Technical Papers
Oct 4, 2021

Plasticity Model for Structural Steel with Lode Angle Dependence

Publication: Journal of Bridge Engineering
Volume 26, Issue 12

Abstract

In recent years, the Lode angle was found to have a significant effect on plasticity and fracture strain of ductile metal under shear dominant loading, and the classical J2 plasticity theory generally overestimates the cases under shear dominant loading. In practice, shear dominant loading is common, that is, fillet-welded joints, partial-penetration welded joints, and metallic shear dampers. Therefore, it is important to study plasticity of structural steel under shear dominant loading and develop corresponding plasticity models for accurate evaluation of the plasticity and fracture of metallic structures. A plasticity model considering the effect of the Lode angle was simplified based on previous studies. Eight types of specimens with different configurations were designed to generate different initial stress states. Three different material tests were conducted to figure out little anisotropy in different locations of steel plate. The integration process for the simplified plasticity model were studied, and a user-defined subroutine in ABAQUS was developed for the model. A postnecking modification method for the true stress–true strain was recommended to evaluate the postnecking behaviors of structural steel through comparison of experimental and numerical simulation results. The simplified single parameter plasticity model proved to have high accuracy for specimens under various stress states, and a detailed calibration process for the material parameter was also introduced.

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Acknowledgments

The financial supports from National Natural Science Foundation of China (NSFC) with Grant No. 51820105013 and No. 51971160 are greatly appreciated. Thanks to Dr. Ruiwen Li for the devoting help during the experiments, and Mr. Zucheng Yao for his valuable discussions.

References

Badie, S. S., M. K. Tadros, H. F. Kakish, D. L. Splittgerber, and M. C. Baishya. 2002. “Large shear studs for composite action in steel bridge girders.” J. Bridge Eng. 7 (3): 195–203. https://doi.org/10.1061/(ASCE)1084-0702(2002)7:3(195).
Bai, Y. L., and T. Wierzbicki. 2008. “A new model of metal plasticity and fracture with pressure and Lode dependence.” Int. J. Plast. 24 (6): 1071–1096. https://doi.org/10.1016/j.ijplas.2007.09.004.
Bao, Y. B., and T. Wierzbicki. 2004. “On fracture locus in the equivalent strain and stress triaxiality space.” Int. J. Mech. Sci. 46 (1): 81–98. https://doi.org/10.1016/j.ijmecsci.2004.02.006.
Brainerd, W. S., C. H. Goldberg, and J. C. Adams. 1996. Programmer’s guide to Fortran 90. New York: Springer-Verlag.
Bridgman, P. W. 1952. Studies in large plastic flow and fracture. New York: McGraw-Hill.
Cazacu, O., and F. Barlat. 2001. “Generalization of Drucker’s yield criterion to orthotropy.” Math. Mech. Solids 6 (6): 613–630. https://doi.org/10.1177/108128650100600603.
Chaboche, J. L. 1989. “Constitutive equations for cyclic plasticity and cyclic viscoplasticity.” Int. J. Plast. 5 (3): 247–302. https://doi.org/10.1016/0749-6419(89)90015-6.
Chen, Y. Y., L. L. Pan, and L. J. Jia. 2017. “Post-buckling ductile fracture analysis of panel zones in welded steel beam-to-column connections.” J. Constr. Steel Res. 132: 117–129. https://doi.org/10.1016/j.jcsr.2017.01.015.
Chusilp, P., T. Usami, H. B. Ge, H. Maeno, and T. Aoki. 2002. “Cyclic shear behaviour of steel box girders: Experiment and analysis.” Earthquake Eng. Struct. Dyn. 31 (11): 1993–2014. https://doi.org/10.1002/eqe.200.
CNS (China National Standardization). 2015. Structural steel for bridge. [In Chinese.] GB/T 714-2015. Beijing: Standards Press of China.
Corte, G. D., M. D’Aniello, and R. Landolfo. 2013. “Analytical and numerical study of plastic overstrength of shear links.” J. Constr. Steel Res. 82: 19–32. https://doi.org/10.1016/j.jcsr.2012.11.013.
de Borst, R., M. A. Crisfield, J. J. C. Remmers, and C. V. Verhoosel. 2012. Non-linear finite element analysis of solids and structures. 2nd ed. Hoboken, NJ: Wiley.
Drucker, D. C. 1950. “Relation of experiments to mathematical theories of plasticity.” J. Appl. Mech. 17 (2): 221. https://doi.org/10.1115/1.4010107.
Dunne, F., and N. Petrinic. 2005. Introduction to computational plasticity. Oxford, UK: Oxford University Press.
El-Bahey, S., and M. Bruneau. 2012. “Bridge piers with structural fuses and bi-steel columns. I: Experimental testing.” J. Bridge Eng. 17 (1): 25–35. https://doi.org/10.1061/(ASCE)BE.1943-5592.0000234.
Erice, B., and F. Gálvez. 2014. “A coupled elastoplastic-damage constitutive model with Lode angle dependent failure criterion.” Int. J. Solids Struct. 51 (1): 93–110. https://doi.org/10.1016/j.ijsolstr.2013.09.015.
Gao, X. S., T. T. Zhang, J. Zhou, S. M. Graham, M. Hayden, and C. Roe. 2011. “On stress-state dependent plasticity modeling: Significance of the hydrostatic stress, the third invariant of stress deviator and the non-associated flow rule.” Int. J. Plast. 27 (2): 217–231. https://doi.org/10.1016/j.ijplas.2010.05.004.
Ge, H. B., X. Chen, and N. Matsui. 2011. “Seismic demand on shear panel dampers installed in steel-framed bridge pier structures.” J. Earthquake Eng. 15 (3): 339–361. https://doi.org/10.1080/13632469.2010.491892.
Hill, R. 1948. “A theory of the yielding and plastic flow of anisotropic metals.” Proc. R. Soc. London 193 (1033): 281–297. https://doi.org/10.1098/rspa.1948.0045.
Hill, R. 1950. The mathematical theory of plasticity. Oxford, UK: Clarendon Press.
Hosford, W. F. 1972. “A generalized isotropic yield criterion.” J. Appl. Mech. 39 (2): 607–609. https://doi.org/10.1115/1.3422732.
Ji, X. D., Y. D. Wang, Q. F. Ma, and T. Okazaki. 2015. “Cyclic behavior of very short steel shear links.” J. Struct. Eng. 142 (2): 04015114. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001375.
Jia, L. J. 2014. “Integration algorithm for a modified Yoshida-Uemori model to simulate cyclic plasticity in extremely large plastic strain ranges up to fracture.” Comput. Struct. 145: 36–46. https://doi.org/10.1016/j.compstruc.2014.08.010.
Jia, L. J., H. B. Ge, K. Shinohara, and H. Kato. 2016a. “Experimental and numerical study on ductile fracture of structural steels under combined shear and tension.” J. Bridge Eng. 21 (5): 04016008. https://doi.org/10.1061/(ASCE)BE.1943-5592.0000845.
Jia, L. J., T. Ikai, K. Shinohara, and H. B. Ge. 2016b. “Ductile crack initiation and propagation of structural steels under cyclic combined shear and normal stress loading.” Constr. Build. Mater. 112: 69–83. https://doi.org/10.1016/j.conbuildmat.2016.02.171.
Jia, L. J., J. Y. Xie, Z. Q. Wang, K. Kondo, and H. B. Ge. 2020. “Initial studies on brace-type shear fuses.” Eng. Struct. 208: 110318. https://doi.org/10.1016/j.engstruct.2020.110318.
Johnson, G. R., and W. H. Cook. 1985. “Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures.” Eng. Fract. Mech. 21 (1): 31–48. https://doi.org/10.1016/0013-7944(85)90052-9.
Karafillis, A. P., and M. C. Boyce. 1993. “A general anisotropic yield criterion using bounds and a transformation weighting tensor.” J. Mech. Phys. Solids 41 (12): 1859–1886. https://doi.org/10.1016/0022-5096(93)90073-O.
Kasai, K., and E. P. Popov. 1986. “General behavior of WF steel shear link beams.” J. Struct. Eng. 112 (2): 362–382. https://doi.org/10.1061/(ASCE)0733-9445(1986)112:2(362).
Kwon, G., M. D. Engelhardt, and R. E. Klingner. 2011. “Experimental behavior of bridge beams retrofitted with postinstalled shear connectors.” J. Bridge Eng. 16 (4): 536–545. https://doi.org/10.1061/(ASCE)BE.1943-5592.0000184.
Li, W. C., F. F. Liao, T. H. Zhou, and H. Askes. 2016. “Ductile fracture of Q460 steel: Effects of stress triaxiality and Lode angle.” J. Constr. Steel Res. 123: 1–17. https://doi.org/10.1016/j.jcsr.2016.04.018.
Lode, W. 1925. “10. Versuche über den einfluß der mittleren hauptspannung auf die fließgrenze.” ZAMM 5 (2): 142–144. https://doi.org/10.1002/zamm.19250050215.
Lou, Y. S., and J. W. Yoon. 2017. “Anisotropic ductile fracture criterion based on linear transformation.” Int. J. Plast. 93: 3–25. https://doi.org/10.1016/j.ijplas.2017.04.008.
Mahin, S. A. 1998. “Lessons from damage to steel buildings during the Northridge earthquake.” Eng. Struct. 20 (4–6): 261–270. https://doi.org/10.1016/S0141-0296(97)00032-1.
Mises, R. V. 1913. “Mechanik der festem Koerper im plastisch deformablem Zustand, Goettingen Nachrichten.” Math. Phys. Klasse 4: 582–592.
Nakashima, M., K. Inoue, and M. Tada. 1998. “Classification of damage to steel buildings observed in the 1995 Hyogoken-Nanbu earthquake.” Eng. Struct. 20 (4–6): 271–281. https://doi.org/10.1016/S0141-0296(97)00019-9.
Neto, E. A. d. S., D. Peric, and D. R. J. Owen. 2008. Computational methods for plasticity. Theory and applications. Chichester, UK: John Wiley & Sons.
Simo, J., and T. Hughes. 1998. Computational inelasticity. New York: Springer-Verlag.
Swift, H. W. 1952. “Plastic instability under plane stress.” J. Mech. Phys. Solids 1 (1): 1–18. https://doi.org/10.1016/0022-5096(52)90002-1.
Tresca, H. 1864. Voce, E. 1948. “The relationship between stress and strain for homogeneous deformation.” J. Inst. Met. 74: 537–562.
Wang, Y. B., Y. F. Lyu, Y. Z. Wang, G. Q. Li, and J. Y. R. Liew. 2020. “A reexamination of high strength steel yield criterion.” Constr. Build. Mater. 230: 116945. https://doi.org/10.1016/j.conbuildmat.2019.116945.
Wu, X. G., and S. M. Han. 2010. “Interface shear connection analysis of ultrahigh-performance fiber-reinforced concrete composite girders.” J. Bridge Eng. 15 (5): 493–502. https://doi.org/10.1061/(ASCE)BE.1943-5592.0000091.
Xiang, P., L. J. Jia, M. Shi, and M. Wu. 2017. “Ultra-low cycle fatigue life of aluminum alloy and its prediction using monotonic tension test results.” Eng. Fract. Mech. 186: 449–465. https://doi.org/10.1016/j.engfracmech.2017.11.006.
Xue, L. 2007. “Damage accumulation and fracture initiation in uncracked ductile solids subject to triaxial loading.” Int. J. Solids Struct. 44 (16): 5163–5181. https://doi.org/10.1016/j.ijsolstr.2006.12.026.
Xue, L. 2008. “Constitutive modeling of void shearing effect in ductile fracture of porous materials.” Eng. Fract. Mech. 75 (11): 3343–3366. https://doi.org/10.1016/j.engfracmech.2007.07.022.
Yoon, J. W., Y. S. Lou, J. H. Yoon, and V. M. Glazoff. 2014. “Asymmetric yield function based on the stress invariants for pressure sensitive metals.” Int. J. Plast. 56: 184–202. https://doi.org/10.1016/j.ijplas.2013.11.008.

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Go to Journal of Bridge Engineering
Journal of Bridge Engineering
Volume 26Issue 12December 2021

History

Received: Mar 9, 2021
Accepted: Jul 26, 2021
Published online: Oct 4, 2021
Published in print: Dec 1, 2021
Discussion open until: Mar 4, 2022

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Authors

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Yang Dong
Graduate Student, Dept. of Disaster Mitigation for Structures, Tongji Univ., Shanghai 200092, China.
Liang-Jiu Jia [email protected]
Associate Professor, State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji Univ., Shanghai 200092, China; Associate Professor, Dept. of Disaster Mitigation for Structures, Tongji Univ., Shanghai 200092, China (corresponding author). Email: [email protected]

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