Abstract
Zirconium alloys are widely used as structure materials in nuclear fuel assembly. However, the poor forming performance of zirconium alloy restricts its application and consequently hinders the development of nuclear industry. In this study, the concept of strain limit is defined, and the influencing mechanisms of different mechanical properties of zirconium alloys on the strain limit of tension-compression area and equi-biaxial area are revealed. The research shows that the variation of sheet thickness t and strength coefficient K has little impact on the strain limit of zirconium alloy. The increase of strain hardening exponent n will significantly raise the strain limit of zirconium alloys in both the tension-compression area and equi-biaxial area. the Lankford coefficient R can improve the strain limit of tension-compression area, but not the equi-biaxial area. Besides, the influencing mechanisms of R and n on the strain limit of zirconium alloy are different. The value of n mainly improves the strain limit by increasing the base point of forming limit curve while the value of R primarily increases the strain limit by changing the slopes of the strain paths in the tension-compression area. Therefore, the value increase of R and n can be considered as an effective way to improve the forming performance of zirconium alloys.
Similar content being viewed by others
References
Trego G, Brachet JC, Vandenberghe V, Portier L, Gélébart L, Chosson R, Soulacroix J et al (2022) Influence of grain size on the high-temperature creep behaviour of M5Framatome1 zirconium alloy under vacuum. J Nucl Mater 560:153503. https://doi.org/10.1016/j.jnucmat.2021.153503
Zhang Y, Qi H, Song X (2021) Expansion deformation behavior of zirconium alloy claddings with different hydrogen concentrations. J Nucl Mater 554:153082. https://doi.org/10.1016/j.jnucmat.2021.153082
Xu L, Xiao Y, van Sandwijk A, Xu Q, Yang Y (2015) Production of nuclear grade zirconium: A review. J Nucl Mater 466:21–28. https://doi.org/10.1016/j.jnucmat.2015.07.010
Lei C, Mao J, Zhang X, Wang L, Chen D (2021) Crack prediction in sheet forming of zirconium alloys used in nuclear fuel assembly by support vector machine method. Energy Rep 7:5922–5932. https://doi.org/10.1016/j.egyr.2021.09.013
Kong Z, Zhang J, Li H, Kong N (2018) Deep drawing and bulging forming limit of dual-phase steel under different mechanical properties. Int J Adv Manuf Technol 97:2111–2124. https://doi.org/10.1007/s00170-018-1980-3
Banabic D, Kami A, Comsa D, Eyckens P (2021) Developments of the Marciniak-Kuczynski model for sheet metal formability: A review. J Mater Process Technol 287:116446. https://doi.org/10.1016/j.jmatprotec.2019.116446
Gensamer M (2017) Strength and Ductility. Metallogr Microstruct Anal 6:171–185. https://doi.org/10.1007/s13632-017-0341-1
Keeler SP (1965) Determination of forming limits in automotive stampings. SAE Technical Paper
Goodwin GM (1968) Application of strain analysis to sheet metal forming problems in the press shop. SAE Technical Paper
Paul SK (2021) Controlling factors of forming limit curve: A review. Adv Ind Manuf Eng 2:100033. https://doi.org/10.1016/j.aime.2021.100033
Wang Z, Zhang W, Luo Q, Zheng G, Li Q, Sun G (2020) A novel failure criterion based upon forming limit curve for thermoplastic composites. Compos B: Eng 202:108320. https://doi.org/10.1016/j.compositesb.2020.108320
Lei C, Mao J, Zhang X, Liu J, Wang L, Chen D (2021) A comparison study of the yield surface exponent of the Barlat yield function on the forming limit curve prediction of zirconium alloys with M-K method. IntJ Mater Form 14:467–484. https://doi.org/10.1007/s12289-021-01616-w
Ma BL, Wan M, Zhang H, Gong XL, Wu XD (2018) Evaluation of the forming limit curve of medium steel plate based on non-constant through-thickness normal stress. J Manuf Process 33:175–183. https://doi.org/10.1016/j.jmapro.2018.05.012
SP K, WG B (1975) Relationship between laboratory material characterization and press-shop formability: micro-alloying 75. New York
Dilmec M, Halkaci HS, Ozturk F, Livatyali H, Yigit O (2013) Effects of sheet thickness and anisotropy on forming limit curves of AA2024-T4. Int J Adv Manuf Technol 67:2689–2700. https://doi.org/10.1007/s00170-012-4684-0
Oh G, Lee K, Huh M, Park JE, Park SH, Engler O (2017) Effect of r-value and texture on plastic deformation and necking behavior in interstitial-free steel sheets. Met Mater Int 23:26–34. https://doi.org/10.1007/s12540-017-6375-8
Lin P, Sun Y, Chi C, Wang W (2017) Effect of plastic anisotropy of ZK60 magnesium alloy sheet on its forming characteristics during deep drawing process. Int J Adv Manuf Technol 88:1629–1637. https://doi.org/10.1007/s00170-016-8816-9
Ghazani MS, Binesh B, Fardi-Ilkhchy A (2019) Effect of strain rate sensitivity and strain hardening exponent of materials on plastic strain distribution and damage accumulation during equal channel angular pressing. Iran J Sci Technol Trans Mech Eng 43:831–844. https://doi.org/10.1007/s40997-018-0198-1
Jalali Aghchai A, Shakeri M, Mollaei DB (2013) Influences of material properties of components on formability of two-layer metallic sheets. Int J Adv Manuf Technol 66:809–823. https://doi.org/10.1007/s00170-012-4368-9
Bertinetti MA, Roatta A, Nicoletti E, Leonard M, Stout M, Signorelli JW (2021) How strain-rate sensitivity creates two forming-limit diagrams: bragard-type versus instability-strain, correlation-coefficient-based temporal curves. J Mater Eng Perform 30:4183–4193. https://doi.org/10.1007/s11665-021-05745-w
Prates PA, Adaixo AS, Oliveira MC, Fernandes JV (2018) Numerical study on the effect of mechanical properties variability in sheet metal forming processes. Int J Adv Manuf Technol 96:561–580. https://doi.org/10.1007/s00170-018-1604-y
Anarestani SS, Morovvati MR, Vaghasloo YA (2015) Influence of anisotropy and lubrication on wrinkling of circular plates using bifurcation theory. Int J Mater Form 8:439–454. https://doi.org/10.1007/s12289-014-1187-6
Dasappa P, Inal K, Mishra R (2012) The effects of anisotropic yield functions and their material parameters on prediction of forming limit diagrams. Int J Solids Struct 49:3528–3550. https://doi.org/10.1016/j.ijsolstr.2012.04.021
Kim M, Rickhey F, Lee H, Kim N (2016) Analytical determination of forming limit curve for zirlo and its experimental validation. J Manuf Process 23:122–129. https://doi.org/10.1016/j.jmapro.2016.06.006
Singh SK, Limbadri K, Singh AK, Ram AM, Ravindran M, Krishna M, Reddy MC et al (2019) Studies on texture and formability of Zircaloy-4 produced by pilgering route. J Market Res 8:2120–2129. https://doi.org/10.1016/j.jmrt.2018.11.018
Wang H, Zhou D, Yan Y, Liu J, Gao B (2022) Effect of pre-straining and subsequent annealing on microstructure and mechanical property of Zr–Sn–Nb–Fe zirconium alloy. Met Mater Int 28:603–617. https://doi.org/10.1007/s12540-020-00905-4
Jia Y, Qiu J, Yang Z (2020) Influence of rolling ways on microstructure of N36 zirconium alloy strip. Heat Treat Met 11:148–154. https://doi.org/10.13251/j.issn.0254-6051.2020.11.027
Dizaji SA, Darendeliler H, Kaftanoğlu B (2018) Prediction of forming limit curve at fracture for sheet metal using new ductile fracture criterion. Eur J Mech A Solids 69:255–265. https://doi.org/10.1016/j.euromechsol.2018.01.003
Ma B, Liu ZG, Jiang Z, Wu X, Diao K, Wan M (2016) Prediction of forming limit in DP590 steel sheet forming: An extended fracture criterion. Mater Des 96:401–408. https://doi.org/10.1016/j.matdes.2016.02.034
Marciniak Z, Kuczyński K (1967) Limit strains in the processes of stretch-forming sheet metal. Int J Mech Sci 9(9):609–620. https://doi.org/10.1016/0020-7403(67)90066-5
Hutchinson J W, Neale K W, Needleman A (1978) Sheet necking—I. Validity of plane stress assumptions of the long-wavelength approximation. 111–126. https://doi.org/10.1007/978-1-4613-2880-3_5
Hutchinson JW, Neale KW (1978) Sheet necking-II. Time-independent behavior. 127–153. https://doi.org/10.1007/978-1-4613-2880-3_6
Wang X, Li Z, Zhou J, Tian F (2012) Application and research progress of zirconium alloy in nuclear industry. Mater Heat Treat 2:71–74.
Author information
Authors and Affiliations
Corresponding authors
Ethics declarations
Ethics approval
Not applicable for that section.
Consent to participate
Not applicable for that section.
Consent for publication
All authors consent to publish their research paper in the International Journal of Material Forming.
Competing of interests
The authors declare no competing interests.
Additional information
Publisher's note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Zhang, X., Mao, J., Lei, C. et al. Effects and quantitative analyses of mechanical properties on strain limit during plastic deformation of zirconium alloys. Int J Mater Form 16, 24 (2023). https://doi.org/10.1007/s12289-023-01746-3
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s12289-023-01746-3