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 consisting of spherical voids, and an intergranular porosity consisting of 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. A 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.

A review of nonlinear FFT-based computational homogenization methods

“…FFT-based methods were developed to compute the conductivity [268] and the thermal diffusivity [199] of porous materials, and for predicting microstructure-induced hotspots in granular media [269]. The elastic and plastic properties of porous materials [270,271] were studied, and the effective yield [272,273] and failure [274] surfaces could be identified.…”

Full-field polycrystal plasticity simulations of neutron-irradiated austenitic stainless steel: A comparison between FE and FFT-based approaches

“…The parameters for SA304L stainless steel used in this study are listed in Tab grains was based on a Poisson-Voronoi diagram. Other types of tessellations could be investigated, such as those of Johnson-Mehl-Avrami-Kolmogorov and Laguerre (see [22]). Keeping in mind that the curvy grain boundaries of such tessellations could lead to meshing problems for finite element calculation (non convexity problems), the polycrystals were limited to Voronoi tessellation.…”

Void coalescence in porous ductile solids containing two populations of cavities

“…In both works, the presence of the second population of cavities lead to a reduction of ductility. The observations made in those analytical works have been completed by numerical micromechanical simulations (Faleskog and Shih, 1997;Khdir et al, 2014;Zybell et al, 2014;Khan and Bhasin, 2017;Boittin et al, 2017), emphasizing that the second population of cavities plays mostly a role on the phenomenon of coalescence of primary voids: the onset of coalescence occurs more quickly and the degradation of the ligament between neighboring primary voids is accelerated by the presence of a second population. Those observations have motivated the development of coalescence models accounting for secondary voids, based on phenomenological extensions of Thomason (1985)'s criterion calibrated with numerical micromechanical simulations Pardoen, 2008, 2009;Tekoglu, 2015).…”