Evolution of Localization Length during Postpeak Response of Steel in Tension: Experimental Study
Publication: Journal of Engineering Mechanics
Volume 146, Issue 7
Abstract
This paper presents an experimental study into the influence of localization length () and its evolution during the postpeak response of cylindrical low-carbon steel bars. A novel longitudinal strain method for the determination of the localization length is compared to the average strain method. Four specimen lengths [38.1 mm (1.5 in.), 76.2 mm (3 in.), 152.4 mm (6 in.), and 304.8 mm (12 in.)] with a diameter of 12.7 mm (0.5 in.) were tested according to ASTM A370 standards. A three-dimensional digital image correlation (3D DIC) measurement system was used to record the longitudinal and transverse deformations along the specimen length. The results indicate that the engineering stress-strain relation up to the peak load is almost identical for all tested specimens. However, the postpeak response shows a steeper softening response for longer specimens. Two methods were used to extract the localization length from the longitudinal engineering strain profile. The average strain method shows a length dependence for different specimen lengths, while the longitudinal strain method eliminates the length dependence. The consistency of the localization length obtained through the longitudinal strain method enables improved generalized analytical relationships. Linear and exponential curve fitting formulae are given to predict the localization length for a generic specimen.
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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. Items available include the data from the experimental tests (load, displacement, longitudinal strain, and transverse strain).
Acknowledgments
Student support for Saif Altai was provided by the Ministry of Higher Education and Scientific Research (MoHESR), Iraq. The opinions, findings, and conclusions or recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of the sponsor.
References
Altai, S. 2019. “Experimental and analytical investigation of localization and post-peak behavior of steel members in tension.” Ph.D. dissertation, Dept. of Civil and Environmental Engineering, Univ. of Missouri-Columbia.
ASTM. 2017. Standard test methods and definitions for mechanical testing of steel products. ASTM A370. West Conshohocken, PA: ASTM.
Audoly, B., and J. W. Hutchinson. 2016. “Analysis of necking based on a one-dimensional model.” J. Mech. Phys. Solids 97 (Dec): 68–91. https://doi.org/10.1016/j.jmps.2015.12.018.
Bao, C., M. Francois, and L. Le Joncour. 2016. “A closer look at the diffuse and localised necking of a metallic thin sheet: Evolution of the two bands pattern.” Strain 52 (3): 244–260. https://doi.org/10.1111/str.12184.
Bažant, Z. P. 1976. “Instability, ductility and size-effect in strain-softening concrete.” J. Eng. Mech. Div. 1976 (Apr): 331–343.
Bažant, Z. P. 2003a. “Asymptotic matching analysis of scaling of structural failure due to softening hinges. I: Theory.” J. Eng. Mech. 129 (6): 641–650. https://doi.org/10.1061/(ASCE)0733-9399(2003)129:6(641).
Bažant, Z. P. 2003b. “Asymptotic matching analysis of structural failure due to softening hinges. II: Implications.” J. Eng. Mech. 129 (6): 651–654. https://doi.org/10.1061/(ASCE)0733-9399(2003)129:6(651).
Bažant, Z. P., and L. Cedolin. 2010. “Stability of structures.” In Vol. 60 of Elastic, inelastic, fracture and damage theories. 1st ed. New York: Oxford University Press.
Bigoni, D. 2012. Nonlinear solid mechanics: Bifurcation theory and material instability. Cambridge, UK: Cambridge University Press.
Chen, Z., Y. Gan, and J. F. Labuz. 2008. “Analytical and numerical study of the size effect on the failure response of hierarchical structures.” Int. J. Multiscale Comput. Eng. 6 (4): 339–348. https://doi.org/10.1615/IntJMultCompEng.v6.i4.50.
Dai, H.-H., X. Zhu, and Z. Chen. 2011. “An analytical study on the post-peak structural response.” J. Appl. Mech. 78 (4): 044501. https://doi.org/10.1115/1.4003740.
Dantec Dynamics. 2017. “ISTRA 4D: Software manual Q-400 system 4.4.6 v2.” Accessed March 24, 2020. https://www.dantecdynamics.com/.
Elices, M., and J. Planas. 1989. “Material models.” In Proc., Fracture Mechanics of Concrete Structures, 16–66. London: Chapman and Hall.
Hill, R., and J. W. Hutchinson. 1975. “Bifurcation phenomena in the plane tension test.” J. Mech. Phys. Solids 23 (4–5): 239–264. https://doi.org/10.1016/0022-5096(75)90027-7.
Jansen, D. C., and S. P. Shah. 1997. “Effect of length on compressive strain softening of concrete.” J. Eng. Mech. 123 (1): 25–35. https://doi.org/10.1061/(ASCE)0733-9399(1997)123:1(25).
Jirásek, M. 2004. “Nonlocal theories in continuum mechanics.” Acta Polytech. 44 (5–6): 16–34.
Jirásek, M., and S. Rolshoven. 2009a. “Localization properties of strain-softening gradient plasticity models. I: Strain-gradient theories.” Int. J. Solids Struct. 46 (11–12): 2225–2238. https://doi.org/10.1016/j.ijsolstr.2008.12.016.
Jirásek, M., and S. Rolshoven. 2009b. “Localization properties of strain-softening gradient plasticity models. II: Theories with gradients of internal variables.” Int. J. Solids Struct. 46 (11–12): 2239–2254. https://doi.org/10.1016/j.ijsolstr.2008.12.018.
Kolwankar, S., A. Kanvinde, M. Kenawy, and S. Kunnath. 2017. “Uniaxial nonlocal formulation for geometric nonlinearity–induced necking and buckling localization in a steel bar.” J. Struct. Eng. 143 (9): 04017091. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001827.
Kotronis, P., S. Al Holo, P. Bésuelle, and R. Chambon. 2008. “Shear softening and localization: Modelling the evolution of the width of the shear zone.” Acta Geotech. 3 (2): 85–97. https://doi.org/10.1007/s11440-008-0061-4.
Li, Y., and D. G. Karr. 2009. “Prediction of ductile fracture in tension by bifurcation, localization, and imperfection analyses.” Int. J. Plast. 25 (6): 1128–1153. https://doi.org/10.1016/j.ijplas.2008.07.001.
Markeset, G., and A. Hillerborg. 1995. “Softening of concrete in compression-localization and size effects.” Cem. Concr. Res. 25 (4): 702–708. https://doi.org/10.1016/0008-8846(95)00059-L.
Needleman, A. 2018. “Effect of size on necking of dynamically loaded notched bars.” Mech. Mater. 116 (Jan): 180–188. https://doi.org/10.1016/j.mechmat.2016.09.007.
Okazawa, S. 2010. “Structural bifurcation for ductile necking localization.” Int. J. Non-Linear Mech. 45 (1): 35–41. https://doi.org/10.1016/j.ijnonlinmec.2009.08.010.
Petit, J., G. Montay, and M. François. 2018. “Strain localization in mild (low carbon) steel observed by acoustic emission: ESPI coupling during tensile test.” Exp. Mech. 58 (5): 743–758. https://doi.org/10.1007/s11340-018-0379-2.
Pijaudier-Cabot, G., Z. P. Bažant, and M. Tabbara. 1988. “Comparison of various models for strain-softening.” Eng. Comput. 5 (2): 141–150. https://doi.org/10.1108/eb023732.
Rolshoven, S., and M. Jirásek. 2002. “Nonlocal formulations of softening plasticity.” In Proc., WCCMV, 5th World Congress on Computational Mechanics, 1–10. Vienna, Austria: Vienna Univ. of Technology.
Schreyer, H. L., and Z. Chen. 1986. “One-dimensional softening with localization.” J. Appl. Mech. 53 (4): 791. https://doi.org/10.1115/1.3171860.
Sideris, P., and M. Salehi. 2016. “A gradient inelastic flexibility-based frame element formulation.” J. Eng. Mech. 142 (7): 04016039. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001083.
Wattrisse, B., A. Chrysochoos, J. M. Muracciole, and M. Némoz-Gaillard. 2001. “Analysis of strain localization during tensile tests by digital image correlation.” Exp. Mech. 41 (1): 29–39. https://doi.org/10.1007/BF02323101.
Yalcinkaya, T., and G. Lancioni. 2014. “Energy-based modeling of localization and necking in plasticity.” Procedia Mater. Sci. 3 (2004): 1618–1625. https://doi.org/10.1016/j.mspro.2014.06.261.
Zhu, F., P. Bai, J. Zhang, D. Lei, and X. He. 2015. “Measurement of true stress–strain curves and evolution of plastic zone of low carbon steel under uniaxial tension using digital image correlation.” Opt. Lasers Eng. 65 (Feb): 81–88. https://doi.org/10.1016/j.optlaseng.2014.06.013.
Zhu, Y., A. Kanvinde, and Z. Pan. 2019. “Analysis of post-necking behavior in structural steels using a one-dimensional nonlocal model.” Eng. Struct. 180 (Feb): 321–331. https://doi.org/10.1016/j.engstruct.2018.11.050.
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©2020 American Society of Civil Engineers.
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Received: Mar 1, 2019
Accepted: Feb 18, 2020
Published online: Apr 28, 2020
Published in print: Jul 1, 2020
Discussion open until: Sep 28, 2020
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