New robust self-consistent homogenization schemes of elasto-viscoplastic polycrystals

Numerical homogenization of nonlinear viscoplastic two-dimensional polycrystals ?

In this paper, we numerically determine the effective stress-strain relation of some two-dimensional polycrystals. These are aggregates of a few tens of perfectly bonded single-crystal (hexagonal atomic lattice) grains, with varying orientations. Each grain obeys a given nonlinear viscoplastic stress-strain relation, which depends on the orientation of the grain. Precise calculations performed ...

Finite element formulation for modelling large deformations in elasto-viscoplastic polycrystals

Anisotropic, elasto-viscoplastic behaviour in polycrystalline materials is modelled using a new, updated Lagrangian formulation based on a three-field form of the Hu-Washizu variational principle to create a stable finite element method in the context of nearly incompressible behaviour. The meso-scale is characterized by a representative volume element, which contains grains governed by single ...

Self-consistent scheme for toughness homogenization

Considering a semi-infinite planar crack propagating along a plane where the local toughness is a random field, the addressed problem is to compute the effective (or homogeneous and macroscopic) toughness. After a brief introduction to the two regimes — strong and weak pinning — that are expected depending on the system size, a self-consistent homogenization scheme is introduced. It is shown th...

Stress hot spots in viscoplastic deformation of polycrystals

The viscoplastic deformation of polycrystals under uniaxial loading is investigated to determine the relationship between hot spots in stress and their location in relation to the microstructure. A 3D full-field formulation based on fast Fourier transforms for the prediction of the viscoplastic deformation of poly-crystals is used with rate-sensitive crystal plasticity. Two measured polycrystal...

Incremental homogenization approach for ageing viscoelastic polycrystals