Large scale finite element simulations of polycrystalline aggregates: applications to X-ray diffraction and imaging for fatigue metal behaviour

Henry Proudhon (1) , Samuel Forest (1) , Wolfgang Ludwig (2, 3)

1 CDM - Centre des Matériaux
2 MATEIS - Matériaux, ingénierie et science [Villeurbanne]
3 ESRF - European Synchrotron Radiation Facility

Large scale finite element simulations of the elastoviscoplastic behaviour of polycrystalline aggregates have become a standard technique to study the stress-strain heterogeneities that develop in grains during deformation. For a long time, comparison between continuum crystal plasticity and experimental field measurements was confined to the observation of surface behaviour. As for example the study of the development of intense deformation bands at the free surface of a polycrystal. Recent 3D experimental techniques open new perspectives in computational crystal plasticity. After reviewing how to define a representative volume element for polycrystal properties and showing that actual 3D computations, including grain shapes and orientations, are really needed to accurately determine the stress and strains distributions, two examples of applications of large scale simulations are described in this paper. First the simulation of 3D coherent X-ray diffraction in a polycrystalline gold sample is detailed. Based on the real geometry of the grains and their columnar nature, a 3D avatar is reconstructed. FE computations are then carried out to evaluate the effect of mechanical and thermal strain of the diffraction pattern resolved in the reciprocal space by complex FFT. Qualitative comparison with the experimental diffraction patterns shows that such computations can help understand the true nature of strain heterogeneities within the material. The second example of application deals with short fatigue crack propagation in polycrystals. One fundamental problem caused by short fatigue cracks is that despite decades of research, so far no reliable prediction of the crack propagation rates, comparable to the well-known Paris law in the long crack regime, could be established. This ``anomalous'' behaviour of short cracks is commonly attributed to factors like their complex three dimensional shapes and the influence of the local crystallographic environment affecting their propagation behaviour via a combination of physical mechanisms. Crystal plasticity computations based on the real grain shapes and orientations obtained thanks to diffraction contrast tomography are carried out using an ideal crack shape. The stress concentration at the crack tip is analysed with respect to possible crack growth directions.

Domaines: Mécanique des matériaux [physics.class-ph]; Mécanique des matériaux [physics.class-ph]

Henry Proudhon, Samuel Forest, Wolfgang Ludwig. Large scale finite element simulations of polycrystalline aggregates: applications to X-ray diffraction and imaging for fatigue metal behaviour. 31st Risø International Symposium on Materials Science, Sep 2010, Roskilde, Denmark. pp.121-139. ⟨hal-00531211⟩