Numerical simulations and modeling of the effective plastic flow surface of a biporous material with pressurizedintergranular voids

Abstract

This study is devoted to the effective plastic flow surface of a biporous polycrystalline material, with an intragranular porosity due to spherical voids, and an intergranular porosity due to larger elongated voids along the grain boundaries. These two populations of voids (or bubbles) with well separated scales and shapes are saturated by a fluid and therefore are subjected to internal pressures. The effect of the intragranular voids is modeled through a GTN (Gurson–Tvergaard–Needleman) criterion in the matrix. Numerical simulations are performed with a FFT-based (Fast Fourier Transforms) method. Particular attention is paid to the effect of the distribution of the intergranular bubbles on the effective plastic flow surface. Different microstructures with different volume fractions and sizes for the intergranular bubbles are tested under three loading conditions (the mean size of the grains being fixed). Two main results are exhibited. First, it is shown that the effect of the relative size of the intergranular bubbles on the effective plastic flow surface depends on the loading direction. Secondly, a comparison is made with the analytical model of (Vincent et al., 2014) and a correction of the porosity relative to the intergranular bubbles is introduced in this analytical model in order to take into account the specific distribution of the intergranular bubbles along the grain boundaries. This correction is expressed as a sum of two power law functions, each of them being significant either for low or for large values of the porosity of intergranular bubbles.