Mécanique

New expressions of the macroscopic criteria of perfectly plastic rigid matrix containing prolate and oblate cavities are presented. The proposed approach, derived in the framework of limit analysis, consists in the consideration of Eshelby-like trial velocity fields for the determination of the macroscopic dissipation. It is shown that the obtained results significantly improve existing criteria for ductile porous media. Moreover, for low stress triaxialities, these new results also agree perfectly with the nonlinear) Hashin-Shtrikhman bound established by Ponte-Castañeda and Suquet. To cite this article: V. Monchiet et al., C. R. Mecanique 335 (2007).

Following the study of which has extended the well-known approach of Gurson (1975), we propose approximate yield criteria for anisotropic plastic voided metals containing non spherical cavities. The plastic anisotropy of the matrix is described by means of Hill's quadratic criterion. The procedure to establish the closed form expression of approximate macroscopic criteria, in which void shape and plastic anisotropic effects are included, is detailed. The new criteria allow us to recover existing results in the cases of spherical and cylindrical voids in an Hill type plastic matrix. Moreover, they agree with previous criteria for non spherical voids in an isotropic plastic matrix. Finally, for validation purposes, we provide, in the general case of non spherical cavities in the anisotropic matrix, a comparison with the numerical exact two field criteria. To cite this article: V. Monchiet et al., C. R. Mecanique 334 (2006).

A micro-macro approach of multiaxial fatigue in unlimited endurance is proposed. It allows one to take into account plasticity and damage mechanisms which occur at the scale of Persistent Slip Bands (PSB). The proposed macroscopic fatigue criterion, which corresponds to microcracks nucleation at the PSB-matrix interface, is derived for different homogenization schemes (Sachs, Lin-Taylor and Kröner). The role of a mean stress and of the hydrostatic pressure in high cycle fatigue is shown; in particular, in the case of Lin-Taylor scheme and linear isotropic hardening rule at microscale, one recovers the linear dependance in pressure postulated by K. Dang Van for the macroscopic fatigue criterion. This dependence is related here to the damage micro-mechanism. Finally, the particular case of affine loading is presented as an illustration. To cite this article: V. Monchiet et al., C. R. Mecanique 334 (2006). Résumé Une modélisation micromécanique couplant plasticité et endommagement en fatigue polycyclique. On propose une approche micro-macro de fatigue multiaxiale en endurance illimitée. Elle permet de prendre en compte des mécanismes de plasticité et d'endommagement apparaissant à l'échelle des Bandes de Glissement Persistantes (BGP). Le critère macroscopique proposé, qui correspond à la nucléation de microfissures à l'interface BGP-matrice, est explicité pour différents schémas d'homogénéisation (Sachs, Lin-Taylor, Kröner). On montre qu'il rend compte du rôle de la contrainte moyenne et d'une pression hydrostatique en fatigue polycyclique ; en particulier, on retrouve, dans le cas du schéma de Lin-Taylor et d'une hypothèse d'écrouissage isotrope linéaire à l'échelle microscopique, la dépendance linéaire en pression postulée par K. Dang Van pour le critère macroscopique de fatigue. Cette dépendance est liée ici au micromécanisme d'endommagement. Enfin, on présente, à titre d'illustration, le cas particulier des chargements affines. Pour citer cet article : V. Monchiet et al., C. R. Mecanique 334 (2006).

In the present Note, we provide new analytical expressions of the components of Hill tensor P (or equivalently the Eshelby tensor S) associated to an arbitrarily oriented crack in orthotropic elastic medium. The crack is modelled as an infinite cylinder along a symmetry axis of the matrix, with low aspect ratio. The three dimensional results obtained show explicitly the interaction between the primary (structural) anisotropy and the crack-induced anisotropy. They are validated by comparison with existing results in the case where the crack is in a symmetry plane. To cite this article: C. Gruescu et al., C. R. Mecanique 333 (2005).  2005 Académie des sciences. Published by Elsevier SAS. All rights reserved.

In this study, we propose a micromechanics-based modification of the Gurson criterion for porous media subjected to arbitrary loadings. The proposed formulation, derived in the framework of limit analysis, consists in the consideration of Eshelbylike exterior point trial velocity fields for the determination of the macroscopic dissipation. This approach is implemented for perfectly plastic rigid von Mises matrix containing spherical voids. After the minimization procedure required by the use of the Eshelby-like trial velocity fields, we derive a two-field estimate of the macroscopic yield function. It is shown that the obtained closed-form estimate provides a significant modification of the Gurson criterion, particularly in the domain of low stress triaxialities. This estimate is first compared with existing criteria. Moreover, its accuracy is assessed through comparison with results derived from numerical exact two-field criterion and with recently available numerical bounds.

In this paper we establish the exact solution for a hollow sphere with a rigid-plastic pressure-sensitive matrix and subjected to hydrostatic tension or compression. The matrix is assumed to obey to a parabolic Mises-Schleicher criterion. The closed-form expressions of the velocity field and of the stress field are provided. These exact solutions, expressed by means of the Lambert W function, allow to assess and discuss existing results.

The combined effects of void shape and matrix anisotropy on the macroscopic response of ductile porous solids is investigated. The Gologanu-Leblond-Devaux's (GLD) analysis of an rigid-ideal plastic (von Mises) spheroidal volume containing a confocal spheroidal cavity loaded axisymmetrically is extended to the case when the matrix is anisotropic (obeying Hill's (1948) anisotropic yield criterion) and the representative volume element (RVE) is subjected to arbitrary deformation. To derive the overall anisotropic yield criterion, a limit analysis approach is used. Conditions of homogeneous boundary strain rate are imposed on every ellipsoidal confocal with the cavity. A two-field trial velocity satisfying these boundary conditions are considered. It is shown that for cylindrical and spherical void geometries, the proposed criterion reduces to existing anisotropic Gurson-like yield criteria. Furthermore, it is shown that for the case when the matrix is considered isotropic, the new results provide a rigorous generalization to the GLD model. Finally, the accuracy of the proposed approximate yield criterion for plastic anisotropic media containing non-spherical voids is assessed through comparison with numerical results.