Effects of the grain size and shape on the flow stress: A dislocation dynamics study

Jiang, Maoyuan; Devincre, Benoît; Monnet, Ghiath

doi:10.1016/j.ijplas.2018.09.008

Cited by 88 publications

(37 citation statements)

References 63 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To overcome this limitation, Aifantis (1984) has proposed in a pioneering work a strain gradient plasticity (SGP) model with a single internal length scale parameter embedded in the conventional plasticity theory. This model is capable of predicting plastic deformation gradients (plastic inhomogeneities), which correlate with size effects as experimentally observed and numerically predicted using dislocation mechanics (Zhou and Lesar, 2012;Dahlberg et al, 2017;Jiang et al, 2019). Plastic deformation gradients can physically be interpreted because they represent the geometrically necessary dislocations (GNDs; Ashby, 1970), which are associated with small scale crystalline incompatibilities (e.g., incompatibility of the mesoscopic plastic distortion).…”

Section: Introductionmentioning

confidence: 86%

Strain gradient crystal plasticity model based on generalized non-quadratic defect energy and uncoupled dissipation

Jebahi

Cai

Abed‐Meraim

2020

International Journal of Plasticity

View full text Add to dashboard Cite

The present paper proposes a flexible Gurtin-type strain gradient crystal plasticity (SGCP) model based on generalized non-quadratic defect energy and uncoupled constitutive assumption for dissipative processes. A power-law defect energy, with adjustable order-controlling index n, is proposed to provide a comprehensive investigation into the energetic length scale effects under proportional and non-proportional loading conditions. Results of this investigation reveal quite different effects of the energetic length scale, depending on the value of n and the type of loading. For n ≥ 2, regardless of the loading type, the energetic length scale has only influence on the rate of the classical kinematic hardening, as reported in several SGCP works. However, in the range of n < 2, this parameter leads to unusual nonlinear kinematic hardening effects with inflection points in the macroscopic mechanical response, resulting in an apparent increase of the yield strength under monotonic loading. More complex effects, with additional inflection points, are obtained under non-proportional loading conditions, revealing new loading history memory-like effects of the energetic length scale. Concerning dissipation, to make the dissipative effects more easily controllable, dissipative processes due to plastic strains and their gradients are assumed to be uncoupled. Separate formulations, expressed using different effective plastic strain measures, are proposed to describe such processes. Results obtained using these formulations show the great flexibility of the proposed model in controlling some major dissipative effects, such as elastic gaps. A simple way to remove these gaps under certain non-proportional loading conditions is provided. Application of the proposed uncoupled formulations to simulate the mechanical response of a sheared strip has led to accurate prediction of the plastic strain distributions, which compare very favorably with those predicted using discrete dislocation mechanics.

show abstract

Section: Introductionmentioning

confidence: 86%

Strain gradient crystal plasticity model based on generalized non-quadratic defect energy and uncoupled dissipation

Jebahi

Cai

Abed‐Meraim

2020

International Journal of Plasticity

View full text Add to dashboard Cite

show abstract

“…Alternatively, Discrete Dislocation Dynamics (DDD) methods first developed by Kubin et al (1992) and later by Needleman (1995), Verdier et al (1998), Schwarz (1999) among others, are able to naturally account for internal length and grain size effects considering discrete distributions of dislocation sources, dislocation mobility, Peach-Koehler force (Peach and Koehler, 1950) on dislocation line or segments and impenetrable grain or phase boundaries. For example, DDD was used to study plasticity size effects on internal stresses in thin films (Espinosa et al, 2005(Espinosa et al, , 2006, micro-specimens (Kiener et al, 2010), grain size effects on the strengthening of polycrystals and Hall-Petch relationship (Biner and Morris, 2002;Lefebvre et al, 2007;Balint et al, 2010;Jiang et al, 2019) and Bauschinger effect (Nicola et al, 2006;Guruprasad et al, 2008;Balint et al, 2010;Jiang et al, 2019;Waheed et al, 2017).…”

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

View full text Add to dashboard Cite

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.

show abstract

“…Further evidence supporting these claims is presented in Ref. 67, where the grain shape effect on the plastic response has been investigated in detail. The use of small cubic grain is thus preferred for the sake of minimizing the computational load.…”

Section: Grain Setups and Dislocation/defect Interaction Implementationmentioning

confidence: 76%

Dislocation spreading and ductile–to-brittle transition in post-irradiated ferritic grains: Investigation of grain size and grain orientation effect by means of 3D dislocation dynamics simulations

Robertson

et al. 2019

J. Mater. Res.

View full text Add to dashboard Cite

show abstract

Effects of the grain size and shape on the flow stress: A dislocation dynamics study

Cited by 88 publications

References 63 publications

Strain gradient crystal plasticity model based on generalized non-quadratic defect energy and uncoupled dissipation

Strain gradient crystal plasticity model based on generalized non-quadratic defect energy and uncoupled dissipation

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

Dislocation spreading and ductile–to-brittle transition in post-irradiated ferritic grains: Investigation of grain size and grain orientation effect by means of 3D dislocation dynamics simulations

Contact Info

Product

Resources

About