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

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.

Automated summary

This paper proposes a method of using discontinuous velocity fields based on FFT numerical results to analyze the strain localization problem of periodic distributions of voids in single crystals. The experimental results show that this new method can provide a good estimation of the macroscopic yield stress.