Strain gradient crystal plasticity with evolving length scale: Application to voided irradiated materials

Scherer, Jean–Michel; Besson, Jacques; Forest, Samuel; Hure, Jérémy; Tanguy, B.

doi:10.1016/j.euromechsol.2019.04.003

Cited by 28 publications

(32 citation statements)

References 48 publications

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“…Although this model remains computationally rather expensive, the results obtained in this work suggest that simulation of structures, such as real specimens, are now within reach in more reasonable computation times. The work initiated in (Scherer et al, 2019) on the evolution of voids in a softening matrix material will be pursued by performing 3D porous unit-cell simulations by taking advantage of the enhanced computational performance of the Lagrange multiplier formulation. The advances obtained in this paper will also be coupled in a future work to recent extensions of standard crystal plasticity to ductile failure (Ling et al, 2016) and damage (Lindroos et al, 2019).…”

Section: Discussionmentioning

confidence: 99%

“…Periodic boundary conditions are imposed on the displacement fluctuation v , micro-slip variable γ χ and Lagrange multiplier λ. As discussed in (Scherer et al, 2019) the analytical solution to this problem, in terms of plastic slip, is a localization band following a sine shape within the [−λ 0 /2; λ 0 /2] region and no slip elsewhere…”

Section: Validation Of the Lagrange Multiplier Implementationmentioning

confidence: 99%

“…From the analytical expression of τ = (F 12 + τ 0 /Z e )/(1/C 44 + 1/Z e ) with 1/Z e = λ 0 /HL derived in (Scherer et al, 2019) it follows that the maximum viscous stress is…”

Section: Computational Efficiencymentioning

confidence: 99%

“…The computational cost of finite element simulation based on strain gradient or micromorphic crystal plasticity is rather high due to the number of additional degrees of freedom and the strong nonlinearities of the problem. A reduced micromorphic crystal plasticity model was proposed by (Wulfinghoff and Böhlke, 2012;Wulfinghoff et al, 2013;Erdle and Böhlke, 2017;Ling et al, 2018;Scherer et al, 2019). It is limited to a single scalar additional degree of freedom, called microslip variable which is bounded to remain close to the cumulative plastic slip by means of the penalty parameter.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Lagrange multiplier based vs micromorphic gradient-enhanced rate-(in)dependent crystal plasticity modelling and simulation

Scherer

Phalke

Besson

et al. 2020

Computer Methods in Applied Mechanics and Engineering

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A reduced strain gradient crystal plasticity theory which involves the gradient of a single scalar field is presented. Rate-dependent and rate-independent crystal plasticity settings are considered. The theory is then reformulated following first the micromorphic approach and second a Lagrange multiplier approach. The finite element implementation of the latter is detailed. Computational efficiency of the Lagrange multiplier approach is highlighted in an example involving regularization of strain localization. The numerical performance improvement is shown to reach up to two orders of magnitude in computation time speedup. Then, size effects predicted by micromorphic and Lagrange multiplier based formulations of strain gradient plasticity are assessed. First of all numerical comparisons are performed on single crystal wires in torsion. Saturation of the size effects induced by the micromorphic approach and absence of saturation with the Lagrange multiplier approach when sample size is decreased are demonstrated. The Lagrange multiplier based formulation is finally applied to characterize size effects predicted for the ductile growth of porous unit-cells at imposed stress triaxiality. Excellent agreement with micromorphic results is obtained.

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Section: Discussionmentioning

confidence: 99%

Section: Validation Of the Lagrange Multiplier Implementationmentioning

confidence: 99%

“…From the analytical expression of τ = (F 12 + τ 0 /Z e )/(1/C 44 + 1/Z e ) with 1/Z e = λ 0 /HL derived in (Scherer et al, 2019) it follows that the maximum viscous stress is…”

Section: Computational Efficiencymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Lagrange multiplier based vs micromorphic gradient-enhanced rate-(in)dependent crystal plasticity modelling and simulation

Scherer

Phalke

Besson

et al. 2020

Computer Methods in Applied Mechanics and Engineering

View full text Add to dashboard Cite

show abstract

“…The scaling predicted from SGP models is almost always reported as τ y ∝ (ℓ/h) α , with α ≃ 1, whereas the experimental data [1,2] reveal a weaker scaling where 0.2 ≤ α ≤ 0.7. A number of extensions of conventional SGP, e.g., by changing the definition of the internal variable in terms of plastic strain and plastic strain gradients [10,[13][14][15][16][17] or by modifying the constitutive length scale by having it evolve with deformation [10,[18][19][20], have been proposed. Although these extensions can give quite different material responses and can be made to fit better to experiments, compared with conventional SGP, currently, there is no indication that they strongly influence the size scaling.…”

Section: Introductionmentioning

confidence: 99%

Size Scaling of Plastic Deformation in Simple Shear: Fractional Strain-Gradient Plasticity and Boundary Effects in Conventional Strain-Gradient Plasticity

Dahlberg

Ortiz

2020

Journal of Applied Mechanics

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A recently developed model based on fractional derivatives of plastic strain is compared with conventional strain-gradient plasticity (SGP) models. Specifically, the experimental data and observed model discrepancies in the study by Mu et al. (2016, “Dependence of Confined Plastic Flow of Polycrystalline Cu Thin Films on Microstructure,” MRS Com. Res. Let. 20, pp. 1–6) are considered by solving the constrained simple shear problem. Solutions are presented both for a conventional SGP model and a model extension introducing an energetic interface. The interface allows us to relax the Dirichlet boundary condition usually assumed to prevail when solving this problem with the SGP model. We show that the particular form of a relaxed boundary condition does not change the underlying size scaling of the yield stress and consequently does not resolve the scaling issue. Furthermore, we show that the fractional strain-gradient plasticity model predicts a yield stress with a scaling exponent that is equal to the fractional order of differentiation.

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Toward robust scalar-based gradient plasticity modeling and simulation at finite deformations

Abatour¹,

Forest²,

Ammar³

et al. 2022

Acta Mech

Self Cite

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Strain gradient plasticity has been the subject of extensive research in the past forty years in order to model size effects in metal plasticity, on the one hand, and provide finite width shear bands in the simulation of localization phenomena, on the other hand. However, the use of the emerging models is still limited to academic applications and has not yet been adopted by industry practitioners. The present paper systematically reviews the pros and the cons of gradient plasticity at finite strains based on gradient of scalar plastic variables, in particular gradient of the cumulative plastic strain. It proposes benchmark tests addressing both size effect modeling and plastic strain localization simulation. It includes new analytical solutions for validation of FE implementation. It focuses on the micromorphic approach to gradient plasticity, as a convenient method for implementation in FE codes. New features of the analysis include the comparison of three distinct formulations of rate-independent gradient plasticity at finite deformations, based on the multiplicative decomposition of the deformation gradient and on quadratic potentials with respect to gradient terms. The performance of micromorphic and Lagrange-multiplier based strain gradient plasticity models is evaluated for various monotonic and cyclic loading conditions including confined plasticity in simple glide and tension, bending and torsion at large deformations. Limitations are pointed out in the case of bending and torsion, which can be overcome for instance by the use of the gradient of equivalent plastic strain model.

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Strain gradient crystal plasticity with evolving length scale: Application to voided irradiated materials

Cited by 28 publications

References 48 publications

Lagrange multiplier based vs micromorphic gradient-enhanced rate-(in)dependent crystal plasticity modelling and simulation

Lagrange multiplier based vs micromorphic gradient-enhanced rate-(in)dependent crystal plasticity modelling and simulation

Size Scaling of Plastic Deformation in Simple Shear: Fractional Strain-Gradient Plasticity and Boundary Effects in Conventional Strain-Gradient Plasticity

Toward robust scalar-based gradient plasticity modeling and simulation at finite deformations

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