A FFT-based numerical implementation of mesoscale field dislocation mechanics: Application to two-phase laminates

Djaka, Komlan Sénam; Berbenni, Stéphane; Taupin, Vincent; Lebensohn, Ricardo A.

doi:10.1016/j.ijsolstr.2018.12.027

Cited by 21 publications

(33 citation statements)

References 131 publications

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“…The evolution law for the shear strength τ c follows the same hypotheses as the strain-hardening models developed by , Puri et al (2011) and Djaka et al (2019):…”

Section: Constitutive Equations Of the Reduced Mfdm Theorymentioning

confidence: 99%

“…The calculation of the components of the Green operator in Fourier space Γ 0 ijkl as part of the solution of the Lippmann-Schwinger equation is performed using a centered finite difference scheme on a rotated grid introduced by Willot (2015), see also Djaka et al (2017Djaka et al ( , 2019.…”

Section: Mfdm-evpfft Numerical Implementationmentioning

confidence: 99%

“…The expression of ∂ε p kl /∂σ mn considering the constitutive equations of the MFDM theory yields (Djaka et al, 2019):…”

Section: Mfdm-evpfft Numerical Implementationmentioning

confidence: 99%

“…where P s = (m s ) sym is the symmetric Schmid tensor. The determination of the expression of ∂ (α × v) kl /∂σ mn is an addition to the standard EVPFFT formulation and is computed as follows (Djaka et al, 2019):…”

Section: Mfdm-evpfft Numerical Implementationmentioning

confidence: 99%

“…In the case of polycrystalline materials, MFDM numerical implementation may take advantage of FFT-based methods, which were already proven to be numerically efficient for elasto-static FDM (Berbenni et al, 2014;Brenner et al, 2014;Djaka et al, 2017) and for the resolution of the dislocation density transport equation at constant applied GND velocity (Djaka et al, 2015) or together with stress equilibrium for two-phase laminate structures (Djaka et al, 2019). Therefore, the objective of this paper is to develop an EVPFFT-based method for MFDM (named MFDM-EVPFFT throughout the paper) for describing grain size effects on flow stress of polycrystals at small strains due to both GNDs and SSDs and local GND dislocation density evolution in the course of monotonic and reversible plastic deformation.…”

mentioning

confidence: 99%

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

Berbenni

Taupin

Lebensohn

2020

Journal of the Mechanics and Physics of Solids

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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.

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“…The evolution law for the shear strength τ c follows the same hypotheses as the strain-hardening models developed by , Puri et al (2011) and Djaka et al (2019):…”

Section: Constitutive Equations Of the Reduced Mfdm Theorymentioning

confidence: 99%

Section: Mfdm-evpfft Numerical Implementationmentioning

confidence: 99%

“…The expression of ∂ε p kl /∂σ mn considering the constitutive equations of the MFDM theory yields (Djaka et al, 2019):…”

Section: Mfdm-evpfft Numerical Implementationmentioning

confidence: 99%

Section: Mfdm-evpfft Numerical Implementationmentioning

confidence: 99%

mentioning

confidence: 99%

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

Berbenni

Taupin

Lebensohn

2020

Journal of the Mechanics and Physics of Solids

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Experimental and numerical investigation of key microstructural features influencing the localization of plastic deformation in Fe-TiB2 metal matrix composite

et al. 2021

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A new generation of iron-based matrix composite reinforced by TiB 2 particles was deformed in tension to investigate at a mesoscopic scale the localization of plastic deformation in relation with characteristic microstructural features of the composite (in particular, ferrite grain boundaries and particle/matrix inter-faces). Large electron back-scattered diffraction (EBSD) maps with improved angular resolution were acquired to evaluate statistically the evolution of the geometrically necessary dislocation (GND) density from the early stage of the deformation. GNDs were found to accumulate preferentially at matrix/particle interfaces with hot-spots located at the tips of elongated particles. Additional length-scale parameters derived from EBSD data evidenced the key influence of two main microstructural features: the particle morphology and the particle clustering. Finally, we present results of an advanced full-field micromechanical model that is best suited to capture these effects, based on an enhanced crystal plasticity elasto-viscoplastic Fast Fourier Transform (EVP-FFT) formulation coupled with a phenomenological continuum Mesoscale Field Dislocation Mechanics (MFDM) theory. By taking the experimental TiB 2 particle distribution into account, the model describes qualitatively the observed effect of particle morphological features on the heterogenous distribution of GNDs.

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A Review of FE-FFT-Based Two-Scale Methods for Computational Modeling of Microstructure Evolution and Macroscopic Material Behavior

Gierden

Kochmann

Waimann

et al. 2022

Arch Computat Methods Eng

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The overall, macroscopic constitutive behavior of most materials of technological importance such as fiber-reinforced composites or polycrystals is very much influenced by the underlying microstructure. The latter is usually complex and heterogeneous in nature, where each phase constituent is governed by non-linear constitutive relations. In order to capture such micro-structural characteristics, numerical two-scale methods are often used. The purpose of the current work is to provide an overview of state-of-the-art finite element (FE) and FFT-based two-scale computational modeling of microstructure evolution and macroscopic material behavior. Spahn et al. (Comput Methods Appl Mech Eng 268:871–883, 2014) were the first to introduce this kind of FE-FFT-based methodology, which has emerged as an efficient and accurate tool to model complex materials across the scales in the recent years.

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A FFT-based numerical implementation of mesoscale field dislocation mechanics: Application to two-phase laminates

Cited by 21 publications

References 131 publications

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

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

Experimental and numerical investigation of key microstructural features influencing the localization of plastic deformation in Fe-TiB2 metal matrix composite

A Review of FE-FFT-Based Two-Scale Methods for Computational Modeling of Microstructure Evolution and Macroscopic Material Behavior

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