On some features of the effective behaviour of porous solids with J2- and J3-dependent yielding matrix behaviour

Ahmed Benallal

doi:10.1016/j.crme.2017.11.002

On some features of the effective behaviour of porous solids with J₂- and J₃-dependent yielding matrix behaviour
[Sur quelques effets de l'angle de Lode sur les caractéristiques macroscopiques de matériaux en rupture ductile]

Ahmed Benallal ¹

¹ LMT, ENS Paris-Saclay/CNRS/Université Paris-Saclay, France

Comptes Rendus. Mécanique, Volume 346 (2018) no. 2, pp. 77-88.

Résumé
Abstract

Les effets du troisième invariant des contraintes sur la surface de charge macroscopique d'un matériau ductile poreux sont analysés dans le cadre de l'approche de Gurson. Ces effets proviennent du processus d'homogénéisation lui-même à cause de l'hétérogénéité des contraintes dans la cellule de Gurson ou encore lorsque le comportement plastique de la matrice dépend du troisième invariant des contraintes. On fournit une représentation paramétrique de la surface de charge valable pour un comportement de la matrice assez général qui permet d'exhiber quelques résultats analytiques, en particulier pour les états de contrainte hydrostatiques et pour des états de cisaillement. Les résultats obtenus pour les chargements hydrostatiques sont étendus au cas où la matrice a un comportement dépendant aussi de la contrainte hydrostatique.

Some features od the constitutive behaviour of voided materials taking into account possible effects of the Lode angle in the yielding behaviour of the matrix are discussed. The Gurson approach is used to this end. After providing a parametric representation of the effective behaviour of such materials, some closed-form results are given for pure shear stress states and also at very high stress triaxialities. In the former case corresponding to a zero macroscopic mean stress, the contour of the yield domain in the π-plane has exactly the shape of the yield surface of the matrix in the deviatoric plane, but a size reduced by a factor $1 - f$ , with f the porosity of the voided material. In the latter, effective yield stresses for the voided material are slightly different from the Gurson result and found to be set by the yield stress at a microscopic stress Lode angle $\frac{π}{3}$ for very high positive triaxiality and by the yield stress at a microscopic stress Lode angle 0 for very high negative triaxiality. This last result is extended for porous materials with yielding depending further on the hydrostatic stress, fully exhibiting the interaction between volumetric and shear interactions on the yielding behaviour of isotropic porous materials. Applications to many usual yielding criteria for the matrix are also provided.

Reçu le : 2017-02-18
Accepté le : 2017-11-08
Publié le : 2017-12-19

DOI : 10.1016/j.crme.2017.11.002

Keywords: Porous material, Lode angle, Effective yielding
Mot clés : Matériau poreux, Angle de Lode, Comportement effectif

Affiliations des auteurs :

Ahmed Benallal ¹

¹ LMT, ENS Paris-Saclay/CNRS/Université Paris-Saclay, France

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     author = {Ahmed Benallal},
     title = {On some features of the effective behaviour of porous solids with {\protect\emph{J}\protect\textsubscript{2}-} and {\protect\emph{J}\protect\textsubscript{3}-dependent} yielding matrix behaviour},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {77--88},
     publisher = {Elsevier},
     volume = {346},
     number = {2},
     year = {2018},
     doi = {10.1016/j.crme.2017.11.002},
     language = {en},
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Ahmed Benallal. On some features of the effective behaviour of porous solids with J₂- and J₃-dependent yielding matrix behaviour. Comptes Rendus. Mécanique, Volume 346 (2018) no. 2, pp. 77-88. doi : 10.1016/j.crme.2017.11.002. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2017.11.002/

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