Shakedown within polycrystals: A direct numerical assessment

It is well known that in high cycle fatigue (HCF), macroscopically, structures undergo elastic shakedown and the stress level commonly determines the lifetime. In this domain, the fatigue phenomena is due to local plasticity at the grain scale. Therefore, some multiscale HCF multiaxial fatigue criteria were proposed, among them the well-known Dang Van criterion. This criterion supposes that in a polycrystal, some misoriented grains can undergo plastic shakedown which conducts to crack initiation. The objective of this work is to validate this assumption by conducting numerical simulations on polycrystalline aggregates. As it is necessary to estimate the stabilized state in each grain of the polycrystal, classical incremental simulations are not the best way as it will be highly time-consuming because of the size of the aggregate. In the recent years, Pommier proposed a method called Direct Cyclic Algorithm to obtain the stabilized response of a structure under cyclic periodic loading, which it is shown to be more efficient compared to an incremental analysis in such situation. However, errors can be obtained in certain case with respect to the incremental solution. In this work, a Crystal Plasticity FEM model, based on dislocation densities, was used. As a first step, an aggregate of 20 grains of AISI 316L stainless steel under strain controlled cyclic loading was studied. Precise comparisons were conducted with incremental analysis and the results show that DCA seems to be an efficient solution in order to estimate the shakedown state of polycrystalline aggregates.