Technical Papers
Jun 27, 2022

Dynamic Hardening Behavior and Ductile Fracture of High-Strength Steel at Intermediate Strain Rates

Publication: Journal of Structural Engineering
Volume 148, Issue 9

Abstract

The mechanical properties of constructional steels at different strain rates were the basis for the dynamic analysis of the progressive collapse of steel structures. The effect of strain rate on the hardening behavior and ductile fracture for the high-strength steel Q690 is investigated in this paper. Quasistatic and intermediate strain-rate experiments were performed. A smooth sheet and a V-shaped notched specimen were carefully designed to cover intermediate and high-stress triaxialities. The experimental results revealed that the effect of strain rate on the hardening behavior is sensitive to stress state. A novel dynamic isotropic hardening law was developed, taking advantage of the Cowper–Symonds and Johnson–Cook hardening models. Also, negative and positive strain-rate effects on the ductility of Q690 were observed in the smooth and notched specimens, respectively. An attempt was made to introduce a new strain-rate term into an uncoupled ductile fracture model to describe the differences of the strain-rate effects at various stress states. The new hardening law and the strain-rate-dependent ductile fracture model were validated with satisfactory accuracy.

Get full access to this article

View all available purchase options and get full access to this article.

Data Availability Statement

Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.

Acknowledgments

The authors would like to gratefully acknowledge the funding support of this research provided by the National Natural Science Foundation of China (No. 51778086), the Shock and Vibration of Engineering Materials and Structures Key Laboratory of Sichuan Province (No. 02180024040012), and the Chongqing Talents Plan for Young Talents (No. CQYC201905055).

References

Bai, Y., 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.
Beatrice, V., S. Bruschi, A. Ghiotti, R. Shivpuri. 2017. “Johnson-Cook based criterion incorporating stress triaxiality and deviatoric effect for predicting elevated temperature ductility of titanium alloy sheets.” Int. J. Mech. Sci. 123 (Apr): 94–105. https://doi.org/10.1016/j.ijmecsci.2017.02.005.
Blaber, J., B. Adair, and A. Antoniou. 2015. “Ncorr: Open-source 2D digital image correlation, MATLAB software.” Exp. Mech. 55 (6): 1105–1122. https://doi.org/10.1007/s11340-015-0009-1.
Cao, J., Z. Sun, L. Huang, and Z. Yin. 2021. “A unified model of ductile fracture considering strain rate and temperature under the complex stress states.” J. Mater. Process Technol. 297 (Nov): 117275. https://doi.org/10.1016/j.jmatprotec.2021.117275.
Cerik, B. C., and J. Choung. 2020. “Rate-dependent combined necking and fracture model for predicting ductile fracture with shell elements at high strain rates.” Int. J. Impact Eng. 146 (Dec): 103697. https://doi.org/10.1016/j.ijimpeng.2020.103697.
Chen, J., J. Li, and Z. Li. 2017a. “Experiment research on rate-dependent constitutive model of Q420 steel.” Constr. Build. Mater. 153 (Oct): 816–823. https://doi.org/10.1016/j.conbuildmat.2017.07.064.
Chen, J., W. Shu, and H. Huang. 2017b. “Rate-dependent progressive collapse resistance of beam-to-column connections with different seismic details.” J. Perform. Constr. Facil. 31 (2): 04016086. https://doi.org/10.1061/(ASCE)CF.1943-5509.0000922.
Chen, J., W. Shu, and J. Li. 2017c. “Constitutive model of Q345 steel at different intermediate strain rates.” Int. J. Steel Struct. 17 (1): 127–137. https://doi.org/10.1007/s13296-016-0122-8.
Chen, W., H. Hao, D. Hughes, Y. Shi, J. Cui, and Z. X. Li. 2015. “Static and dynamic mechanical properties of expanded polystyrene.” Mater. Des. 69 (Mar): 170–180. https://doi.org/10.1016/j.matdes.2014.12.024.
Chiyatan, T., and V. Uthaisangsuk. 2020. “Mechanical and fracture behavior of high strength steels under high strain rate deformation: Experiments and modeling.” Mater. Sci. Eng. 779 (Mar): 139125. https://doi.org/10.1016/j.msea.2020.139125.
Cowper, G. R., and P. S. Symonds. 1957. Strain hardening and strain rate effects in the impact loading of cantilever beams, 28. Fort Belvoir, VA: Defense Technical Information Center.
Das, Y. B., A. N. Forsey, T. H. Simm, K. M. Perkins, M. E. Fitzpatrick, S. Gungor, and R. J. Moat. 2016. “In situ observation of strain and phase transformation in plastically deformed 301 austenitic stainless steel.” Mater. Des. 112 (Dec): 107–116. https://doi.org/10.1016/j.matdes.2016.09.057.
Dong, J. H., D. Y. Kong, Z. Zheng, B. Yang, and M. Elchalakani. 2020. “A dislocation-movement-and-void-growth-motivated ductile fracture criterion considering size effect.” Int. J. Solids Struct. 206 (Dec): 137–152. https://doi.org/10.1016/j.ijsolstr.2020.09.013.
Du, R., C. Mareau, Y. Ayed, E. Giraud, and P. D. Santo. 2020. “Experimental and numerical investigation of the mechanical behavior of the AA5383 alloy at high temperatures.” J. Mater. Process. Technol. 281 (Jul): 116609. https://doi.org/10.1016/j.jmatprotec.2020.116609.
Erice, B., C. C. Roth, and D. Mohr. 2018. “Stress-state and strain-rate dependent ductile fracture of dual and complex phase steel.” Mech. Mater. 116 (Jan): 11–32. https://doi.org/10.1016/j.mechmat.2017.07.020.
Forni, D., B. Chiaia, and E. Cadoni. 2016. “Strain rate behaviour in tension of S355 steel: Base for progressive collapse analysis.” Eng. Struct. 119 (Jul): 164–173. https://doi.org/10.1016/j.engstruct.2016.04.013.
Gatea, S., H. Ou, B. Lu, and G. McCartney. 2017. “Modelling of ductile fracture in single point incremental forming using a modified GTN model.” Eng. Fract. Mech. 186 (Dec): 59–79. https://doi.org/10.1016/j.engfracmech.2017.09.021.
Gurson, A. L. 1977. “Continuum theory of ductile rupture by void nucleation and growth: Part I—Yield criteria and flow rules for porous ductile media.” J. Eng. Mater. Technol. 99 (1): 2–15. https://doi.org/10.1115/1.3443401.
He, J., Z. Cui, F. Chen, Y. Xiao, and L. Ruan. 2013. “The new ductile fracture criterion for 30Cr2Ni4MoV ultra-super-critical rotor steel at elevated temperatures.” Mater. Des. 52 (Dec): 547–555. https://doi.org/10.1016/j.matdes.2013.05.080.
Huh, H., K. Ahn, J. H. Lim, H. W. Kim, and L. J. Park. 2014. “Evaluation of dynamic hardening models for BCC, FCC, and HCP metals at a wide range of strain rates.” J. Mater. Process. Technol. 214 (7): 1326–1340. https://doi.org/10.1016/j.jmatprotec.2014.02.004.
Huh, H., S. J. Lim, Y. S. Lou, N. Park, M. Piao, and G. Joo. 2018. “Ductile fracture criterion of metals based on mechanism maps at a wide range of strain rates.” In Proc., 2nd Int. Conf. on Impact Loading of Structures and Materials. Plenary Lecture. Xi’an, China: Northwestern Polytechnical Univ.
Jia, W., L. Ma, Q. Le, C. Zhi, and P. Liu. 2019. “Deformation and fracture behaviors of AZ31B Mg alloy at elevated temperature under uniaxial compression.” J. Alloys Compd. 783 (Apr): 863–876. https://doi.org/10.1016/j.jallcom.2018.12.260.
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.
Kang, W., S. Cho, H. Huh, and D. Chung. 1999. “Modified Johnson-Cook model for vehicle body crashworthiness simulation.” Int. J. Veh. Des. 21 (4–5): 424–435. https://doi.org/10.1504/IJVD.1999.005594.
Khan, A. S., and S. Huang. 1992. “Experimental and theoretical study of mechanical behavior of 1100 aluminum in the strain rate range 10−5–104 s−1.” Int. J. Plast. 8 (4): 397–424. https://doi.org/10.1016/0749-6419(92)90057-J.
Kumar, G. D. C., V. A. Kumar, R. K. Gupta, S. V. S. N. Murty, and B. P. Kashyap. 2019. “Effect of Strain rate and temperature on the tensile flow behavior and microstructure evolution in Fe-0.3 Pct C-CrMoV grade steel.” Metall. Mater. Trans. A 50 (1): 161–178. https://doi.org/10.1007/s11661-018-4963-y.
Lee, S., and H. Huh. 2021. “Shear stress hardening curves of AISI 4130 steel at ultra-high strain rates with Taylor impact tests.” Int. J. Impact Eng. 149 (Mar): 103789. https://doi.org/10.1016/j.ijimpeng.2020.103789.
Li, M., Z. Zong, H. Hao, X. Zhang, J. Lin, and G. Xie. 2019. “Experimental and numerical study on the behaviour of CFDST columns subjected to close-in blast loading.” Eng. Struct. 185 (Apr): 203–220. https://doi.org/10.1016/j.engstruct.2019.01.116.
Lin, S. C., D. Li, and B. Yang. 2019. “Experimental study and numerical simulation on damage assessment of reinforced concrete beams.” Int. J. Impact Eng. 132 (Oct): 103323. https://doi.org/10.1016/j.ijimpeng.2019.103323.
Liu, J., Y. Tian, and S. L. Orton. 2015. “Resistance of flat-plate buildings against progressive collapse. II: System response.” J. Struct. Eng. 141 (12): 04015054. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001295.
Lou, Y., J. W. Yoon, and H. Huh. 2014. “Modeling of shear ductile fracture considering a changeable cut-off value for stress triaxiality.” Int. J. Plast. 54 (Mar): 56–80. https://doi.org/10.1016/j.ijplas.2013.08.006.
Mohr, D., and S. J. Marcadet. 2015. “Micromechanically-motivated phenomenological Hosford–Coulomb model for predicting ductile fracture initiation at low stress triaxialities.” Int. J. Solids Struct. 67–68 (Aug): 40–55. https://doi.org/10.1016/j.ijsolstr.2015.02.024.
Needleman, A., and V. Tvergaard. 1984. “An analysis of ductile rupture in notched bars.” J. Mech. Phys. Solids 32 (6): 461–490. https://doi.org/10.1016/0022-5096(84)90031-0.
Pandya, K. S., C. C. Roth, and D. Mohr. 2020. “Strain rate and temperature dependent fracture of aluminum alloy 7075: Experiments and neural network modeling.” Int. J. Plast. 135 (Dec): 102788. https://doi.org/10.1016/j.ijplas.2020.102788.
Preston, D. J., D. L. Tonks, and D. C. Wallace. 2003. “Model of plastic deformation for extreme loading conditions.” J. Appl. Phys. 93 (1): 211–220. https://doi.org/10.1063/1.1524706.
Rice, J. R., and D. M. Tracey. 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.
Roth, C. C., and D. Mohr. 2014. “Effect of strain rate on ductile fracture initiation in advanced high strength steel sheets: Experiments and modeling.” Int. J. Plast. 56 (May): 19–44. https://doi.org/10.1016/j.ijplas.2014.01.003.
Song, J. H., and H. Huh. 2007. “The effect of strain rate on the material characteristics of Nickel-based superalloy Inconel 718.” Key Eng. Mater. 340–341 (Jun): 283–288. https://doi.org/10.4028/www.scientific.net/KEM.340-341.283.
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.
Valoppi, B., S. Bruschi, A. Ghiotti, and R. Shivpuri. 2017. “Johnson-Cook based criterion incorporating stress triaxiality and deviatoric effect for predicting elevated temperature ductility of titanium alloy sheets.” Int. J. Mech. Sci. 123 (Apr): 94–105. https://doi.org/10.1016/j.ijmecsci.2017.02.005.
Voce, E. 1948. “The relationship between stress and strain for homogeneous deformations.” J. Inst. Met. 74 (11): 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 (Jan): 116945. https://doi.org/10.1016/j.conbuildmat.2019.116945.
Wu, J., Y. Zhou, R. Zhang, C. Liu, and Z. Zhang. 2020. “Numerical simulation of reinforced concrete slab subjected to blast loading and the structural damage assessment.” Eng. Fail. Anal. 118 (Dec): 104926. https://doi.org/10.1016/j.engfailanal.2020.104926.
Xia, P., F. Vercruysse, R. Petrov, I. Sabirov, M. Castillo-Rodríguez, and P. Verleysen. 2019. “High strain rate tensile behavior of a quenching and partitioning (Q&P) Fe-0.25C-1.5Si-3.0Mn steel.” Mater. Sci. Eng. 745 (Feb): 53–62. https://doi.org/10.1016/j.msea.2018.12.064.
Xiang, P., L. J. Jia, K. Ke, Y. Chen, and H. Ge. 2017. “Ductile cracking simulation of uncracked high strength steel using an energy approach.” J. Constr. Steel Res. 138 (Nov): 117–130. https://doi.org/10.1016/j.jcsr.2017.07.002.
Xie, F., B. Gu, and H. Qian. 2021. “Experimental study on the dynamic behavior of steel frames during progressive collapse.” J. Constr. Steel Res. 177 (Feb): 106459. https://doi.org/10.1016/j.jcsr.2020.106459.
Xu, D. M., X. L. Wan, J. X. Yu, G. Xu, and G. Q. Li. 2019. “Effect of strain rate on microstructures and mechanical properties of Fe–18Cr–8Ni steel.” Mater. Sci. Technol. 35 (2): 195–203. https://doi.org/10.1080/02670836.2018.1548113.
Yin, Q., C. Soyarslan, K. Isik, and A. E. Tekkaya. 2015. “A grooved in-plane torsion test for the investigation of shear fracture in sheet materials.” Int. J. Solids Struct. 66 (Aug): 121–132. https://doi.org/10.1016/j.ijsolstr.2015.03.032.
Zerilli, F. J., and R. W. Armstrong. 1987. “Dislocation-mechanics-based constitutive relations for material dynamics calculations.” J. Appl. Phys. 61 (5): 1816–1825. https://doi.org/10.1063/1.338024.
Zhang, X., Y. Shi, and Z. X. Li. 2019. “Experimental study on the tensile behavior of unidirectional and plain weave CFRP laminates under different strain rates.” Composites, Part B: Eng. 164 (May): 524–536. https://doi.org/10.1016/j.compositesb.2019.01.067.
Zhou, J., X. Gao, J. C. Sobotka, B. A. Webler, and B. V. Cockeram. 2014. “On the extension of the Gurson-type porous plasticity models for prediction of ductile fracture under shear-dominated conditions.” Int. J. Solids Struct. 51 (18): 3273–3291. https://doi.org/10.1016/j.ijsolstr.2014.05.028.

Information & Authors

Information

Published In

Go to Journal of Structural Engineering
Journal of Structural Engineering
Volume 148Issue 9September 2022

History

Received: Dec 16, 2021
Accepted: Apr 4, 2022
Published online: Jun 27, 2022
Published in print: Sep 1, 2022
Discussion open until: Nov 27, 2022

Permissions

Request permissions for this article.

Authors

Affiliations

Ph.D. Candidate, School of Civil Engineering, Chongqing Univ., No. 83 Shabei St., Shapingba District, Chongqing 400045, China; Shock and Vibration of Engineering Materials and Structures Key Laboratory of Sichuan Province, Southwest Univ. of Science and Technology, No. 59,Middle Section of Qinglong Ave., Fucheng District, Mianyang City, Sichuan Province 621010, China. ORCID: https://orcid.org/0000-0002-5087-5409. Email: [email protected]
Mohamed Elchalakani [email protected]
Senior Lecturer, School of Civil, Environmental and Mining Engineering, Univ. of Western Australia, Crawley, WA 6009, Australia. Email: [email protected]
Associate Professor, Shock and Vibration of Engineering Materials and Structures Key Laboratory of Sichuan Province, Southwest Univ. of Science and Technology, No. 59, Middle Section of Qinglong Ave., Fucheng District, Mianyang City, Sichuan Province 621010, China. Email: [email protected]
Associate Professor, School of Civil Engineering, Chongqing Univ., No. 83, Shabei St., Shapingba District, Chongqing 400045, China. Email: [email protected]
Professor, School of Civil Engineering, Chongqing Univ., No. 83, Shabei St., Shapingba District, Chongqing 400045, China (corresponding author). ORCID: https://orcid.org/0000-0001-5374-9208. Email: [email protected]

Metrics & Citations

Metrics

Citations

Download citation

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

Cited by

  • Strain-rate and stress-state dependent ductile fracture model of S690 high-strength steel, Journal of Constructional Steel Research, 10.1016/j.jcsr.2023.107852, 204, (107852), (2023).

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share