A rate-independent crystal plasticity model with a smooth elastic–plastic transition and no slip indeterminacy

Forest, Samuel; Rubin, M. B.

doi:10.1016/j.euromechsol.2015.08.012

Cited by 32 publications

(27 citation statements)

References 41 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The Clausius-Duhem inequality (30) can now be written in terms of the newly introduced, intermediate quantities by noting that…”

Section: Alternative Formulation Of Constitutive Equationsmentioning

confidence: 99%

“…They are given in Table 1. The parameters for the elasto-viscoplastic behavior, given in Table 2, are chosen based on reported values in the literature [30,31] with the exception of the parametersη and C which are taken from [7], where it was demonstrated thatη < η φ should hold for mobile grain boundaries.…”

Section: Coupling Functions Mobility Functions and Model Parametersmentioning

confidence: 99%

See 1 more Smart Citation

A Cosserat–phase-field theory of crystal plasticity and grain boundary migration at finite deformation

Ask

Forest

Appolaire

et al. 2018

Continuum Mech. Thermodyn.

Self Cite

View full text Add to dashboard Cite

In metallic polycrystals, an important descriptor of the underlying microstructure is the orientation of the crystal lattice of each grain. During thermomechanical processing, the microstructure can be significantly altered through deformation, nucleation of new subgrains and grain boundary migration. Cosserat crystal plasticity provides orientation as a degree of freedom and is therefore a natural choice for the development of a coupled framework to deal with concurrent viscoplasticity and grain growth. In order to take into account grain boundary motion, the Cosserat theory is adapted with inspiration from orientation phase-field models. This allows for the microstructure at a material point to evolve on the one hand due to deformation-induced lattice reorientation and on the other hand due to a sweeping grain boundary. With a proper separation of plastic evolution in the bulk of the grain and in the grain boundary, the model can successfully capture grain boundary migration due to lattice curvature and due to statistically stored dislocations.Keywords Cosserat crystal plasticity · Phase-field method · Grain boundary migration Communicated by Francesco dell'Isola.A. Ask · S. Forest (B) · K. Ammar MINES ParisTech,

show abstract

“…The Clausius-Duhem inequality (30) can now be written in terms of the newly introduced, intermediate quantities by noting that…”

Section: Alternative Formulation Of Constitutive Equationsmentioning

confidence: 99%

Section: Coupling Functions Mobility Functions and Model Parametersmentioning

confidence: 99%

A Cosserat–phase-field theory of crystal plasticity and grain boundary migration at finite deformation

Ask

Forest

Appolaire

et al. 2018

Continuum Mech. Thermodyn.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Each grain is considered as an initially homogeneous single crystal. To ease the interpretation of the numerical results, a rate-independent formulation is selected, using the single crystal plasticity model recently proposed by Forest and Rubin (2016). An advantage of using a rate-independent model coupled with a small strain assumption is the numerical efficiency which is crucial when simulating hundreds of cycles under various load amplitudes.…”

Section: Crystal Plasticity Modelmentioning

confidence: 99%

“…with the Macaulay brackets < x >= Max(x, 0). In the present work following Forest and Rubin (2016), the rate of slip on each slip system is replaced by a rate-independent formulation of the form:…”

Section: Crystal Plasticity Modelmentioning

confidence: 99%

“…A rate-independent crystal plasticity model formulation is used to avoid the contamination of the final results by viscosity effects. The selected crystal plasticity model 70 by (Forest and Rubin, 2016) exhibits a smooth elasto-plastic transition and is strictly rate-independent. In what follows, finite element simulations of polycrystalline aggregates will be shown to provide a realistic description of ratcheting and mean stress relaxation in face centered cubic (FCC) metals, without resorting to complex memory variables in contrast to macroscopic approaches.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Crystal plasticity modeling of the cyclic behavior of polycrystalline aggregates under non-symmetric uniaxial loading: Global and local analyses

Farooq

Cailletaud

Forest

et al. 2020

International Journal of Plasticity

Self Cite

View full text Add to dashboard Cite

When a sample is cyclically loaded under a mean stress or strain, incremental strain ratcheting or mean stress relaxation phenomena are usually observed. Experiments show that for metallic materials there is generally no full mean stress relaxation as well as saturation of macroscopic strain ratcheting. In contrast, most macroscopic constitutive models produce both quantities in excess, and complex sets of additional internal variables must be introduced to improve the modeling. Little attention has been paid to model such phenomena using polycrystal aggregates especially going up to the regime of cyclic mechanical stability. In this work based on an elementary crystal plasticity model for FCC crystals and large scale finite element, it is be shown that the interaction between different grains is sufficient to cater for such complex phenomena. Light is shed on how different regions of the polycrystal accommodate each other and how the classical definition of constant rate strain ratcheting or a zero mean stress is nearly impossible to apply to a polycrystalline aggregate. In addition, it is shown that even if a macroscopic stable hysteresis stress strain loop is observed, ratcheting phenomena can still be observed at the local scale. The distributions of different constitutive quantities within a polycrystal are also analyzed which gives a new insight into what is happening inside a polycrystal in terms of stress and strain redistribution. In particular, the existence of evolving bimodal distributions of stress and accumulated plastic strain is evidenced and related to the occurrence of plastic shakedown and incomplete mean stress relaxation. Two numerical criteria to detect strain ratcheting are finally proposed and discussed. Kang et al., 2010). Mean stress in this article is defined as (Σ max + Σ min )/2 where Σ max and Σ min are the 15 maximum and minimum applied stresses in a cyclically loaded component. The stress amplitude is defined as Σ max −Σ min /2. With regards to asymetric strain controlled cyclic loadings, it is also known that under a given stress amplitude, increasing the mean stress, or increasing the applied mean stress under constant amplitude, both increase the rate of ratcheting (Goodman, 1984). On the other hand, experimental observations indicate levels of mean stress for which there is very low ratcheting and the mechanical state of the material converges 20 towards plastic shakedown (Pellissier-Tanon et al., 1982). Similarly, for asymmetric strain controlled loading conditions, a cyclic mean stress is observed, and several experimental studies (Wehner and Fatemi, 1991;Nikulin et al., 2019;Prithivirajan and Sangid, 2018) have deciphered the corresponding physical mechanisms. These observations show that for a given positive mean strain, and a low strain amplitude, the mean stress does not completely relax to zero. Also, increasing the strain amplitude leads to a nonlinear decrease of the 25

show abstract

Crystal plasticity algorithm based on the quasi‐extremal energy principle

Petryk

Kursa

2022

Numerical Meth Engineering

View full text Add to dashboard Cite

The direct incremental energy minimization in rate‐independent plasticity does not account for the skew‐symmetric part of the tangent stiffness matrix. In crystal plasticity, this corresponds to neglecting the asymmetry of the matrix of interaction moduli for active slip‐systems. This limitation has been overcome in the recently proposed quasi‐extremal energy principle (QEP) applicable to nonpotential problems. In the present article it is shown how to extend QEP to finite increments in the backward‐Euler computational scheme. A related constitutive algorithm is proposed which enables automatic selection of active slip systems using an energetic criterion, along any path of large deformation of a rate‐independent single crystal with a nonsymmetric slip‐system interaction matrix. Numerical examples have been calculated for a fcc single crystal subjected to simple shear or uniaxial tension. The slip system activity predicted by using the QEP algorithm has been found to be more reliable in describing the actual plastic response of metal crystals than conventional rate‐dependent modeling in cases where the selection of active slip‐systems is essential.

show abstract

A rate-independent crystal plasticity model with a smooth elastic–plastic transition and no slip indeterminacy

Cited by 32 publications

References 41 publications

A Cosserat–phase-field theory of crystal plasticity and grain boundary migration at finite deformation

A Cosserat–phase-field theory of crystal plasticity and grain boundary migration at finite deformation

Crystal plasticity modeling of the cyclic behavior of polycrystalline aggregates under non-symmetric uniaxial loading: Global and local analyses

Crystal plasticity algorithm based on the quasi‐extremal energy principle

Contact Info

Product

Resources

About