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The asymmetric pre-yielding behaviour during tension and compression for a rolled AZ31 Mg alloy

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Abstract

Tensile and compressive pre-yield mechanical behavior of a rolled AZ31 Mg alloy sheet was studied by cyclic loading–unloading tests along rolling direction (RD) and transverse direction (TD). The results show that the mechanical response of pre-yielding is not linear elasticity. Microplasticity with irreversible strain and energetic dissipation is observed during tension. While anelasticity with reversible strain and dissipative energy is detected during compression. A stress dependent varied elastic modulus model was built by introducing a stress factor to capture the asymmetric behavior. Three model parameters are tensile yield strength, initial elastic modulus and critical modulus at tensile yield point. Consequently, this model is verified by comparison with the experimental observations. The anelastic and micro-plastic deformation are ascribed to the glide of mobile dislocations. The asymmetric behavior of tension and compression is clarified by the nucleation mechanism of {10–12} twinning.

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References

  1. Song J, She J, Chen D, Pan F (2020) Latest research advances on magnesium and magnesium alloys worldwide. J Magnes Alloy 8:1–41. https://doi.org/10.1016/j.jma.2020.02.003

    Article  Google Scholar 

  2. Xu T, Yang Y, Peng X, Song J, Pan F (2019) Overview of advancement and development trend on magnesium alloy. J Magnes Alloy 7:536–544. https://doi.org/10.1016/j.jma.2019.08.001

    Article  Google Scholar 

  3. Pan F, Yang M, Chen X (2016) A review on casting magnesium alloys: modification of commercial alloys and development of new alloys. J Mater Sci Technol 32:1211–1221. https://doi.org/10.1016/j.jmst.2016.07.001

    Article  Google Scholar 

  4. You S, Huang Y, Kainer KU, Hort N (2017) Recent research and developments on wrought magnesium alloys. J Magnes Alloy 5:239–253. https://doi.org/10.1016/j.jma.2017.09.001

    Article  Google Scholar 

  5. Rabeeh BM, Rokhlin SI, Soboyejo WO (1996) Microplasticity and fracture in a Ti-15V-3Cr-3Al-3Sn Alloy. Scripta Mater 35:1429–1434. https://doi.org/10.1016/S1359-6462(96)00328-4

    Article  Google Scholar 

  6. Chen Z, Gandhi U, Lee J, Wagoner RH (2016) Variation and consistency of Young’s modulus in steel. J Mater Proc Technol 227:227–243. https://doi.org/10.1016/j.jmatprotec.2015.08.024

    Article  Google Scholar 

  7. Maaß R, Derlet PM (2018) Micro-plasticity and recent insights from intermittent and small-scale plasticity. Acta Mater 143:338–363. https://doi.org/10.1016/j.actamat.2017.06.023

    Article  Google Scholar 

  8. Zhang W, Ao S, Oliveira JP, Li C, Zeng Z, Wang A, Zhen L (2020) On the metallurgical joining mechanism during ultrasonic spot welding of NiTi using a Cu interlayer. Scripta Mater 178:414–417. https://doi.org/10.1016/j.scriptamat.2019.12.012

    Article  Google Scholar 

  9. Shen JJ, Zeng Z, Nematollahi M, Schell N, Maawad E, Vasin RN, Safaei K, Poorganji B, Elahinia M, Olivera JP (2021) In-situ synchrotron X-ray diffraction analysis of the elastic behavior of martensite and H-phase in a NiTiHf high temperature shape memory alloy fabricated by laser powder bed fusion. Addit Manuf Lett 1:100003. https://doi.org/10.1016/j.addlet.2021.100003

    Article  Google Scholar 

  10. Oliveira JP, Shen JJ, Zeng Z, Park JM, Choi YT, Schell N, Maawad E, Zhou N, Kim HS (2022) Dissimilar laser welding of a CoCrFeMnNi high entropy alloy to 316 stainless steel. Scripta Mater 206:114219. https://doi.org/10.1016/j.scriptamat.2021.114219

    Article  Google Scholar 

  11. Li Q, Yu Q, Zhang J, Jiang Y (2010) Effect of strain amplitude on tension-compression fatigue behavior of extruded Mg6Al1ZnA magnesium alloy. Scripta Mater 62:778–781. https://doi.org/10.1016/j.scriptamat.2010.01.052

    Article  Google Scholar 

  12. Shao S, Khonsari MM, Wang J, Shamsaei N, Li N (2018) Frequency dependent deformation reversibility during cyclic loading. Mater Res Lett 6:390–397. https://doi.org/10.1080/21663831.2018.1469172

    Article  Google Scholar 

  13. Mozafari F, Thamburaja P, Srinivasa AR, Moslemi N (2019) A rate independent inelasticity model with smooth transition for unifying low-cycle to high-cycle fatigue life prediction. Int J Mech Sci 159:325–335. https://doi.org/10.1016/j.ijmecsci.2019.05.017

    Article  Google Scholar 

  14. Zhang F, Sun P, Li X, Zhang G (2001) A comparative study on microplastic deformation behavior in a SiCp/2024Al composite and its unreinforced matrix alloy. Mater Lett 49:69–74. https://doi.org/10.1016/S0167-577X(00)00344-X

    Article  Google Scholar 

  15. Chen Z, Bong HJ, Li D, Wagoner RH (2016) The elastic-plastic transition of metals. Int J Plast 83:178–201. https://doi.org/10.1016/S0749-6419(01)00054-7

    Article  Google Scholar 

  16. Cleveland RM, Ghosh AK (2002) Inelastic effects on springback in metals. Int J Plast 18:769–785. https://doi.org/10.1016/S0749-6419(01)00054-7

    Article  MATH  Google Scholar 

  17. Wagoner RH, Lim H, Lee M-G (2013) Advanced Issues in springback. Int J Plast 45:3–20. https://doi.org/10.1016/j.ijplas.2012.08.006

    Article  Google Scholar 

  18. Torkabadi A, Perdahcioglu ES, Meinder VT, Van den Boogaard AH (2017) On the nonlinear anelastic behavior of AHSS. Int J Solids Struct 151:2–8. https://doi.org/10.1016/j.ijsolstr.2017.03.009

    Article  Google Scholar 

  19. Sun L, Wagoner RH (2011) Complex unloading behavior: Nature of the deformation and its consistent constitutive representation. Int J Plast 27:1126–1144. https://doi.org/10.1016/j.ijplas.2010.12.003

    Article  MATH  Google Scholar 

  20. Mareau C, Favier V, Weber B, Galtier A, Berveiller M (2012) Micromechanical modeling of the interactions between the microstructure and the dissipative deformation mechanisms in steels under cyclic loading. Int J Plast 32–33:106–120. https://doi.org/10.1016/j.ijplas.2011.12.004

    Article  Google Scholar 

  21. Van Liempt P, Sietsma J (2016) A physically based yield criterion I. Determination of the yield stress based on analysis of pre-yield dislocation behaviour. Mater Sci Eng A 662:80–87. https://doi.org/10.1016/j.msea.2016.03.013

    Article  Google Scholar 

  22. Arechabaleta Z, Van Liempt P, Sietsma J (2016) Quantification of dislocation structures from anelastic deformation behaviour. Acta Mater 115:314–323. https://doi.org/10.1016/j.actamat.2016.05.040

    Article  Google Scholar 

  23. Vreeland T Jr, Wood DS, Clark DS (1953) Preyield plastic and anelastic microstrain in low-carbon steel. Acta Mater 1:414–421. https://doi.org/10.1016/0001-6160(53)90123-0

    Article  Google Scholar 

  24. Zhang L, Zhu P (1991) Preyield microplastic deformation behavior in metals. Mechanical Behaviour of Materials VI. Proceedings of the Sixth International Conference. Kyoto, 673–678.

  25. Vellaikal G (1969) Some observations on microyielding in copper polycrystals. Acta Mater 17:1145–1154. https://doi.org/10.1016/0001-6160(69)90091-1

    Article  Google Scholar 

  26. Fantozzi G, Esnouf C, Benoit W, Ritchie IG (1982) Internal friction and microdeformation due to the intrinsic properties of dislocations: The Bordoni relaxation. Prog Mater Sci 27:311–451. https://doi.org/10.1016/0079-6425(82)90003-2

    Article  Google Scholar 

  27. Tian Q, Luo H, Yi R, Fan X, Ma Y, Shi D, Gao J (2019) Study of micro-plastic deformation in pure iron before macro-yielding using acoustic emission, electron backscattered diffraction and transmission electron microscopy. Mater Sci Eng A 771:138645. https://doi.org/10.1016/j.msea.2019.138645

    Article  Google Scholar 

  28. Fan GD, Zheng MY, Hu XS, Wu K, Gan WM, Brokmeier HG (2013) Internal friction and microplastic deformation behavior of pure magnesium processed by equal channel angular pressing. Mater Sci Eng A 561:100–108. https://doi.org/10.1016/j.msea.2012.10.083

    Article  Google Scholar 

  29. Fan GD, Zheng MY, Ju CH, Hu XS, Wu K, Gan WM, Brokmeier HG (2013) Effect of grain size on cyclic microplasticity of ECAP processed commercial pure magnesium. J Mater Sci 48:1239–1248. https://doi.org/10.1007/s10853-012-6865-5

    Article  Google Scholar 

  30. Zhou AG, Basu S, Barsoum MW (2008) Kinking nonlinear elasticity, damping and microyielding of hexagonal close-packed metals. Acta Mater 56:60–67. https://doi.org/10.1016/j.actamat.2007.08.050

    Article  Google Scholar 

  31. Zhou AG, Barsoum MW (2009) Kinking nonlinear elasticity and the deformation of magnesium. Metall Mater Trans A 40A:1741–1756. https://doi.org/10.1007/s11661-009-9845-x

    Article  Google Scholar 

  32. Fallahi H, Tabarroki M, Davies C (2020) Evolution of anelastic behavior and twinning in cyclic loading of extruded magnesium alloy ZM21. Mater Sci Eng A 770:138520. https://doi.org/10.1016/j.msea.2019.138520

    Article  Google Scholar 

  33. Drozdenko D, Caperk J, Clausen B, Vinogradoc A, Mathis K (2019) Influence of the solute concentration on the anelasticity in Mg-Al alloys: A multiple-approach study. J Alloy Compd 786:779–790. https://doi.org/10.1016/j.jallcom.2019.01.358

    Article  Google Scholar 

  34. Wang H, Wu PD, Wang J (2013) Modeling inelastic behavior of magnesium alloys during cyclic loading-unloading. Int J Plast 47:49–64. https://doi.org/10.1016/j.ijplas.2013.01.007

    Article  Google Scholar 

  35. Chandola N, Pasiliao C, Cazacu O, Revil-Baudard B (2016) On modeling the mechanical behavior and texture evolution of rolled AZ31B Mg for complex loadings involving strain path changes. Magnes Technol 245-250.https://doi.org/10.1002/9781119274803.ch49

  36. Hama T, Takuda H (2011) Crystal-plasticity finite-element analysis of inelastic behavior during unloading in a magnesium alloy sheet. Int J Plast 27(7):1072–1092. https://doi.org/10.1016/j.ijplas.2010.11.004

    Article  MATH  Google Scholar 

  37. Hama T, Kariyazaki Y, Hosokawa N, Fujimoto H, Takuda H (2012) Work-hardening behaviors of magnesium alloy sheet during in-plane cyclic loading. Mater Sci Eng A 551(8):209–217. https://doi.org/10.1016/j.msea.2012.05.009

    Article  Google Scholar 

  38. Hama T, Kitamura N, Takuda H (2013) Effect of twinning and detwinning on inelastic behavior during unloading in a magnesium alloy sheet. Mater Sci Eng A 583:232–241. https://doi.org/10.1016/j.msea.2013.06.070

    Article  Google Scholar 

  39. Lou XY, Li M, Boger RK, Agnew SR, Wagoner RH (2007) Hardening evolution of AZ31B Mg sheet. Int J Plast 23:44–86. https://doi.org/10.1016/j.ijplas.2006.03.005

    Article  MATH  Google Scholar 

  40. Barnett MR, Nave MD, Ghaderi A (2012) Yield point elongation due to twinning in a magnesium alloy. Acta Mater 60:1433–1443. https://doi.org/10.1016/j.actamat.2011.11.022

    Article  Google Scholar 

  41. Timar G, Barnett MR, Quinta da Fonseca J (2017) Discontinuous yielding in wrought magnesium. Comput Mater Sci 132:81–91. https://doi.org/10.1016/j.commatsci.2017.02.010

    Article  Google Scholar 

  42. Hielscher R, Schaeben H (2008) A novel pole figure inversion method: Specification of the MTEX algorithm. J Appl Cryst 41:1024–1037. https://doi.org/10.1107/S0021889808030112

    Article  Google Scholar 

  43. Yang C, Shi B, Peng Y, Pan F (2019) Loading path dependent distortional hardening of Mg alloys: Experimental investigation and constitutive modeling on cruciform specimens. Int J Mech Sci 160:282–297. https://doi.org/10.1016/j.ijmecsci.2019.06.046

    Article  Google Scholar 

  44. Li Q, Jin M, Zou Z, Zhao S, Zhang Q, Li P (2017) Experiment research on tensile and compression cyclic loading of sheet metal. Procedia Eng 207:1916–1921. https://doi.org/10.1016/j.proeng.2017.10.961

    Article  Google Scholar 

  45. Yi S-B, Davies CHJ, Brokmeier H-G, Bolmaro RE, Kainer KU, Homeyer J (2006) Deformation and texture evolution in AZ31 magnesium alloy during uniaxial loading. Acta Mater 54:549–562. https://doi.org/10.1016/j.actamat.2005.09.024

    Article  Google Scholar 

  46. Catorceno LLC, de Abreu HFG, Padilha AF (2018) Effects of cold and warm cross-rolling on microstructure and texture evolution of AZ31B magnesium alloy sheet. J Magnes Alloy 6:121–133. https://doi.org/10.1016/j.jma.2018.04.004

    Article  Google Scholar 

  47. Wang YN, Wang JC (2003) Texture analysis in hexagonal materials. Mater Chem Phys 81:11–26. https://doi.org/10.1016/S0254-0584(03)00168-8

    Article  Google Scholar 

  48. Hirsch J, Al-Samman T (2013) Superior light metals by texture engineering: Optimized aliuminum and magnesium alloys for automotive applications. Acta Mater 61:818–843. https://doi.org/10.1016/j.actamat.2012.10.044

    Article  Google Scholar 

  49. Mayama T, Noda M, Chiba R, Kuroda M (2011) Crystal plasticity analysis of texture development in magnesium alloy during extrusion. Int J Plast 27:1916–1935. https://doi.org/10.1016/j.ijplas.2011.02.007

    Article  MATH  Google Scholar 

  50. Chapuis A, Liu Q (2015) Simulations of texture evolution for HCP metals: Influence of the main slip systems. Comput Mater Sci 97:121–126. https://doi.org/10.1016/j.commatsci.2014.10.017

    Article  Google Scholar 

  51. Zhao J, Jiang B, Tao A, Chai Y, Liu B, Sheng H, Yang T, Sheng G, Zhang D, Pan F (2020) Deformation behavior and texture evolution in an extruded Mg-Li sheet with non-basal texture during tensile deformation. Mater Charact 159:110041. https://doi.org/10.1016/j.matchar.2019.110041

    Article  Google Scholar 

  52. Li L, Zhang C, Lv H, Li C, Wen Z, Jiang J (2021) Texture development and tensile properties of Mg–Yb binary alloys during hot extrusion and subsequent annealing. J Magnes Alloy In press. https://doi.org/10.1016/j.jma.2021.05.001

    Article  Google Scholar 

  53. Wang Y, Li F, Wang Y, Xiao XM (2021) Texture property and weakening mechanism of Mg-3Al-1Zn alloy by interactive alternating forward extrusion. J Magnes Alloy In press. https://doi.org/10.1016/j.jma.2021.05.007

    Article  Google Scholar 

  54. Hu L, Lv H, Shi L, Chen Y, Chen Q, Zhou T, Li M, Yang M (2021) Research on deformation mechanism of AZ31 magnesium alloy sheet with non-basal texture during uniaxial tension at room temperature: A visco-plastic self-consistent analysis. J Magnes Alloy In press. https://doi.org/10.1016/j.jma.2020.12.008

    Article  Google Scholar 

  55. Dobron P, Drozdenko D, Fekete K, Knapek M, Bohlen J, Chmelik F (2021) The slip activity during the transition from elastic to plastic tensile deformation of the Mg-Al-Mn sheet. J Magnes Alloy 9:1057–1067. https://doi.org/10.1016/j.jma.2020.12.010

    Article  Google Scholar 

  56. Li D, Wagoner RH (2021) The nature of yielding and anelasticity in metals. Acta Mater 206:116625. https://doi.org/10.1016/j.actamat.2021.116625

    Article  Google Scholar 

  57. Van Dokkum JS, Bos C, Offerman SE, Sietsma J (2021) Influence of dislocations on the apparent elastic constants in single metallic crystallites: an analytical approach. Mater 20:101178. https://doi.org/10.1016/j.mtla.2021.101178

    Article  Google Scholar 

  58. Yoshida F, Uemori T, Fujiwara K (2002) Elastic–plastic behavior of steel sheets under in-plane cyclic tension–compression at large strain. Int J Plast 18:633–659. https://doi.org/10.1016/S0749-6419(01)00049-3

    Article  MATH  Google Scholar 

  59. Guo Q, Zairi F, Guo X (2018) An intrinsic dissipation model for high-cycle fatigue life prediction. Int J Mech Sci 140:163–171. https://doi.org/10.1016/j.ijmecsci.2018.02.047

    Article  Google Scholar 

  60. Yoshida F, Amaishi T (2020) Model for description of nonlinear unloading-reloading stress-strain response with special reference to plastic-strain dependent chord modulus. Int J Plast 130:102708. https://doi.org/10.1016/j.ijplas.2020.102708

    Article  Google Scholar 

  61. Jeong J, Alfeider M, Konetschnik R, Kiener D, Ho OhS (2018) In-situ TEM observation of 10–12 twin-dominated deformation of Mg pillars: Twinning mechanism, size effects and rate dependency. Acta Mater 158:407–421. https://doi.org/10.1016/j.actamat.2018.07.027

    Article  Google Scholar 

  62. Zhang S-L, Xuan F-Z, Guo S-J, Zhao P (2017) The role of anelastic recovery in the creep-fatigue interaction of 9–12% Cr steel at high temperature. Int J Mech Sci 122:95–103. https://doi.org/10.1016/j.ijmecsci.2017.01.018

    Article  Google Scholar 

  63. Zhou G, Jeong W, Homer ER, Fullwood DT, Lee MG, Kim JH, Lim H, Zbib H, Wagoner RH (2020) A predictive strain-gradient model with no undetermined constants or length scales. J Mech Phys Solids 145:104178. https://doi.org/10.1016/j.jmps.2020.104178

    Article  MathSciNet  Google Scholar 

  64. Agnew SR, Duygulu O (2005) Plasticity anisotropy and the role of non-basal slip in magnesium alloy AZ31B. Int J Plast 21:1161–1193. https://doi.org/10.1016/j.ijplas.2004.05.018

    Article  MATH  Google Scholar 

  65. Wang J, Yadav SK, Hirth JP, Tome CN, Beyerlein IJ (2013) Pure-shuffle nucleation of deformation twins in hexagonal-close-packed metals. Mater Res Lett 1:126–132. https://doi.org/10.1080/21663831.2013.792019

    Article  Google Scholar 

  66. McCabe RJ, Arul Kumar M, Liu W, Tome CN, Capolungo L (2021) Revealing the effect of local stresses on twin growth mechanisms in titanium using synchrotron X-ray diffraction. Acta Mater 221:117359. https://doi.org/10.1016/j.actamat.2021.117359

    Article  Google Scholar 

  67. Jia Y, Jiang S, Tan J, Lu Z, Jiang J, Wang X (2021) The evolution of local stress during deformation twinning in a Mg-Gd-Y-Zn alloy. Acta Mater 222:117452. https://doi.org/10.1016/j.actamat.2021.117452

    Article  Google Scholar 

  68. Li J, Li X, Yu M, Sui M (2020) Nucleation mechanism of 10–12 twin with low Schmid factor in hexagonal close-packed metals. Mater Sci Eng A 791:139542. https://doi.org/10.1016/j.msea.2020.139542

    Article  Google Scholar 

  69. Nicolo M, Ventura D, Kalacska S, Casari D, Edwards TEJ, Sharma A, Michler J, Loge R, Maeder X (2021) 10–12 twinning mechanism during in situ micro-tensile loading of pure Mg: role of basal slip and twin-twin interactions. Mater Des 197:109206. https://doi.org/10.1016/j.matdes.2020.109206

    Article  Google Scholar 

  70. Capolungo L, Beyerlein IJ (2008) Nucleation and stability of twins in hcp metals. Phys Rev B 78:1–19. https://doi.org/10.1103/PhysRevB.78.024117

    Article  Google Scholar 

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Acknowledgements

G. Zhu and B. Shi are grateful for fruitful discussions with Prof. Hongwang Zhang from Yanshan University.

Funding

Financial was supported from the projects by the NSFC [51771166], the Hebei Natural Science Foundation [E2019203452, E2021203011], the central government guiding local science and technology development [216Z1001G], the talent project of human resources and social security department of Hebei province [A202002002], the key project of department of education of Hebei province [ZD2021107], Cultivation project for Basic Research and Innovation of Yanshan University [2021LGZD002], and [P2020-013] from the State Key Laboratory of Materials Processing and Die & Mould Technology.

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  1. National Engineering Research Center for Equipment and Technology of Cold Rolled Strip, School of Mechanical Engineering, Yanshan University, Qinhuangdao, 066004, People’s Republic of China

    Guoguo Zhu, Chong Yang, Ge Shen, Yan Peng & Baodong Shi

  2. State Key Laboratory of Metastable Materials Science and Technology, Yanshan University, Qinhuangdao, 066004, People’s Republic of China

    Baodong Shi

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  1. Guoguo Zhu
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Zhu, G., Yang, C., Shen, G. et al. The asymmetric pre-yielding behaviour during tension and compression for a rolled AZ31 Mg alloy. Int J Mater Form 15, 26 (2022). https://doi.org/10.1007/s12289-022-01683-7

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