Elastostatic field distributions in polycrystals and cracked media

François Willot (1, 2) , Renald Brenner (3) , Hervé Trumel (4)

1 CDM - Centre des Matériaux
2 CMM - Centre de Morphologie Mathématique
3 DALEMBERT - Institut Jean Le Rond d'Alembert
4 CEA Le Ripault - CEA Le Ripault

This work addresses the problem of the reconstruction of the local fields distribution occurring in heterogeneous linear elastic solids. The constitutive heterogeneities are crystals and cracks. Through comparisons with FFT computations, it is shown that self-consistent estimates together with an assumption of normal distribution at the phase scale provide an accurate description of the elastostatic field histograms in polycrystals without cracks. In the case of inter and transgranular cracks, full-field FFT simulations indicate that the field histograms present van Hove singularities. Their natures are determined analytically in the low-density regime, in the case of an homogeneous medium containing cracks.

Mots clés: Polycrystals; Cracked media; Field fluctuation; Self-consistent Methods; Micromechanics; Van Hove singularities

Domaines: Matériaux

François Willot, Renald Brenner, Hervé Trumel. Elastostatic field distributions in polycrystals and cracked media. Philosophical Magazine, 2020, 100 (6), pp.661-687. ⟨10.1080/14786435.2019.1699669⟩. ⟨hal-02425491⟩