Modélisation multi-échelle du comportement électrique de nano-composites Cu-Nb

Abstract

is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. le lien entre la conductivitéélectrique effective et la microstructure, deux méthodes d'homogénéisation sont appliquées : l'une, en champs moyens (modèle auto-cohérent généralisé), dans laquelle une microstructure formée de motifs co-cylindriques répartis aléatoirement est considérée, et l'autre, en champs complets (éléments finis), dans laquelle l'aspect périodique de la microstructure expérimentale est pris en compte. Les effets de la taille des constituantsélémentaires (nm), de la température, ainsi que de la densité de dislocations, sur la conductivité locale sont considérés. Le caractère multi-échelle du matériau est pris en compte grâceà un processus itératif. Les conductivités effectives longitudinale et transversale obtenues avec les deux méthodes sont en excellent accord, montrant un moindre effet de la distribution des fibres sur ces propriétés. Ces résultats reproduisentégalement les données expérimentales disponibles. Mots clés : Composites architecturés / matériaux polycristallins / méthodes d'homogénéisation / modélisation multi-échelle / conductivitéélectriqueAbstract -Multiscale modeling of the electrical behavior of Cu-Nb nanocomposites. Nanostructured and architectured copper niobium composite wires are very good candidates for the generation of very high magnetic fields as they combine both high strength and high electrical conductivity. They are fabricated by co-deformation of a Cu-Nb composite assembly. A multiscale microstructure formed by 85 3 Cu-Nb elementary patterns with dimensions of the order of nanometers, is obtained. In order to investigate the link between the effective electrical conductivity and the wire microstructure, two homogenization methods are applied: first, using a mean field theory (generalized self-consistent model) in which a microstructure formed by co-cylindrical long fibers with a random distribution is considered, and second a full field method (Finite Elements) in which the periodic character of the experimental microstructure is taken into account. The size effect of components (nm), temperature, and dislocation density are taken into account into the definition of the local conductivity. The multiscale character of the material is taken into consideration through an iterative process. The longitudinal and transverse effective conductivities obtained by both methods perfectly match with each other, showing the limited influence of the effect of fiber distribution for this behavior. Results also compare well with the available experimental data.

Multiscale modeling of the anisotropic electrical conductivity of architectured and nanostructured Cu-Nb composite wires and experimental comparison

“…Due to ADB processing, the architecture of Cu-Nb wires is quasiaxisymmetric with respect to x 1 . As a result, the effective material behavior is expected to be transverse isotropic [19,20]. For the conductivity along the transverse direction x 2 or x 3 , a more delicate measurement is needed due to the small sample size, compared with the measurement of longitudinal conductivity [50].…”

“…The GSC scheme [19,37] is developed in the following way: (i) (nþ1)-layered cylindrical problem and (ii) n-layered problem embedded in the HEM where the effective electrical conductivity e s $ is determined by the self-consistent scheme [40,52], as illustrated in Fig. 3(a).…”

“…Among the mean-field models, the Generalized Self-Consistent scheme (denoted GSC hereafter) was initially developed to study the elastic behavior of multi-coated fiber-reinforced composites [39]. Later, the GSC scheme was extended for diffusion phenomena [37,40,41], and this model has been found to be very efficient to estimate the effective electrical conductivity of Cu-Nb wires [19]. As for the full-field analysis, we have proposed a Finite Element Method (FEM) method with periodic boundary conditions (denoted PH, for Periodic Homogenization) [19].…”

“…Later, the GSC scheme was extended for diffusion phenomena [37,40,41], and this model has been found to be very efficient to estimate the effective electrical conductivity of Cu-Nb wires [19]. As for the full-field analysis, we have proposed a Finite Element Method (FEM) method with periodic boundary conditions (denoted PH, for Periodic Homogenization) [19]. FEM PH is adapted to the case of periodic fiber distribution, as observed experimentally (see Fig.…”

Multiscale modeling of the elasto-plastic behavior of architectured and nanostructured Cu-Nb composite wires and comparison with neutron diffraction experiments

“…Previous studies on the Cu-Nb nanocomposite wires and laminates have focused on textures and their evolution (Lim and Rollett, 2009;Dubois, 2010;Lee et al, 2012;Hansen et al, 2013;Medy, 2016), elasticity (Gu et al, 2017a), dislocation glide (Thilly et al, 2001;Misra and Hoagland, 2007), grain size dependent yield stress/yield criterion (Misra and Hoagland, 2007;Thilly et al, 2009;Nizolek et al, 2015), Bauschinger effect (Thilly et al, 2007;Badinier et al, 2014), hardness (Thilly et al, 2002), ultimate tensile strength (Vidal et al, 2007), Cu-Nb interfaces (Mayeur et al, 2013(Mayeur et al, , 2015Beyerlein et al, 2014), and thermal stability and internal stresses (Vidal, 2006;Dubois et al, 2010;Beyerlein et al, 2014). The electrical behavior of Cu-Nb composites was studied by Gu et al (2015Gu et al ( , 2017b.…”