Testing and Analysis of Additively Manufactured Stainless Steel Corrugated Cylindrical Shells in Compression
Publication: Journal of Engineering Mechanics
Volume 149, Issue 4
Abstract
Initial geometric imperfections have been identified as the main cause for the large discrepancies between experimental and theoretical buckling loads of thin-walled circular cylindrical shells under axial compression. The extreme sensitivity to imperfections has been previously addressed and mitigated through the introduction of stiffeners; however, sensitivity still remains. Optimized corrugated cylindrical shells are largely insensitive to imperfections and hence exhibit excellent load-bearing capacities, but their complex geometries make their construction difficult and costly using conventional manufacturing techniques. This was overcome in the present study through additive manufacturing (AM). Nine optimized corrugated shells with different diameter-to-thickness ratios, together with one reference circular cylindrical shell, were additively manufactured by means of powder bed fusion (PBF) from austenitic and martensitic precipitation hardening stainless steel. The structural behavior of the AM shells was then investigated experimentally with the testing program comprising tensile coupon tests, measurements of basic geometric properties, and axial compression tests. Numerical analyses were also conducted following completion of the physical experiments. The experimental and numerical results verified the effectiveness of optimized corrugated cylindrical shells in achieving improved local buckling capacity and reduced imperfection sensitivity. Initial recommendations for the structural design of the studied cross-sections are made.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
Some data for the PBF 316L stainless steel shells, 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 acknowledge the contribution of the LUT Laser Laboratory for building the test specimens and the financial support from the China Scholarship Council. We are grateful to the copyright holder (Ernst & Sohn) for permission to reproduce part of the article “Optimisation and compressive testing of additively manufactured stainless steel corrugated shells” from Proceedings of 9th European Conference on Steel and Composite Structures (Eurosteel 2021) (Zhang et al. 2021b).
References
Afkhami, S., V. Javaheri, E. Dabiri, H. Piili, and T. Björk. 2022. “Effects of manufacturing parameters, heat treatment, and machining on the physical and mechanical properties of 13Cr10Ni1.7Mo2Al0.4Mn0.4Si steel processed by laser powder bed fusion.” Mater. Sci. Eng., A 832 (Jan): 142402. https://doi.org/10.1016/j.msea.2021.142402.
Araar, M., M. Derbali, and J. F. Jullien. 1998. “Buckling of the multi-vaulted ‘Aster’ shell under axial compression alone or combined with an external pressure.” Struct. Eng. Mech. 6 (7): 827–839. https://doi.org/10.12989/sem.1998.6.7.827.
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.
Asgari, H., and M. Mohammadi. 2018. “Microstructure and mechanical properties of stainless steel CX manufactured by direct metal laser sintering.” Mater. Sci. Eng., A 709 (Jan): 82–89. https://doi.org/10.1016/j.msea.2017.10.045.
Ashraf, M., L. Gardner, and D. A. Nethercot. 2006. “Compression strength of stainless steel cross-sections.” J. Constr. Steel Res. 62 (1–2): 105–115. https://doi.org/10.1016/j.jcsr.2005.04.010.
CEN (European Committee for Standardization). 2006. Design of steel structures—Part 1-5: Plated structural elements. EN 1993-1-5:2006, Eurocode 3. Brussels, Belgium: CEN.
CEN (European Committee for Standardization). 2015. Design of steel structures—Part 1-4: General rules—Supplementary rules for stainless steels. EN 1993-1-4:2006+A1:2015, Eurocode 3. Brussels, Belgium: CEN.
CEN (European Committee for Standardization). 2016. Metallic materials—Tensile testing—Part 1: Method of test at room temperature. EN ISO 6892-1. Brussels, Belgium: CEN.
CEN (European Committee for Standardization). 2017. Design of steel structures—Part 1-6: Strength and stability of shell structures. EN 1993-1-6:2007+A1:2017, Eurocode 3. Brussels, Belgium: CEN.
Combescure, A., and J. F. Jullien. 2015. “ASTER Shell: A simple concept to significantly increase the plastic buckling strength of short cylinders subjected to combined external pressure and axial compression.” Adv. Model. Simul. Eng. Sci. 2 (1): 1–27. https://doi.org/10.1186/s40323-015-0047-3.
EOS (Electro Optical Systems). 2017. EOS stainless steel 316L material data sheet. Krailling, BY: EOS.
EOS (Electro Optical Systems). 2019. EOS stainless steel CX material data sheet. Krailling, BY: EOS.
Gardner, L. 2022. “Metal additive manufacturing in structural engineering—Review, advances, opportunities and outlook.” In Current perspectives and new directions in mechanics, modelling and design of structural systems. Boca Raton, FL: CRC Press.
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., and M. Theofanous. 2008. “Discrete and continuous treatment of local buckling in stainless steel elements.” J. Constr. Steel Res. 64 (11): 1207–1216. https://doi.org/10.1016/j.jcsr.2008.07.003.
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.
Hilburger, M. W., M. P. Nemeth, and J. H. Starnes. 2006. “Shell buckling design criteria based on manufacturing imperfection signatures.” AIAA J. 44 (3): 654–663. https://doi.org/10.2514/1.5429.
Huang, C., P. Kyvelou, R. Zhang, T. B. Britton, and L. Gardner. 2022. “Mechanical testing and microstructural analysis of wire arc additively manufactured steels.” Mater. Des. 216 (Apr): 110544. https://doi.org/10.1016/j.matdes.2022.110544.
Hutchinson, J. W., and J. C. Frauenthal. 1969. “Elastic postbuckling behavior of stiffened an barreled cylindrical shells.” J. Appl. Mech. 36 (4): 784–790. https://doi.org/10.1115/1.3564771.
Kanyilmaz, A., et al. 2021. “Role of metal 3D printing to increase quality and resource-efficiency in the construction sector.” Addit. Manuf. 50 (Feb): 102541. https://doi.org/10.1016/j.addma.2021.102541.
Kianersi, D., A. Mostafaei, and A. A. Amadeh. 2014. “Resistance spot welding joints of AISI 316L austenitic stainless steel sheets: Phase transformations, mechanical properties and microstructure characterizations.” Mater. Des. 61 (Sep): 251–263. https://doi.org/10.1016/j.matdes.2014.04.075.
Knapp, R. H. 1977. “Pseudo-cylindrical shells: A new concept for undersea structures.” J. Eng. Ind. 99 (2): 485–492. https://doi.org/10.1115/1.3439263.
Meng, X., and L. Gardner. 2020a. “Cross-sectional behaviour of cold-formed high strength steel circular hollow sections.” Thin-Walled Struct. 156 (Nov): 106822. https://doi.org/10.1016/j.tws.2020.106822.
Meng, X., and L. Gardner. 2020b. “Testing of hot-finished high strength steel SHS and RHS under combined compression and bending.” Thin-Walled Struct. 148 (Mar): 106262. https://doi.org/10.1016/j.tws.2019.106262.
Meng, X., L. Gardner, A. J. Sadowski, and J. M. Rotter. 2020. “Elasto-plastic behaviour and design of semi-compact circular hollow sections.” Thin-Walled Struct. 148 (Mar): 106486. https://doi.org/10.1016/j.tws.2019.106486.
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.
NASA (National Aeronautics and Space Administration). 1968. Bucking of thin-walled circular cylinders. NASA SP-8007. Washington, DC: NASA.
NASA (National Aeronautics and Space Administration). 2020. Buckling of thin-walled circular cylinders. NASA SP-8007. 2nd ed. Washington, DC: NASA.
Niloufari, A., H. Showkati, M. Maali, and S. M. Fatemi. 2014. “Experimental investigation on the effect of geometric imperfections on the buckling and post-buckling behavior of steel tanks under hydrostatic pressure.” Thin-Walled Struct. 74 (Jan): 59–69. https://doi.org/10.1016/j.tws.2013.09.005.
Ning, X., and S. Pellegrino. 2015. “Imperfection-insensitive axially loaded thin cylindrical shells.” Int. J. Solids Struct. 62 (Jun): 39–51. https://doi.org/10.1016/j.ijsolstr.2014.12.030.
Ning, X., and S. Pellegrino. 2017. “Experiments on imperfection insensitive axially loaded cylindrical shells.” Int. J. Solids Struct. 115–116 (Jun): 73–86. https://doi.org/10.1016/j.ijsolstr.2017.02.028.
Ramberg, W., and W. R. Osgood. 1943. Description of stress-strain curves by three parameters. Technical Note, No. 902. Washington, DC: National Advisory Committee for Aeronautics.
Rasmussen, K. J. R. 1990. Compression tests of stainless steel tubular columns. Investigation Rep. No. S770. Sydney, Australia: Centre for Advanced Structural Engineering.
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.
Reitinger, R., K. U. Bletzinger, and E. Ramm. 1994. “Shape optimization of buckling sensitive structures.” Comput. Syst. Eng. 5 (1): 65–75. https://doi.org/10.1016/0956-0521(94)90038-8.
Reitinger, R., and E. Ramm. 1995. “Buckling and imperfection sensitivity in the optimization of shell structures.” Thin-Walled Struct. 23 (1–4): 159–177. https://doi.org/10.1016/0263-8231(95)00010-B.
Sanjari, M., A. Hadadzadeh, H. Pirgazi, A. Shahriari, B. S. Amirkhiz, L. A. I. Kestens, and M. Mohammadi. 2020. “Selective laser melted stainless steel CX: Role of built orientation on microstructure and micro-mechanical properties.” Mater. Sci. Eng., A 786 (Jun): 139365. https://doi.org/10.1016/j.msea.2020.139365.
Schafer, B. W., M. Grigoriu, and T. Peköz. 1996. “A probabilistic examination of the ultimate strength of cold-formed steel elements.” In Proc., 13th Int. Specialty Conf. on Cold-Formed Steel Structures. Rolla, MO: Missouri Univ. of Science and Technology.
Schafer, B. W., and T. Peköz. 1998. “Computational modeling of cold-formed steel: Characterizing geometric imperfections and residual stresses.” J. Constr. Steel Res. 47 (3): 193–210. https://doi.org/10.1016/S0143-974X(98)00007-8.
Singer, J., J. Arbocz, and C. D. Babcock. 1971. “Buckling of imperfect stiffened cylindrical shells under axial compression.” AIAA J. 9 (1): 68–75. https://doi.org/10.2514/3.6125.
Teng, J. G., X. Lin, J. M. Rotter, and X. L. Ding. 2005. “Analysis of geometric imperfections in full-scale welded steel silos.” Eng. Struct. 27 (6): 938–950. https://doi.org/10.1016/j.engstruct.2005.01.013.
Wagner, H. N. R., C. Hühne, K. Rohwer, S. Niemann, and M. Wiedemann. 2017. “Stimulating the realistic worst case buckling scenario of axially compressed unstiffened cylindrical composite shells.” Compos. Struct. 160 (Jan): 1095–1104. https://doi.org/10.1016/j.compstruct.2016.10.108.
Weingarten, V. I., E. J. Morgan, and P. Seide. 1965. “Elastic stability of thin-walled cylindrical and conical shells under axial compression.” AIAA J. 3 (3): 500–505. https://doi.org/10.2514/3.2893.
Ye, J., P. Kyvelou, F. Gilardi, H. Lu, M. Gilbert, and L. Gardner. 2021. “An end-to-end framework for the additive manufacture of optimized tubular structures.” IEEE Access 9 (Dec): 165476–165489. https://doi.org/10.1109/ACCESS.2021.3132797.
Yoshimura, Y. 1955. On the mechanism of buckling of a circular cylindrical shell under axial compression. Washington, DC: National Advisory Committee for Aeronautics.
Yu, C., and B. Schafer. 2005. Distortional buckling of cold-formed steel members in bending. Baltimore: American Iron and Steel Institute.
Yuan, H. X., Y. Q. Wang, Y. J. Shi, and L. Gardner. 2014. “Stub column tests on stainless steel built-up sections.” Thin-Walled Struct. 83 (Oct): 103–114. https://doi.org/10.1016/j.tws.2014.01.007.
Yun, X., L. Gardner, and N. Boissonnade. 2018. “Ultimate capacity of I-sections under combined loading—Part 1: Experiments and FE model validation.” J. Constr. Steel Res. 147 (Aug): 408–421. https://doi.org/10.1016/j.jcsr.2018.04.016.
Yun, X., Z. Wang, and L. Gardner. 2021. “Full-range stress–strain curves for aluminum alloys.” J. Struct. Eng. 147 (6): 04021060. https://doi.org/10.1061/(ASCE)ST.1943-541X.0002999.
Zhang, R., L. Gardner, C. Buchanan, V. P. Matilainen, H. Piili, and A. Salminen. 2021a. “Testing and analysis of additively manufactured stainless steel CHS in compression.” Thin-Walled Struct. 159 (Feb): 107270. https://doi.org/10.1016/j.tws.2020.107270.
Zhang, R., L. Gardner, X. Meng, C. Buchanan, V. Matilainen, H. Piili, and A. Salminen. 2021b. “Optimisation and compressive testing of additively manufactured stainless steel corrugated shells.” In Proc., 9th European Conf. on Steel and Composite Structures (Eurosteel 2021). Berlin, DE: John Wiley & Sons.
Zhang, R., X. Meng, and L. Gardner. 2022. “Shape optimisation of stainless steel corrugated cylindrical shells for additive manufacturing.” Eng. Struct. 270 (Nov): 114857. https://doi.org/10.1016/j.engstruct.2022.114857.
Zhang, Z., G. Shi, L. Hou, and L. Zhou. 2021c. “Geometric dimension and imperfection measurements of box-T section columns using 3D scanning.” J. Constr. Steel Res. 183 (Aug): 106742. https://doi.org/10.1016/j.jcsr.2021.106742.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 149 • Issue 4 • April 2023
Copyright
© 2023 American Society of Civil Engineers.
History
Received: Jun 29, 2022
Accepted: Nov 6, 2022
Published online: Jan 23, 2023
Published in print: Apr 1, 2023
Discussion open until: Jun 23, 2023
Authors
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.