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, Les perturbations ont le même nombre d'onde ? 1 = 23?/L 01 . Le gradient de vitesse initial est? 11 = 1000 s ?1, Évolution temporelle des taux de croissance ?/? 11 (voir l'équation 4.5) et ? T /? 11

, 12) en fonction du nombre d'onde à t = 260 µs (déformation nominale ? 11 = 0, 26), Amplitude normalisée de la fonction de courant (équation 4.8) et de la perturbation de la température

, ) b) ? T /? 11 (voir équation 4.11) et par l'approche classique (voir équation 4.4) en fonction du nombre d'onde pour ? = 0, 1 et 0, 2. Les résultats sont présentés en utilisant la condition initiale CI7 définie dans la Table 4.5. La loi de comportement est donnée par l'équation (4.10) avec les paramètres de la Table 4.4. L'instant considéré est t = 1 ms correspondant à une déformation nominale ? 11 = 1 ; le gradient de vitesse initial est? 11 = 1000 s ?1

, Différents modèles d'analyse des prémices du développement de l'instabilité plastique de striction

, La prédiction du modèle XLSA et l'instant de localisation relevé par le modèle par éléments finis sont présentés. Le nombre d'onde de la perturbation est ? 1 = 12?/L 01 . La plaque est soumise à un gradient de vitesse initial? 11 = 10000 s ?1 . La loi de comportement du matériau est décrite par l'équation (5.5) avec les paramètres de la Table 5.1. Le modèle ABAQUS utilise le maillage M 4 défini dans la Table (5.2). Les demi-dimensions sont L 01 = 10 cm et L 03 = 1 cm

C. , Erreur relative sur le taux de croissance instantanée de? à t = 100 µs (voir équation C.8) en fonction du pas de temps en échelle log-log. Deux valeurs du nombre N de polynômes d'interpolation sont considérées. Les pentes associées aux erreurs d'ordre 1 et 2 sont représentées, p.170

, Liste des tableaux

, A 0 est un facteur d'amplitude qui n'influence pas les résultats présentés, donc aucune valeur n'est spécifiée. CI4 est une fonction périodique avec ? = 5?/2. Deux valeurs de gradients de vitesse initial sont testées :? 11 = 1 000 s ?1, Définition des conditions initiales. CI1, CI2 et CI3 sont calculées à partir de l'Analyse Linéaire de Stabilité Classique, vol.10, pp.0-1

. .. ,

, Définition des conditions initiales pour le cas d'un matériau non sensible à la vitesse de déformation lorsque l'écoulement est stable à t = 0, vol.87

, Plusieurs valeurs du paramètre m de sensibilité à la vitesse de déformation seront adoptées : m = 0, 01 et m = 0, 05

, Plusieurs valeurs du paramètre ? d'adoucissement thermique seront adoptées : ? = 0, 1 et ? = 0

, Définition des conditions initiales pour la perturbation mécanique et la perturbation thermique. Le comportement du matériau est thermoviscoplastique

, Paramètres adoptés pour la loi de comportement décrite par l'équation (5.5). 122 5.2 Caractéristiques des différents maillages utilisés pour définir un maillage de référence

, La plaque est soumise à un gradient de vitesse initial? 11 = 10000 s ?1 . La loi de comportement du matériau est décrite par l'équation (5.5) avec les paramètres de la Table 5.1. Le modèle ABAQUS utilise le maillage M 4 défini dans la Table (5.2). Les demidimensions sont L 01 = 10 cm et L 03 = 1 cm, Instant t loc de localisation relevé dans le modèle par éléments finis pour les différentes amplitudes A du défaut