Du polycristal au multicristal : vers un mésoscope numérique

Abstract

La compréhension des mécanismes d'endommagement, notamment intergranulaires des polycristaux passe par la connaissance précise des champs mécaniques (contraintes, déformations) à l'échelle mésoscopique. Le but de cette étude est de les déterminer par simulation numérique. Pour cela nous considérerons un motif multicristallin inclus dans un milieu homogène équivalent. Ce milieu obéit au comportement expérimental du matériau (ici du 316 L(N) à chaud) à l'échelle macroscopique; le comportement cristallin microscopique est lui aussi connu. Une simulation par un code de calcul pa.r éléments finis prenant en compte l'aspect cristallin du motif et celui continu de la matrice nous donnera les champs mécaniques dans le motif. Nous définirons le cadre théorique de ce "mésoscope numérique", en insistant sur le concept de relocalisation et sur sa position vis à vis des modèles de passage micro-macro. Puis, nous aborderons les difficultés du choix du motif multicristallin et de la cohérence entre la loi de comportement du milieu homogène équivalent et celle des cristaux. Nous donnerons ensuite les résultats de l'identification des paramètres de la loi macroscopique. Enfin, le traitement numérique par éléments finis du problème sera abordé, et nous discuterons des premiers résultats. Nous 'conclurons sur les évolutions et les possibilités de ce nouvel outil, notamment pour la description du comportement des joints de grains.

Numerical strategy for unbiased homogenization of random materials

“…Some authors () have intended to do so by intercalating between the heterogeneous model of interest and the boundary conditions of a homogeneous medium, with the appropriate homogenized tensor. As the properties of the medium do not vary in space, the corresponding mesh does not need to be heavily refined, and the boundary conditions can therefore be pushed away in a cost‐effective manner.…”

“…The idea of coupling the microstructure to a homogenized medium to limit the influence of the boundary conditions was already developed in and , but with three major differences: (1) the microstructure is here random, although it was deterministic (and heterogeneous) in the previous papers; (2) the coupling is here made over a volume rather than along a surface; and (3) the approach is coupled to an iterative scheme to identify the value of the effective tensor, although it was previously only used to perform direct computations, for a given value of the homogenized tensor.…”

Prediction of the Scatter of Crack Initiation under High Cycle Fatigue

“…The parameters are representative of AISI 316L stainless steel at 550°C. The crystalline plastic behaviour was described in detail in [7]. The parameters are obtained by inverse identification; i.e a 1000 grains aggregate has the macroscopic behaviour.…”

A “Numerical Mesoscope” for the Investigation of Local Fields in Rate-Dependent Elastoplastic Materials at Finite Strain

“…On the other hand, direct numerical simulation of aggregates of several thousands of grains, i.e., large enough to be a good approximation of a RYE, in addition to being hardly tractable, cannot yield reliable predictions of debonding in actual polycrystals: although they are statistically representa tive of these polycrystals with respect to their crystallographic texture or their average grain shape, they cannot coincide with them at the scale of a few grains. In what follows, by applying the concept of "numerical mesoscope" (lliraud et al [6]), we consider the microheterogeneous subdomain under investigation as embedded with a perfect interface in a large homogeneous matrix. This matrix, which obeys the experimentally defined overall behavior of the studied material, is subjected to homogeneous stress or strain boundary conditions, so that, due to its own mechanical response, different mechanical conditions, which are expected to be more realistic, are transferred to the boundary of the considered subdomain.…”