京都大学 / 新制・課程博士 / 博士(工学) / 甲第23156号 / 工博第4800号 / 新制||工||1750(附属図書館) / 京都大学大学院工学研究科材料工学専攻 / (主査)教授 辻 伸泰, 教授 奥田 浩司, 教授 安田 秀幸 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

L'élaboration de nouveaux alliages maintient un fort intérêt pour le phénomène d’instabilité plastique, ou l'effet Portevin-Le Chatelier (PLC), provoqué par l'interaction des dislocations avec des atomes de soluté. Par ailleurs, l'effet PLC attire l'intérêt comme un exemple remarquable d'auto-organisation dans les systèmes dynamiques. Il est associé à des motifs complexes de séries de chutes de contrainte liées à la nucléation et au mouvement des bandes de déformation dans le matériau déformé, et nécessite une compréhension de l'auto-organisation des dislocations. La déformation plastique des alliages Al-Mg est sujette à l'instabilité dans une large gamme de conditions expérimentales. Pour cette raison, les alliages Al-Mg binaires ont longtemps servi d'objets modèles pour l'étude de l'effet PLC. En même temps, l'utilisation pratique des alliages binaires Al-Mg est limitée en raison d’une faible résistance mécanique. Une amélioration significative de leurs propriétés peut être atteinte en ajoutant des solutés supplémentaires, conduisant en particulier à la formation de précipités. En outre, une forte réduction de la taille de grains du polycristal pourrait être une technique clé pour produire des matériaux à haute résistance et ténacité. Cependant, il existe très peu d'information, souvent contradictoire, sur l'instabilité PLC dans les alliages Al-Mg à grains fins et contenant des précipités. Le but de l'étude de cette thèse a été d'étudier les caractéristiques spécifiques de l'effet PLC dans les alliages à base AlMg, avec et sans nanoparticules, à gros grains et à grains fins, ces derniers obtenus par une méthode de déformation plastique sévère. Grâce à l’application de méthodes d’extensométrie locale, notamment de la technique de corrélation d’images, ces études ont révélé une persistance non habituelle de la propagation des bandes de déformation dans les alliages comprenant des précipités et/ou des grains fins. Ce mode dynamique est observé dans un large intervalle de vitesses de déformation, tandis qu’il n’apparait qu’à haute vitesse dans des alliages modèles AlMg. Par ailleurs, l’analyse des distributions statistiques des amplitudes des chutes de contrainte a révélé une tendance vers une statistique en loi puissance, caractéristique du mode de propagation. Ce phénomène est attribué à une modification du couplage spatial entre les dislocations, due à la concentration de contraintes internes. La combinaison de ces études avec l’analyse de l’émission acoustique a mis en évidence une influence de la microstructure sur la compétition entre un facteur aléatoire et la synchronisation des dislocations. Enfin, l’étude par corrélation d’images a permis d’observer une interrelation entre l’instabilité PLC et la formation de la striction. / The elaboration of new alloys sustains a strong interest to the phenomenon of unstable plastic flow, or the Portevin–Le Chatelier (PLC) effect, caused by interaction of dislocations with solute atoms. Moreover, this effect attracts interest as a rich example of self-organization in dynamical systems. It is associated with complex patterns of stress serrations related to nucleation and motion of deformation bands in the deforming material, and requires understanding of self-organization of dislocations. Plastic deformation of Al-Mg alloys is prone to instability in a wide range of experimental conditions. For this reason, binary Al-Mg alloys served for a long time as model objects for investigation of the PLC effect. At the same time, the practical use of binary Al-Mg alloys is limited because of their low strength. A significant improvement of their properties can be achieved by additional alloying, in particular, leading to precipitation. Further, extensive grain refinement could be a key technique used to produce tough and high- strength materials. However, there exists very limited and often contradictory information on the PLC instability in fine-grained Al-Mg alloys containing precipitates. The objective of the present thesis was to investigate specific features of the PLC effect in AlMg-based alloys with and without nanoscale particles, both in coarse-grained and fine-grained states, the latter obtained by severe plastic deformation. Using local extensometry methods, particularly the image correlation technique, these studies revealed an unusual persistence of the propagation of deformation bands in alloys with precipitates and/or fine grains. This dynamic mode is observed in a wide range of strain rates, whereas it only appears at high strain rate in model Al-Mg alloys. Moreover, the analysis of statistical distributions of stress drop amplitudes revealed a tendency to power law statistics characteristic of the propagation mode. This phenomenon was attributed to a modification of the spatial coupling between dislocations due to the concentration of internal stresses. The combination of these studies with the acoustic emission analysis uncovered an influence of the microstructure on the competition between a random factor and the dislocation synchronization. Finally, the study by the image correlation made it possible to observe an interrelation between the PLC instability and the neck formation.

Récemment, les observations in-situ par laminographie aux rayons X (au synchrotron) montrent que les multiples bandes de localisation sont les précurseurs de l'endommagement et éventuellement de la rupture en biseau. Ces bandes peuvent être liées aux phénomènes de vieillissement par la déformation (type effet de L"uders ou Portevin-Le Chatelier (PLC)) dont l'influence sur la rupture est encore mal compris. Ces effets sont pourtant observés dans de nombreux alliages industriels comme les aluminiums de la série 2000 ou 5000, ou par exemple, dans le cas des aciers C-Mn pour lesquels un creux de ductilité est observé dans la gamme de température o'u ces effets sont les plus marqués.L'objectif de la thèse consiste à caractériser l'effet PLC et évaluer son influence sur le développement de l'endommagement et donc sur la rupture finale. D'abord, l'effet de vieillissement sur l'écrouissage a été introduit dans un modèle basé sur la densité de dislocations en utilisant les résultats dans la littérature. Ensuite, certains alliages d'aluminium de la série 2000 et un acier C-Mn ont été étudiés par essais mécaniques avec corrélation d'images.Le déclenchement prématuré de localisation a été observé pendant les essais de relaxation, de déchargement et de changement de vitesse pour certains alliages d'aluminium.Les bandes autour de l'entaille dans l'éprouvette d'acier C-Mn ont été observées à haute température. Deux modes de rupture différents ont été observés dans les deux températures. Ces résultats sont comparés avec ceux du modèle KEMC. Enfin, un modèle de comportement couplant les effets de vieillissement (type KEMC) et d'endommagement (type Rousselier) a été développé pour tenter d'expliquer les interactions observées expérimentalement entre ces deux phénomènes. / Recently, in-situ observations by X-ray laminography (at synchrotron) show that the multiple localization bands are the precursors of damage and possibly the slant fracture. These bands can be related to the strain ageing effect (L"uders or Portevin-Le Chatelier (PLC)) whose influence on the fracture is still poorly understood. These effects are observed in many industrial alloys such as 2000 or 5000 series aluminium alloys, or, for example, in the C-Mn steels for which a ductility drop is observed in the temperature range where these effects are most pronounced.The aim of the thesis is to characterize the PLC effect and to evaluate its influence on the development of ductile damage and therefore on the final fracture. Firstly, the influence of strain ageing on strain hardening was introduced in a model based on the dislocation density using results from the literature. Secondly, several 2000 series aluminium alloys and a C-Mn steel were investigated by mechanical tests combined with Digital Image Correlation. The premature triggering of localization bands was observed in tensile tests involving relaxation, unloading and strain rate jump for certain aluminium alloys. The bands around the notch in the specimens of C-Mn steel were observed at high temperature. Two different modes of fracture were observed at the two temperatures. These results are compared with those produced with the KEMC model. Thirdly, a constitutive model combining the strain ageing (type KEMC) and damage (type Rousselier) was developed in order to explain the experimentally observed interactions between these two phenomena.

Les instabilités plastiques désignent une famille de comportements non-linéaires que l’on rencontre dans plusieurs matériaux solides. Elles correspondent à une évolution hétérogène de la déformation sous un chargement homogène, et se manifestent par un écrouissage irrégulier accompagné de bandes de localisation d’épaisseur millimétrique dont la cinétique est sensible, entre autres, à la température et à la vitesse de chargement. Ce phénomène freine considérablement l’usage des tôles d’aluminium-magnésium dans l’industrie. En effet, il a des conséquences esthétiques et mécaniques néfastes dont il est difficile de prédire l'évolution à l'étape de conception. Des modèles de comportement dédiés peuvent reproduire les bandes de localisation mais peinent à estimer précisément leur cinématique. De plus, ils sont sujets à des complications comme la sensibilité à la discrétisation, un coût de calcul considérable ou encore l’identification expérimentale délicate de leurs paramètres. L’objectif de ces travaux est donc de proposer un cadre dans lequel la cinématique des bandes de localisation est prédite de façon fidèle. Dans un premier temps, l’alliage d’étude est caractérisé par des essais de traction où la cinétique de bandes individuelles est traquée à l'aide de la corrélation d'images numériques. Les quantités d'intérêt sont identifiées à l'échelle non-locale des bandes de déformation : leur géométrie, leur distribution spatio-temporelle, la déformation qu'elles portent et l'énergie qu'elles échangent. S'appuyant sur ces résultats expérimentaux, un modèle de comportement est formulé à l'échelle des bandes de localisation. Il encapsule toutes les conséquences macroscopiques des instabilités plastiques et s’émancipe donc des complications évoquées plus tôt. Finalement, une stratégie numérique est proposée pour la simulation unidimensionnelle des essais, avec pour objectif de démontrer la faisabilité de l'approche. Ce travail constitue une première contribution à la simulation des bandes de localisation au travers d'une modélisation directe de leur cinétique. Les perspectives suggérées portent en particulier sur trois aspects. D'abord, la caractérisation de la cinétique des bandes de déformation à l'échelle inférieure à la nucléation. Aussi, le déploiement en 2D et l'amélioration du modèle proposé pour le traitement robuste de cas industriels. Enfin, l'utilisation du cadre développé pour la prise en charge d'autres physiques non-locales. / Plastic instabilities refer to a wide family of material nonlinearities met in several solid materials. They correspond to a heterogeneous strain response under homogeneous loading conditions, and manifest as an erratic workhardening accompanied by strain localization bands that kinetics are sensitive to temperature and loading rate, among other material properties. This phenomenon hinders the industrial use of aluminium-magnesium alloys. It involves harmful mechanical and aesthetic consequences that can hardly be predicted at the design step. Constitutive models can recreate localization bands but they fail to accurately predict their kinematics. Moreover, they are subjected to several issues such as mesh sensitivity, a high computational cost or a complex parameters identification. The purpose of this work is to build a framework in which bands kinematics can be reliably predicted. First, the studied alloy is characterized by means of tensile tests in which the kinetics of individual bands are tracked using digital image correlation. Quantities of interest are then identified at the non-local scale of bands: their morphology, spatiotemporal distribution, the strain they carry and the energy they exchange. Based on these experimental results, a constitutive model is derived at the scale of localization bands. It embeds all the aforementioned macroscopic consequences of plastic instabilities. A numerical strategy is then proposed to tackle unidimensional simulations, with the purpose of justifying the feasibility of the approach. This work constitutes a first contribution to the simulation of localization bands through a direct modeling of their kinetics. The considered outlooks focus on three main aspects. First, the experimental characterization of instabilities beneath the bands scale. Also, the twodimensional deployment and the improvement of the model to fit concrete and industrial applications. Lastly, the use of the proposed framework for a greater variety of non-local behaviors.

<p> The use of AA 5754 Al-Mg alloy for automotive applications is limited by its rapid shear failure process, due to shear banding. This failure mechanism is further complicated by the presence of inhomogeneous plastic deformation, so-called Portevin-Le Chatelier (PLC) effect, during deformation. Therefore, the purpose of this study was primarily to investigate the impact of Portevin-Le Chatelier (PLC) banding towards shear banding in this commercial alloy. The second objective was to study the PLC banding as a function of prior deformation under positive strain rate sensitivity condition.</p> <p> The experimental work involved pre-straining experiments coupled with a non-contact strain measurement technique. Pre-straining experiments were carried out by deforming the sample at 223 K, at which the PLC effect is significantly suppressed, up to a prescribed amount of true strain prior to room temperature testing. A non-contact strain measurement technique, based on digital image correlation (DIC), was utilized in order to observe PLC band behavior during tensile tests at room temperature and subsequently to measure the amount of plastic strain carried within the band.</p> <p> The results showed the appearance of random nucleation deformation bands, associated with type B PLC banding, with short distance propagation during constant strain rate tensile test at room temperature. A change in the nature of PLC banding, marked by distinct band propagation, was observed once a critical amount of pre-strain is given. However, there is no evidence of a relationship between two existing phenomena, PLC banding and shear banding, in this alloy.</p> / Thesis / Master of Applied Science (MASc)

Les études récentes de la déformation plastique à l'aide de techniques expérimentales à haute résolution témoignent que les processus de déformation sont souvent caractérisés par des effets collectifs qui émergent à une échelle mésoscopique, intermédiaire entre celle de défauts cristallins et celle d'une éprouvette macroscopique. Notamment, la méthode de l'émission acoustique (EA) révèle, dans divers conditions expérimentales, l'intermittence de la déformation plastique, qui se manifeste par une propriété de l'invariance d'échelle, caractéristique de phénomènes d'auto-organisation. L'objectif de la thèse a été d'étudier la structure inhérente de l'EA pour différents mécanismes de déformation plastique, d'examiner sa dépendance à la vitesse de déformation et à l'écrouissage du matériau, et d'appréhender les liens entre les petites échelles de temps, liées à l'organisation des défauts, et celles qui relèvent de l'approche continue de la plasticité. L'étude a été réalisée sur des alliages AlMg et des alliages base Mg, dont la déformation plastique est accompagnée d'une forte activité acoustique et contrôlée par différents mécanismes physiques : l'effet Portevin-Le Chatelier (PLC) dans les premiers et une combinaison du maclage et du glissement des dislocations dans les deuxièmes. L'utilisation de la technique d'enregistrement continue de l'EA ("data streaming") a permis de montrer que le comportement apparent - discrète ou continue - de l'EA accompagnant l'effet PLC dépend de l'échelle de temps d'observation et du paramètre physique étudié. Cependant, contrairement à une vision traditionnelle, il se trouve que l'EA a un caractère intermittent pendant l'écoulement macroscopiquement lisse tant que pendant l'instabilité macroscopique de la déformation plastique. Grace aux méthodes d'analyse issues de la théorie des systèmes dynamiques non linéaires, telles que l'analyse multifractale, une tendance à la transition entre la dynamique invariante d'échelle et les comportements caractérisés par des échelles intrinsèques a été trouvée lors de l'écrouissage des matériaux. Enfin, nous avons prouvé que les distributions statistiques en loi puissance persistent dans des larges intervalles de variation des paramètres, conventionnellement utilisés pour individualiser les événements acoustiques. Ce résultat est d'une importance générale car il s'applique à tous les processus avalancheux émergeant dans différents systèmes dynamiques / Recent studies of plastic deformation using high-resolution experimental techniques testify that deformation processes are often characterized by collective effects that emerge on a mesoscopic scale, intermediate between the scale of individual crystal defects and that of the macroscopic sample. In particular, the acoustic emission (AE) method reveals intermittency of plastic deformation in various experimental conditions, which is manifested by the property of scale invariance, a characteristic feature of self-organized phenomena. The objective of the dissertation was to study the inherent structure of AE for different mechanisms of plastic deformation, to examine its dependence on the strain rate and strain hardening of the material, and to understand the relationships between short time scales related to organization of defects and those relevant to the continuous approach of plasticity. The study was performed on AlMg and Mg-based alloys, the plastic deformation of which is accompanied by a strong acoustic activity and controlled by different physical mechanisms: the Portevin-Le Chatelier (PLC) effect in the first case and a combination of twinning and dislocation glide in the second case. Application of a technique of continuous AE recording ("data streaming") allowed proving that the apparent behavior, discrete or continuous, of AE accompanying the PLC effect depends on the time scale of observation and the physical parameters surveyed. However, unlike the traditional view, it appears that AE has an intermittent character during both stress serrations and macroscopically smooth flow. Using methods of the theory of nonlinear dynamical systems, such as the multifractal analysis, a tendency to a transition between the scale-invariant dynamics and the behaviors characterized by intrinsic scales was detected during work hardening. Finally, we proved that the power-law statistical distributions persist in wide ranges of variation of parameters conventionally used to individualize acoustic events. This result is of general importance because it applies to all avalanche-like processes emerging in dynamical systems

L'étude a pour but de caractériser et d'analyser le comportement mécanique du Ti 6242-Si dans un large domaine de températures, de vitesses de sollicitation et de trajets de chargement. En effet une viscoplasticité plus marquée au voisinage de l'ambiante qu'à plus haute température caractérise de nombreux alliages de titane et de zirconium. Ce comportement inhabituel est à relier à des phénomènes d'interactions entre dislocations et atomes interstitiels (O, C, N, H), généralement décrits par les termes de " vieillissement dynamique " ou " vieillissement statique ". Les microstructures de déformation observées en microscopie électronique en transmission sur certains de ces états de déformation particuliers choisis au travers de tout le domaine de températures exploré, apportent des éclairages ponctuels sur les bases physiques possibles d'une interprétation à l'échelle microscopique des phénomènes observés et mesurés à l'échelle macroscopique. Les résultats obtenus sont alors interprétés à partir de la mobilité relative des dislocations ou groupements de dislocations, de leur interaction avec des solutés en sursaturation dans ce matériau, ou de la structure de cœur particulière de ces dislocations à basse température. L'essai de relaxation, grâce à la large gamme de vitesses de déformation qu'il couvre, a permis d'évaluer dans quelles proportions les différents régimes de déformation se mélangent à chaque température. En effet, deux modes plastiques profondément différents, en se combinant, régissent la viscoplasticité macroscopique : - dans le domaine des hautes températures (ou des faibles vitesses de déformation), le mode traînage est dominant : les dislocations coins traînent des atmosphères de solutés. - dans le domaine des basses températures (ou des vitesses élevées), c'est au contraire le mode friction qui prévaut : les dislocations se déplacent rapidement, les atomes de solutés restant quasi immobiles et ne jouant qu'un rôle de durcissement de solution solide. Dans le domaine de recouvrement de ces deux modes plastiques propres - domaine d'existence du phénomène PLC - de brusques changements de comportement peuvent donc apparaître, car la plasticité en mode friction a tendance à se rassembler localement sous forme de " bandes de vitesse ", alors que le reste de la structure ou de l'éprouvette continue à se déformer beaucoup plus lentement en mode traînage, jusqu'à atteindre le " blocage " aux plus basses températures. La plasticité du matériau est intrinsèquement hétérogène. L'étude fine des données de relaxation met en évidence la présence de " bouffées de plasticité " (strain bursts) très localisées dans le temps et dans l'espace (échelle mésoscopique). Le taux de corrélation de ces événements élémentaires détermine l'amplitude et la forme des manifestations macroscopiques (bandes de vitesse, serrations, crochets de traction,...). Les essais mécaniques ont donc permis de déterminer les frontières des différents domaines de comportement de l'alliage étudié et d'y mesurer certains paramètres macroscopiques caractéristiques tels que les énergies et les volumes d'activation apparents de ces modes plastiques. Aux températures élevées (600°C - 450°C), le mode traînage est omniprésent. Le régime de vieillissement dynamique domine au pic du domaine de l'anomalie de comportement, vers 400°C. À cette température, les capacités de restauration du matériau sont très limitées : la faible amplitude de relaxation qu'il présente est suivie d'un blocage strict de la plasticité. Le domaine des températures intermédiaires, entre 300°C et 200°C, est caractérisé par le blocage quasi-instantané de la plasticité. Dans le domaine des basses températures de l'anomalie (autour de 150°C), la plasticité est rétablie grâce à la prédominance du mode friction, et les durcissements de vieillissement et d'écrouissage s'additionnent. Enfin, à température ambiante, c'est-à-dire au voisinage de la limite basse du domaine, le vieillissement statique se manifeste.

Materials when subjected to deformation exhibit unstable plastic flow beyond the elastic limit. In certain range of temperature and strain rates many solid state solutions, both interstitial as well as substitutional, exhibit the phenomenon of serrated yielding which also goes by the name, the Portevin - Le Chatelier (PLC) effect. The origin of this plastic instability is due to the interaction of dislocations with solute atoms. The objective of the thesis is to provide a dynamical systems approach to the study of this plastic flow instability. The thesis work discusses, within the framework of a model, the connection between microscopic dislocation mechanisms and macroscopic mechanical response of the specimen as stress drops in stress-strain curves. An extension of the model to the associated deformation bands is also considered. The emphasis is on the dynamical aspects of the instability. The methods of nonlinear dynamics like geometrical slow manifold and Poincare map formalism are applied for the first time to study the PLC effect. However, the approach and techniques transcend this particular application as the techniques are equally well applicable for many other physical systems as well, in particular, systems involving multiple time scales. The material covered should be of interest to investigators in the materials science, in particular, those, involved in the dislocation patterning and self organization of dislocations. Many theoretical models for the PLC effect exist in literature. Although the physical phenomenon is inherently dynamic, the conventional theoretical models do not involve any dynamical aspect. A dynamical model for this effect, due to Ananthakrishna, Sahoo and Valsakumar provides an explanation in terms of the dynamic interactions between different dislocation species and evolution of densities of these dislocation species. This model is known to reproduce several of the experimental results. It is within the perspective of this model and its extensions we analyze the PLC effect. The macroscopic manifestation of the PLC effect is the repeated load drops or serration in stress-strain curves (beyond the yield point). Each of the load drop is associated with the formation of a spatial dislocation band and its subsequent propagation. From the perspective of a dynamical system, the changeover from the stress-strain curve with single yield drop to repeated yield drops (the PLC effect) corresponds to a Hopf bifurcation wherein equilibrium state changes over to a periodic steady state. These repeated load drops correspond to auto oscillations of the applied stress (in the absence of any periodic driving force). In particular, as implied by the slow loading and sudden load drops, these oscillations are classified as relaxation oscillations. Relaxation oscillations are a result of disparate time scales of dynamics of the participating modes. Within the context of the model, this refers to very different time scales of evolution of densities of mobile (fast), immobile (slow) dislocations and those with a cloud of solute atoms (not too slow). The focus of attention in the thesis work is on these auto relaxation oscillations. There are several methodologies in nonlinear dynamical systems to study the oscillatory behavior of multidimensional systems with multiple time scales. An effective way is to study the reduced dynamical system in an appropriate space without sacrificing the required dynamical information. To this end, we discuss two techniques which compliment each other. 1.Slow manifold approach: This method utilizes the presence of multiple time scales dynamics. Advantage is that the information on the nature of evolution of the periodic orbit is retained. The limitation is that the transition from one stable state to another as parameter is varied cannot be dealt with. 2.Poincare maps:This approach utilizes the recurrent behavior of the period orbit. This is a convenient methodology to study the nature of stability of periodic orbits. However, in this, the information about the nature of evolution is lost. Both the above techniques provide good description in the presence of high dissipation or larger separation of time scales of the participating modes. For slow manifold analysis, this leads to exact slow manifold structure while in the case of Poincare maps, it leads to simpler, lower dimensional attractors. Specific issues that are dealt with using these approaches and others in this thesis are the following. To start with, we first provide a comprehensive overview of the dynamical behavior as envisaged by the model system in physically relevant two parameter space. The existence of relaxation oscillations bounded by back-to-back Hopf bifurcation is a good representation of the fact that the PLC effect manifests only in a window of strain rates. Within this boundary of Hopf bifurcations relaxation oscillations destabilize to give rise to new states of order, including the chaotic states. The changes in the nature of these oscillations with control parameters is projected through the bifurcation diagrams and analyzed using techniques like Floquet multipliers, Lyapunovs exponents etc. After the identification of the relevant parameter space for the monoperiodic relaxation oscillations, we focus our attention on the time scales involved in these relaxation oscillations and its connection to the time scales apparent in serrations of the stress-strain curve of the PLC effect. This characteristic feature of the PLC effect, the stick-slip nature of stress-strain curves, is believed to result from the negative strain rate dependence of the flow stress. The latter is assumed to arise from a competition of the relevant time scales involved in the phenomenon. However, in the previous works, the identification and the role of the time scales in the dynamical phenomenon is not clear. The motivation of this part of the work is to identify the time scales involved in the stress drops of the time series and their origin. Since the dynamics involves distinct time scales, in the long time limit, the evolution is controlled only by the slow modes. Hence, the adiabatic elimination or quasi-steady state approximation of the fast modes leads to an invariant manifold, the slow manifold which is useful for the analysis of time scales. The geometry of the slow manifold which is atypical with two connected pieces is shown to be at the root of the relaxation oscillations. The analysis of the slow manifold structure helps to understand the time scales of the dynamics operating in different regions of the slow manifold. The analysis also helps us to provide a proper dynamical interpretation for the negative branch of the strain rate sensitivity of the flow stress. The slow-fast dynamical nature manifests itself through multiperiodic oscillations also, in the form of mixed mode oscillations (MMOs), which are oscillations with both large amplitude excursions as well as small amplitude loops. In MMOs, the small amplitude oscillatory loops are confined to one part of the slow manifold (around the fixed point) and the large amplitude excursions arise as jumps from one piece of the slow manifold to the other. More generally, MMOs are a characteristic feature of a family of dynamical systems which also exhibit alternate periodic-chaotic sequences in bifurcation portraits. Usually, the origin of these features is explained in terms of either the approach to a homoclinic bifurcation duo to a saddle fixed point (Shilnikov scenario) or a saddle orbit (Gavrilov-Shilnikov scenario). However, the dynamical model exhibits features from both the above scenarios. The emphasis of this study is on explaining the origin of the incomplete approach to a global bifurcation in the dynamical model. Apart from attempting to understand the complex bifurcation sequences, an additional motivation for this study is the apparent lack of systematic investigation into the incomplete approach to global bifurcation exhibited by a variety of physical systems. The method of the analysis is general and applicable to the family of MMO systems. In the model, using the structure of the bifurcation sequences, and the equilibrium fixed point, a local analysis shows that the approach to homoclinicity is asymptotic at best, and is a result of the ‘softening' of eigenvalues of the saddle equilibrium point. This softening, in turn, is a consequence of back-to-back Hopf bifurcation which reflects the constraint of the physical phenomenon, namely, the occurrence of the multiple stress drops only in an interval of the strain rates. The characteristic features, namely, MMOs, alternate periodic-chaotic sequences, and incomplete approach to homoclinicity are related to each other and arise as a consequence of the atypical slow manifold structure. The slow manifold structure analysis assumes that the evolution of the system is constrained within the neighborhood of the slow manifold which also implies that the dynamical system involves high dissipation. Hence, the dimension of the effective dynamics in the long time limit is reduced. The analysis reveals information regarding the structure of the periodic orbit for a given set of parameter values but does not provide any information regarding the nature of stability of the periodic orbits. However, any insight into the mechanism of the instability of the periodic orbits in the model may lead to a better understanding of the underlying physical phenomenon. Poincare maps and equivalent discrete dynamical systems provide a convenient means to obtain such an insight on the nature of the periodic solutions of the dynamical system. This methodology compliments the invariant slow manifold analysis, since in Poincare maps, the nature of the stability information is preserved at the expense of the structure of the periodic orbit. However, these two methodologies are not exclusive to each other, since the slow manifold structure as well as Poincare maps may be constructed using a common factor, namely, extremal values of the fast variable of the dynamical system. The methodologies adopted for the analysis assumes large dissipation arising out of the multiple time scale behavior such that the next maximal amplitude (NMA) maps can be modeled by one dimensional discrete dynamical systems. The dynamical portrait of the model shows differing nature of dynamics and consequently Poincare maps with different geometrical shapes in the {m,c) plane. Within the framework of one dimensional maps, these shapes can be schematically reconstructed using minimal information regarding the principal periodic orbit embedded in higher dimension and its nature of stability. This suggests that one dimensional maps might be sufficient to represent the higher dimensional dynamical system. For most of the parameter space, the NMA maps of the dynamical model possess characteristic features of a locally smooth maximum and asymptotically long tail. These features have been observed in many other physical systems, both experimental and model systems. Hence, this analysis is focused on a broader issue of Poincare maps in a family of dynamical systems with multiple time scale dynamics and mixed mode oscillations. Here, the dynamical model has been used as a representative dynamical system for this family. The scope of the study is to understand the dynamical features of the MMO systems within the framework of one dimensional systems. Specifically, by using some general constraints on the one dimensional map, we first analyze the basic mechanism that is responsible for the reversal of periodic sequences of RLk type which corresponds to the dominant periodic states of the MMO systems. This in turn allows us to understand the period adding sequences as well. The analysis also helps to demonstrate that the width of the periodic states contained within the chaotic regions bounded by two successive periodic states of the form RLk is smaller than that for RLk .To this end, we first construct a model map which mimics the dominant bifurcation sequences of MMO systems. This map is utilized to verify the analytical results for the parameter width of the periodic windows. This analysis also throws light on the origin of the ordered structure of the isolas of RLk periodic orbits, in MMO systems, which was shown to be the result of a back-to-back Hopf bifurcation. The results indicate the ubiquity in the qualitative dynamical features of physical systems from widely differing origin, exhibiting alternate periodic-chaotic sequences. Although the model for the PLC effect is successful in describing the features of the phenomenon, a shortcoming of the dynamical model has been the absence of the spatial aspect. A dominant process in the PLC effect is the movement of dislocations (mainly through cross glide) which is essentially nonlocal. This feature has been incorporated into the dynamical model through a 'diffusive' term for the mobile dislocations. Preliminary results indicate that various types of band propagation, as seen in experiments, are recovered. It is known that the solute atmosphere aggregation occurs primarily during the waiting time of the mobile dislocations after its arrest. As another extension, the present model has been revised to incorporate these aging effects also. An outline of the thesis is as follows. Focus of this thesis work is on the dynamical aspects of the PLC effect. The phenomenology and few techniques in nonlinear dynamics are introduced in Chapters 1 and 2. Chapter 3 provides a comprehensive tour of dynamical behavior of the model in physically relevant two-parameter space. The rest of the work is presented in three parts (six chapters). In the first part of the thesis, the structure of the relaxation oscillations in the phase space is analyzed using the topology of the slow manifold. A connection between the slow manifold structure and the negative strain rate sensitivity of the flow stress is attempted using this analysis (Chapter 4). As a natural extension, the approach is utilized for the analysis of multiperiodic relaxation oscillations also. The emphasis is on the connection between the dynamical behavior of the model and incomplete approach to a global bifurcation (Chapter 5). In the second part of the thesis, the stability properties of periodic orbits are analyzed in detail using the Poincare map formalism, complimenting the study on the structure of periodic orbits using slow manifold. The structure and gross features of the Poincare map are reproduced utilizing only minimum information regarding the principal periodic orbit in the multidimensional space (Chapter 6). Within the framework of one dimensional systems, we analyze the mechanisms responsible for the structure of bifurcation portraits of MMO systems (Chapter 7). Third and the last part, of work focuses on modeling the spatial aspect of the PLC effect and refinement of the dynamical model (Chapters). The last chapter, Chapter9, is devoted for discussion of the results and scope for future work.