Contribution au calcul des effets de voisinage dans les agrégats polycristallins en combinant la théorie d’Eshelby à une approche de type automate cellulaire

Abstract

The aim of this PhD thesis, conducted in co-supervision between ISAE-ENSMA / Pprime Institute and the Ecole de Technologie Supérieure (ETS) of Montreal / LOPFA was to develop a tool for the generation of polycrystalline aggregates and the calculation of elastic fields by taking into account the neighborhood effects of each grain. This tool was designed for a statistic employment in order to identify the most harmful neighborhood configurations as well as the influence of the morphology, the elastic anisotropy of the material and of the type of loading on these configurations. Although some existing models allow to estimate local fields, they tend to underestimate the neighborhood effect and when this effect is taken into account, the computational cost is often prohibitive. The advanced tool is an extension of the previous work by [Bretin et al., 2019] based on Cellular Automata (CA). The full-field simulations previously used to compute each neighbor individual effect on a grain were first replaced by analytical calculations with the Equivalent Inclusion Method (EIM) [Eshelby, 1957 ; Eshelby, 1959 ; Eshelby, 1961]. A unified EIM code able to deal with an elastic inhomogeneity, isotropic or anisotropic (via the assignation of a crystallographic orientation (CO)), spatially oriented in an isotropic medium under uniform loading at infinity, was developed to this aim. Each new functionality introduced in the code was carefully validated by comparisons to Finite Element (FE) reference solutions, both inside and outside the inhomogeneity along different paths from the interface. Such a systematic evaluation, for internal and external points, allows to be confident in the reliability of the final program and constitutes an original contribution of the present work. The EIM code was then introduced in the CA. At second, the Bretin’s model and underlying CA, originally devoted to regular aggregates (Kelvin type) were extended in order to deal with more realistic aggregates. A module for the aggregates generation (Voronoï, Laguerre, Johnson-Mehl) was incorporated to this aim as well as a module for the identification of the irregular neighborhood of each grain and at last, a module to approximate the grains by equivalent inertia spheroïds. The results of the extended model were compared to FE full-field calculations in order to appreciate the accuracy and the calculation time several orders of magnitude lower. In a second part, the EIM code was exploited in order to analyse the influence of various characteristics (shape, aspect ratio, nature, spatial and eventual crystallographic orientations) of an isolated inhomogeneity on the inside and outside stress field. A second study, this time statistical, was then carried out with 316L and Titanium aggregates under uniaxial strain loading and shear-strain loading. The role of the elastic anisotropy and of the crystallographic orientation of neighbors was clearly demonstrated. Finally, additional work was undertaken in order to insert a new minority phase into an existing aggregate, here carbides "appearing" in a microstructure previously chemically homogeneous. The effect of these carbides is significant but localized.

Date	10 Oct 2024
Original language	French
Awarding Institution	École de technologie supérieure
Supervisor	Philippe Bocher (Supervisor) & Carole Nadot-Martin (Co-supervisor)