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![Amount of slip, γ1\documentclass[12pt]{minimal} \usepackage{amsmath}...](publication/317746593/figure/fig4/AS:960229487435785@1605947958735/Amount-of-slip-g1documentclass12ptminimal-usepackageamsmath-usepackagewasysym_Q320.jpg)
In this paper we discuss issues related to the theoretical as well as the computational format of gradient-extended crystal viscoplasticity. The so-called primal format uses the displacements, the slip of each slip system and the dissipative stresses as the primary unknown fields. An alternative format is coined the semi-dual format, which in addit...
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... The differences arise near the external boundaries due to how boundary conditions are imposed by the two formulations. A recent work of Carlsson et al. (2017) compared both methods for a tricrystal plate with micro-hard GB condition and obvious differences have been reported. Motivated by this, it is urgent to confirm that whether these two methods will lead to differences for the GB model (ρ−method GB modeling can be found in van ; Peng et al. (2019) and γ−method such as Özdemir and Yalçinkaya (2014); Gottschalk et al. (2016); Yalçinkaya et al. (2018)). ...
Au cours des dernières décennies, les développements significatifs de la microélectronique et des systèmes micro-électromécaniques (MEMS) ont conduit à une augmentation spectaculaire de la demande en produits miniaturisés. La fabrication de ces produits à micro-échelle est souvent une tâche difficile en raison de la présence d'effets de taille qui rendent inapplicables les règles simples basées sur la similarité pour réduire l'échelle des procédés de formage conventionnels. Dans les procédés de microformage, les effets de taille peuvent influencer les paramètres des matériaux et des procédés et doivent être soigneusement pris en compte. Lorsque les dimensions géométriques des composants passent du niveau conventionnel (macroscopique) au niveau microscopique, les comportements des matériaux associés ne sont plus indépendants de la taille. L'influence des effets de taille sur ces comportements a reçu un fort intérêt scientifique ces dernières années et plusieurs travaux ont été publiés sur le sujet. Le présent travail de thèse vise à corroborer ces travaux en proposant un outil numérique flexible pour modéliser les effets de taille dans les composants polycristallins miniaturisés.Pour modéliser différents types d'effets de taille polycristallins, l'outil numérique proposé consiste en un couplage entre la théorie de plasticité cristalline à gradients de déformation (SGCP) et la modélisation de joints de grains (GB). Dans le cadre de ce couplage, un modèle flexible de type Gurtin basé sur l'approche de Gurtin (2007) a été développé. Une version en petites déformations de ce modèle a d'abord été proposée pour étudier l'influence des paramètres impliqués sur la prédiction des effets de taille en l'absence d'effets de grandes déformations. Une extension aux grandes déformationsa ensuite été proposée pour permettre des applications en grandes déformations. Le modèle SGCP implémenté permet de prédire les effets de premier et de second ordre à l'intérieur des grains. Pour capter les effets de taille dus aux joints de grains, une extension aux grandes déformations du modèle GB proposé par Gurtin (2008) a été effectuée dans un cadre entièrement lagrangien tenant compte de la distorsion plastique du réseau. L'application des modèles SGCP et GB à l’étude des effets de taille dans les structures polycristallines montre une bonne reproduction qualitative des effets de taille communément observés expérimentalement.Comme application, l'outil numérique proposé a été utilisé pour faire un premier pas vers la modélisation des effets de taille sur les modes de localisation dans les structures mono- et poly-cristallines. Cet outil numérique sera utilisé à l'avenir pour modéliser les effets de taille sur la formabilité des tôles métalliques ultra-minces.
Motivated by experimental findings on sheet-metal forming, this article concerns the modeling of evolving anisotropies in finite plasticity. A covariant formulation of plasticity is employed in conjunction with evolution equations for the structural tensors that characterize the symmetry group of the yield function. A specific model is implemented into a finite element code to simulate tension and torsion tests. The results are then compared to experiments.
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This paper presents the application of variationally consistent selective homogenization applied to a polycrystal with a subscale model of gradient‐enhanced crystal inelasticity. Although the full gradient problem is solved on Statistical Volume Elements (SVEs), the resulting macroscale problem has the formal character of a standard local continuum. A semi‐dual format of gradient inelasticity is exploited, whereby the unknown global variables are the displacements and the energetic micro‐stresses on each slip‐system. The corresponding time‐discrete variational formulation of the SVE‐problem defines a saddle point of an associated incremental potential. Focus is placed on the computation of statistical bounds on the effective energy, based on virtual testing on SVEs and an argument of ergodicity. As it turns out, suitable combinations of Dirichlet and Neumann conditions pertinent to the standard equilibrium and the micro‐force balance, respectively, will have to be imposed. Whereas arguments leading to the upper bound are quite straightforward, those leading to the lower bound are significantly more involved; hence, a viable approximation of the lower bound is computed in this paper. Numerical evaluations of the effective strain energy confirm the theoretical predictions. Furthermore, heuristic arguments for the resulting macroscale stress‐strain relations are numerically confirmed.
