La technologie de micro indentation est un des moyens de caractérisation (à partir de petits échantillons) qui s'est imposé ces derniers temps dans différents domaines (pharmaceutique, génie civil, industrie pétrolière etc.). Il répond à un certain nombre d'exigences en matière de solution au problème d'échantillonnage. Cette thèse est consacrée à la caractérisation des propriétés mécanique des géomatériaux, et spécialement pour les roches pétrolières comme l'argilite, le grès, la craie ... qui ont été utilisées pour les différentes études expérimentales menées au cours de la thèse. Après avoir présenté la méthode de dépouillement du test d'indentation pour un milieu isotrope, nous avons développé une méthode semi-analytique basée sur la fonction de Green pour caractériser le milieu isotrope transverse en déterminant les cinq paramètres élastique de ce milieu. L'influence des différentes sollicitations (mécaniques, thermiques, hydriques) sur les propriétés mécaniques des roches a été étudiée en utilisant la technologie de micro indentation avec la méthode de dépouillement isotrope transverse. Nous avons essayé de caractériser les paramètres de rupture (C et f) à l'aide du test d'indentation et d'un test de micro compression simple (MCS) effectué par la même machine d'indentation. Par l'essai d'indentation et une méthode d'analyse inverse, nous avons identifié les paramètres d'une loi de comportement élastoplastique (Drucker Prager). En l'absence d'une solution directe du problème d'indentation en régime plastique, nous avons eu recours à une modélisation numérique par un code de calcule élément finis (ABAQUS) pour déterminer la courbe d'indentation calculée. Cette détermination s'est révélée tout à fait probante et a été de plus validée par une simulation d'essais de compression triaxiale sur le même matériau. / The technology of micro indentation is one of the techniques ofmateriaJ characterization (by using small specimens) in various fields (mechanical engineering, civil engineering, oil industry, and pharmaceutical industry). Its main advantage lies in a certain number of practical requirements as regards the solution to the problem of small specimens. The present study is devoted the characterization of the mechanical properties of geomaterials, especially rocks involved in petroleum engineering. After having presented the methodology of the indentation test for isotropic rocks, we developed a semi-analytical method based on the use of Green function to characterize transverse isotropic rocks (five elastic parameters of these rocks). The influence of the various loadings (mechanical, thermal, hydrous) on the rock mechanics properties was studied by using the technology of micro indentation and the methodology proposed for isotropic transverse were used. Moreover, we characterize the failure parameters (C and f) by a combined approach of the indentation test and a test of micro compression (MCS) carried out the indentation device. Finally, we use inverse analysis in order to identify the parameters of a Drucker Prager mode!. ln the absence of a direct solution of the problem of indentation (in plastic regime), we had recourse to a numerical modelling by a finite element code (ABAQUS) to determine the calculated curve of indentation. This determination appeared completely convincing and moreover was validated by a simulation of triaxial compression tests on the same material

Although existing continuum models for the elasto-viscoplastic response of amorphous polymeric materials phenomenologically capture the large deformation response of these materials in a reasonably acceptable manner, they do not adequately account for the creep response of these materials at stress levels below those causing “macro-yield”, as well as the Bauschinger-type reverse yielding phenomena at strain levels less than ≈ 30% associated with the macro-yield transient. Anand [1] has recently generalized the model of Anand and Gurtin [2] to begin to capture these important aspects of the mechanical response of such materials. In this work, we summarize Anand’s constitutive model and apply it to the amorphous polymeric solid poly(methyl methacrylate) (PMMA), at ambient temperature and compressive stress states under which this material does not exhibit crazing. We describe our compression-tension and creep experiments on this material from which the material parameters in the model were determined. We have implemented the constitutive model in the finite-element computer program ABAQUS/Explicit [3], and using this finite-element program, we show numerical results for some representative problems in micro-indentation of PMMA, and compare them against corresponding results from physical experiments. The overall predictions of the details of the load, P, versus depth of indentaion, h, curves are very encouraging. / Singapore-MIT Alliance (SMA)

Proton Exchange Membrane (PEM) fuel cell stack requires gaskets and seals in each cell to keep the hydrogen and air/oxygen within their respective regions. The stability of the gaskets is critical to the operating life as well as the electrochemical performance of the fuel cell. Chemical degradation of five elastomeric gasket materials in a simulated and an aggressive accelerated fuel cell solution at PEM operating temperature for up to 63 weeks was investigated in this work. The five materials are Copolymeric Resin (CR), Liquid Silicone Rubber (LSR), Fluorosilicone Rubber (FSR), Ethylene Propylene Diene Monomer Rubber (EPDM), and Fluoroelastomer Copolymer (FKM). In order to assess the durability of the materials, observation of chemical degradation level, dynamic mechanical analysis, and micro-indentation test were adopted in this study. This experimental result showed that the influence of the chemical reaction could affect the material surface condition. Also, the chemical reaction could affect material¡¦s mechanical properties had been changed over the soaking time. By considering the level of chemical degradation and mechanical properties, the experimental results showed that EPDM is recommended as the best choice of sealing material for using in a PEMFC.

Currently, the maintenance and repair of civil engineering infrastructures (especially bridges and highways) have become increasingly important, as these structures age and deteriorate. Interface between two different mixes or strengths of concrete also appear in large concrete structures involving mass concreting such as dams, nuclear containment vessels, cooling towers etc., since joints between successive lifts are inevitable. These joints and interfaces are potential sites for crack formation, leading to weakening of mechanical strength and subsequent failure. In case of a bi-material interface, the stress singularities are oscillatory in nature and the fracture behavior of a concrete-concrete bi-material interface is much more complicated. A comprehensive experimental work has been undertaken for characterization of the behavior of different concrete-concrete interfaces under static and fatigue loading. The effect of specimen size on the concrete-concrete interfaces is studied and the non-linear fracture parameters such as fracture energy, mode I fracture toughness, critical crack tip opening displacement, critical crack length, length of process zone, brittleness number, size of process zone, crack growth resistance curve and tension softening diagram. These parameters are required for modeling the concrete-concrete interfaces in non-linear finite element analysis. Presently, the advanced non-destructive techniques namely acoustic emission, digital image correlation and micro-indentation have great capabilities to characterize the fracture behavior. The damage in plain concrete and concrete interface specimens is characterized both qualitatively and quantitatively using acoustic emission technique by measuring the width of fracture process zone and width of damage zones. The DIC technique is used to obtain the fracture parameters such as mode I and mode II fracture toughness and critical energy release rate. The micro-mechanical properties are obtained by performing depth-sensing micro-indentation tests on the concrete-concrete interfaces. Civil engineering structures such as long-span bridges, offshore structures, airport pavements and gravity dams are frequently subjected to variable-amplitude cyclic loadings in actual conditions. Hence, in order to understand the fracture behaviour under fatigue loading, the fatigue crack growth in plain concrete and concrete-concrete interface is also studied using the acoustic emission technique. An attempt is made to apply the Paris’ law, which is applicable to mechanical behaviour of metals, for acoustic emission count data. All these studies show that, as the difference in the compressive strength of concrete on either side of the interface increases, the load carrying capacity decreases and the fracture parameters indicate the increase in the brittleness of the specimens. It is concluded that the repair concrete should be selected in such a way that its elastic properties are as those of the parent concrete.

Les aspects biologiques ne sont généralement pas considérés lors de la conception des ouvrages de génie civil, malgré que la biocolonisation puisse affecter leur durabilité. Cette thèse s’intéresse à l’encrassement biologique des matériaux cimentaires en eau de rivière. Un essai de biocolonisation phototrophe accélérée, simulant les conditions en rivière a été mis au point et validé. Il a permis l’étude de pâtes cimentaires de différentes formulations. La colonisation a été évaluée par le taux de recouvrement de la surface, estimé par une méthode proposée d’analyse d’images. Une étude de l’influence de la rugosité sur la bioréceptivité du matériau a été réalisée à travers plusieurs paramètres de différentes natures et la densité de pics (paramètre d’espacement) a montré l’influence la plus déterminante. Un modèle a été proposé pour expliquer cette influence et a donné des résultats satisfaisants. Les influences de la porosité et du pH semblent être limitées dans les conditions de l’essai. Enfin, la micro-indentation a été adaptée pour l’évaluation mécanique de la détérioration des pâtes cimentaires sur de faibles épaisseurs. Cette technique pourra être utilisée pour évaluer la biodétérioration. / The biological aspects are generally not considered in the design of civil engineering works, although the biocolonisation may affect their durability. This thesis focuses on biofouling of cementitious materials in river water. A laboratory accelerated test of phototrophic biocolonisation, simulating the river conditions, was developed and validated. It allowed the study of cement pastes of different formulations. Colonization was assessed by the recovery rate of the surface, estimated by a proposed method of image analysis. A study of the roughness influence on the bioreceptivity of the material was conducted through several roughness parameters of different natures, and the peaks density (a spacing parameter) showed the most decisive influence. A model was proposed to explain this influence and gave satisfactory results. The influences of porosity and pH appeared to be limited in the test conditions. Finally, micro-indentation was adapted to the mechanical evaluation of the deterioration of thin layers of cement pastes. This technique may be used to evaluate the biodeterioration.

La restauration des peintures d'art consiste à restaurer la lisibilité d'une œuvre d'art et à préserver son intégrité. La plupart des techniques consiste à déposer des solvants juste en surface afin de ne dissoudre que la couche de vernis. Cependant, les couches sous-jacentes risquent d'être endommagées par la pénétration de ces solvants, causant éventuellement un gonflement ou un craquèlement de ces dernières. Du fait de la complexité physico- chimique de la couche picturale, nous proposons d'étudier la pénétration de solvants dans un nanoporeux modèle issu du séchage contrôlé de dispersions aqueuses de nanoparticules de silice. Le séchage et la consolidation de ces dispersions colloïdales jusqu'à l'apparition de craquelures de séchage sont étudiés. La réflectivité de neutrons et la diffusion de neutrons aux petits angles permettent d'accéder à la structuration des systèmes en surface et en volume, respectivement, au cours du séchage. L’étude expérimentale des ouvertures de craquelures dues au séchage, associée à un modèle de poroélasticité que nous développons, renseigne sur les propriétés mécaniques des systèmes consolidés et du tableau « Jeanne d'Arc en prison » (1824) du peintre français Louis Crignier (1790-1824). La caractérisation du milieu poreux formé après la consolidation est réalisée par imagerie de neutrons et permet de déterminer la perméabilité et les porosités des milieux. Enfin, nous présentons la dynamique d'imprégnation d'une goutte sessile de solvant dans plusieurs milieux poreux, qui diffèrent de par leur taille de pores. Notre montage expérimental permet une quantification précise et directe des écoulements au-dessus et à l'intérieur du milieu poreux. Des mesures de propriétés mécaniques sont réalisées avant et après imprégnation par micro-indentation. / Art painting restoration aims to restore the readability of a painting and to preserve its integrity. Most of the techniques consist of depositing solvents on the surface of the painting to dissolve the varnish layer. However, the sublayers can be damaged by the penetration of the solvent, possibly resulting in swelling or cracking processes. Due to the physical and chemical complexity of the pictorial layer, we propose to study solvent penetration in model nano porous media obtained by controlled drying of aqueous silica nanoparticles dispersions. Drying and the consolidation process of these colloidal dispersions are studied until drying cracks appear. Neutron reflectivity and small angle neutron scattering provide structural information on particles near the interface between the dispersion and the air and in the bulk, respectively, during drying. The experimental study of drying cracks, associated to a poroelastic model, inform on mechanical properties of consolidated model systems and of the painting “Jeanne d'Arc en prison” (1824) by the French painter Louis Crignier (1790-1824). Characterization of the porous media obtained after consolidation is carried out with neutron imaging to determine the permeability and the porosities of the porous media. Finally, we present the dynamics of imbibition of sessile solvent drops on several porous media with different pore sizes. Our experimental set-up provides a precise and a direct quantification of the different flows outside and through the porous media. Mechanical properties are performed before and after solvent imbibition, by micro-indentation testing.

There is great need to understand the mechanical properties of lead-free alloys—an alternative of lead-based alloys—to address the environmental problems associated with the use of lead-based materials in microelectronics. In this work, the microstructures of Bi57In26Sn17 lead-free alloy were examined using Optical Microscopy and Energy Dispersive X-ray Spectroscopy analysis. The micro-indentation technique was used to study the mechanical properties of Bi57In26Sn17 lead-free alloy. The experimental results of the hardness and contact modulus were presented and discussed. Local creep during the indentation was observed from the load-displacement curves. The Vickers hardness (HV) increases with the decrease of the indentation depth, suggesting that the alloy exhibits indentation size effect.

Ce travail de thèse a eu comme objectif la mise en place et la validation d’une méthodologie expérimentale pour le suivi de l’évolution in-vitro de substituts osseux à base de phosphates de calcium. Du phosphate dicalcique dihydraté (DCPD, CaHPO4·2H2O) et du phosphate tricalcique bêta (β-TCP, β-Ca3(PO4)2) ont été choisis comme matériaux modèles de deux grandes classes de substituts osseux: les “biosolubles” (sujets à dissolution après implantation) et les “biorésorbables” (sujets à résorption cellulaire après implantation). Pour l’étude des phénomènes de dissolution et de reprécipitation observés lorsque les phosphates de calcium sont plongés en solution, ces matériaux ont été produits sous forme d’échantillons microporeux (60% de porosité pour le DCPD, 75% pour le β-TCP) et soumis à des tests de dissolution in-vitro en conditions statiques ou dynamiques (sans ou avec renouvellement du liquide) dans différentes solutions tamponnées à pH physiologique (TRIS et PBS) et pour des durées s’étalant entre 30 minutes et 2 mois. L’analyse des propriétés physico-chimiques, microstructurales et mécaniques des échantillons avant et après immersion a permis d’évaluer l’influence du type de milieu et des conditions de test choisies sur l’évolution des échantillons. Une attention particulière a été prêtée à la caractérisation mécanique: la technique de micro-indentation instrumentée sphérique a été préférée à autres essais plus conventionnels. Cette technique permet d’évaluer plusieurs paramètres tels que la dureté et le module de Young de façon quasi non-destructive et à une échelle locale. En conséquence, l’utilisation de la micro-indentation s’est avérée d’une grande aide pour le suivi des caractéristiques d’échantillons dégradés qui présentaient un gradient de propriétés entre la surface (où le processus de dégradation commence) et le cœur (sujet à des changements sur plus long terme). La dernière partie de cette étude a été dédiée à l’étude du deuxième phénomène qui entraine la résorption de substituts osseux in-vivo, à savoir la résorption cellulaire. Pour cela des essais cellulaires avec des cellules précurseurs d’ostéoclastes ont été réalisés sur des échantillons denses de β-TCP pur ou dopé avec 5% molaire de magnésium. L’addition de cet élément est censée modifier les propriétés du matériau (notamment sa solubilité) et, par conséquence, modifier le comportement cellulaire. Les résultats des tests ont confirmé la cytocompatibilité des deux types de β-TCP, mais ont également mis en avant une difficulté d’activation des ostéoclastes. Deux des causes possibles seraient liées à la topographie de surface des échantillons et au relargage des ions calcium suite à la dissolution du matériau. / The present Ph.D. thesis work was aimed to establish and assess an experimental methodology to monitor the in-vitro evolution of calcium phosphate (CaP) bone substitutes. Dicalcium phosphate dihydrate and beta-tricalcium phosphate were chosen as model of two main classes of bone substitutes: “biosoluble” ones (which undergo dissolution after implantation) and “bioresorbable” ones (which undergo cellular resorption after implantation). In order to study the dissolution and precipitation phenomena, which take place once CaPs are immersed in solution, these materials were produced in the form of micro-porous samples (60% of porosity for DCPD, 75% for β-TCP) and used for dissolution tests in-vitro in static and dynamic conditions (without or with liquid renewal) in different buffered solutions at physiologic pH (TRIS and PBS) and for periods of time ranging between 30 minutes and 2 months. The analysis of the physico-chemical, microstructural and mechanical properties of the samples before and after immersion allowed to evaluate the influence of the chosen medium and immersion conditions on the evolution of the specimens. Particular attention was paid to the mechanical characterisation: instrumented spherical micro-indentation was preferred to other more conventional tests. This technique enables the evaluation of several parameters such as the hardness and the Young’s modulus in a quasi-non-destructive way and on a local scale. As a consequence, the use of micro-indentation proved to be of great help for monitoring the characteristics of the degraded specimens, which presented a gradient of properties between the surface (where the degradation process starts) and the core (subject to changes on a longer period). The last part of this work was focused on the study of the second main phenomenon, which takes part in the in-vivo resorption of bone substitutes, that is to say the cellular resorption. For this purpose, cellular tests with osteoclast-precursor cells were carried out on dense samples made of pure and magnesium-doped β-TCP (5 mol.% of Mg). The addition of magnesium was aimed to modify the properties of the material and, as a consequence, the cellular behavior. The results confirmed the cytocompatibility of both types of β-TCP, but they also showed a difficult activation of osteoclasts. Two of the possible causes would be linked to the topography of the surface of the specimens and to the release of calcium ions due to the dissolution of the material.

Ultra high performance fibre reinforced concrete (UHPFRC) is a relatively new fibre reinforced cementitious composite and has become very popular in construction applications. Extensive experimental studies have been conducted, demonstrating its superior properties such as much higher strength, ductility and durability than conventional fibre reinforced concrete (FRC) and high performance concrete. However, the material's damage and fracture mechanisms at meso/micro scales are not well understood, limiting its wider applications considerably. This study aims at an in-depth understanding of the damage and fracture mechanisms of UHPFRC, combining microscale in-situ X-ray computed tomography (µXCT) experiments and mesoscale image-based numerical modelling. Firstly, in-situ µXCT tests of small-sized UHPFRC specimens under wedge splitting loading were carried out, probably for the first time in the world, using an in-house designed loading rig. With a voxel resolution of 16.9µm, the complicated fracture mechanisms are clearly visualised and characterised using both 2D images and 3D volumes at progressive loading stages, such as initiating of micro-cracks, arresting of cracks by fibres, bending and pulling out of fibres and spalling of mortar at the exit points of inclined fibres. Secondly, based on the statistics of pores in the µXCT images obtained for a 20mm cube specimen, an efficient two-scale analytical-numerical homogenisation method was developed to predict the effective elastic properties of the UHPFRC. The large number of small pores were first homogenised at microscale with sand and cement paste, using elastic moduli from micro-indentation tests. 3D mesoscale finite element models were built at the second scale by direct conversion of the µXCT images, with fibres and large pores were faithfully represented. The effects of the volume fraction and the orientation of steel fibres on the elastic modulus were investigated, indicating that this method can be used to optimise the material micro-structure. Thirdly, 3D mesoscale finite element models were built for the specimen used in the in-situ µXCT wedge splitting test, with embedded fibre elements directly converted from the µXCT images. The fracture behaviour in the mortar was simulated by the damage plasticity model available in ABAQUS. Finally, 2D mesoscale finite element models were developed to simulate the fracture behaviour of UHPFRC using cohesive interface elements to simulate cracks in the mortar, and randomly distributed two-noded 1D fibres and connector elements to simulate the pull-out behaviour of fibres. This approach offers a link between the fibres pull-out behaviour and the response of the whole composite at the macroscale, thus it can be used to conduct parametric studies to optimise the material properties.

Recent studies demonstrate that mechanical deformation of small volume systems can be significantly different from those of the bulk. One such interesting length scale dependent property is the increase in the yield stress with decrease in diameter of micrometer rods, particularly when the diameter is below a micrometer. Intermittent flow may also result when the diameter of the rods is decreased below a certain value. The second such property is the intermittent plastic deformation during nano-indentation experiments. Here again, the instability manifests due to smallness of the sample size, in the form of force fluctuations or displacement bursts. The third such length scale dependent property manifests as ’smaller is stronger’ property in indentation experiments on thin films, commonly called as the indentation size effect (ISE). More specifically, the ISE refers to the increase in the hardness with decreasing indentation depth, particularly below a fraction of a micrometer depth of indentation. The purpose of this thesis is to extend nonlinear dynamical approach to plastic deformation originally introduced by Anantha krishna and coworkers in early 1980’s to nano and micro-indentation process. More specifically, we address three distinct problems : (a) intermittent force/load fluctuations during displacement controlled mode of nano-indentation, (b) displacement bursts during load controlled mode of nano-indentation and (c) devising an alternate framework for the indentation size effect. In this thesis, we demonstrate that our approach predicts not just all the generic features of nano-and micro-indentation and the ISE, the predicted numbers also match with experiments. Nano-indentation experiments are usually carried-out either in a displacement controlled (DC) mode or load controlled (LC) mode. The indenter tip radius typically ranges from few tens of nanometer to few hundreds of nanometers-meters. Therefore, the indented volume is so small that the probability of finding a dislocation is close to zero. This implies that dislocations must be nucleated for further plastic deformation to proceed. This is responsible for triggering intermittent flow as indentation proceeds. While several load drops are seen beyond the elastic limit in the DC controlled experiments, several displacement jumps are seen in the LC experiments. In both cases, the stress corresponding to load maximum on the elastic branch is close to the theoretical yield stress of an ideal crystal, a feature attributed to the absence of dislocations in the indented volume. Hardness is defined as the ratio of the load to the imprint area after unloading and is conventionally measured by unloading the indenter from desired loads to measure the residual plastic imprint area. Then, the hardness so calculated is found to increase with decreasing indentation depth. However, such size dependent effects cannot be explained on the basis of conventional continuum plasticity theories since all mechanical properties are independent of length scales. Early theories suggest that strong strain gradients exist under the indenter that require geometrically necessary dislocations (GNDs) to relax the strain gradients. In an effort to explain the the size effect, these theories introduce a length scale corresponding to the strain gradients. One other feature predicted by subsequent models of the ISE is the linear relation between the square of the hardness and the inverse of the indentation depth. Early investigations on the ISE did recognize that GNDs were required to accommodate strain gradients and that the hardness H is determined by the sum of the statistically stored dislocation (SSD) and GND densities. Following these steps, Nix and Gao derived an expression for the hardness as a function of the indentation depth z. The relevant variables are the SSD and GND densities. An expression for the GND density was obtained by assuming that the GNDs are contained within a hemispherical volume of mean contact radius. The authors derive an expression for the hardness H as a function of indentation depth z given by [ HH 0 ]2 = 1+ zz ∗ . The intercept H0 represents the hardness arising only from SSDs and corresponds to the hardness in the limit of large sample size. The slope z ∗ can be identified as the length scale below which the ISE becomes significant. The authors showed that this linear relation was in excellent agreement with the published results of McElhaney et al for cold rolled polycrystalline copper and single crystals of copper, and single crystals of silver by Ma and Clarke. Subsequent investigations showed that the linear relationship between H2 verses 1/z breaks down at small indentation depths. Much insight into nano-indentation process has come from three distinct types of studies. First, early studies using bubble raft indentation and later studies using colloidal crystals (soft matter equivalent of the crystalline phase) allowed visualization of dislocation nucleation mechanism. Second, more recently, in-situ transmission electron microscope studies of nano-indentation experiments have been useful in understanding the dislocation nucleation mechanism in real materials. Third, considerable theoretical understanding has come largely from various types of simulation studies such as molecular dynamics (MD) simulations, dis¬location dynamics simulations and multiscale modeling simulations (using MD together with dislocation dynamics simulations). A major advantage of simulation methods is their ability to include a range of dislocation mechanisms participating in the evolution of dislocation microstructure starting from the nucleation of a dislocation, its multiplication, formation of locks, junctions etc. However, this advantage is offset by the serious limitations set by short time scales inherent to the above mentioned simulations and the limited size of simulated volumes that can be implemented. Thus, simulation approaches cannot impose experimental parameters such as the indentation rates or radius of the indenter and thickness of the sample, for example in MD simulations. Indeed, the imposed deformation rates are often several orders of magnitude higher than the experimental rates. Consequently, the predicted values of force, indentation depth etc., differ considerably from those reported by experiments. For these reasons, the relevance of these simulations to real materials has been questioned. While several simulations, particularly MD simulation predict several force drops, there are no simulations that predict displacement jumps seen in LC mode experiments. The inability of simulation methods to adopt experimental parameters and the mismatch of the predicted numbers with experiments is main motivation for devising an alternate framework to simulations that can adopt experimental parameters and predict numbers that are comparable to experiments. The basic premise of our approach is that describing time evolution of the relevant variables should be adequate to capture most generic features of nano and micro-indentation phenomenon. In the particular case under study, this point of view is based on the following observation. While one knows that dislocations are the basic defects responsible for plastic deformation occurring inside the sample, the load-indentation depth curve does not include any information about the spatial location of dislocation activity inside the sample. In fact, the measured load and displacement are sample averaged response of the dislocation activity in the sample. This suggests that it should be adequate to use sample averaged dislocation densities to obtain load-indentation depth curve. Keeping this in mind, we devise a method for calculating the contribution from plastic deformation arising from dislocation activity in the entire sample. This is done by setting up rate equations for the relevant sample averaged dislocation densities. The first problem we consider is the force/load fluctuations in displacement controlled nano-indentation. We devise a novel approach that combines the power of nonlinear dynamics with the evolution equations for the mobile and forest dislocation densities. Since the force serrations result from plastic deformation occurring inside the sample, we devise a method for calculating this contribution by setting-up a system of coupled nonlinear time evolution equations for the mobile and forest dislocation densities. The approach follows closely the steps used in the Anantha krishna (AK) model for the Portevin-Le Chatelier (PLC) effect. The model includes nucleation, multiplication and propagation of dislocation loops in the time evolution equation for the mobile dislocation density. We also include other well known dislocation transformation mechanisms to forest dislocation. Several of these dislocation mechanisms are drawn from the AK model for the PLC effect. To illustrate the ability of the model to predict force fluctuations that match experiments, we use the work of Kiely at that employs a spherical indenter. The ability of the approach is illustrated by adopting experimental parameters such as the indentation rate, the radius the indenter etc. The model predicts all the generic features of nano-indentation such as the Hertzian elastic branch followed by several force drops of decreasing magnitudes, and residual plas¬ticity after unloading. The stress corresponding to the elastic force maximum is close to the yield stress of an ideal solid. The predicted values for all the quantities are close to those reported by experiments. Our model allows us to address the indentation-size effect including the ambiguity in defining the hardness in the force drop dominated regime. At large indentation depths where the load drops disappear, the hardness shows decreasing trend, though marginal. The second problem we consider is the load controlled mode of indentation where sev¬eral displacement jumps of decreasing magnitudes are seen. Even though, the LC mode is routinely used in nano-indentation experiments, there are no models or simulations that predict the generic features of force-displacement curves, in particular, the existence of sev¬eral displacement jumps of decreasing magnitudes. The basic reason for this is the inability of these methods to impose constant load rate during displacement jumps. We then show that an extension of the model for the DC mode predicts all the generic features when the model is appropriately coupled to an equation defining the load rate. Following the model for DC mode, we retain the system of coupled nonlinear time evolution equations for mobile and forest dislocation densities that includes nucleation, multiplication, and propagation threshold mechanisms for mobile dislocations, and other dislocation transformation mechanisms. The commonly used Berkovich indenter is considered. The equations are then coupled to the force rate equation. We demonstrate that the model predicts all the generic features of the LC mode nano-indentation such as the existence of an initial elastic branch followed by several displacement jumps of decreasing magnitudes, and residual plasticity after unloading for a range of model parameter values. In this range, the predicted values of the load, displacement jumps etc., are similar to those found in experiments. Further, optimized set of parameter values can be easily determined that provide a good fit to the load-indentation depth curve of Gouldstone et al for single crystals of Aluminum. The stress corresponding to the maximum force on the Berkovich elastic branch is close to the theoretical yield stress. We also elucidate the ambiguity in defining hardness at nanometer scales where the displacement jumps dominate. The approach also provides insights into several open questions. The third problem we consider is the indentation size effect. The conventional definition of hardness is that it is the ratio of the load to the residual imprint area. The latter is determined by the residual plastic indentation depth through area-depth relation. Yet, the residual plastic indentation depth that is a measure of dislocation mobility, never enters into most hardness models. Rather, the conventional hardness models are based on the Taylor relation for the flow stress that characterizes the resistance to dislocation motion. This is a complimentary property to mobility. Our idea is to provide an alternate way of explaining the indentation size effect by devising a framework that directly calculates the residual plastic indentation depth by integrating the Orowan expression for the plastic strain rate. Following our general approach to plasticity problems, we set-up a system of coupled nonlinear time evolution equations for the mobile, forest (or the SSD) and GND densities. The model includes dislocation multiplication and other well known dislocation transformation mechanisms among the three types of dislocations. The main contributing factor for the evolution of the GND density is determined by the mean strain gradient and the number of sites in the contact area that can activate dislocation loops of a certain size. The equations are then coupled to the load rate equation. The ability of the approach is illustrated by adopting experimental parameters such as the indentation rates, the geometrical quantities defining the Berkovich indenter including the nominal tip radius and other parameters. The hardness is obtained by calculating the residual plastic indentation depth after unloading by integrating the Orowan expression for the plastic strain rate. We demonstrate that the model predicts all features of the indentation size effect, namely, the increase in the hardness with decreasing indentation depth and the linear relation between the square of the hardness and inverse of the indentation depth, for all but 200nm, for a range of parameter values. The model also predicts deviation from the linear relation of H2 as a function of 1/z for smaller depths consistent with experiments. We also show that it is straightforward to obtain optimized parameter values that give a good fit to polycrystalline cold-worked copper and single crystals of silver. Our approach provides an alternate way of understanding the hardness and indentation size effect on the basis of the Orowan equation for plastic flow. This approach must be contrasted with most models of hardness that use the SSD and GND densities as parameters. The thesis is organized as follows. The first Chapter is devoted to background material that covers physical aspects of different kinds of plastic deformation relevant for the thesis. These include the conventional yield phenomenon and the intermittent plastic deformation in bulk materials in alloys exhibiting the Portevin-Le Chatelier (PLC) effect. We then provide background material on nano-and micro-indentation, both experimental aspects and the current status of the DC controlled and LC controlled modes of nano-indentation. Results of simulation methods are briefly summarized. The chapter also provides a survey of hardness models and the indentation size effect. A critical survey of experiments on dislocation microsructure that contradict / support certain predictions of the NixGao model. The current status of numerical simulations are also given. The second Chapter is devoted to introducing the basic steps in modeling plastic deformation using nonlinear dynamical approach. In particular, we describe how the time evolution equations are constructed based on known dislocation mechanisms such as nucleation, multiplication formations of junctions etc. We then consider a model for the continuous yield phenomenon that involves only the mobile and forest densities coupled to constant strain rate condition. This problem is considered in some detail to illustrate how the approach can be used for modeling nano-indentation and indentation size effect. The third Chapter deals with a model for displacement controlled nano-indentation. The fourth Chapter is devoted to adopting these equation to the load controlled mode of nano¬indentation. The fifth Chapter is devoted to modeling the indentation size effect based on calculating residual plastic indentation depth after unloading by using the Orowan’s expression for the plastic strain rate. We conclude the thesis with a Summary, Discussion and Conclusions.