Theoretical and numerical analysis of void coalescence in porous ductile solids under arbitrary loadings

Torki, Mohammad E.; Tekoğlu, Cihan; Leblond, Jean-Baptiste; Benzerga, A. Amine

doi:10.1016/j.ijplas.2017.02.011

Cited by 46 publications

(29 citation statements)

References 37 publications

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“…Note that the numerical results presented in Fig. 8 are slightly different from the ones reported in [64] due to different void shapes (cylindrical for [64] vs. spheroidal in this study).…”

Section: Comparisons To Numerical Resultscontrasting

confidence: 74%

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Anisotropic coalescence criterion for nanoporous materials

Hure

2017

Journal of the Mechanics and Physics of Solids

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Ductile fracture through void growth and coalescence depends significantly on the plastic anisotropy of the material and on void size, as shown by experiments and/or numerical simulations through several studies. Macroscopic (homogenized) yield criteria aiming at modeling nanoporous materials have been proposed only for the growth regime, i.e. non-interacting voids. The aim of this study is thus to provide a yield criterion for nanoporous materials relevant for the coalescence regime, i.e. when plastic flow is localized between voids. Through homogenization and limit analysis, and accounting for interface stresses at the void-matrix interface, analytical coalescence criterion is derived under the following conditions: axisymmetric loading, orthotropic material obeying Hill's plasticity, cylindrical voids in cylindrical unit-cell. Incidentally, an orthotropic extension of the existing isotropic modeling of interface stresses through limit analysis is described and used. The proposed coalescence criterion is then extended to account for combined tension and shear loading conditions. Numerical limit analyses have been performed under specific conditions / materials parameters to get supposedly exact (up to numerical errors) results of coalescence stress. A good agreement between the analytical coalescence criteria derived in this study and numerical results is found for elongated spheroidal voids, making them usable to predict the onset of void coalescence in ductile fracture modeling of nanoporous materials.

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“…Note that the numerical results presented in Fig. 8 are slightly different from the ones reported in [64] due to different void shapes (cylindrical for [64] vs. spheroidal in this study).…”

Section: Comparisons To Numerical Resultscontrasting

confidence: 74%

“…For combined tension and shear loading conditions, pseudo-periodic boundary conditions are used on the lateral surface of the cylindrical unit-cell: ∀z v(x, y, z) = C ste (z). The boundary conditions used in this study are the same as the ones used recently in [64]. Interface stresses are accounted for in two different ways.…”

Section: Numerical Simulationsmentioning

confidence: 99%

Anisotropic coalescence criterion for nanoporous materials

Hure

2017

Journal of the Mechanics and Physics of Solids

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“…26 and numerical results is found to be good, similarly to what have been already shown in [60]. Some discrepancies appear for oblate voids for low applied shear stress, as already discussed in the previous section and attributed to the effect of the unit-cell [61]. Restricting to pure shear loading conditions, a strong effect of the crystallographic orientation is observed on the coalescence stress, up to a factor two for the FCC material with orientation [100] and [111], respectively.…”

Section: Combined Tension and Shear Loading Conditionssupporting

confidence: 85%

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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“…However, shear stress effects are not accounted for by the Thomason model. To address this issue, Tekoglu et al (2012) and Torki et al (2017) have extended the Thomason approach combining shear and tensile loading. Reddi et al (2019) have obtained similar results by using the multi-surface yield criterion developed by Keralavarma and Chockalingam (2016); Keralavarma (2017).…”

Section: Introduction and Motivationsmentioning

confidence: 99%

A micromechanics-based non-local damage to crack transition framework for porous elastoplastic solids

Leclerc

Nguyễn

Pardoen³

et al. 2020

International Journal of Plasticity

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The failure process of ductile porous materials is simulated by representing the damage nucleation, growth and coalescence stages up to crack initiation and propagation using a physically-based constitutive model. In particular, a non-local damage to crack transition framework is developed to predict the fracture under various loading conditions while minimising case-dependent calibration process. The formulation is based on a discontinuous Galerkin method, making it computationally efficient and scalable. The initial stable damage process is simulated using an implicit non-local damage model ensuring solution uniqueness beyond the onset of softening relying on the Gurson-Tvergaard-Needleman (GTN) model. Once the coalescence criterion is satisfied, which can physically arise before or during the softening stage, a cohesive band is introduced. Within the cohesive band, a void coalescencebased governing law is solved, accounting for the stress triaxiality state and material history, in order to capture the near crack tip failure process in a micromechanically sound way. Two coalescence models are then successively considered and compared. First, with a view to model verification towards literature results, a numerical coalescence model detects crack initiation at loss of ellipticity of a local model, and the crack opening is governed by ad-hoc parameters of the GTN model. Alternatively, the Thomason criterion is used to detect crack nucleation during the softening stage while the Thomason coalescence model governs the crack opening process. This latter model is able to reproduce slant and cup-cone failure modes in plane-strain and axisymmetric specimens, respectively.

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Theoretical and numerical analysis of void coalescence in porous ductile solids under arbitrary loadings

Cited by 46 publications

References 37 publications

Anisotropic coalescence criterion for nanoporous materials

Anisotropic coalescence criterion for nanoporous materials

A coalescence criterion for porous single crystals

A micromechanics-based non-local damage to crack transition framework for porous elastoplastic solids

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