Coalescence of voids by internal necking: Theoretical estimates and numerical results

Morin, Léo; Leblond, Jean-Baptiste; Benzerga, A. Amine

doi:10.1016/j.jmps.2014.11.009

Cited by 56 publications

(71 citation statements)

References 40 publications

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“…These additional features would inevitably lead to well known phenomena in porous materials such as material softening, void shape effects, deformation localization (c.f. Danas and Ponte Castañeda (2012)) and ultimately void coalescence (see for instance (Benzerga, 2002;Pardoen and Hutchinson, 2000;Morin et al, 2015)). Such a work is underway and will be presented elsewhere.…”

Section: Resultsmentioning

confidence: 99%

A model for porous single crystals with cylindrical voids of elliptical cross-section

Mbiakop¹,

Constantinescu²,

Danas³

2015

International Journal of Solids and Structures

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International audienceThis work presents a rate-dependent constitutive model for porous single crystals with arbitrary number of slip systems and orientations. The single crystal comprises cylindrical voids with elliptical cross-section at arbitrary orientations and is subjected to general plane-strain loadings. The proposed model, called modified variational model (MVAR), is based on the nonlinear variational homogenization method, which makes use of a linear comparison porous single crystal material to estimate the response of the nonlinear porous single crystal. The MVAR model is validated by periodic finite element simulations for a large number of parameters including general in-plane crystal anisotropy, general in-plane void shapes and orientations, various creep exponents (i.e., nonlinearity) and general plane strain loading conditions. The MVAR model, which at the present state involves no calibration parameters, is found to be in good agreement with the finite element results for all cases considered in this work. The model is then used in a predictive manner to investigate the complex response of porous single crystals in several cases with strong coupling between the anisotropy of the crystal and the (morphological) anisotropy induced by the shape and orientation of the voids

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Section: Resultsmentioning

confidence: 99%

A model for porous single crystals with cylindrical voids of elliptical cross-section

Mbiakop¹,

Constantinescu²,

Danas³

2015

International Journal of Solids and Structures

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“…and (2) a trial velocity field kinematically admissible with boundary conditions and verifying the property of incompressibility. Regarding the latter point, several trial velocity fields have been provided in previous studies [8,57,58,59,21] for cylindrical porous unit-cell with cylindrical void, which have been shown to lead to good estimates of coalescence stress for both isotropic and (Hill)-anisotropic materials. For crystal plasticity as defined in Section 3.1.1, an analytical expression for the microscopic dissipation (Eq.…”

Section: Homogenization and Limit-analysismentioning

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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“…Such geometry, which stands as an approximation of a unit-cell of a (doubly)-periodic array of hexagonal lattice under periodic boundary conditions ( Fig. 2), allows to derive analytical estimates of (nano)-voids coalescence in the frame of limit analysis [50]. As detailed for example in [51] through comparisons of analytical criterion to finite-element simulations results, coalescence criterion derived for cylindrical void can a priori be used to describe spheroidal void.…”

Section: Geometry and Boundary Conditionsmentioning

confidence: 99%

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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Coalescence of voids by internal necking: Theoretical estimates and numerical results

Cited by 56 publications

References 40 publications

A model for porous single crystals with cylindrical voids of elliptical cross-section

A model for porous single crystals with cylindrical voids of elliptical cross-section

A coalescence criterion for porous single crystals

Anisotropic coalescence criterion for nanoporous materials

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