A Multiscale Discussion of Fatigue and Shakedown for Notched Structures

The aim of this paper is to analyse the fatigue phenomena in the presence of stress gradients. It is well-known that most fatigue criteria fail to predict the lifetime of components in the presence of high stress concentrations or stress gradients, as it is the case in the neighbourhood of cracks, holes notches and encountered for example in riveted or threaded structures. This paper proposes a numerical approach in the framework of the high cycle fatigue domain in order to give a first qualitative answer to this difficult question. We start from the numerical calculation of macroscopic loading corresponding to some fatigue experiments on specimens with an inclusion of metallic grains embedded in a macroscopic matrix. The computed fields are then analysed in terms of the Dang Van or the Papadopoulos HCF criteria, which are based on the estimation of the shakedown limit at the grain scale. The Dang Van infinite lifetime prediction is based on the assumption that fatigue occurs if at least one grain fails, i.e. reaches plastic shakedown. The predictions at mesoscopic and macroscopic scales are close if the macroscopic stress distribution is homogeneous. However in the case of the stress gradient, lifetime predicted at the macroscopic scale is underestimated when compared to the predictions made at the mesoscopic scale. Another result is that the gap between microscopic and macroscopic predictions obtained from these numerical calculations can roughly be estimated by a diminution of stress of the same order of magnitude as found in the experiments and phenomenological observations.