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An important failure mechanism in ductile metals and their alloys is by growth and coalescence of microscopic voids. In structural materials, the voids nucleate at inclusions and second-phase particles by decohesion of the particle–matrix interface or by particle cracking. Void growth is driven by plastic deformation of the surrounding matrix. Early micromechanical treatments of this phenomenon considered the growth of isolated voids. Later, constitutive equations for porous ductile solids were developed based on homogenization theory. Among these, the most widely known model was developed by Gurson for spherical and cylindrical voids.
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... Based on unit-cell studies, Pardoen and Hutchinson (2000) extended Thomason (1985) coalescence criterion for general spheroidal void by defining w as the void aspect ratio. Additionally, the coefficients α and β are defined as a function of isotropic hardening exponent: (Benzerga and Leblond, 2010). and Gologanu et al. (2001a) further extended the Thomason (1985) coalescence criterion for the combined tension and shear loadings. ...
... However, for low values of stress triaxiality ratio, experiments have revealed that the void shape changes from spherical to general spheroids. In this regard, Gologanu et al. (1993Gologanu et al. ( , 1994 changes with the plastic deformation (see Benzerga and Leblond, 2010). Recently, Madou and Leblond (2012a, 2012b and further extended this approach to general spheroidal void shapes. ...
Thesis
La mise en forme des tôles minces est sans aucun doute l’un des procédés de fabrication les plus utilisés de nos jours dans divers secteurs industriels, tels que l’automobile, l’aérospatiale, l’électroménager et l’industrie alimentaire. Divers défauts dans la tôle peuvent apparaître durant sa mise en forme par déformation plastique, tels que le plissement, la striction ou la rupture. Plus précisément, ce travail de thèse se concentre sur l’étude de l’apparition des instabilités plastiques inhérentes au matériau lui-même, telles que la striction diffuse et la striction localisée, limitant ainsi sa formabilité. Le concept de courbes limites de formage (CLF) fournit les limites de déformations que les tôles peuvent supporter sans l’apparition de défauts indésirables. Ce présent travail contribue au développement d’outils théoriques et numériques pour la prédiction des CLF, ce qui permet de fournir une approche complémentaire aux essais expérimentaux à des fins de caractérisation de la formabilité des tôles minces. Pour cela, des modèles constitutifs phénoménologiques, basés sur le modèle original de Gurson, sont considérés dans la présente contribution. Concernant la prédiction des instabilités plastiques, plusieurs critères de striction diffuse et localisée, basés sur la théorie de la bifurcation et l’approche multi-zone (imperfection initiale), sont combinés aux modèles de comportement. Ces critères sont analysés et hiérarchisés en termes d’ordre de prédiction de la striction. Globalement, les résultats numériques montrent que, pour l’ensemble des lois de comportement considérées, le critère de bifurcation générale constitue une borne inférieure à tous les critères de bifurcation, en termes de prédiction de la striction. En ce qui concerne la prédiction de la striction localisée, le critère de perte d’ellipticité apparaît comme une borne supérieure à tous les critères de bifurcation, ainsi qu’à l’approche d’imperfection initiale.
... To assess the performance of the proposed coupling model, four kinds of specimens including a plate, a notched tension specimen, a pure shear specimen, and a Sandia benchmark specimen are selected based on the numerical testing procedure of the micro-mechanical damage models for ductile fracture suggested by Benzerga et al. [64]. These specimens cover different stress states, e.g., the initial stress triaxiality for the notched tension specimen is 0.65 approximately, and that for the pure shear specimen is zero. ...
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... It is well established that the dominating fracture mechanism in ductile materials is nucleation, growth and coalescence of microscopic voids [25,26]. The voids may be initially present in the material [27], created from coarse deformation bands or intersecting slip planes [28], nucleated at broken constituent particles [29,30] or at particles/inclusions by decohesion between the matrix-particle interface [31,32]. ...
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Prediction of ductile fracture in structural metallic materials requires some representation of microstructural effects, including the plastic anisotropy that is associated with initial or induced polycrystalline textures and the microscopic processes of void growth and coalescence. With the objective of characterizing existing continuum models, we present a finite-element study of cylindrical unit cells, consisting of spheroidal voids embedded in an orthotropic Hill matrix, subjected to proportional loading paths. Two-dimensional axisymmetric calculations are employed for the case of transverse isotropy and axisymmetric loading about the void axis. The effective cell model responses are compared with predictions from an extended model of anisotropic void growth, which is the subject of an accompanying paper.