Abstract
Typically, structures fail due to buckling if loaded by compression. However, it is important to notice that–especially in lightweight structures–there are several situations in which instabilities, such as buckling or wrinkling, can be observed under tensile loads. In the present paper, a number of problems, dealing with buckling under tensile loads, are presented. Some solutions already contained in former papers of the author are reconsidered, compared to recent results, and extended. Further new results are presented. Bifurcation buckling under tensile loading of beams, plates (with and without cut-outs), rolled metal strips, thin cell walls of metal foams, and of thin metallic films on polymer substrates is treated in this paper. It is made clear that in all cases of buckling under tensile loads eventually compressive stresses are responsible for the loss of stability. Thus, one should carefully differentiate between “buckling under tension” and “buckling under tensile loads”. Nonconservative loads as well as material instabilities under tension, such as necking, are not considered in this paper.
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References
Ziegler, F.: Mechanics of Solids and Fluids, 2nd edn. Springer, Berlin (1995)
Ziegler, H.: Principles of Structural Satbility, 1st edn. Blaisdell Publishing Company, New York (1968)
Ziegler, F., Rammerstorfer, F.G.: Thermoelastic stability. In: Hetnarski, R.B. (ed.) Thermal Stresses III, pp. 107–189. North-Holland Publishing Company, Amsterdam (1989)
Daxner, T., Rammerstorfer, F.G., Fischer, F.D.: Instability phenomena during the conical expansion of circular cylindrical shells. Comput. Methods Appl. Mech. Eng. 194, 2591–2603 (2005)
Datta, P.K., Biswas, S.: Research advances on tension buckling behaviour of aerospace structures: a review. Int. J. Aeronaut. Space Sci. 12, 1–15 (2011)
Brighenti, R.: Buckling sensitivity analysis of cracked thin plates under membrane tension or compression loading. Nucl. Eng. Des. 239, 965–980 (2009)
Tomita, Y., Shindo, A.: Onset and growth of wrinkles in thin square plates subjected to diagonal tension. Int. J. Mech. Sci. 30, 921–931 (1988)
Segedin, R.H., Collins, I.F., Segedin, C.M.: The elastic wrinkling of rectangular sheets. Int. J. Mech. Sci. 30, 719–732 (1988)
Friedl, N., Rammerstorfer, F.G., Fischer, F.D.: Buckling of stretched strips. Comp. Struct. 78, 185–190 (2000)
Rammerstorfer, F.G., Pahr, D.H., Daxner, T., Vonach, W.K.: Buckling in thin walled micro and meso structures of lightweight materials and material compounds. Comput. Mech. 37, 470–478 (2006)
Daxner, T., Pahr, D.H., Rammerstorfer, F.G.: Micro- and meso-instabilities in structured materials and sandwich structures. In: Falzon, G., Aliabadi, M.H. (eds.) Buckling and Postbuckling Structures: Experimental, Analytical and Numerical Studies, pp. 453–495. Imperial College Press, London (2008)
Rammerstorfer, F.G., Fischer, F.D., Friedl, N.: Buckling of free infinite strips under residual stresses and global tension. J. Appl. Mech. 68, 399–404 (2001)
Toth, F., Rammerstorfer, F.G., Cordill, M.J., Fischer, F.D.: Detailed modelling of delamination buckling of thin films under global tension. Acta Mater. 61, 2425–2433 (2013)
Buckingham, E.: On physically similar systems; illustrations of the use of dimensional equations. Phys. Rev. 4, 345–376 (1914)
Shimizu, S.: Tension buckling of plate having a hole. Thin Walled Struct. 45, 827–833 (2007)
Bringhenti, R.: Buckling of cracked thin plates under tension or compression. Thin Walled Struct. 42, 209–224 (2005)
Jacques, N., Portier-Ferry, M.: On mode localisation in tensile plate buckling. C. R. Mec. 333, 804–809 (2005)
Sipos, A.A., Fehér, E.: Disappearance of stretch-induced wrinkles of thin sheets: a study of orthotropic films. Int. J. Sol. Struct. 97–98, 275–283 (2016)
Nayyar, V., Ravi-Chandar, K., Huang, R.: Stretch-induced wrinkling of polyethylene thin sheets: experiments and modeling. Int. J. Solids Struct. 51, 1847–1858 (2014)
Rammerstorfer, F.G., Daxner, T.: Berechnungs- und Design-Konzepte für den Leichtbau. In: Degischer, H.P., Lüftl, S. (eds.) Leichtbau, pp. 14–49. Wiley-VCH, Weinheim (2009)
Firmberger, G., Rammerstorfer, F.G.: FEM simulations of buckling and post-buckling of stretched rectangular plates with cut-outs or cracks. ILSB-Report 299, TU Vienna (2017)
Abdelkhalek, S., Zahrouni, H., Legrand, N., Potier-Ferry, M.: Post-buckling modelling for strips under tension and residual stresses using asymptotic numerical method. Int. J. Mech. Sci. 104, 126–137 (2015)
Fischer, F.D., Rammerstorfer, F.G., Friedl, N.: Residual stress-induced center wave buckling of rolled strip metal. J. Appl. Mech. 70, 84–90 (2003)
Fischer, F.D., Friedl, N., Noé, A., Rammerstorfer, F.G.: A study of the buckling behaviour of strips and plates with residual stresses. Steel Res. Int. 76, 327–335 (2005)
Marx, V.M., Toth, F., Wiesinger, A., Berger, J., Kirchlechner, C., Cordill, M.J., Fischer, F.D., Rammerstorfer, F.G., Dehm, G.: The influence of a brittle Cr interlayer on the deformation behavior of thin Cu films on flexible substrates: experiment and model. Acta Mater. 89, 278–289 (2015)
Cordill, M.J., Fischer, F.D., Rammerstorfer, F.G., Dehm, G.: Adhesion energies of Cr thin films on polyimide determined from buckling: experiment and model. Acta Mater. 58, 5520–5531 (2010)
Mukherjee, B., Barta, R.C., Dillard, D.A.: Edge debonding in peeling of a thin flexible plate from an elastomer layer: a cohesive zone model analysis. J. Appl. Mech. (2017). https://doi.org/10.11115/1.4034988
Acknowledgements
Open access funding provided by TU Wien (TUW). Parts of the paper stem from a project financially supported by the Austrian Science Funds (FWF) under the project number P 22648. Furthermore, the contributions from colleagues from the TU Wien, the Montanunversität (MU) Leoben, from the Erich Schmid Institute (ESI) of the Austrian Academy of Sciences, from the Max-Planck-Institut für Eisenforschung GmbH (Düsseldorf), as well as from the industrial partners (BWG Duisburg) to the papers are acknowledged. Their names are in the authors lists of the respective papers.
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This paper is dedicated to the memory of Franz Ziegler
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Rammerstorfer, F.G. Buckling of elastic structures under tensile loads. Acta Mech 229, 881–900 (2018). https://doi.org/10.1007/s00707-017-2006-1
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DOI: https://doi.org/10.1007/s00707-017-2006-1