Application of shakedown theory to fatigue analysis of structures

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.