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

Abstract

is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. 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 10 7 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.

An affine formulation for the self-consistent modeling of elasto-viscoplastic heterogeneous materials based on the translated field method

“…In the case of the FFT-based spectral method, a 3D microstructure was generated using the procedure proposed by Robert et al (2012). The different grains were initially approximated by spheroids being randomly positioned but not superimposed.…”

Experimental and numerical study of the evolution of stored and dissipated energies in a medium carbon steel under cyclic loading

“…The simulations were performed with a polycrystal of 512 grains with orientations representative of the crystallographic texture of the real material. The generation of the polycrystalline aggregate was achieved thanks to the procedure proposed by Robert et al (2012). The different grains were initially approximated by spheroids being randomly positioned but not superimposed.…”

Competition between microstructure and defect in multiaxial high cycle fatigue

“…For both 2D and 3D models, an homogeneous isotropic matrix embeds the polycrystal. The process used to generate the 2D polycrystalline geometries is described in [10]. Both smooth and notched microstructures are studied.…”

“…A promising approach, consisting in computing, by FE method, the mechanical response of explicitly modelled polycrystalline aggregates, allows to take into account microstructural details generally neglected in the homogenisation schemes and to deepen the analysis of the mesoscopic mechanical responses of metals under cyclic multiaxial loading. In recent years, several works have involved this kind of numerical simulations to contribute to the study of the HCF behaviour [8][9][10][11][12]. The present study falls within this framework and a specific effort is made to quantify the multiaxial fatigue performance of metals in the presence of defects through statistical modeling of the microstructure.…”