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A model of porous plastic single crystals based on fractal slip lines distribution

Article dans une revue avec comité de lecture
Author
PAUX, Joseph
1003313 Institut de Thermique, Mécanique, Matériaux [ITheMM]
MORIN, Léo
86289 Laboratoire Procédés et Ingénierie en Mécanique et Matériaux [PIMM]
BRENNER, Renald
413221 Sorbonne Université [SU]

URI
http://hdl.handle.net/10985/22240
DOI
10.1016/j.jmps.2022.104948
Date
2022-10
Journal
Journal of the Mechanics and Physics of Solids

Abstract

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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