DOI QR코드

DOI QR Code

A numerical framework of the phenomenological plasticity and fracture model for structural steels under monotonic loading

  • He, Qun (Department of Building and Real Estate, The Hong Kong Polytechnic University) ;
  • Yam, Michael C.H. (Department of Building and Real Estate, The Hong Kong Polytechnic University) ;
  • Xie, Zhiyang (State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University) ;
  • Lin, Xue-Mei (Department of Building and Real Estate, The Hong Kong Polytechnic University) ;
  • Chung, Kwok-Fai (Chinese National Engineering Research Centre for Steel Construction (Hong Kong Branch), The Hong Kong Polytechnic University)
  • Received : 2021.09.12
  • Accepted : 2022.08.22
  • Published : 2022.08.25

Abstract

In this study, the classical J2 flow theory is explicitly proved to be inappropriate to describe the plastic behaviour of structural steels under different stress states according to the reported test results. A numerical framework of the characterization of the strain hardening and ductile fracture initiation involving the effect of stress states, i.e., stress triaxiality and Lode angle parameter, is proposed based on the mechanical response of structural steels under monotonic loading. Both effects on strain hardening are determined by correction functions, which are implemented as different modules in the numerical framework. Thus, other users can easily modify them according to their test results. Besides, the ductile fracture initiation is determined by a fracture locus in the space of stress triaxiality, Lode angle parameter, and fracture strain. The numerical implementation of the proposed model and the corresponding code are provided in this paper, which are also available on GitHub. The validity of the numerical procedure is examined through single element tests and the accuracy of the proposed model is verified by existing test results.

Keywords

Acknowledgement

The work described in this paper is fully supported by a grant from the Chinese National Engineering Research Centre (CNERC) for Steel Construction (Hong Kong Branch) at The Hong Kong Polytechnic University (Project No. 1-BBV4).

References

  1. Bai, Y. (2008), Effect of Loading History in Necking and Fracture, Ph.D. Dissertation, Massachusetts Institute of Technology, Boston, USA. https://dspace.mit.edu/handle/1721.1/43148.
  2. Bai, Y. and Wierzbicki, T. (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.
  3. Bai, Y. and Wierzbicki, T. (2009), "Application of extended Mohr-Coulomb criterion to ductile fracture", Int. J. Fract., 161(1), 1. https://doi.org/10.1007/s10704-009-9422-8.
  4. Barsoum, I., Faleskog, J. and Pingle, S. (2011), "The Influence of the Lode Parameter on Ductile Failure Strain in Steel", Procedia Eng., 10, 69-75. https://doi.org/10.1016/j.proeng.2011.04.014.
  5. Barsoum, I. and Faleskog, J. (2007a), "Rupture mechanisms in combined tension and shear-Experiments", Int. J. Solids Struct., 44(6), 1768-1786. https://doi.org/10.1016/j.ijsolstr.2006.09.031.
  6. Barsoum, I. and Faleskog, J. (2007b), "Rupture mechanisms in combined tension and shear-Micromechanics", Int. J. Solids Struct., 44(17), 5481-5498. https://doi.org/10.1016/j.ijsolstr.2007.01.010.
  7. Besson, J. (2010). "Continuum models of ductile fracture: A review", Int. J. Damage Mech., 19(1), 3-52. https://doi.org/10.1177/1056789509103482.
  8. Bonora, N. (1997), "A nonlinear CDM model for ductile failure", Eng. Fract. Mech., 58(1), 11-28. https://doi.org/10.1016/S0013-7944(97)00074-X.
  9. Bridgman, P.W. (1964), Studies in Large Plastic Flow and Fracture with Special Emphasis on the Effects of Hydrostatic Pressure. Harvard University Press, Cambridge, USA
  10. Chi, W.M., Kanvinde, A.M. and Deierlein, G.G. (2006), "Prediction of ductile fracture in steel connections using SMCS criterion", J. Struct. Eng., 132(2), 171-181. https://doi.org/10.1061/(ASCE)0733-9445(2006)132:2(171).
  11. Dassault Systemes Simulia Corporation (2020), ABAQUS Analysis User's Manual Version 2020.
  12. Hancock, J.W. and Mackenzie, A.C. (1976), "On the mechanisms of ductile failure in high-strength steels subjected to multi-axial stress-states", J. Mech. Phys. Solids, 24(2), 147-160. https://doi.org/10.1016/0022-5096(76)90024-7.
  13. He, Q., Chen, Y., Ke, K., Yam, M.C.H. and Wang, W. (2019), "Experiment and constitutive modeling on cyclic plasticity behavior of LYP100 under large strain range", Constr. Build. Mater., 202, 507-521. https://doi.org/10.1016/j.conbuildmat.2018.12.146.
  14. Ho, H.C., Xiao, M., Hu, Y.F., Guo, Y.B., Chung, K.F., Yam, M.C. H. and Nethercot, D.A. (2020), "Determination of a full range constitutive model for high strength S690 steels", J. Constr. Steel Res., 174, 106275. https://doi.org/10.1016/j.jcsr.2020.106275.
  15. Huang, X., Ge, J., Zhao, J. and Zhao, W. (2020), "A continuous damage model of Q690D steel considering the influence of Lode parameter and its application", Constr. Build. Mater., 262, 120067. https://doi.org/10.1016/j.conbuildmat.2020.120067.
  16. Huanga, X. and Zhao, J. (2017), "A cumulative damage model for extremely low cycle fatigue cracking in steel structure", Struct. Eng. Mech., 62(2), 225-236. https://doi.org/10.12989/sem.2017.62.2.225.
  17. Jia, L.J., Ge, H., Shinohara, K. and Kato, H. (2016), "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.
  18. Jia, L.J., Ikai, T., Kang, L., Ge, H. and Kato, T. (2016), "Ductile cracking simulation procedure for welded joints under monotonic tension", Struct. Eng. Mech., 60(1), 51-69. https://doi.org/10.12989/SEM.2016.60.1.051.
  19. Jia, L.J. and Kuwamura, H. (2014), "Ductile fracture simulation of structural steels under monotonic tension", J. Struct. Eng., 140(5), 04013115. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000944.
  20. Johnson, G.R. and Cook, W. H. (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.
  21. Kang, L., Ge, H. and Fang, X. (2016), "An improved ductile fracture model for structural steels considering effect of high stress triaxiality", Constr. Build. Mater., 115, 634-650. https://doi.org/10.1016/j.conbuildmat.2016.04.083.
  22. Kang, L., Ge, H., Suzuki, M. and Wu, B. (2018), "An average weight whole-process method for predicting mechanical and ductile fracture performances of HSS Q690 after a fire", Constr. Build. Mater., 191, 1023-1041. https://doi.org/10.1016/j.conbuildmat.2018.10.068.
  23. Kanvinde, A.M. and Deierlein, G.G. (2006), "The void growth model and the stress modified critical strain model to predict ductile fracture in structural steels", J. Struct. Eng., 132(12), 1907-1918. https://doi.org/10.1061/(ASCE)0733-9445(2006)132:12(1907).
  24. Kanvinde, A.M. and Deierlein, G.G. (2007), "Cyclic void growth model to assess ductile fracture initiation in structural steels due to ultra low cycle fatigue", J. Eng. Mech., 133(6), 701-712. https://doi.org/10.1061/(ASCE)0733-9399(2007)133:6(701).
  25. Kanvinde, A.M., Fell, B.V., Gomez, I.R. and Roberts, M. (2008), "Predicting fracture in structural fillet welds using traditional and micromechanical fracture models", Eng. Struct., 30(11), 3325-3335. https://doi.org/10.1016/j.engstruct.2008.05.014.
  26. Kong, D.Y., Ren, L.M., Yang, B., Zhou, X.H. and Elchalakani, M. (2020), "Comparative study of uncoupled ductile-fracture models on fracture prediction of structural steels under monotonic loading", J. Eng. Mech., 146(8), 04020080. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001807.
  27. Kong, D.Y. and Yang, B. (2020), "Enhanced voids growth model for ductile fracture prediction of high-strength steel q690d under monotonic tension: experiments and numerical simulation", J. Struct. Eng., 146(6), 04020107. https://doi.org/10.1061/(ASCE)ST.1943-541X.0002658.
  28. Lemaitre, J. (1985), "A continuous damage mechanics model for ductile fracture." J. Eng. Mater. Technol., 107(1), 83-89. https://doi.org/10.1115/1.3225775.
  29. Li, D., Uy, B., Wang, J. and Song, Y. (2020), "Behaviour and design of grade 10.9 high-strength bolts under combined actions", Steel Compos. Struct., 35(3), 327-341. https://doi.org/10.12989/SCS.2020.35.3.327.
  30. Li, H., Fu, M. W., Lu, J. and Yang, H. (2011), "Ductile fracture: Experiments and computations", Int. J. Plast., 27(2), 147-180. https://doi.org/10.1016/j.ijplas.2010.04.001.
  31. Li, W., Liao, F., Zhou, T. and Askes, H. (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.
  32. Liao, F., Wang, W. and Chen, Y. (2012), "Parameter calibrations and application of micromechanical fracture models of structural steels", Struct. Eng. Mech., 42(2), 153-174. https://doi.org/10.12989/sem.2012.42.2.153.
  33. Liao, F., Wang, W. and Chen, Y. (2015), "Ductile fracture prediction for welded steel connections under monotonic loading based on micromechanical fracture criteria", Eng. Struct., 94, 16-28. https://doi.org/10.1016/j.engstruct.2015.03.038.
  34. Lin, X.M., Yam, M.C.H., Chung, K.F. and Lam, A.C.C. (2021), "A study of net-section resistance of high strength steel bolted connections", Thin-Walled Struct., 159, 107284. https://doi.org/10.1016/j.tws.2020.107284.
  35. Liu, Y., Kang, L. and Ge, H. (2019). "Experimental and numerical study on ductile fracture of structural steels under different stress states", J. Constr. Steel Res., 158, 381-404. https://doi.org/10.1016/j.jcsr.2019.04.001.
  36. Lou, Y. and Huh, H. (2013), "Prediction of ductile fracture for advanced high strength steel with a new criterion: Experiments and simulation." J. Mater. Process. Technol., 213(8), 1284-1302. https://doi.org/10.1016/j.jmatprotec.2013.03.001
  37. Lou, Y. and Yoon, J.W. (2018). "Anisotropic yield function based on stress invariants for BCC and FCC metals and its extension to ductile fracture criterion." Int. J. Plast., 101, 125-155. https://doi.org/10.1016/j.ijplas.2017.10.012.
  38. Myers, A.T., Kanvinde, A.M. and Deierlein, G.G. (2010), "Calibration of the smcs criterion for ductile fracture in steels: specimen size dependence and parameter assessment", J. Eng. Mech., 136(11), 1401-1410. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000178.
  39. Park, T., Abu-Farha, F. and Pourboghrat, F. (2019), "An evolutionary yield function model based on plastic work and non-associated flow rule", Metals, 9(5), 611. https://doi.org/10.3390/met9050611.
  40. Pineau, A., Benzerga, A.A. and Pardoen, T. (2016), "Failure of metals I: Brittle and ductile fracture", Acta Mater., 107, 424-483. https://doi.org/10.1016/j.actamat.2015.12.034.
  41. Rice, J.R. and Tracey, D.M. (1969), "On the ductile enlargement of voids in triaxial stress fields∗", J. Mech. Phys. Solids, 17(3), 201-217. https://doi.org/10.1016/0022-5096(69)90033-7.
  42. Safaei, M., Lee, M.G., Zang, S. and De Waele, W. (2014), "An evolutionary anisotropic model for sheet metals based on nonassociated flow rule approach", Comput. Mater. Sci., 81, 15-29. https://doi.org/10.1016/j.commatsci.2013.05.035.
  43. Simo, J.C. and Hughes, T.J.R. (1998), Computational Inelasticity. Springer, New York, USA
  44. Stoughton, T.B. (2002), "A non-associated flow rule for sheet metal forming", Int. J. Plast., 18(5), 687-714. https://doi.org/10.1016/S0749-6419(01)00053-5.
  45. Wang, Jia, Uy, B., Li, D. and Song, Y. (2020), "Progressive collapse analysis of stainless steel composite frames with beamto-column endplate connections", Steel Compos. Struct., 36(4), 427-446. https://doi.org/10.12989/SCS.2020.36.4.427.
  46. Wang, J. and Sun, Q. (2019), "Seismic behavior of Q690 circular HCFTST columns under constant axial loading and reversed cyclic lateral loading", Steel Compos. Struct., 32(2), 199-212. https://doi.org/10.12989/SCS.2019.32.2.199.
  47. Wang, M., Shi, Y. and Wang, Y. (2012), "Equivalent constitutive model of steel with cumulative degradation and damage", J. Constr. Steel Res., 79, 101-114. https://doi.org/10.1016/j.jcsr.2012.07.028.
  48. Wang, M., Shi, Y. and Wang, Y. (2015), "Application of steel equivalent constitutive model for predicting seismic behavior of steel frame", Steel Compos. Struct., 19(5), 1055-1075. https://doi.org/10.12989/SCS.2015.19.5.1055.
  49. Wang, Y.B., Lyu, Y.F., Wang, Y.Z., Li, G.Q. and Richard Liew, J.Y. (2020), "A reexamination of high strength steel yield criterion", Constr. Build. Mater., 230, 116945. https://doi.org/10.1016/j.conbuildmat.2019.116945.
  50. Wang, Y.Z., Li, G.Q., Wang, Y.B., Lyu, Y.F. and Li, H. (2020), "Ductile fracture of high strength steel under multi-axial loading", Eng. Struct., 210, 110401. https://doi.org/10.1016/j.engstruct.2020.110401.
  51. Wen, H. and Mahmoud, H. (2016), "New model for ductile fracture of metal alloys. i: monotonic loading", J. Eng. Mech., 142(2), 04015088. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001009.
  52. Wierzbicki, T., Bao, Y., Lee, Y.-W., and Bai, Y. (2005), "Calibration and evaluation of seven fracture models", Int. J. Mech. Sci., 47(4), 719-743. https://doi.org/10.1016/j.ijmecsci.2005.03.003.
  53. Xie, Z. and Chen, Y. (2022), "Numerical study of the robustness of steel moment connections under catenary effect", Eng. Struct., 252, 113658. https://doi.org/10.1016/j.engstruct.2021.113658.
  54. Xue, L. (2007), Ductile Fracture Modeling: Theory, Experimental Investigation and Numerical Verification, Ph.D. Dissertation, Massachusetts Institute of Technology, Boston, USA. https://dspace.mit.edu/handle/1721.1/40876.
  55. Xue, L. and Wierzbicki, T. (2008), "Ductile fracture initiation and propagation modeling using damage plasticity theory", Eng. Fract. Mech., 75(11), 3276-3293. https://doi.org/10.1016/j.engfracmech.2007.08.012.
  56. Yan, S., Zhao, X. and Wu, A. (2018), "Ductile fracture simulation of constructional steels based on yield-to-fracture stress-strain relationship and micromechanism-based fracture criterion", J. Struct. Eng., 144(3), 04018004. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001970.
  57. Yang, F., Veljkovic, M. and Liu, Y. (2020), "Ductile damage model calibration for high-strength structural steels", Constr. Build. Mater., 263, 120632. https://doi.org/10.1016/j.conbuildmat.2020.120632.
  58. Zhu, J., Xia, Y., Luo, H., Gu, G. and Zhou, Q. (2014), "Influence of flow rule and calibration approach on plasticity characterization of DP780 steel sheets using Hill48 model", Int. J. Mech. Sci., 89, 148-157. https://doi.org/10.1016/j.ijmecsci.2014.09.001.
  59. Zhuang, C., Mu, L., Zhang, J., Jiang, R. and Jia, Z. (2021), "Ductile fracture characterization of a36 steel and comparative study of phenomenological models", J. Mater. Civ. Eng., 33(1), 04020421. https://doi.org/10.1061/(ASCE)MT.1943-5533.0003543.