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A coalescence criterion for isotropic porous materials with inhomogeneous yield stress
[Un critère de coalescence pour matériaux poreux isotropes de limite d’élasticité inhomogène]
Jérémy Hure1 orcid   ; Léo Morin2, 3 orcid
1Université Paris-Saclay, CEA, Service d’Étude des Matériaux Irradiés, 91191, Gif-sur-Yvette, France
2Univ. Bordeaux, CNRS, Bordeaux INP, I2M, UMR 5295, F-33400 Talence, France
3Arts et Metiers Institute of Technology, CNRS, Bordeaux INP, I2M, UMR 5295, F-33400 Talence, France
Comptes Rendus. Mécanique, Volume 354 (2026), pp. 679-703

The aim of this work is to study theoretically and numerically the effect of the inhomogeneity of the yield stress on void coalescence for isotropic porous ductile materials. Such inhomogeneities may arise due to strain hardening prior to void coalescence. Sequential limit analysis is applied to a cylindrical unit cell containing a coaxial cylindrical void in a von Mises matrix material with a radially dependent yield stress. An estimate of the coalescence criterion is obtained for combined tensile and shear loading. The criterion relies on 1D integrals, but two approximations are also provided to obtain analytical expressions. Numerical limit analysis based on FFT simulations is performed to get exact, up to numerical errors, coalescence stresses, and to assess the theoretical expressions. A good agreement is found between the analytical coalescence criterion and the numerical results for a large set of void shape, porosities and yield stress distributions. The coalescence criterion is finally used to assess the effect of strain-hardening on the orientation of void coalescence plane, as well as to describe the full yield locus — accounting for both void growth and coalescence — of porous isotropic materials, for axisymmetric loading conditions.

L’objectif de ce travail est d’étudier théoriquement et numériquement l’effet de l’inhomogénéité spatiale de la limite d’élasticité, résultant par exemple de l’écrouissage, sur la coalescence de cavités dans les matériaux poreux. L’analyse limite séquentielle est appliquée à une cellule cylindrique contenant une cavité cylindrique coaxiale. La plasticité de la matrice est décrite par le critère de von Mises en considérant une dépendance radiale de la limite d’élasticité. Un critère de coalescence est obtenu pour des chargements combinant traction et cisaillement. Le critère dépend d’intégrales unidimensionnelles, mais deux approximations sont proposées pour obtenir des expressions analytiques. Des simulations d’analyse limite numérique par méthode FFT sont réalisées pour obtenir le critère exact de coalescence et pour évaluer les expressions théoriques obtenues. Un bon accord est observé entre le critère théorique et les résultats numériques pour une large plage de valeurs de rapports d’aspects de la cavité, de porosités et de distribution spatiale de limite d’élasticité. Le critère de coalescence est finalement utilisé pour évaluer l’effet de l’écrouissage sur l’orientation du plan de coalescence, et pour décrire le critère de plasticité de matériaux poreux isotropes pour des conditions de chargement axisymétriques.

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Révisé le :
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DOI : 10.5802/crmeca.377
Keywords: Porous ductile solids, void coalescence, limit analysis, FFT-based simulations
Mots-clés : Matériaux poreux, coalescence de cavités, analyse limite, simulations FFT

Jérémy Hure  1   ; Léo Morin  2 , 3

1 Université Paris-Saclay, CEA, Service d’Étude des Matériaux Irradiés, 91191, Gif-sur-Yvette, France
2 Univ. Bordeaux, CNRS, Bordeaux INP, I2M, UMR 5295, F-33400 Talence, France
3 Arts et Metiers Institute of Technology, CNRS, Bordeaux INP, I2M, UMR 5295, F-33400 Talence, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
Jérémy Hure; Léo Morin. A coalescence criterion for isotropic porous materials with inhomogeneous yield stress. Comptes Rendus. Mécanique, Volume 354 (2026), pp. 679-703. doi: 10.5802/crmeca.377
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