Full-Range Stress–Strain Curves for Aluminum Alloys
Publication: Journal of Structural Engineering
Volume 147, Issue 6
Abstract
Aluminum alloys are being increasingly used in a wide range of construction applications owing to their sound mechanical properties, lightness in weight, strong corrosion resistance, ability to be formed into complex and efficient cross-sectional shapes, and natural aesthetics. Aluminum alloys are characterized by a rounded stress–strain response, with no sharply defined yield point. Such behavior can be accurately represented using Ramberg–Osgood-type equations. In the present study, use of a two-stage Ramberg–Osgood model to describe the full-range stress–strain behavior of aluminum alloys is proposed and, following careful analysis of a comprehensive database of aluminum alloy coupon test data assembled from the literature, standardized values or predictive expressions for the required input parameters are derived. The experimental database includes over 700 engineering stress–strain curves obtained from 56 sources and covers five common aluminum alloy grades: 5052-H36, 6061-T6, 6063-T5, 6082-T6, and 7A04-T6. The developed model is shown to be more accurate in predicting the full-range stress–strain response of aluminum alloys than existing expressions, and is suitable for use in the analytical modeling, numerical simulation, and advanced design of aluminum alloy structures.
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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.
Acknowledgments
The authors would like to thank Dr. Meini Su from the University of Manchester, Prof. Xiaonong Guo and Dr. Feng Zhou from Tongji University, Prof. Ximei Zhai from Harbin Institute of Technology, Prof. Jihua Zhu from Shenzhen University, Dr. Mei Liu from Shandong University, Dr. Cao Hung Pham from the University of Sydney, and Prof. Yuanqing Wang from Tsinghua University for the provision of experimental stress–strain curves.
References
AA (Aluminum Association). 2010. Aluminum design manual. Washington, DC: AA.
Aalberg, A. 2015. “Design of aluminium beam ends with flange copes.” Thin-Walled Struct. 94 (Sep): 593–602. https://doi.org/10.1016/j.tws.2015.06.003.
Alsanat, H., S. Gunalan, H. Guan, P. Keerthan, and J. Bull. 2019. “Experimental study of aluminium lipped channel sections subjected to web crippling under two flange load cases.” Thin-Walled Struct. 141 (Aug): 460–476. https://doi.org/10.1016/j.tws.2019.01.050.
Arrayago, I., E. Real, and L. Gardner. 2015. “Description of stress–strain curves for stainless steel alloys.” Mater. Des. 87 (Dec): 540–552. https://doi.org/10.1016/j.matdes.2015.08.001.
AS (Standards Australia). 2007. Metallic materials—Tensile testing at ambient temperature. AS 1391. Sydney, NSW, Australia: AS.
AS (Standards Australia). 1997. Aluminum structures part 1: Limit state design. AS/NZS 1664.1. Sydney, NSW, Australia: AS.
ASTM. 2013. Standard test methods for tension testing of metallic materials. ASTM E8/E8M-15a. West Conshohocken, PA: ASTM.
Baehre, R. 1966. Trycktastravorav elastoplastikt material-nagrafragestallninga [Comparison between structural behaviour of elastoplastic material]. [In German.]. Stockholm, Sweden: De Arne Johnson Ingenjorsbyra.
Brando, G., G. Sarracco, and G. De Matteis. 2015. “Strength of an aluminum column web in tension.” J. Struct. Eng. 141 (7): 04014180. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001138.
CEN (European Committee for Standardization). 2007. Eurocode 9: Design of aluminum structures—Part 1-1: General rules—General rules and rules for buildings. BS EN 1999-1-1. Brussels, Belgium: CEN.
CEN (European Committee for Standardization). 2009. Metallic materials—Tensile testing—Part 1: Method of test at ambient temperature. BS EN ISO 6892-1. Brussels, Belgium: CEN.
Chen, W., H. Deng, S. Dong, and Z. Zhu. 2018. “Numerical modelling of lockbolted lap connections for aluminium alloy plates.” Thin-Walled Struct. 130 (Sep): 1–11. https://doi.org/10.1016/j.tws.2018.04.010.
Chen, Y., R. Feng, and J. Xu. 2017. “Flexural behaviour of CFRP strengthened concrete-filled aluminium alloy CHS tubes.” Constr. Build. Mater. 142 (Jul): 295–319. https://doi.org/10.1016/j.conbuildmat.2017.03.040.
Chen, Y., M. Li, X. Yang, and W. Luo. 2020. “Damage and failure characteristics of CFRP/aluminum single lap joints designed for lightweight applications.” Thin-Walled Struct. 153 (Aug): 106802. https://doi.org/10.1016/j.tws.2020.106802.
Cho, Y., and T. Kim. 2016. “Estimation of ultimate strength in single shear bolted connections with aluminum alloys (6061-T6).” Thin-Walled Struct. 101 (Apr): 43–57. https://doi.org/10.1016/j.tws.2015.11.017.
Davies, A. W., and T. M. Roberts. 1999. “Resistance of welded aluminum alloy plate girders to shear and patch loading.” J. Struct. Eng. 125 (8): 930–938. https://doi.org/10.1061/(ASCE)0733-9445(1999)125:8(930).
De Matteis, G., A. Mandara, and F. M. Mazzolani. 2000. “T-stub aluminium joints: Influence of behavioural parameters.” Comput. Struct. 78 (1–3): 311–327. https://doi.org/10.1016/S0045-7949(00)00081-X.
Dundu, M. 2018. “Evolution of stress–strain models of stainless steel in structural engineering applications.” Constr. Build. Mater. 165 (Mar): 413–423. https://doi.org/10.1016/j.conbuildmat.2018.01.008.
Đuričić, Đ., S. Aleksić, B. Šćepanović, and D. Lučić. 2017. “Experimental, theoretical and numerical analysis of K-joint made of CHS aluminium profiles.” Thin-Walled Struct. 119 (Oct): 58–71.
Dwight, J. 1998. Aluminium design and construction. London: E & FN Spon.
Faella, C., F. M. Mazzolani, V. Piluso, and G. Rizzano. 2000. “Local buckling of aluminum members: Testing and classification.” J. Struct. Eng. 126 (3): 353–360. https://doi.org/10.1061/(ASCE)0733-9445(2000)126:3(353).
Feng, R., Z. Chen, C. Shen, K. Roy, B. Chen, and J. B. Lim. 2020. “Flexural capacity of perforated aluminium CHS tubes—An experimental study.” Structures 25 (Jun): 463–480. https://doi.org/10.1016/j.istruc.2020.03.025.
Feng, R., W. Sun, C. Shen, and J. Zhu. 2017. “Experimental investigation of aluminum square and rectangular beams with circular perforations.” Eng. Struct. 151 (Nov): 613–632. https://doi.org/10.1016/j.engstruct.2017.08.053.
Feng, R., and B. Young. 2015. “Experimental investigation of aluminum alloy stub columns with circular openings.” J. Struct. Eng. 141 (11): 04015031. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001265.
Feng, R., W. Zhu, H. Wan, A. Chen, and Y. Chen. 2018. “Tests of perforated aluminium alloy SHSs and RHSs under axial compression.” Thin-Walled Struct. 130 (Sep): 194–212. https://doi.org/10.1016/j.tws.2018.03.017.
Fieber, A., L. Gardner, and L. Macorini. 2020. “Structural steel design using second-order inelastic analysis with strain limits.” J. Constr. Steel Res. 168 (May): 105980. https://doi.org/10.1016/j.jcsr.2020.105980.
Fukumoto, Y. 1996. “New constructional steels and structural stability.” Eng. Struct. 18 (10): 786–791. https://doi.org/10.1016/0141-0296(96)00008-9.
Gardner, L. 2019. “Stability and design of stainless steel structures—Review and outlook.” Thin-Walled Struct. 141 (Aug): 208–216. https://doi.org/10.1016/j.tws.2019.04.019.
Gardner, L., and M. Ashraf. 2006. “Structural design for non-linear metallic materials.” Eng. Struct. 28 (6): 926–934. https://doi.org/10.1016/j.engstruct.2005.11.001.
Gardner, L., Y. Bu, P. Francis, N. R. Baddoo, K. A. Cashell, and F. McCann. 2016. “Elevated temperature material properties of stainless steel reinforcing bar.” Constr. Build. Mater. 114 (Jul): 977–997. https://doi.org/10.1016/j.conbuildmat.2016.04.009.
Gardner, L., A. Insausti, K. T. Ng, and M. Ashraf. 2010. “Elevated temperature material properties of stainless steel alloys.” J. Constr. Steel Res. 66 (5): 634–647. https://doi.org/10.1016/j.jcsr.2009.12.016.
Gardner, L., and X. Yun. 2018. “Description of stress-strain curves for cold-formed steels.” Constr. Build. Mater. 189 (Nov): 527–538. https://doi.org/10.1016/j.conbuildmat.2018.08.195.
Gardner, L., X. Yun, A. Fieber, and L. Macorini. 2019. “Steel design by advanced analysis: Material modeling and strain limits.” Engineering 5 (2): 243–249. https://doi.org/10.1016/j.eng.2018.11.026.
Guo, X. N. 2006. “Theoretical and experimental research on the aluminum alloy structure members.” [In Chinese.] Ph.D. thesis, College of Civil Engineering, Tongji Univ.
Guo, X. N., L. Tao, S. Zhu, and S. Zong. 2020. “Experimental investigation of mechanical properties of aluminum alloy at high and low temperatures.” J. Mater. Civ. Eng. 32 (2): 06019016. https://doi.org/10.1061/(ASCE)MT.1943-5533.0003002.
He, L., C. Liu, Z. Wu, and J. Yuan. 2019. “Stability analysis of an aluminum alloy assembly column in a modular support structure.” Thin-Walled Struct. 135 (Feb): 548–559. https://doi.org/10.1016/j.tws.2018.11.026.
Hill, H. N. 1944. Determination of stress-strain relations from the offset yield strength values. Washington, DC: National Advisory Committee for Aeronautics.
Hopperstad, O. S., M. Langseth, and T. Tryland. 1999. “Ultimate strength of aluminium alloy outstands in compression: Experiments and simplified analysis.” Thin-Walled Struct. 34 (4): 279–294. https://doi.org/10.1016/S0263-8231(99)00013-0.
Hradil, P., A. Talja, E. Real, E. Mirambell, and B. Rossi. 2013. “Generalized multistage mechanical model for nonlinear metallic materials.” Thin-Walled Struct. 63 (Feb): 63–69. https://doi.org/10.1016/j.tws.2012.10.006.
Huang, Y., and B. Young. 2014. “The art of coupon tests.” J. Constr. Steel Res. 96 (May): 159–175. https://doi.org/10.1016/j.jcsr.2014.01.010.
Huynh, L. A. T., C. H. Pham, and K. J. R. Rasmussen. 2019. “Mechanical properties and residual stresses in cold-rolled aluminium channel sections.” Eng. Struct. 199 (Nov): 109562. https://doi.org/10.1016/j.engstruct.2019.109562.
Islam, S. Z., and B. Young. 2012. “Web crippling of aluminium tubular structural members strengthened by CFRP.” Thin-Walled Struct. 59 (Oct): 58–69. https://doi.org/10.1016/j.tws.2012.05.002.
Jiang, S., Z. Xiong, X. Guo, and Z. He. 2018. “Buckling behaviour of aluminium alloy columns under fire conditions.” Thin-Walled Struct. 124 (Mar): 523–537. https://doi.org/10.1016/j.tws.2017.12.035.
Jiang, Y., H. Ma, J. R. Liew, and F. Fan. 2020. “Testing of aluminum alloyed bolted joints for connecting aluminum rectangular hollow sections in reticulated shells.” Eng. Struct. 218 (Sep): 110848. https://doi.org/10.1016/j.engstruct.2020.110848.
Kim, T., and Y. Cho. 2014. “Investigation on ultimate strength and failure mechanism of bolted joints in two different aluminum alloys.” Mater. Des. 58 (Jun): 74–88. https://doi.org/10.1016/j.matdes.2014.01.045.
Liu, H., J. Ying, Y. Meng, and Z. Chen. 2019a. “Flexural behavior of double-and single-layer aluminum alloy gusset-type joints.” Thin-Walled Struct. 144 (Nov): 106263. https://doi.org/10.1016/j.tws.2019.106263.
Liu, M., L. Zhang, P. Wang, and Y. Chang. 2015. “Buckling behaviors of section aluminum alloy columns under axial compression.” Eng. Struct. 95 (Jul): 127–137. https://doi.org/10.1016/j.engstruct.2015.03.064.
Liu, Y., H. Liu, and Z. Chen. 2019b. “Post-fire mechanical properties of aluminum alloy 6082-T6.” Constr. Build. Mater. 196 (Jan): 256–266. https://doi.org/10.1016/j.conbuildmat.2018.10.237.
Ma, H., Y. Jiang, C. Li, Z. Yu, and F. Fan. 2020. “Performance analysis and comparison study of two aluminum alloy joint systems under out-of-plane and in-plane loading. An experimental and numerical investigation.” Eng. Struct. 214 (Jul): 110643. https://doi.org/10.1016/j.engstruct.2020.110643.
May, J. E., and C. C. Menzemer. 2005. “Strength of bolted aluminum alloy tension members.” J. Struct. Eng. 131 (7): 1125–1134. https://doi.org/10.1061/(ASCE)0733-9445(2005)131:7(1125).
Mazzolani, F. M. 1972. “Characterization of the law and buckling of aluminum columns.” Constr. Metal 3.
Mazzolani, F. M. 1995. Aluminium alloy structures. 2nd ed. London: E & FN Spon.
Mazzolani, F. M., V. Piluso, and G. Rizzano. 2011. “Local buckling of aluminum alloy angles under uniform compression.” J. Struct. Eng. 137 (2): 173–184. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000289.
Mirambell, E., and E. Real. 2000. “On the calculation of deflections in structural stainless steel beams: An experimental and numerical investigation.” J. Constr. Steel Res. 54 (1): 109–133. https://doi.org/10.1016/S0143-974X(99)00051-6.
Quach, W. M., and J. F. Huang. 2011. “Stress-strain models for light gauge steels.” Procedia Eng. 14: 288–296. https://doi.org/10.1016/j.proeng.2011.07.035.
Quach, W. M., J. G. Teng, and K. F. Chung. 2008. “Three-stage full-range stress-strain model for stainless steels.” J. Struct. Eng. 134 (9): 1518–1527. https://doi.org/10.1061/(ASCE)0733-9445(2008)134:9(1518).
Ramberg, W., and W. R. Osgood. 1943. Description of stress-strain curves by three parameters. Washington, DC: National Advisory Committee for Aeronautics.
Rasmussen, K. J. R. 2003. “Full-range stress–strain curves for stainless steel alloys.” J. Constr. Steel Res. 59 (1): 47–61. https://doi.org/10.1016/S0143-974X(02)00018-4.
Rønning, L., A. Aalberg, and P. K. Larsen. 2010. “An experimental study of ultimate compressive strength of transversely stiffened aluminium panels.” Thin-Walled Struct. 48 (6): 357–372. https://doi.org/10.1016/j.tws.2010.01.015.
Rouholamin, M., S. Gunalan, K. Poologanathan, and H. Karampour. 2020. “Experimental study of roll-formed aluminium lipped channel beams in shear.” Thin-Walled Struct. 153 (Aug): 106687. https://doi.org/10.1016/j.tws.2020.106687.
Shi, M., P. Xiang, and M. Wu. 2018. “Experimental investigation on bending and shear performance of two-way aluminum alloy gusset joints.” Thin-Walled Struct. 122 (Jan): 124–136. https://doi.org/10.1016/j.tws.2017.10.002.
Su, M. N., and B. Young. 2019. “Material properties of normal and high strength aluminium alloys at elevated temperatures.” Thin-Walled Struct. 137 (Apr): 463–471. https://doi.org/10.1016/j.tws.2019.01.012.
Su, M. N., B. Young, and L. Gardner. 2014. “Testing and design of aluminum alloy cross sections in compression.” J. Struct. Eng. 140 (9): 04014047. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000972.
Su, M. N., B. Young, and L. Gardner. 2015. “Continuous beams of aluminum alloy tubular cross sections. I: Tests and FE model validation.” J. Struct. Eng. 141 (9): 04014232. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001214.
Tajeuna, T. A., F. Légeron, P. Labossière, M. Demers, and S. Langlois. 2015. “Effect of geometrical parameters of aluminum-to-steel bolted connections.” Eng. Struct. 102 (Nov): 344–357. https://doi.org/10.1016/j.engstruct.2015.08.010.
Tryland, T., M. Langseth, and O. S. Hopperstad. 1999. “Nonperfect aluminum beams subjected to concentrated loading.” J. Struct. Eng. 125 (8): 900–909. https://doi.org/10.1061/(ASCE)0733-9445(1999)125:8(900).
Walport, F., L. Gardner, and D. A. Nethercot. 2019. “A method for the treatment of second order effects in plastically-designed steel frames.” Eng. Struct. 200 (Dec): 109516. https://doi.org/10.1016/j.engstruct.2019.109516.
Wang, Y. J., F. Fan, H. Qian, and X. M. Zhai. 2013. “Experimental study on constitutive model of high-strength aluminum alloy 6082-T6.” J. Build. Struct. 34 (6): 113–120.
Wang, Y. Q., and Z. X. Wang. 2016. “Experimental investigation and FE analysis on constitutive relationship of high strength aluminum alloy under cyclic loading.” Adv. Mater. Sci. Eng. 2016: 1–16. https://doi.org/10.1155/2016/2941874.
Wang, Y. Q., Z. X. Wang, X. G. Hu, J. K. Han, and H. J. Xing. 2016. “Experimental study and parametric analysis on the stability behavior of 7A04 high-strength aluminum alloy angle columns under axial compression.” Thin-Walled Struct. 108 (Nov): 305–320. https://doi.org/10.1016/j.tws.2016.08.029.
Wang, Z. X., Y. Q. Wang, J. Sojeong, and Y. W. Ouyang. 2018a. “Experimental investigation and parametric analysis on overall buckling behavior of large-section aluminum alloy columns under axial compression.” Thin-Walled Struct. 122 (Jan): 585–596. https://doi.org/10.1016/j.tws.2017.11.003.
Wang, Z. X., Y. Q. Wang, X. Yun, L. Gardner, and X. G. Hu. 2020. “Experimental and numerical study of fixed-ended high strength aluminum alloy angle section columns.” J. Struct. Eng. 146 (10): 04020206. https://doi.org/10.1061/(ASCE)ST.1943-541X.0002773.
Wang, Z. X., Y. Q. Wang, J. Zhang, M. Liu, and Y. W. Ouyang. 2018b. “Experimental investigation on deformation performance and stiffness of TEMCOR joints in aluminum alloy spatial reticulated shell structures.” In Vol. 23 of Proc., IASS Annual Symposia, 1–8. Madrid, Spain: International Association for Shell and Spatial Structures.
Wang, Z. X., Y. Q. Wang, Y. Zhang, L. Gardner, and Y. W. Ouyang. 2019. “Experimental investigation and design of extruded aluminium alloy T-stubs connected by swage-locking pins.” Eng. Struct. 200 (Dec): 109675. https://doi.org/10.1016/j.engstruct.2019.109675.
Yalçın, M. M., and K. Genel. 2019. “On the axial deformation characteristic of PVC foam-filled circular aluminium tube: Effect of radially-graded foam filling.” Thin-Walled Struct. 144 (Nov): 106335. https://doi.org/10.1016/j.tws.2019.106335.
Yuan, H. X., Y. Q. Wang, T. Chang, X. X. Du, Y. D. Bu, and Y. J. Shi. 2015. “Local buckling and postbuckling strength of extruded aluminium alloy stub columns with slender I-sections.” Thin-Walled Struct. 90 (May): 140–149. https://doi.org/10.1016/j.tws.2015.01.013.
Yun, X., and L. Gardner. 2017. “Stress-strain curves for hot-rolled steels.” J. Constr. Steel Res. 133 (Jun): 36–46. https://doi.org/10.1016/j.jcsr.2017.01.024.
Zha, Y., and T. Moan. 2003. “Experimental and numerical prediction of collapse of flatbar stiffeners in aluminum panels.” J. Struct. Eng. 129 (2): 160–168. https://doi.org/10.1061/(ASCE)0733-9445(2003)129:2(160).
Zhao, Y., X. Zhai, and J. Wang. 2019. “Buckling behaviors and ultimate strengths of 6082-T6 aluminum alloy columns under eccentric compression—Part I: Experiments and finite element modeling.” Thin-Walled Struct. 143 (Oct): 106207. https://doi.org/10.1016/j.tws.2019.106207.
Zhou, F., and B. Young. 2009. “Concrete-filled aluminum circular hollow section column tests.” Thin-Walled Struct. 47 (11): 1272–1280. https://doi.org/10.1016/j.tws.2009.03.014.
Zhou, F., and B. Young. 2018. “Concrete-filled double-skin aluminum circular hollow section stub columns.” Thin-Walled Struct. 133 (Dec): 141–152. https://doi.org/10.1016/j.tws.2018.09.037.
Zhou, F., and B. Young. 2019. “Aluminium alloy channels subjected to web crippling.” Adv. Struct. Eng. 22 (7): 1617–1630. https://doi.org/10.1177/1369433218819564.
Zhu, J. H., Z. Q. Li, M. N. Su, and B. Young. 2019. “Behaviour of aluminium alloy plain and lipped channel columns.” Thin-Walled Struct. 135 (Feb): 306–316. https://doi.org/10.1016/j.tws.2018.11.010.
Zhu, J. H., and B. Young. 2006. “Experimental investigation of aluminum alloy circular hollow section columns.” Eng. Struct. 28 (2): 207–215. https://doi.org/10.1016/j.engstruct.2005.07.012.
Zhu, P., Q. Zhang, X. Luo, Y. Ouyang, and J. Yin. 2020. “Experimental and numerical studies on ductile-fracture-controlled ultimate resistance of bars in aluminum alloy gusset joints under monotonic tensile loading.” Eng. Struct. 204 (Feb): 109834. https://doi.org/10.1016/j.engstruct.2019.109834.
Zhu, S., X. Guo, X. Liu, and S. Jiang. 2018. “Bearing capacity of aluminum alloy members under eccentric compression at elevated temperatures.” Thin-Walled Struct. 127 (Jun): 574–587. https://doi.org/10.1016/j.tws.2018.02.030.
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Journal of Structural Engineering
Volume 147 • Issue 6 • June 2021
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© 2021 American Society of Civil Engineers.
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Received: Jul 4, 2020
Accepted: Jan 6, 2021
Published online: Mar 24, 2021
Published in print: Jun 1, 2021
Discussion open until: Aug 24, 2021
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