FFT-based interface decohesion modelling by a nonlocal interphase

Sharma, Luv; Peerlings, R.H.J.; Shanthraj, Pratheek; Roters, Franz; Geers, M.G.D.

doi:10.1186/s40323-018-0100-0

Cited by 26 publications

(20 citation statements)

References 28 publications

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“…For polycrystals, the different constitutive regimes solved with FFT-based methods include: linear elasticity (Lebensohn, 2001;Brenner et al, 2009); linear viscosity (Lebensohn et al, 2005); thermoelasticity (Vinogradov and Milton, 2008;Anglin et al, 2014;Donegan and Rollett, 2015); rigid-viscoplasticity (Lebensohn, 2001;Lebensohn et al, 2008Lebensohn et al, , 2009Lee et al, 2011;Rollett et al, 2010); smallstrain crystal plasticity elasto-viscoplasticity, i.e. CP-EVPFFT Grennerat et al, 2012;Suquet et al, 2012); large-strain elasto-viscoplasticity (Eisenlohr et al, 2013;Shanthraj et al, 2015;Kabel et al, 2016;Vidyasagar et al, 2018;Lucarini and Segurado, 2018); dilatational plasticity ; lower-order (Lucarini and Segurado, 2018) and higher-order strain-gradient plasticity (Lebensohn and Needleman, 2016); curvature-driven plasticity (Upadhyay et al, 2016); transformation plasticity (Richards et al, 2013;Otsuka et al, 2018); fatigue (Rovinelli et al, 2017a,b); and quasi-brittle damage (Li et al, 2012;Sharma et al, 2012). FFT-based methods were also applied to field dislocation mechanics (FDM) and field disclination mechanics (Brenner et al, 2014;Berbenni et al, 2014;Djaka et al, 2015;Berbenni et al, 2016;Djaka et al, 2017;Berbenni and Taupin, 2018), and discrete dislocation dynamics (DDD) problems (Bertin et al, 2015;Graham et al, 2016;…”

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confidence: 99%

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

Djaka

Berbenni

Taupin

et al. 2020

International Journal of Solids and Structures

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confidence: 99%

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

Djaka

Berbenni

Taupin

et al. 2020

International Journal of Solids and Structures

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“…The different constitutive regimes solved with FFT-based methods include: linear elasticity (Lebensohn, 2001;Brenner et al, 2009); linear viscosity (Lebensohn et al, 2005); linear elasticity with eigenstrains or thermoelasticity (Vinogradov and Milton, 2008;Anglin et al, 2014;Donegan and Rollett, 2015;Eloh et al, 2019); rigid-viscoplasticity (Lebensohn, 2001;Lebensohn et al, 2008Lebensohn et al, , 2009Lee et al, 2011;Rollett et al, 2010); small-strain crystal plasticity elasto-viscoplasticity, i.e. CP-EVPFFT (Lebensohn et al, 2012;Grennerat et al, 2012;Suquet et al, 2012); large-strain elasto-viscoplasticity (Eisenlohr et al, 2013;Shanthraj et al, 2015;Kabel et al, 2016;Vidyasagar et al, 2018;Lucarini and Segurado, 2019); dilatational plasticity ; lower-order (Haouala et al, 2020) and higher-order (Lebensohn and Needleman, 2016) straingradient crystal plasticity; curvature-driven plasticity (Upadhyay et al, 2016); transformation plasticity (Richards et al, 2013;Otsuka et al, 2018); twinning (Mareau and Daymond, 2016;Paramatmuni and Kanjarla, 2019), fatigue (Rovinelli et al, 2017(Rovinelli et al, , 2018Lucarini and Segurado, 2019); and quasi-brittle damage (Li et al, 2012;Sharma et al, 2012). FFT-based methods were also applied to field dislocation mechanics (FDM) and field disclination mechanics (Brenner et al, 2014;Berbenni et al, 2014;…”

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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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“…This ratio is maintained throughout the analysis. In an FFT based solution for problems involving heterogeneity of model parameters, the numerical convergence issues are expected [30]. provides a systematic analysis of the influence of this contrast of the mechanical response.…”

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confidence: 99%

An FFT-based spectral solver for interface decohesion modelling using a gradient damage approach

et al. 2019

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This work presents a fast Fourier transform (FFT) based method that can be used to model interface decohesion. The inability of an FFT solver to deal with sharp interfaces discards the use of conventional cohesive zones to model the interfacial mechanical behaviour within this framework. This limitation is overcome by approximating sharp interfaces (e.g. grain/phase boundaries) with an interphase. Within the interphase, the background plastic constitutive behaviour is inherited from the respective adjacent grains. The anisotropic kinematics of the decohesion process is modelled using a damage deformation gradient that is constructed by mapping the opening strains (in normal and tangential modes) to the associated projection tensors. The degradation (damage) of the interfacial opening resistances is modelled via a dimensionless nonlocal damage variable that prevents localisation of damage within the interphase. This nonlocal variable results from the solution of a gradient damage based regularisation equation within the interphase subdomain. The damage field is constrained to the interphase region by applying a relatively large penalisation on the damage gradients inside the interphase. The extent of nonlocality ensures that the damage is largely uniform in the direction perpendicular to the interphase, thus making its thickness the theoretical lengthscale for dissipation. To achieve model predictions that are objective with respect to the interphase thickness, scaling relations of the model parameters are proposed. The numerical performance is shown for a uniform opening case and then for a propagating crack. Finally, an application to an artificial polycrystal is shown.

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FFT-based interface decohesion modelling by a nonlocal interphase

Cited by 26 publications

References 28 publications

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

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

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

An FFT-based spectral solver for interface decohesion modelling using a gradient damage approach

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