A model of porous plastic single crystals based on fractal slip lines distribution
Article dans une revue avec comité de lecture
The ductile failure of crystalline materials is strongly linked to the growth of intragranular voids. The estimation of the overall yield criterion thus requires to take into account the anisotropic plastic behavior of the single crystal. In the framework of the kinematic limit-analysis approach, this problem has been considered up to now with Gurson-type isotropic trial velocity fields. In the present work, a different class of piecewise constant velocity fields is proposed based on a detailed analysis of FFT numerical results on the strain localization in porous single crystals with periodic distributions of voids. This original approach is implemented for the model 2D problem of a square or hexagonal array of cylindrical voids in a hexagonal close-packed single crystal with in-plane prismatic slip systems. For equibiaxial loadings, the assumption of discontinuous velocity field provides a good approximation of the smooth jumps observed in the numerical results. Consistently, this new proposal leads to a significant improvement on the macroscopic yield stress with respect to the estimate based on an isotropic velocity field. Our theoretical estimate almost coincides with the FFT numerical results for all the unit-cells and crystalline orientations considered.
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Article dans une revue avec comité de lecturePAUX, Joseph; MORIN, Léo; BRENNER, Renald (Elsevier, 2022-10)The ductile failure of crystalline materials is strongly linked to the growth of intragranular voids. The estimation of the overall yield criterion thus requires to take into account the anisotropic plastic behavior of the ...
Article dans une revue avec comité de lectureMORIN, Léo; BRENNER, Rénald; SUQUET, Pierre M. (IOP Publishing, 2019)The aim of this paper is to investigate the numerical implementation of the field dislocation mechanics (FDM) theory for the simulation of dislocation-mediated plasticity. First, the mesoscale FDM theory of Acharya and Roy ...
Article dans une revue avec comité de lectureMORIN, Léo; BRENNER, Renald; DERRIEN, Katell; DORHMI, Khaoula (Elsevier, 2021)The aim of this paper is to develop a periodic smoother based on splines for FFT-based solvers. Spurious oscillations in FFT-based methods are shown to be due to pseudo-spectral differentiation of discontinuous fields. An ...
A self-consistent estimate for linear viscoelastic polycrystals with internal variables inferred from the collocation method Article dans une revue avec comité de lectureVU, QH; BRENNER, Renald; CASTELNAU, Olivier; MOULINEC, H; SUQUET, P (IOP Publishing, 2012)The correspondence principle is customarily used with the Laplace–Carson transform technique to tackle the homogenization of linear viscoelastic heterogeneous media. The main drawback of this method lies in the fact that ...
Article dans une revue avec comité de lectureMASSON, Renaud; BRENNER, Renald; CASTELNAU, Olivier (Elsevier Masson, 2012)An approximate self-consistent modelling is proposed to estimate the effective viscoelastic response of polycrystals presenting an ageing constitutive behaviour. This approach makes use of the equivalence between the ...