A fast Fourier transform-based mesoscale field dislocation mechanics study of grain size effects and reversible plasticity in polycrystals

Abstract

To cite this version:Stéphane Berbenni, Vincent Taupin, Ricardo Lebensohn. A fast Fourier transform-based mesoscale field dislocation mechanics study of grain size effects and reversible plasticity in polycrystals. AbstractA numerical implementation of a non-local polycrystal plasticity theory based on a mesoscale version of the field dislocation mechanics theory (MFDM) of Acharya and Roy (2006) is presented using small-strain elasto-viscoplastic fast Fourier transformbased (EVPFFT) algorithm developed by Lebensohn et al. (2012). In addition to considering plastic flow and hardening only due to SSDs (statistically stored dislocations) as in the classic EVPFFT framework, the proposed method accounts for the evolution of GND (geometrically necessary dislocations) densities solving a hyperbolic-type partial differential equation, and GND effects on both plastic flow and hardening. This allows consideration of an enhanced strain-hardening law that includes the effect of the GND density tensor. The numerical implementation of a reduced version of the MFDM is presented in the framework of the FFT-based augmented Lagrangian procedure of Michel et al. (2001). A Finite Differences scheme combined with discrete Fourier transforms is applied to solve both incompatibility and equilibrium equations. The numerical procedure named MFDM-EVPFFT is used to perform full field simulations of polycrystal plasticity considering different grain sizes and their mechanical responses during monotonic tensile and reversible tension-compression tests. Using Voronoi tessellation and periodic boundary conditions, voxelized representative volume elements (RVEs) with different grain sizes are generated. With MFDM-EVPFFT, a Hall-Petch type scaling law is obtained in contrast with the conventional crystal plasticity EVPFFT. In the case of reversible plasticity, a stronger Bauschinger effect is observed with the MFDM-EVPFFT approach in comparison with conventional EVPFFT. The origin of these differences is analyzed in terms of heterogeneity, GND density and stress evolutions during the compression stage.

Particle interspacing effects on the mechanical behavior of a Fe–TiB2 metal matrix composite using FFT-based mesoscopic field dislocation mechanics

“…3a, b, the macroscopic tensile stress is more sensitive to the particle interspacing effect for the multiple slip orientation #1 than for the single slip orientation #2. No scaling law of the macroscopic flow stress has been identified here, in contrast with grain-size effect for which the well-known Hall-Petch's law was obtained from other simulations, not reported here, see [46]. In contrast with the MFDM-EVP-FFT predictions, results obtained with the conventional CP-EVP-FFT model are size independent.…”

“…The change in grain size from d g = 6.2 µm to d g = 1.24 µm between the two sets of simulations clearly induces an increase of the macroscopic tensile stress. As it was reported in [46], this effect cannot be obtained with conventional CP-EVP-FFT, which is insensitive to grain size. Also, the dependence of macroscopic flow stress with grain size was shown to follow a Hall-Petch scaling law.…”

“…elasto-viscoplastic FFT formulation [39], denoted CP-EVP-FFT here, was adapted to consider PMFDM equations in its reduced version. This implementation, abbreviated MFDM-EVP-FFT, was originally developed and demonstrated for two-phase laminate composites by [45] and applied to Voronoi polycrystals with different average grain sizes under monotonic tensile and reversible tension-compression loadings to study the Bauschinger effect [46]. Compared to FE, FFT-based methods may be advantageous to avoid mesh generation [47] and less time-consuming (in some major cases except exascale calculations) [48].…”

Stress fields of finite-size dislocation walls and prediction of back stress induced by geometrically necessary dislocations at grain boundaries

“…Most techniques indicate the existence of a large GND density close to GBs even after a small plastic deformation. On the modeling side, such feature was reproduced by crystal plasticity calculations of polycrystalline aggregates (Berbenni et al, 2020, Cordero et al, 2012, Haouala et al, 2020, Sun et al, 2019. In a recent investigation based on Dislocation Dynamics (DD) simulations (Jiang et al, 2019), it was also shown that the dislocation storage rate dρ/dγ recorded inside grains agrees with a prediction of Ashby (Ashby, 1970), i.e., is proportional to the inverse of grain size 1/d.…”

A numerical study of reversible plasticity using continuum dislocation mechanics

“…These original CP FFT-based implementations showed the feasibility of efficiently solving the micromechanical behavior of complex polycrystalline unit cells. FFT-based methods were also recently extended to consider constitutive behavior based on field dislocation mechanics (FDM) [50][51][52][53] and MFDM [54][55][56], and were also coupled with DDD methods [57][58][59], providing better efficiency to these powerful and numerically-demanding formulations.…”