A multiscale approach of fatigue and shakedown for notched structures

Abstract

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. Proposed is a numerical approach in the framework of the high cycle fatigue domain in order to give a qualitative answer. The work starts from the numerical computation 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 HCF (high cycle fatigue) criterion [1], which is based on the estimation of the shakedown limit at the grain scale. The 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 computations can roughly be estimated by a diminution of stress of the same order of magnitude as found in the experiments and phenomenological observations

Micro-mechanical modelling of high cycle fatigue behaviour of metals under multiaxial loads

“…The authors find that the Dang Van equivalent stress and the Fatemi and Socie equivalent slip amplitude do not highlight the well know critical character of the grains at the free surface when considering high cycle fatigue behaviour. Bertolino et al (2007) use the concept proposed by Dang Van, whereby elastic shakedown of the grains can be seen as a limit for crack initiation. They therefore sought to determine, using numerical models, the critical load above which at least one grain does not elastically shakedown.…”

Comparison between defects and micro-notches in multiaxial fatigue – The size effect and the gradient effect

“…In other words and as numerically shown by Bertolino et al [16], when the stress gradient is high, fewer grains are subject to plastic deformation and consequently to crack initiation. On the contrary, with a uniform stress distribution over a larger scale, for example for the biggest defects, the situation is closer to the case of a smooth specimen.…”

“…Recently, Bertolino et al [16] showed, by means of microstructural simulations, that the stress gradient occurring at the notch tip can strongly influence the probability of finding a favourably oriented grain at the notch root. This leads to an average increase in the fatigue strength, which can be correlated to the intensity of the stress gradient.…”

Rail surface crack initiation analysis using multi-scale coupling approach

“…In order to capture the multi-scale behavior present at a material, numerous multi-scale modelling approaches has been proposed to fulfill different purpose of engineering applications (Li et al, 2010, Yang et al, 2014, Bertolino et al, 2007. However, in the research field of railway engineering, few investigations on wheel-rail interaction using multi-scale approach have been reported so far.…”