Effects of grain size distribution and stress heterogeneity on yield stress of polycrystals: A numerical approach

Lavergne, Francis; Brenner, Rénald; Sab, Karam

doi:10.1016/j.commatsci.2013.04.061

Cited by 24 publications

(18 citation statements)

References 41 publications

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“…On the other hand, localized phenomena, such as internal stresses, plastic stored energy, void nucleation or cracking, require more accurate estimates of the heterogeneity of microscopic mechanical fields and, hence, richer representations of the microstructure. Whereas the most realistic grain shapes and size distributions are obtained after simulated annealing processes ( Cruz-Fabiano et al, 2014;Sieradzki and Madej, 2013 ), it is common to rely on a definition of the grains based on Voronoï ( Diard et al, 2005;Dobrzynski et al, 2011;Fritzen et al, 2009;Gonzalez et al, 2014;Quey et al, 2011;Resk et al, 2009;Sweeney et al, 2012 ) or Laguerre-Voronoï ( Hitti et al, 2012;Lavergne et al, 2013 ) cells.…”

Section: Introductionmentioning

confidence: 99%

“…One option is to use the level set approach in order to define the grains and to immerse the microstructure in an unstructured finite element mesh ( Dobrzynski et al, 2011;Resk et al, 2009 ). In the simplest case, the RVE is discretized in the form of an array of voxels, as is required when relying on fast Fourier transforms ( Brenner et al, 2009;Eisenlohr et al, 2013;Lavergne et al, 2013 ).…”

Section: Introductionmentioning

confidence: 99%

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Finite element modeling of periodic polycrystalline aggregates with intergranular cracks

Kowalski

Delannay

Yan

et al. 2016

International Journal of Solids and Structures

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a b s t r a c tThe present study addresses the prediction of the mechanical response of model polycrystalline aggregates in which the anisotropy of individual crystals induces high internal stresses as well as microcracks. A novel procedure is proposed in order to automatically generate finite element (FE) meshes that conform to the polycrystalline microstructure. The meshes obtained are periodic in 3-D and they contain cohesive zone elements along all grain boundaries. The FE model is applied to two materials with significant elastic anisotropy at the crystal level: stainless steel and graphite. A self-consistent equivalent inclusion solution is shown to produce a valid mean-field estimate of the effective stiffness of the polycrystal. This reference solution is used in order to optimize the assignment of lattice orientations to individual grains prior to the FE simulations. It is demonstrated that relying on such model polycrystals increases the accuracy of FE predictions at an affordable computational cost. The influence of internal cracks on the macroscopic response depends on the anisotropy of individual crystals.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Finite element modeling of periodic polycrystalline aggregates with intergranular cracks

Kowalski

Delannay

Yan

et al. 2016

International Journal of Solids and Structures

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“…This method revealed to be efficient for considering grain size distribution effects on the macroscopic flow stress of polycrystals (Berbenni et al, 2007;Lavergne et al, 2013) but the size effect does not come from deformation gradients that exist at more local scale reflecting the inhomogeneous nature of slip in the presence of grain boundaries. These intra-granular spatial gradients of lattice orientation, e.g.…”

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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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“…(7). A commercial strip of 22MnVNb6 microalloyed low carbon cast steel 30.00 mm long, with a rectangular cross section, 20.00 mm wide by 5.00 mm thick was applied on the tests [28][29][30][31]. The research material having chemical composition showed in Table 1.…”

Section: Methodsmentioning

confidence: 99%

Estimation of Ferrite Grain Size and Mechanical Properties of a 22MnVNb6 Microalloyed Low Carbon Cast Steel

Pluphrach

Yamsai

2017

Period. Polytech. Mech. Eng.

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Effects of grain size distribution and stress heterogeneity on yield stress of polycrystals: A numerical approach

Cited by 24 publications

References 41 publications

Finite element modeling of periodic polycrystalline aggregates with intergranular cracks

Finite element modeling of periodic polycrystalline aggregates with intergranular cracks

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

Estimation of Ferrite Grain Size and Mechanical Properties of a 22MnVNb6 Microalloyed Low Carbon Cast Steel

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