Influence of the Yield Surface Curvature on the Forming Limit Diagrams Predicted by Crystal Plasticity Theory

Akpama, Holanyo K.; Bettaieb, Mohamed Ben; Abed‐Meraim, Farid

doi:10.1590/1679-78252456

Cited by 3 publications

(3 citation statements)

References 29 publications

(36 reference statements)

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“…Among them, one may mention the lattice rotation, the convective stress components involved in the expression of the tangent modulus, and the slip system activity governed by the Schmid law, which represents the most important factor. Indeed, with a regular form of the Schmid law, which rounds off corners at the yield surface, the strong reduction in the determinant of the acoustic tensor cannot be observed (Akpama et al, 2016). Fur-thermore, it is also observed from Figure 4 that the predictions given by the polycrystalline aggregate with 50 grains exhibit much more oscillations than those obtained with the other polycrystalline aggregates, which comprise a larger number of grains.…”

Section: Fld Predictionsmentioning

confidence: 87%

Prediction of Plastic Instability in Sheet Metals During Forming Processes Using the Loss of Ellipticity Approach

Akpama

Bettaieb

Abed‐Meraim

2017

Lat. Am. j. solids struct.

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The prediction of plastic instability in sheet metals during forming processes represents nowadays an ambitious challenge. To reach this goal, a new numerical approach, based on the loss of ellipticity criterion, is proposed in the present contribution. A polycrystalline model is implemented as a user-material subroutine into the ABAQUS/Implicit finite element (FE) code. The polycrystalline constitutive model is assigned to each integration point of the FE mesh. To derive the mechanical behavior of this polycrystalline aggregate from the behavior of its microscopic constituents, the multiscale self-consistent scheme is used. The mechanical behavior of the single crystals is described by a finite strain rateindependent constitutive framework, where the Schmid law is used to model the plastic flow. The condition of loss of ellipticity at the macroscale is used as plastic instability criterion in the FE modeling. This numerical approach, which couples the FE method with the self-consistent scheme, is used to simulate a deep drawing process, and the above criterion is used to predict the formability limit of the studied sheets during this operation.

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Section: Fld Predictionsmentioning

confidence: 87%

Prediction of Plastic Instability in Sheet Metals During Forming Processes Using the Loss of Ellipticity Approach

Akpama

Bettaieb

Abed‐Meraim

2017

Lat. Am. j. solids struct.

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“…As to tensor

, it represents the 2D macroscopic tangent modulus relating the in-plane components of the nominal stress rate tensor to the in-plane components of the velocity gradient. The analytical expression for the 2D tangent modulus

is derived from the general expression of the 3D tangent modulus by the classical relation [ 20 ]:

…”

Section: Theoretical Frameworkmentioning

confidence: 99%

“…In this case, the destabilizing mechanism required to predict bifurcation localization at realistic limit strain levels is an obvious consequence of the crystal plasticity multi-slip and the associated yield surface vertex effects, which is taken into account by using this classical Schmid law. The effect of a regularization of this Schmid law (by substituting the vertices at the yield surface by rounded corners) on the prediction of the ductility limit has been recently analyzed in [ 20 ]. It has been demonstrated that the limit strains predicted in the range of positive strain paths are unrealistically high when the regularized version of the Schmid law is used to model the plastic flow at the single crystal scale.…”

Section: Introductionmentioning

confidence: 99%

Influence of the Non-Schmid Effects on the Ductility Limit of Polycrystalline Sheet Metals

Bettaieb

Abed‐Meraim

2018

Materials

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The yield criterion in rate-independent single crystal plasticity is most often defined by the classical Schmid law. However, various experimental studies have shown that the plastic flow of several single crystals (especially with Body Centered Cubic crystallographic structure) often exhibits some non-Schmid effects. The main objective of the current contribution is to study the impact of these non-Schmid effects on the ductility limit of polycrystalline sheet metals. To this end, the Taylor multiscale scheme is used to determine the mechanical behavior of a volume element that is assumed to be representative of the sheet metal. The mechanical behavior of the single crystals is described by a finite strain rate-independent constitutive theory, where some non-Schmid effects are accounted for in the modeling of the plastic flow. The bifurcation theory is coupled with the Taylor multiscale scheme to predict the onset of localized necking in the polycrystalline aggregate. The impact of the considered non-Schmid effects on both the single crystal behavior and the polycrystal behavior is carefully analyzed. It is shown, in particular, that non-Schmid effects tend to precipitate the occurrence of localized necking in polycrystalline aggregates and they slightly influence the orientation of the localization band.

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An elasto-plastic self-consistent model for damaged polycrystalline materials: Theoretical formulation and numerical implementation

Paux

Bettaieb

Badreddine

et al. 2020

Computer Methods in Applied Mechanics and Engineering

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Influence of the Yield Surface Curvature on the Forming Limit Diagrams Predicted by Crystal Plasticity Theory

Cited by 3 publications

References 29 publications

Prediction of Plastic Instability in Sheet Metals During Forming Processes Using the Loss of Ellipticity Approach

Prediction of Plastic Instability in Sheet Metals During Forming Processes Using the Loss of Ellipticity Approach

Influence of the Non-Schmid Effects on the Ductility Limit of Polycrystalline Sheet Metals

An elasto-plastic self-consistent model for damaged polycrystalline materials: Theoretical formulation and numerical implementation

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