Effect of (α + β) heat treatment on the mechanical properties of Zircaloy-4. J. Nucl. Mater. 185, 87–95 (1991)

    Article  CAS  Google Scholar 

  161. C.J. Bennett, A comparison of material models for the numerical simulation of spike-forging of a CrMoV alloy steel. Comput. Mater. Sci. 70, 114–122 (2013). https://doi.org/10.1016/j.commatsci.2013.01.003

    Article  CAS  Google Scholar 

  162. L.X. Li, K.P. Rao, Y. Lou, D.S. Peng, A study on hot extrusion of Ti–6Al–4 V using simulations and experiments. Int. J. Mech. Sci. 44, 2415–2425 (2002). https://doi.org/10.1016/S0020-7403(02)00173-X

    Article  Google Scholar 

  163. Z. Wang, L. Qi, G. Wang, H. Li, M.S. Dargusch, Constitutive equation for the hot deformation behavior of Csf/AZ91D composites and its validity for numerical simulation. Mech. Mater. 102, 90–96 (2016). https://doi.org/10.1016/j.mechmat.2016.08.011

    Article  Google Scholar 

  164. W. Zhang, Y. Liu, L. Wang, B. Liu, Numerical simulation and physical analysis for dynamic behaviors of P/M TiAl alloy in hot-packed forging process. Trans. Nonferrous Met. Soc. China (English Ed.) 22, 901–906 (2012). https://doi.org/10.1016/S1003-6326(11)61263-6

    Article  CAS  Google Scholar 

  165. L. Li, J. Zhou, J. Duszczyk, Determination of a constitutive relationship for AZ31B magnesium alloy and validation through comparison between simulated and real extrusion. J. Mater. Process. Technol. 172, 372–380 (2006). https://doi.org/10.1016/j.jmatprotec.2005.09.021

    Article  CAS  Google Scholar 

  166. Z. Wang, L. Qi, J. Zhou, J. Guan, J. Liu, A constitutive model for predicting flow stress of Al18B 4O33w/AZ91D composite during hot compression and its validation. Comput. Mater. Sci. 50, 2422–2426 (2011). https://doi.org/10.1016/j.commatsci.2011.03.020

    Article  CAS  Google Scholar 

  167. J. Zhou, L. Li, J. Duszczyk, Computer simulated and experimentally verified isothermal extrusion of 7075 aluminium through continuous ram speed variation. J. Mater. Process. Technol. 146, 203–212 (2004). https://doi.org/10.1016/j.jmatprotec.2003.10.018

    Article  CAS  Google Scholar 

  168. Y.S. Jang, D.C. Ko, B.M. Kim, Application of the finite element method to predict microstructure evolution in the hot forging of steel. J. Mater. Process. Technol. 101, 85–94 (2000). https://doi.org/10.1016/S0924-0136(99)00460-4

    Article  Google Scholar 

  169. L. Cheng, H. Chang, B. Tang, H. Kou, J. Li, Simulation of microstructure for hot pack-forging of a high Nb containing TiAl alloy. Xiyou Jinshu Cailiao Yu Gongcheng/Rare Met. Mater. Eng. 43, 36–41 (2014). https://doi.org/10.1016/s1875-5372(14)60048-5

    Article  CAS  Google Scholar 

  170. X. Li, L. Duan, J. Li, X. Wu, Experimental study and numerical simulation of dynamic recrystallization behavior of a micro-alloyed plastic mold steel. Mater. Des. 66, 309–320 (2015). https://doi.org/10.1016/j.matdes.2014.10.076

    Article  CAS  Google Scholar 

  171. K.K. Saxena, K. Chetan, K. Vaibhav, K.V. Mani Krishna, V. Pancholi, S.K. Jha, D. Srivastava, Constitutive analysis of Zr–1Nb alloy for different phase regions. Mater. Perform. Charact. 8, 20190020 (2019). https://doi.org/10.1520/mpc20190020

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Kuldeep K. Saxena.

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

Saxena, K.K., Pancholi, V. Zr–Nb Alloys and Its Hot Deformation Analysis Approaches. Met. Mater. Int. 27, 2106–2133 (2021). https://doi.org/10.1007/s12540-020-00812-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12540-020-00812-8

Keywords

Navigation