Abstract
The weakest link theory, sometimes proposed to analyze size effects on the plastic behaviour of single crystals, is introduced in 3D numerical simulations of polycrystals. The approach relies on a random distribution of sources in space and strength associated to a crystal plasticity law with constant per layer Critical Resolved Shear Stresses (CRSS). It is able to reproduce: (1) the grain size dependence of the yield stress given by the Hall–Petch law, (2) intense slip band localization patterns as often observed at the grains surface, especially pronounced in quenched or irradiated metals, but difficult to reproduce by numerical simulation.
Highlights
The present note lies in the context of the numerical simulation of polycrystals in the framework of continuum mechanics using the Finite Element method associated to Crystal Plasticity for the constitutive non-linear behaviour
The problem comes from the fact that the weakest link theory cannot be represented in this approach as neighbouring voxels are interacting in the mechanical simulation
−0.5 g deduced from the numerical simulation appears intuitive as we introduced a Critical Resolved Shear Stresses (CRSS) sample size dependence D−0.5, it was forgetting the fact that the macroscopic yield stress results from a homogenization procedure on a rather complex microstructure
Summary
The present note lies in the context of the numerical simulation of polycrystals in the framework of continuum mechanics using the Finite Element method associated to Crystal Plasticity for the constitutive non-linear behaviour. Lionel Gélébart such as non-local crystal plasticity [4] or variants of Dislocation Field Mechanics [5] have been proposed to introduce size effects in the simulation of polycrystals [6,7] These models essentially take into account an additional hardening arising from the gradients of the plastic deformation through the dislocation density tensor. The weakest link model is well suited to analyse results obtained on single crystalline samples submitted to micro-tensile (or compression) tests, whether experimentally [19] or numerically with Dislocation Dynamics [19,20]. The extension of this idea to the size-dependent macroscopic yield stress of 3D polycrystals seems promising but is not straightforward. This can be done classically with 3D numerical simulations accounting for crystal plasticity, but it raises the question of representing the variability (location and CRSS) associated to dislocation sources within grains
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