Anisotropic coalescence criterion for nanoporous materials

Hure, Jérémy

doi:10.1016/j.jmps.2017.08.001

Cited by 14 publications

(22 citation statements)

References 59 publications

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“…Average Taylor factors (Eqs. 22,24,28) are computed by adaptative quadrature scheme where the integrand function (local Taylor factor) relies on Taylor's minimum shear principle solved through linear programming [70].…”

Section: Coalescence Criterion For Porous Crystalsmentioning

confidence: 99%

A coalescence criterion for porous single crystals

Hure¹

2019

Journal of the Mechanics and Physics of Solids

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Voids can be observed at various scales in ductile materials, frequently of sizes lower than the grain size, leading to porous single crystals materials. Two local deformation modes of porous ductile (single crystals) materials have been identified and referred to as void growth and void coalescence, the latter being characterized by strong interactions between neighboring voids. A simple semi-analytical coalescence criterion for porous single crystals with periodic arrangement of voids is proposed using effective isotropic yield stresses associated with a criterion derived for isotropic materials. An extension of the coalescence criterion is also proposed to account for shear with respect to the coalescence plane. Effective yield stresses are defined using Taylor theory of single crystal deformation, and rely ultimately on the computation of average Taylor factors. Arbitrary sets of slip systems can be considered. The coalescence criterion is assessed through comparisons to numerical limit-analysis results performed using a Fast-Fourier-Transform based solver. A good agreement is observed between the proposed criterion and numerical results for various configurations including different sets of slip systems (Face-Centered-Cubic, Hexagonal-Close-Packed), crystal orientations, void shapes and loading conditions. The competition between void growth and void coalescence is described for specific conditions, emphasizing the strong influence of both crystal orientation and void lattice, as well as their interactions.

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Section: Coalescence Criterion For Porous Crystalsmentioning

confidence: 99%

A coalescence criterion for porous single crystals

Hure¹

2019

Journal of the Mechanics and Physics of Solids

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“…A size dependent homogenized model for isotropic porous materials is described in this study based on yield criteria derived for nanoporous material in growth [43] and coalescence [46] regimes, and adding evolutions laws for the hardening, porosity, cell and void aspect ratios. The latter has been calibrated through comparisons to reference finite strain porous unit cell simulations incorporating interfacial stresses.…”

Section: Resultsmentioning

confidence: 99%

“…The key ingredients of the size-dependent homogenized model for isotropic porous materials are the yield criteria derived in [43] in the growth regime, i.e. without strong interactions between voids, and in [46] for the coalescence regime, i.e. when adjacent voids strongly interact [50].…”

Section: Constitutive Equationsmentioning

confidence: 99%

“…Considering interface stresses, sizedependent isotropic yield criteria for both spherical and spheroidal voids in the growth regime have been derived in [42,43] and validated in [44,45], the latter describing a homogenized model based on the yield criterion for spherical voids [42]. A coalescence criterion has been proposed considering interface stresses, for spheroidal voids [46]. All these yield criteria for porous materials were derived in the continuum mechanics framework, assuming that plastic flow occurs at a scale well below the void size, which might be questionable for very small voids.…”

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confidence: 99%

“…In addition, no size-dependent homogenized model for porous materials including void growth and coalescence regimes, as well as voids shape effects, has been described in the literature.Therefore, the aim of this study is to provide a size-and shape-dependent homogenized model for isotropic porous materials, with a description of the numerical implementation as well as validation of the model through comparisons to unit cells simulations. Yield criteria proposed in [43] for the growth regime and [46] for the coalescence regime that consider spheroidal (nano-)voids are used. In section 2, the constitutive equations are detailed, as well as the numerical implementation.…”

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A size-dependent ductile fracture model: Constitutive equations, numerical implementation and validation

Scherer

Hure

2019

European Journal of Mechanics - A/Solids

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Size effects have been predicted at the micro-or nano-scale for porous ductile materials from Molecular Dynamics, Discrete Dislocation Dynamics and Continuum Mechanics numerical simulations, as a consequence of Geometrically Necessary Dislocations or due to the presence of a void matrix interface. As voids size decreases, higher stresses are needed to deform the material, for a given porosity. However, the majority of the homogenized models for porous materials used in ductile fracture modeling are size-independent, even though micrometric or nanometric voids are commonly observed in structural materials. Based on yield criteria proposed in the literature for nanoporous materials, a size-dependent homogenized model for porous materials is proposed for axisymmetric loading conditions, including void growth and coalescence as well as void shape effects. Numerical implementation of the constitutive equations is detailed. The homogenized model is validated through comparisons to porous unit cells finite element simulations that consider interfacial stresses, consistently with the model used for the derivation of the yield criteria, aiming at modeling an additional hardening at the void matrix interface. Potential improvements of the model are finally discussed with respect to the theoretical derivation of refined yield criteria and evolution laws. cell simulations [16,17,18]. Homogenized yield criteria for porous single crystals have been developed to account for the effects of crystal orientation [19,20,21,22,23].Most of these homogenized models for porous materials are size-independent, assuming implicitly that only void volume fraction matters irrespectively of void size, although porous materials with voids ranging from micrometric [13] down to nanometric sizes [24,25] are encountered in industrial applications. Moreover, size effects have been predicted from theoretical and numerical studies. A first kind of size effect, occurring when voids size is lower than the dislocation mean free-path, has been revealed through Discrete Dislocation Dynamics (DDD) simulations [26]. In such situations, dislocations exhaustion can lead to the absence of void growth under mechanical loading. A second kind of size effect is related, in a broad sense, to an additional hardening at or close to the void matrix interface. Strain gradient (crystal-)plasticity models -accounting for the presence of Geometrically Necessary Dislocations [27] to extend conventional plasticity to lower scales -have been used in porous unit cells simulations (see [28,29,30,31] and reference therein), showing a strong effect of the void size on both void growth rate and strength of the porous material, consistently with DDD simulations [32]. Numerous Molecular Dynamics (MD) studies have also been performed to assess the strength of (nano-)porous materials, considering voids in an initially dislocation free matrix material ([33, 34, 35] and references therein). Plasticity occurs through dislocation emission from void matrix interface [36], and an influence...

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Comparison between the Marciniak and Kuczyński imperfection approach and bifurcation theory in the prediction of localized necking for porous ductile materials

Nasir

Chalal

Abed‐Meraim

2022

Int J Adv Manuf Technol

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To prevent the occurrence of localized necking, the concept of forming limit diagram is often used, thus playing an important role in sheet metal forming processes. The aim of the present study is to develop a numerical tool for the theoretical prediction of forming limit diagrams, which would be a cost-effective procedure as compared to experimental measurements. The proposed numerical tool is based on the Marciniak and Kuczyński imperfection approach combined with the Gurson-Tvergaard-Needleman damage model, which is implemented into the MATLAB program within the framework of plane-stress conditions. Forming limit diagrams have been predicted by assuming both geometric (thickness) as well as material initial imperfections in the Marciniak and Kuczyński imperfection approach. These forming limit diagrams, for different sizes of geometric or material imperfections, are also compared with the forming limit diagram obtained by using the bifurcation theory. It is shown that the bifurcationbased forming limit diagram provides an upper bound as compared to the Marciniak and Kuczyński imperfection approach predictions. The results also reveal that, irrespective of the imperfection type considered in the Marciniak and Kuczyński imperfection approach, the corresponding forming limit diagram tends to that predicted by bifurcation theory when the size of initial imperfection tends to zero. Additionally, the predicted ductility limits are lowered as the magnitude of initial imperfection increases; however, the decrease in the ductility limits at balanced biaxial tension is more significant than for the other strain-path ratios. The results for the forming limit diagrams indicate that the predicted ductility limits are more sensitive to the initial imperfection in the thickness and the isotropic hardening coefficient as compared to the other types of material imperfections. Moreover, the initial imperfection in the critical porosity is the most influential one among the Gurson-Tvergaard-Needleman damage parameters.

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Anisotropic coalescence criterion for nanoporous materials

Cited by 14 publications

References 59 publications

A coalescence criterion for porous single crystals

A coalescence criterion for porous single crystals

A size-dependent ductile fracture model: Constitutive equations, numerical implementation and validation

Comparison between the Marciniak and Kuczyński imperfection approach and bifurcation theory in the prediction of localized necking for porous ductile materials

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