This study on the Bauschinger effect of extruded magnesium AZ31B during low-cycle fatigue (LCF) addresses the limited quantification of cyclic plasticity and tension–compression asymmetry in biodegradable Mg alloys for temporary orthopaedic fixation. Fully reversed (Rε = −1), strain-controlled LCF tests were conducted at strain amplitudes of 0.006, 0.008, and 0.010 mm/mm (n = 3 per level) to characterize the Bauschinger response through stress-, strain-, and backstress-based indices. The Bauschinger effect factor decreased monotonically from 0.984 to 0.947, the normalized Bauschinger strain ratio fell from 0.843 to 0.680, and the backstress indicator rose more than threefold, from 0.93 to 3.18 MPa, with increasing strain amplitude. SEM fractography confirmed this trend, showing a transition from rough, serrated ridges at 0.006 mm/mm to facet-dominated, heavily torn surfaces at 0.010 mm/mm, consistent with intensifying slip–twinning heterogeneity and grain-boundary strain incompatibility underlying the Bauschinger effect. An empirical strain-life relation achieved a leave-one-out MAPE of 7.24%, closely matching the Coffin–Manson–Basquin fit (in-sample MAPE = 1.45%). Together, these results quantify how the Bauschinger effect in extruded AZ31B intensifies with strain amplitude and link this behaviour to fatigue-life prediction, offering a mechanistic basis for LCF-based screening of Mg-alloy implant candidates.

Mg AZ31B, Low-cycle fatigue, Bauschinger effect, Kinematic hardening, Strain-life model

[1] L. Song, G. Duan, C. Han, J. Zhou, H. Liu, Y. Liu, B. Wu, Enhanced low-cycle fatigue life of an extruded AZ31B alloy after pre-ratcheting deformation. Materialia, 39, 2025: 102379.
https://doi.org/10.1016/j.mtla.2025.102379
[2] I. Sukmana, F. Ibrahim, M. Badaruddin, H. Nur, Low cycle fatigue properties of extruded magnesium AZ31B. FME Transactions, 50(3), 2022: 422–432.
https://doi.org/10.5937/fme2203422S
[3] P. Rider, Ž. Perić Kačarević, A. Elad, D. Rothamel, G. Sauer, F. Bornert, P. Windisch, D. Hangyási, B. Molnar, B. Hesse, M. Assad, F. Witte, Biodegradation of a magnesium alloy fixation screw used in a guided bone regeneration model in beagle dogs. Materials, 15(12), 2022: 4111.
https://doi.org/10.3390/ma15124111
[4] S. Söntgen, L. Keilig, K. Kabir, A. Weber, S. Reimann, K. Welle, C. Bourauel, Mechanical and numerical investigations of biodegradable magnesium alloy screws for fracture treatment. Journal of Biomedical Materials Research Part B: Applied Biomaterials, 111(1), 2022: 7–15. https://doi.org/10.1002/jbm.b.35127
[5] Y. Luo, F. Liu, Z. Chen, Y. Luo, W. Li, J. Wang, A magnesium screw with optimized geometry exhibits improved corrosion resistance and favors bone fracture healing. Acta Biomaterialia, 178, 2024: 320–329. https://doi.org/10.1016/j.actbio.2024.03.002
[6] J. Sun, Z. Li, S. Liu, T. Xia, J. Shen, Biodegradable magnesium screw, titanium screw and direct embedding fixation in pedicled vascularized iliac bone graft transfer for osteonecrosis of the femoral head: a randomized controlled study. Journal of Orthopaedic Surgery and Research, 18(1), 2023: 523. https://doi.org/10.1186/s13018-023-04012-z
[7] Ž. Perić Kačarević, P. Rider, A. Elad, D. Tadic, D. Rothamel, G. Sauer, F. Bornert, P. Windisch, D. B. Hangyási, B. Molnar, T. Kämmerer, B. Hesse, E. Bortel, M. Bartosch, F. Witte, Biodegradable magnesium fixation screw for barrier membranes used in guided bone regeneration. Bioactive Materials, 14, 2022: 15–30. https://doi.org/10.1016/j.bioactmat.2021.10.036
[8] M. Nasr Azadani, A. Zahedi, O.K. Bowoto, B.I. Oladapo, A review of current challenges and prospects of magnesium and its alloy for bone implant applications. Progress in Biomaterials, 11(1), 2022: 1–26. https://doi.org/10.1007/s40204-022-00182-x
[9] Y. Zhou, A. Zhang, J. Wu, S. Guo, Q. Sun, Application and perspectives: Magnesium materials in bone regeneration. ACS Biomaterials Science & Engineering, 10(6), 2024: 3514–3527.
https://doi.org/10.1021/acsbiomaterials.3c01713
[10] Y. Gao, H. Huang, X. Jiang, T. Ha, Y. Li, K. Zhang, C. Wang, L. Wang, Y. Fan, Effect of mechanical loading on osseointegration combined with degradation behavior of magnesium bone screw in vivo. Applied Materials Today, 32, 2023: 101793. https://doi.org/10.1016/j.apmt.2023.101793
[11] M. Ye, Y.K. Wu, Y.F. Lv, C. Xin, Q. Wang, Variation of low-cycle fatigue life in TA5 alloy as a function of different cyclic deformation mechanisms. Journal of Materials Engineering and Performance, 35, 2026: 6757-6767. https://doi.org/10.1007/s11665-025-12043-2
[12] G. Liu, J. Han, Y. Li, Y. Guo, X. Yu, S. Yuan, Z. Nie, C. Tan, C. Guo, Effects of inorganic ions, organic particles, blood cells, and cyclic loading on in vitro corrosion of Mg–Al alloys. Journal of Magnesium and Alloys, 11(7), 2023: 2429–2441. https://doi.org/10.1016/j.jma.2021.08.034
[13] H.-G. Nguyen, S.-J. Young, T.-D. Le, T.-N. Vu, T.-H. Fang, Bauschinger effect on high-entropy alloy under cyclic deformation. Intermetallics, 183, 2025: 108830.
https://doi.org/10.1016/j.intermet.2025.108830
[14] J. Chen, X. Xiao, S. Xiong, J. Wang, H. Huang, B. Yang, Low cycle fatigue behavior of Cu-Cr-Zr alloy with different cold deformation. Fatigue & Fracture of Engineering Materials & Structures, 46(1), 2023: 3–16. https://doi.org/10.1111/ffe.13842
[15] W. Wang, C. Fang, Y. Ji, Y. Lu, M. C. H. Yam, Experimental and numerical studies on Fe–Mn–Si alloy dampers for enhanced low-cycle fatigue resistance. Journal of Structural Engineering, 148(11), 2022: 04022170. https://doi.org/10.1061/(ASCE)ST.1943-541X.0003459
[16] M.A. Bakkar, R. Saha, D. Das, Low-cycle fatigue performance and failure analysis of reinforcing bar. Metals and Materials International, 27(12), 2021: 4952–4966. https://doi.org/10.1007/s12540-020-00839-x
[17] X. Chen, J. Yue, X. Wu, J. Lei, X. Fang, A damage-coupled elasto-plastic constitutive model of marine high-strength steels under low-cycle fatigue loading. International Journal of Pressure Vessels and Piping, 205, 2023: 104982. https://doi.org/10.1016/j.ijpvp.2023.104982
[18] Z. Wang, S. Wu, Y. Lei, Q. Kan, G. Kang, Damage evolution of extruded magnesium alloy from deformation twinning and dislocation slipping in uniaxial stress-controlled low cycle fatigue. International Journal of Fatigue, 164, 2022: 107124. https://doi.org/10.1016/j.ijfatigue.2022.107124
[19] C.-H. Li, Z. Vidmar, B. Saxey, M. Reynolds, C.-M. Uang, A procedure for assessing low-cycle fatigue life of buckling-restrained braces. Journal of Structural Engineering, 148(2), 2022: 04021259. https://doi.org/10.1061/(ASCE)ST.1943-541X.0003237
[20] A. Mandal, K.D. Sharma, S. Bagui, K. Barat, S. Patra, A. Karmakar, Tempering-microstructure reciprocity on low-cycle fatigue properties of Cu-modified quenched-and-tempered steel. Materials Science and Engineering: A, 950, 2026: 149474. https://doi.org/10.1016/j.msea.2025.149474
[21] H. Ban, X. Yang, L. Hai, Y. Shi, Low-cycle fatigue behaviour and fracture feature of stainless-clad bimetallic steel. Journal of Constructional Steel Research, 196, 2022: 107437.
https://doi.org/10.1016/j.jcsr.2022.107437
[22] M. Li, S. Maskill, Z. Wen, Z. Yue, W. Sun, A miniaturized thin-plate low-cycle fatigue test method at elevated temperature. Fatigue & Fracture of Engineering Materials & Structures, 45(5), 2022: 1361–1378. https://doi.org/10.1111/ffe.13665
[23] L. Pagliari, R. Gerosa, D. Panzeri, F. Concli, High- and low-cycle fatigue of a 6060 aluminium alloy. WIT Transactions on the Built Environment, 216, 2025: 37–49. https://doi.org/10.2495/HPSM250041
[24] Z. Lyu, C. Liu, D. Xie, R. Feng, D. Yu, Y. Chen, K. An, Y. Gao, H. Wang, P.K. Liaw, Low cycle fatigue performances of Al_0.3CoCrFeNi high entropy alloys: In situ neutron diffraction studies on the precipitation effects. Intermetallics, 168, 2024: 108241. https://doi.org/10.1016/j.intermet.2024.108241
[25] Y. Gao, G. Shi, X. Wang, Mechanical properties of low-yield-point steels subjected to low-cycle structural damage. Journal of Constructional Steel Research, 183, 2021: 106733.
https://doi.org/10.1016/j.jcsr.2021.106733
[26] H. Alwahsh, S. Salawdeh, Y. Jiang, J. Goggins, Extremely low-cycle fatigue testing of structural carbon steel for a novel self-centring system. In: Civil Engineering Research in Ireland conference 2024 (CERI2024), 29-30 August 2024, Galway, Ireland, pp.500-505. https://doi.org/10.13025/29497
[27] Z. Zeng, G. Li, S.-W. Liu, D.-H. Huang, Y.-P. Liu, S.-L. Chan, Low-cycle fatigue of laser-arc hybrid-welded S960 high-strength steel joints. Journal of Constructional Steel Research, 236, 2026: 110040. https://doi.org/10.1016/j.jcsr.2025.110040
[28] C. Bai, L. Lan, R. Xin, S. Gao, B. He, Microstructure evolution and cyclic deformation behavior of Ti-6Al-4V alloy fabricated by electron-beam melting during low-cycle fatigue. International Journal of Fatigue, 159, 2022: 106784. https://doi.org/10.1016/j.ijfatigue.2022.106784
[29] L. Ávila de Oliveira Silva, G. Adinolfi Colpaert Sartori, D. Bondarchuk, I.M. Oliveira Anício Costa, C. Mesplont, J.-B. Vogt, Effect of interlamellar spacing on the low-cycle fatigue behavior of a fully pearlitic steel. Metallography, Microstructure, and Analysis, 10(5), 2021: 692–699.
https://doi.org/10.1007/s13632-021-00775-1
[30] X. Liu, F. Yuan, Y. Zhu, X. Wu, Extraordinary Bauschinger effect in gradient-structured copper. Heterostructured Materials, 2021: 361–370. https://doi.org/10.1201/9781003153078-23
[31] T. Touch, S. Kishiki, S. Yamada, Low-cycle fatigue performances including large plastic strain of SUS821L1 lean duplex stainless steel. Proceedings of the 11^th International Conference on Behaviour of Steel Structures in Seismic Areas. Lecture Notes in Civil Engineering, 519, 2024: 162–171.
https://doi.org/10.1007/978-3-031-62884-9_14
[32] B. Xu, B. Huang, S. Tang, X. Xu, H. Peng, C. Wang, Q. Wang, Effects of temperature, loading frequency, stress amplitude, and stress ratio on the low-cycle fatigue behavior of FeMnSiCrNi shape-memory alloys. Acta Mechanica Solida Sinica, 39, 2026: 133-151. https://doi.org/10.1007/s10338-025-00617-5
[33] M. Buttard, T. Lenoir, B. Chéhab, C. Josserond, A. Deschamps, J.-J. Blandin, G. Martin, Bauschinger effect in an aluminium alloy designed for laser powder-bed fusion. Materialia, 34, 2024: 102093. https://doi.org/10.1016/j.mtla.2024.102093
[34] P. Zhu, J. Lin, R. Xiao, H. Zhou, Unravelling the physical origin of the Bauschinger effect in glassy polymers. Journal of the Mechanics and Physics of Solids, 168, 2022: 105046.
https://doi.org/10.1016/j.jmps.2022.105046
[35] O. Bouaziz, H.S. Kim, J. Lee, Y. Estrin, Bauschinger effect or kinematic hardening: Bridging microstructure and continuum mechanics. Metals and Materials International, 29(2), 2023: 280–292. https://doi.org/10.1007/s12540-022-01227-3
[36] X. Zhu, X. Yang, W. Huang, M. Liu, X. Wang, M. Li, Modeling the Bauschinger effect through the reversibility of dislocation slip in an Al–Cu–Li alloy. Materials Science and Engineering: A, 902, 2024: 146574. https://doi.org/10.1016/j.msea.2024.146574
[37] S. Gao, K. Yoshino, D. Terada, Y. Kaneko, N. Tsuji, Significant Bauschinger effect and backstress strengthening in ultrafine-grained pure aluminum fabricated by severe plastic deformation. Scripta Materialia, 211, 2022: 114503. https://doi.org/10.1016/j.scriptamat.2022.114503
[38] X. Du, S. Shuang, J. Zhao, Z. Fu, Q. Kan, X. Zhang, Extra strengthening and Bauschinger effect in a gradient high-entropy alloy: A molecular-dynamics study. International Journal of Mechanical Sciences, 264, 2024: 108829. https://doi.org/10.1016/j.ijmecsci.2023.108829
[39] P. Vourna, N.D. Papadopoulos, K. Argiris, P.P. Falara, E. Hristoforou, Magnetic evaluation of the Bauschinger effect in marine engineering steels. NDT & E International, 139, 2023: 102933. https://doi.org/10.1016/j.ndteint.2023.102933
[40] W. He, M. Wan, B. Meng, Size effect on nonlinear unloading behavior and the Bauschinger effect of a Ni-based superalloy ultrathin sheet. International Journal of Mechanical Sciences, 231, 2022: 107563. https://doi.org/10.1016/j.ijmecsci.2022.107563
[41] A. Ellermann, B. Scholtes, The Bauschinger effect in different heat-treatment conditions of 42CrMo4. International Journal of Structural Changes in Solids – Mechanics and Applications, 3(1), 2011: 1–13.
[42] M. Kreins, K. Büßenschütt, S. Wesselmecking, U. Krupp, On the impact of nanoscale γ′′ precipitates on the Bauschinger effect in single- and polycrystal Ni-base superalloy 718. Materials Science and Engineering: A, 856, 2022: 144008. https://doi.org/10.1016/j.msea.2022.144008
[43] R.R. Adigamov, V.A. Andreev, S.O. Rogachev, E.S. Fedotov, G.E. Khadeev, V.S. Yusupov, Bauschinger effect in alternating deformation. Steel in Translation, 52(7), 2022: 639–647.
https://doi.org/10.3103/S0967091222070026
[44] Z. Hu, M.C. Gibson, A.P. Parker, Swage autofrettage finite-element analysis incorporating a user function to model the actual Bauschinger effect. International Journal of Pressure Vessels and Piping, 191, 2021: 104372. https://doi.org/10.1016/j.ijpvp.2021.104372
[45] A. Martinez-Pechero, E. Demir, C. Hardie, Y. Zayachuk, A. Widdowson, E. Tarleton, Modelling the Bauschinger effect in copper during preliminary load cycles. Acta Materialia, 289, 2025: 120886.
https://doi.org/10.1016/j.actamat.2025.120886
[46] S. Lu, D. Huang, C. Liang, Y. Feng, Orientation-dependent yield and Bauschinger effects in two-dimensional Yukawa solids. Physical Review Research, 6(3), 2024: 033211.
https://doi.org/10.1103/PhysRevResearch.6.033211
[47] C.J. Geng, B.L. Wu, X.H. Du, Y.D. Wang, Y.D. Zhang, F. Wagner, C. Esling, Low cycle fatigue behavior of the textured AZ31B magnesium alloy under the asymmetrical loading. Materials Science and Engineering: A, 560, 2013: 618–626. https://doi.org/10.1016/j.msea.2012.10.004