Abstract
Fatigue failure is final result of complex microscopic phenomena which occur under cyclic loading. Traditionally this phenomenon is studied by different ways depending on the fatigue regime and on the field of interest: fatigue limit analysis, life prediction in high or in low cycle fatigue, thermal fatigue... The diversity of proposed approaches is so great that design engineers meet many difficulties to have a clear idea of the fatigue calculations which have to be done. The purpose of this paper is to present an original unified approach to both high and low cycle fatigue based on shakedown theories and dissipated energy. The discussion starts with an explanation of fatigue phenomena at different scales (microscopic, mesoscopic, and macroscopic). Then some useful aspects of shakedown theory in relation with fatigue are presented. Applications to modeling of high cycle fatigue is then introduced: for instance, some multiaxial fatigue criteria (Dang Van, Papadopoulos) are essentially based on the hypothesis of elastic shakedown at the mesoscopic scale and therefore a bounded cumulated dissipated energy. In the low cycle fatigue regime, some recent results show that we can speak of a plastic shakedown at both mesoscopic and macroscopic scale and a cumulated energy bounded by the failure energy. These ideas are also justified by some infrared thermography test results permitting a direct determination of the fatigue limit.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Bignonnet, A. (1999). Fatigue design in automotive industry. In Dang Van, K. and Papadopoulos, I.V., eds, High Cycle Metal Fatigue, From Theory to Applications, CISM Courses and Lectures N° 392, International Center for Mechanical Sciences, Springer: Wien, New-York. 145–167
Charkaluk, E., Bignonnet, A., Constantinescu, A. and Dang Van K. (2001). Fatigue design of structures under thermomechanical loading. Fat. Fracture of Eng. Mat. Struct (Accepted for publication).
Dang Van, K. (1999). Fatigue analysis by the multiscale approach. In Dang Van, K. and Papadopoulos, I.V., eds, High Cycle Metal Fatigue, From Theory to Applications, CISM Courses and Lectures N° 392, International Center for Mechanical Sciences, Springer: Wien, New-York. 57–88.
Drucker, D.C. (1963). On the macroscopic theory of inelastic stress-strain-time-temperature behaviour. Advances in Materials Research in the NATO Nations (AGAR Dograph 62) Pergamon press. 641–651.
Fayard, J.L., Bignonnet, A. and Dang Van, K., (1996). Fatigue design criterion for welded structures. Fatigue Fract. Engng. Mater. Struct. 19: 723–729.
Halphen, B. and Nguyen, Q.S., (1975). Sur les matériaux standards généralisés. J. Mécanique, 14: 1–37.
Koiter, W.T. (1960). General theorems for elastic-plastic solids. In Sneddon, J.N. and Hill, R., eds., Progress in Solid Mechanics, Amsterdam: Amsterdam: North-Holland. 165–221.
Lemaitre, J. and Chaboche, J.L. (1990). Mechanics of Solid Materials. Cambridge: University Press.
Luong, M.P. and Dang Van, K. (1992) Infrared thermographie evaluation of fatigue limit in metal. Proc. 27th QUIRT Eurotherm Seminar, Paris.
Luong, M.P. (1995). Infrared thermographie scanning of fatigue in metals. Nuclear Eng. and Design 158, 363–376
Maitournam, H. (1999). Finite elements applications numerical tools and specific fatigue problems. In Dang Van, K. and Papadopoulos, I.V., eds, High Cycle Metal Fatigue, From Theory to Applications, CISM Courses and Lectures N° 392, International Center for Mechanical Sciences, Springer: Wien, New-York. 169–187
Mandel, J., Halphen, B. and Zarka, J. (1977). Adaptation d’une structure élastoplastique à écrouissage cinématique. Mech. Res. Comm., 4: 309–314.
Nguyen, Q.S. (2000). Stability and Nonlinear Solid Mechanics. J. Wiley & Sons.
Orowan, E. (1939). Theory of the fatigue of metals. Proc. Roy. Soc. London, A, 171: 79–106.
Papadopoulos, I.V. (1987). Fatigue Polycyclique des Métaux: une Nouvelle Approche. Ph.D. Dissertation, Ecole Nationale des Ponts et Chaussées, Paris.
Papadopoulos, I.V. (1999). Multiaxial fatigue limit criterion of metals. In Dang Van, K. and Papadopoulos, I.V., eds, High Cycle Metal Fatigue, From Theory to Applications, CISM Courses and Lectures N° 392, International Center for Mechanical Sciences, Springer: Wien, New-York. 89–143.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Wien
About this chapter
Cite this chapter
Dang Van, K. (2002). Application of Shakedown Theory to Fatigue Analysis of Structures. In: Weichert, D., Maier, G. (eds) Inelastic Behaviour of Structures under Variable Repeated Loads. International Centre for Mechanical Sciences, vol 432. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2558-8_18
Download citation
DOI: https://doi.org/10.1007/978-3-7091-2558-8_18
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-83687-3
Online ISBN: 978-3-7091-2558-8
eBook Packages: Springer Book Archive