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

Abstract

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 elasto-plastic 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.