Cosserat continuum modelling of grain size effects in metal polycrystals

Zeghadi, Asmahana; Forest, Samuel; Gourgues, Anne-Françoise; Bouaziz, Olivier

doi:10.1002/pamm.200510021

Cited by 14 publications

(8 citation statements)

References 9 publications

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“…The fact that Table 3. the Cosserat extra-hardening stress was found to be bounded, irrespective of the value of higher order moduli, may explain that the grain size effects for aggregates of Cosserat crystals are systematically underestimated in Forest et al (2000) and Zeghadi et al (2005). It is expected that predicted size-effects will be more pronounced for the microcurl model that with the Cosserat model.…”

Section: Discussionmentioning

confidence: 78%

Size effects in generalised continuum crystal plasticity for two-phase laminates

Cordero

Gaubert

Forest

et al. 2010

Journal of the Mechanics and Physics of Solids

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Section: Discussionmentioning

confidence: 78%

Size effects in generalised continuum crystal plasticity for two-phase laminates

Cordero

Gaubert

Forest

et al. 2010

Journal of the Mechanics and Physics of Solids

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“…More refined models are necessary to account for size effects and dislocation/grain boundary interaction. The continuum modelling of grain size effects was tackled in (Forest et al, 2000;Zeghadi et al, 2005) where additional continuity requirements are grain morphology is a second prerequisite for a realistic prediction of the strain field in a given set of surface grains. It can be obtained in the case of samples with one grain within the thickness (Eberl et al, 2002), by successive polishing and EBSD mapping of the sample as in (Stölken, 2000;Erieau and Rey, 2004;Musienko, 2005), or by micro-diffraction or neutron diffraction (Nielsen et al, 2001;Letouzé et al, 2002;Gundlach et al, 2004).…”

Section: Lattice Rotation Fieldmentioning

confidence: 99%

Ensemble averaging stress–strain fields in polycrystalline aggregates with a constrained surface microstructure – Part 2: crystal plasticity

Zeghadi

Forest

Gourgues

et al. 2007

Philosophical Magazine

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The effect of three-dimensional grain morphology on the deformation at a free surface in polycrystalline aggregates is investigated by means of a large scale finite element and statistical approach. For a given 2D surface at z = 0 containing 39 grains with given crystal orientations, eight 3D random polycrystalline aggregates are constructed having different 3D grain shapes and orientations except at z = 0, based on an original 3D image analysis procedure. They are subjected to overall tensile loading conditions. The continuum crystal plasticity framework is adopted and the resulting plastic strain fields at the free surface z = 0 are analysed. Ensemble average and variance maps of the plastic strain field at the observed free surface are computed. In the case of elastoplastic copper grains, fluctuations ranging between 2% and 80% are found in the equivalent plastic slip level at a given material point of the observed surface from one realization of the microstructure to another. The obtained fields are compared to the prediction based on the associated columnar grain microstructure, often used in literature.

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“…On the other hand, strain gradient plasticity continuum theories (Fleck and Hutchinson, 1993;Smyshlyaev and Fleck, 1996;Fleck and Hutchinson, 2001;Niordson and Hutchinson, 2003;Gudmundson, 2004;Zeghadi et al, 2005;Gurtin and Anand, 2009;Niordson and Legarth, 2010;Fleck and Willis, 2009;Fleck et al, 2015;El-Naaman et al, 2019) are also able to predict size dependent responses of polycrystals like Hall-Petch behavior and reversible plasticity effects due to GNDs. These theories integrate the Nye tensor characterizing the plastic deformation incompatibility and strain gradient effects in continuum crystal plasticity simulations.…”

mentioning

confidence: 99%

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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Cosserat continuum modelling of grain size effects in metal polycrystals

Cited by 14 publications

References 9 publications

Size effects in generalised continuum crystal plasticity for two-phase laminates

Size effects in generalised continuum crystal plasticity for two-phase laminates

Ensemble averaging stress–strain fields in polycrystalline aggregates with a constrained surface microstructure – Part 2: crystal plasticity

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

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