Vol. 4, No. 2, 2009

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Numerical exploration of the Dang Van high cycle fatigue criterion: application to gradient effects

Felix Hofmann, Gratiela Bertolino, Andrei Constantinescu and Mohamed Ferjani

Vol. 4 (2009), No. 2, 293–308

The objective of this paper is to show that a number of key features of the Dang Van high cycle fatigue criterion can be observed using simple polycrystalline computational models.

This paper presents a series of numerical computations for an inclusion consisting of 156 grains embedded in a homogeneous matrix. The grains are modeled using a polycrystalline single slip elastoplastic model, whilst the matrix is considered as elastic. As expected the numerical simulations confirm the theoretical prediction on which the Dang Van fatigue criterion is based, that if a large enough number of grains is considered under uniform loading, a grain with the least favourable lattice orientation will always be present. This grain will constitute the weakest link in the assembly and thus its fatigue life largely determines the fatigue life of the bulk material.

Next the question of stress-gradients in the high cycle fatigue regime is addressed. An example of stress gradients appears around notches as they create stress concentrations in structures. It is a well known problem that fatigue criteria have to be locally arranged using stress-factors or critical distances in order to give satisfactory predictions. The work presented here shows that an analysis of the problem at the grain scale explains the apparent discrepancy when using classical fatigue criteria. The discussion is based on a numerical model of single slip crystal plasticity and the Dang Van fatigue criterion.

high cycle fatigue, fatigue criterion, polycrystalline plasticity, stress gradient, notch
Received: 14 December 2007
Revised: 14 June 2008
Accepted: 17 July 2008
Published: 12 April 2009
Felix Hofmann
Department of Engineering Science
Oxford University
Parks Road
Oxford, OX1 3PJ
United Kingdom
Gratiela Bertolino
Centro Atomico Bariloche
8400 San Carlos de Bariloche
Río Negro
Andrei Constantinescu
Laboratoire de Mécanique des Solides - CNRS
École Polytechnique
91128 Palaiseau
Mohamed Ferjani
Institut Français du Pétrole
1-4 rue Bois-Préau
92852 Rueil-Malmaison