Abstract
This paper is concerned with the elastic plastic response of a two-bar system with temperature-dependent elastic coefficients under cyclic thermomechanical loadings. Such materials are characterized by lack of results concerning the asymptotic behaviors and conditions for shakedown occurrence. This study shows that the considered simple structure is sufficiently complex to experience different periodic long term behaviors as in classical elastoplasticity. In order to understand how Melan-Koiter method works for such materials, the evolution of the structure’s response until the stabilization of the plastic strain (‘shakedown’) or the asymptotic dissipative behavior (‘alternating plasticity’ or ‘ratcheting’) is analytically addressed and the Bree diagram is then constructed. The main result of this work is that the residual stress and strain fields are time-dependent even when shakedown occurs. Incidently, we proved that Halphen’s conjecture (Halphen in C. R. Méc. 33:617–621, 2005) giving a sufficient condition for shakedown occurrence is not a necessary condition. Finally, numerical results performed by an incremental finite element procedure are presented.
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References
Constantinescu, A., Van Dang, K., Maitournam, H.: A unified approach for high and low cycle fatigue based on shakedown concepts. Eng. Mater. Struct. 26, 567–568 (2003)
Bleich, H.: Über die bemessung statisch unbestimmter stahltragwerke unter berüschsichtigung der elastisch-plastischen verhaltens des baustoffes. J. Bauingenieur 19, 261–269 (1932)
Melan, E.: Theorie statisch unbestimmter Systeme aus ideal-plastischem Baustoff. Sitzber. Akad. Wiss. Wien, IIa 145, 195–218 (1936)
Melan, E.: Zur plastizität des räumlichen Kontinuums. Ing.-Arch. 8, 116–126 (1938)
Koiter, W.: General problems for elastic-plastic solids. In: Sneddon, Hill (ed.) Progress in Solid Mechanics, vol. 4, pp. 165–221. North-Holland, Amsterdam (1960)
Pham, D.C.: Shakedown static and kinematic theorems for elastic-plastic limited linear kinematic-hardening solids. Eur. J. Mech. A, Solids 56, 1905–1915 (2008)
Pham, D.C.: On shakedown theory for elastic-plastic materials and extensions. J. Mech. Phys. Solids 56, 1905–1915 (2008)
Bouby, C., de Saxcé, G., Tritsch, J.-B.: A comparison between analytical calculations of the shakedown load by the bipotential approach and step-by-step computations for elastoplastic materials with nonlinear kinematic hardening. Int. J. Solids Struct. 43, 2670–2692 (2006)
Prager, W.: Shakedown in elastic plastic media subjected to cycles of load and temperature. In: La Plasticità nella Scienza delle Costruzioni. Proc. A. Dannuso Symp, Zanichelli, Bologna, pp. 239–244 (1956)
Borino, G.: Consistent shakedown theorems for materials with temperature dependent yield functions. Int. J. Solids Struct. 37, 3121–3147 (2000)
Khôi Vu, D., Staat, M.: Shakedown analysis of structures made of materials with temperature-dependent yield stress. Int. J. Solids Struct. 44, 4524–4540 (2007)
Halphen, B.: Elastic perfectly plastic structures with temperature dependent elastic coefficients. C. R., Méc. 33, 617–621 (2005)
König, J.A.: A shakedown theorem for temperature dependent elastic moduli. Bull. Acad. Pol. Sci., Ser. Sci. Tech. 17, 161 (1968)
Halphen, B., di Domizio, S.: Evolution des structures élastoplastiques dont les coefficients d’élasticité dépendent de la température. In: 17ème congrès français de mécanique, Troyes (2005)
di Domezio, S.: Structures élastoplastiques sous chargement cyclique: équation d’évolution de la contrainte résiduelle. Stage at Ecole Polytechnique (2005)
Zarka, J., Frelat, J., Inglebert, G., Kasmai-Navidi, P.: A New Approach in Inelastic Analysis of Structures. Ecole Polytechnique, Paris (1990)
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Oueslati, A., de Saxcé, G., Hasbroucq, S. (2013). Inelastic Behavior of a Two-Bar System with Temperature-Dependent Elastic Modulus Under Cyclic Thermomechanical Loadings. In: de Saxcé, G., Oueslati, A., Charkaluk, E., Tritsch, JB. (eds) Limit State of Materials and Structures. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-5425-6_8
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DOI: https://doi.org/10.1007/978-94-007-5425-6_8
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