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

An analysis of high cycle multiaxial fatigue behaviour is conducted through the numerical simulation of polycrystalline aggregates using the finite element method. The metallic material chosen for investigation is pure copper, which has a Face Centred Cubic (FCC) crystalline microstructure. The elementary volumes are modelled in 2D using an hypothesis of generalised plane strain and consist of 300 equi-probability, randomly oriented grains with equiaxed geometry. The aggregates are loaded at levels equivalent to the average macroscopic fatigue strength at 1E7 cycles. The goal is to compute the mechanical quantities at the mesoscopic scale (i.e., average within the grain) after stabilization of the local cyclic behaviour. The results show that the mesoscopic mechanical variables are characterised by high dispersion. A statistical analysis of the response of the aggregates is undertaken for different loading modes: fully reversed tensile loads, torsion and combined in-phase tension–torsion. Via the calculation of the local mechanical quantities for a sufficiently large number of different microstructures, a critical analysis of certain multiaxial endurance criteria (Crossland, Dang Van and Matake) is conducted. In terms of material behaviour models, it is shown that elastic anisotropy strongly affects the scatter of the mechanical parameters used in the different criteria and that its role is predominant compared to that of crystal plasticity. The analysis of multiaxial endurance criteria at both the macroscopic and mesoscopic scales clearly show that the critical plane type criteria (Dang Van and Matake) give an adequate estimation of the shear stress but badly reflect the scatter of the normal stress or the hydrostatic stress