Granular materials are in abundance in nature and are estimated to constitute over 75% of all raw materials passing through the industry. Granular or particulate solids are thus of considerable interest to many industrial sectors and research communities, where many unsolved challenges still remain. This thesis investigates the micro- and macro-phenomena in densely packed particulate systems by means of the Discrete Element Method (DEM), which is a numerical tool for analysing the internal complexities of granular material as the mechanical interactions are considered at the grain scale. It presents an alternative approach to phenomenological continuum approaches when studying localisation problems and finite deformation problems in granular materials. In order to develop a comprehensive theoretical understanding of particulate matter and to form a sound base to improve industrial processes, it is desirable to study the mechanical behaviour of granular solids subject to a variety of loading conditions. In this thesis, three loading actions were explored in detail, which are biaxial compression, rigid object penetration and progressive formation of granular piles. The roles of particle shape and contact friction in each of these loading scenarios were investigated. The resulting packing structures were compared and studied to provide a micromechanical insight into the development of contact force network which governs the collective response. The interparticle contact forces and displacements were then used to evaluate the equivalent continuum stress and strain components thus providing the link between micro- and macroscopic descriptions. The information collected from the evolution of strong contact network illustrates the underlying mechanism of force transmission and propagation. DEM simulations presented in this thesis demonstrate strong capability in predicting the bulk behaviour as well as capturing local phenomenon occurring in the system. The research first simulates a testing environment of biaxial compression in DEM, in which the phenomenon of strain localisation was investigated, with special attention given to the interpretation of underlying failure mechanism. Several key micromechanical quantities of interest were extracted to understand the bifurcation instability, such as force chains, contact orientation, particle rotation and void ratio. In the simulation of progressive formation of granular piles, a counterintuitive pressure profile with a significant pressure dip under the apex was predicted for three models under certain conditions. Both particle shape and preparation history were shown to be important in the resulting pressure distribution. During the rigid body penetration into a granular sample, the contact forces were used to evaluate the equivalent continuum stress components. Significant stress concentration was developed around the punch base which further led to successive collapse and reformation of force chains. Taking the advantage of micromechanical analysis at particle scale, two distinct bearing failure mechanisms were identified as the penetration proceeded. To further quantify the nature of strain mobilisation leading to failure, Particle Image Velocimetry (PIV) was employed to measure the deformation over small strain interval in association with shear band propagation in the biaxial test and deformation pattern in the footing test. The captured images from DEM simulation and laboratory experiments were evaluated through PIV correlation. This optical measuring technique is able to yield a significant improvement in the accuracy and spatial resolution of the displacement field over highly strained and localised regions. Finally, a series of equivalent DEM simulations were also conducted and compared with the physical footing experiments, with the objective of evaluating the capability of DEM in producing satisfactory predictions.

Ti-6Al-4V is the most widely used titanium alloy and is typically used in stages of gas turbine engines, due to its high strength-to-weight ratio, corrosion resistance and high strength at moderate temperatures. However, the alloy is susceptible to the development of strong textures during thermomechanical processing that leads to a preferred crystallographic orientation. These are referred to as macrozones and are thought to develop during the β to α phase transformation, as a result of the retention of large prior β grains during processing and variant selection. Macrozones are clusters of neighbouring grains with a common crystallographic orientation that may act as one single grain during loading and have been shown to cause scatter in the fatigue life. The focus of the current work was based on the analysing the strain behaviour of soft, hard and no macrozones within the microstructure, during various loading conditions. The local strain behaviour was studied at a micro and nanoscale, using the digital image correlation (DIC) technique, which utilises microstructural images recorded during mechanical loading. On a microscale, the no-macrozone and strong-macrozone condition loaded at 0% exhibited homogeneous strain behaviour. The strong-macrozone condition loaded at 45% and 90% to the extrusion direction, respectively, developed pronounced high strain bands correlating to regions that were favourably oriented for prismatic and basal slip, respectively. Characterisation of the slip bands provided a detailed understanding of the deformation behaviour at the nanoscale and the slip system was subsequently determined for each grain using slip trace analysis. Prismatic slip was the dominant slip system in all conditions, particularly in the soft-oriented macrozone regions of the strong-macrozone condition loaded at 45 degrees. Shear strains of 10 times the appliedstrain were observed. Further investigations on the strong-macrozone condition loaded at 45 degrees to ED during standard and dwell fatigue demonstrated early failure in the dwell sample, with higher strain accumulation for dwell.

Modéliser la localisation de la déformation dans les géomatériaux de manière objective nécessite l'utilisation de méthodes capables de régulariser le problème aux limites en introduisant une longueur caractéristique. Dans le cadre de ce travail de thèse, nous avons choisis d'utiliser les milieux à microstructures de types second gradient. Une question, alors se pose quant à l'identification des paramètres constitutifs qui interviennent dans la formulation de ces milieux. L'objectif de cette thèse est de mettre en place une méthode d'identification d'une loi de comportement enrichie de type second gradient. L'identification paramétrique d'une loi constitutive écrite dans un formalisme de milieu enrichi de type second gradient local est étudiée. Une partie de l'identification peut-être réalisée à partir d'essais homogènes, mais l'identification complète nécessite de considérer des modes de déformation à forts gradients, comme cela est le cas en présence d'une localisation de la déformation. La procédure d'identification développée s'appuie sur des résultats expérimentaux d'essais mécaniques sur le grès de Vosges, pour lesquels le mode de déformation des échantillons a été caractérisé à l'aide de mesures de champs cinématiques, y compris en régime localisé. Un certain nombre d'observables peuvent être extraits de ces essais, qui servent à appuyer la comparaison entre calculs numériques et observations expérimentales. L'identification nécessite le calcul d'une matrice de sensibilité pour l'optimisation des observables. Afin de calculer cette matrice, deux études de sensibilité sont effectuées. Ces études consistent à évaluer l'influence de la variation de chaque paramètre constitutif sur les données sélectionnées. La première étude de sensibilité porte sur la partie homogène des essais, elle permet l'optimisation d'un certain nombre de paramètres qui jouent un rôle uniquement dans cette partie. La deuxième étude concerne le régime de déformation localisé. Celle-ci permet le calcul de la matrice de sensibilité. Grâce à cette matrice, il est possible de démarrer l'optimisation des observables. Ainsi, chaque observable pourra être optimisé indépendamment des autres. A l'issue de cette optimisation un jeu de paramètre est proposé. Il permet de reproduire de manière fiable, les essais expérimentaux à 20 et 30 MPa de confinement. / The strain localisation modelling of geomaterials requires the use of enhanced models, able to regularise the boundary value problem, by introducing a characteristic length. In this research work, we have chosen to use second gradient models. A question then arises, concerning the identification of second gradient constitutive parameters. This PhD research work aimed to develop an identification method to obtain theses parameters. The study proposed here covers a parametric identification of a constitutive law written in the local second gradient formalism. A part of this identification may be performed through homogenous tests, however the complete identification requires the consideration of high gradient deformation modes, as it is the case where localized deformation is observed. The identification procedure developed uses experimental results from mechanical tests on Vosges sandstone, for which the deformation mode was characterised by kinematic field measurement, including the localized regime. A certain number of observable data can be extracted from these tests, they are then used for the comparison between experimental and numerical data. It is necessary to compute the sensitivity matrix in order to optimise the observables data. In this sense, two sensitivity studies have been carried out, allowing the evaluation of the influence of each constitutive parameter on the selected data. This first analyse concern the homogenous part of the tests. Constitutive parameters involved in this part can be then optimized. The second analyse concerns the localized regime and the sensitivity matrix computation. Once this is achieved, the optimization of the observable data can be conducted. Each observable data can be optimised independently. A set of constitutive parameters is proposed. It allows a good matching between experimental and numerical results at two confining pressures ; 20 and 30 MPa.

In recent years there has been a growing demand to produce lightweight high pressure die cast (HPDC) parts for structural applications to decrease vehicle mass and to reduce manufacturing costs. Due to the coupled rapid heat flow and complex flow/deformation that occur in the process, the formation of microstructure and defects in HPDC are still not fully understood. Developing a better understanding of microstructure formation is essential to enable advances in die design and process optimisation, as well as alloy development, to improve the quality and productivity of HPDC components. Therefore, this thesis aims to enhance this understanding by conducting detailed microstructural analysis of samples produced in controlled HPDC experiments. In the first series of experiments, various microstructure characterisation techniques were used to study salient HPDC microstructural features. The microstructures of castings were characterised at different length scales, from the scale of the casting to the scale of the eutectic interlamellar spacing. The results show that the salient as-cast microstructural features, e.g. externally solidified crystals (ESCs), defect bands, surface layer, grain size distribution, porosity and hot tears were similar for both two HPDC-specific Al alloys used, AlSi4MgMn and AlMg5Si2Mn. The formation of these features has been explained by considering the influence of flow and solidification during each stage of the HPDC process. The formation of defect bands is further studied by investigating the ratio between band thickness ( ) and average grain size in the band ( ). Suitable methods for measuring w and dsb in HPDC have been developed. The w/dsb relationship of defect bands has been investigated in HPDC specimens from a range of alloys, casting geometries and band locations within castings. The bands were measured to be 7-18 mean grains wide. This is substantial evidence that defect bands form due to strain localisation in partially solidified alloys during cold-chamber and hot-chamber HPDC. At the end of solidification, dilatant shear bands contain a higher eutectic volume fraction and/or porosity content than adjacent material. In the cross-section of the AM50 Mg alloy, the centrally-located band contains a much higher volume fraction of concentrated porosity than the second-outermost band and insignificant porosity was found in the outermost band. The level of porosity in bands was attributed to the relative difficulty of feeding shrinkage for each band location. As the feeding of material during the intensification stage is important for the reduction of porosity, the influence of intensification pressure (IP) and gate thickness on the transport of material through the gate during the latter stages of HPDC were investigated. Microstructural characterisation of the gate region indicated a marked change in feeding mechanism with increasing IP and gate size. Castings produced with a high IP and/or thick gate contained a relatively low fraction of total porosity and shear band-like features existed through the gate, suggesting that semi-solid strain localisation in the gate is involved in feeding during the pressure intensification stage. When a low IP is combined with a thin gate, no shear band was observed in the gate and feeding was less effective, resulting in a higher level of porosity in the HPDC component. As equiaxed primary crystals are subjected to intense shear during HPDC, their agglomeration and bending behaviour were investigated in the last series of experiment. Samples produced by near-static cooling, HPDC and Thixomoulding®, where the solidifying crystals experience different levels of mechanical stresses, were characterised. The electron backscatter diffraction (EBSD) technique was used to acquire grain misorientation data which is linked to the crystal agglomeration and bending behaviour during solidification. The number fraction of low-energy grain boundaries in HPDC and Thixomoulded samples was substantially higher than in ‘statically cooled’ samples. This is attributed to the much higher shear stresses and pressure applied on the solidifying alloy in HPDC and Thixomoulding, which promote crystal collisions and agglomeration. In-grain misorientations were found to be significant only in branched dendritic crystals which were subjected to significant shear stresses. This is related to the increased bending moment acting on long protruding dendrite arms compared to more compact crystal morphologies.

Plagioclase is the most abundant mineral in the lower crust and it is thus important to constrain the behaviour of plagioclase during deformation. Anorthosites, which are plagioclase-rich rocks, are common in Archaean cratons but their origin and rheological importance is still debated. The aims of this thesis are to 1) describe a newly discovered Archaean anorthosite complex (Naajat Kuuat, SW Greenland), investigate its origin and a possible genetic relationship between the anorthosite and associated mafic-ultramafic rocks and 2) to study the rheology and deformation mechanisms in plagioclase-rich rocks. The main focus of this thesis is on the deformation studies. (1) Geochemical whole-rock analyses from the Naajat Kuuat complex are indicative for an origin near a subduction zone setting. A genetic link by crystal fractionation between the anorthosite and associated mafic-ultramafic units is inferred. (2) Deformation behaviour of plagioclase is assessed from analyses of three anorthosite units deformed during different conditions. Samples were analysed using the electron backscatter diffraction technique (EBSD) in combination with optical and chemical analyses. All three case studies show significant strain localisation related to grain size reduction. A wet anorthosite deformed at dry conditions (T ~675-700°C) was dynamically recrystallised. Continuous bands of recrystallised grains developed a texture yet display microstructures and grain relationships indicative for grain size sensitive creep, suggesting that the rheology followed a Newtonian flow law. In the other two studies, samples with initially dry and wet composition, respectively, have experienced deformation during fluid present conditions at T ~550-620°C. These two samples show that fluids effectively caused reactions, replacements and aided strain localisation during deformation at mid crustal conditions. / At the time of the doctoral defence the following papers were unpublished and had a status as follows: Paper 1: Manuscript; Paper 2 Manuscript; Paper 3 Manuscript.

Abstract The effect of austenite pancaking in the non-recrystallisation regime on microstructure and mechanical properties, especially bendability, was investigated in direct-quenched ultrahigh-strength strip steels with martensitic-bainitic microstructures. Lowering the finishing rolling temperature (FRT) increased total reduction in the non-recrystallisation region (R tot). Niobium microalloying increased Rtot while variations in C, Mn and Mo did not affect Rtot to the same extent as Nb. A decrease in the FRT increased the incidence of softer microstructures such as ferrite and granular bainite in the subsurface layers. The microstructures at the centreline were comprised of auto-tempered martensite with some bainite. An increase in Rtot strengthens the intensities of the ~{554}<225>α and ~{112}<110>α texture components at the centreline and the components ~{112}<111>α and ~{110}<112>α - {110}<111>α at the strip subsurface. Bendability is poorer with the bend axis perpendicular rather than parallel to the rolling direction (RD) and is further impaired with increasing hardness below the sheet surface. An intense ~{112}<111>α shear texture combined with upper bainite containing MA islands in the subsurface region is shown to be detrimental to bendability when the bend axis is perpendicular to the RD. This anisotropy of bendability can be explained by the appearance of geometric softening in grain clusters belonging to this texture component when the bend axis is perpendicular to the RD. Shear localisation is prevented, however, by the presence of a sufficiently thick subsurface microstructure having adequate work hardening capacity, i.e., ferrite + granular bainite rather than ferrite + upper bainite. The strain required to initiate strain localisation can be increased and good bendability thereby achieved—even in the presence of detrimental texture components—by ensuring the presence of a sufficiently soft subsurface layer extending to a depth of approximately 5% of the total sheet thickness. The above beneficial microstructures can be obtained and good bendability ensured in direct-quenched strip steel with a yield stress above 900 MPa together with good impact toughness, provided a suitable combination of chemical composition and processing parameters is selected and sufficient attention is paid to steelmaking operations to obtain a proper inclusion structure. / Tiivistelmä Austeniitin muokkauksen vaikutusta mikrorakenteeseen ja mekaanisiin ominaisuuksiin, erityisesti särmättävyyteen, tutkittiin suorasammutetuilla martensiittis-bainiittisilla suurlujuusnauhateräksillä. Kuumavalssauksen lopetuslämpötilan lasku kasvatti austeniitin kokonaisreduktiota ei-rekristallisaatioalueella. Mikroseostus niobilla kasvatti myös kokonaisreduktiota, kun taasen muutokset C-, Mn- ja Mo -pitoisuuksissa eivät vaikuttaneet yhtä voimakkaasti. Valssauksen lopetuslämpötilan lasku kasvatti pehmeämpien mikrorakenteiden, kuten ferriitin ja granulaarisen bainiitin, määrää nauhan pintakerroksessa. Terästen keskilinjan mikrorakenteet koostuivat pääasiassa itsepäässeestä martensiitista sekä pienestä määrästä bainiittia. Kokonaisreduktion kasvu voimisti ~{554}<225>α - ja ~{112}<110>α -tekstuurikomponentteja keskilinjalla sekä ~{112}<111>α- ja ~{110}<112>α - {110}<111>α -komponentteja nauhan pintakerroksessa. Särmättävyys oli huonompi särmän ollessa poikittain valssaussuuntaan nähden kuin pitkittäin. Pintakerroksen kovuuden kasvu heikensi särmättävyyttä. Pintakerroksen voimakas ~{112}<111>α -leikkaustekstuuri, yläbainiitin ja MA-saarekkeiden läsnä ollessa, osoittautui haitalliseksi särmän ollessa poikittain valssaussuuntaan nähden. Särmättävyyden anisotrooppisuus voidaan selittää geometrisella pehmenemisellä rakeissa, joissa kyseinen tekstuurikomponentti on voimakas. Leikkausmyötymän paikallistuminen estyy, kun pinnassa on riittävän paksu hyvän muokkauslujittumiskyvyn omaava kerros, mikä sisältää esim. ferriittiä ja granulaarista bainiittia, mutta ei ferriittiä ja yläbainiittia. Särmättävyys osoittautui pysyvän hyvänä huolimatta haitallisesta tekstuurikomponentista, kun pehmeä pintakerros ulottui noin 5 % syvyydelle levyn paksuudesta. Edellä mainitut mikrorakenteet ja hyvä särmättävyys voidaan saavuttaa suorasammutetuilla yli 900 MPa myötölujuuden nauhateräksillä yhdessä hyvän iskusitkeyden kanssa, kunhan valitaan sopiva kemiallisen koostumuksen ja valmistusparametrien yhdistelmä sekä kiinnitetään huomiota teräksen sulkeumapuhtauteen.

Nous présentons deux approches différentes pour décrire le couplage hydromécanique des géomatériaux. Dans une approche de type phénoménologique nous traitons le milieu poreux comme un milieu continu équivalent dont les interactions entre la phase fluide et le squelette solide constituent le couplage du mélange à l'échelle macroscopique. En caractérisant le comportement de chaque phase nous arrivons à décrire le comportement couplé du milieu couplé saturé.Nous utilisons cette approche pour modéliser des essais expérimentaux faits sur un cylindre creux pour une roche argileuse (argile de Boom). Les résultats expérimentaux montrent de façon claire que le comportement de cette roche est fortement anisotrope. Nous avons choisi de modéliser ces essais en utilisant une lois de comportement élasto-plastique pour laquelle la partie élastique est transversalement isotrope.Le problème aux conditions aux limites étudié met en évidence des déformations localisées autour du forage intérieur. Afin de décrire de façon objective le développement de ces bandes de cisaillement nous avons considéré un milieu continu local de type second gradient qui permet d'introduire une longueur interne. De ce fait nous avons pu étudier le problème d'unicité en montrant qu'un changement de la discrétisation temporelle du problème aux limites peut conduire à des solutions différentes.Dans la deuxième approche étudiée nous caractérisons la microstructure du matériau avec des grains et un réseau de canaux pour la phase fluide. À l'aide d'un processus numérique d'homogénéisation nous arrivons à calculer numériquement la contrainte du mélange et le flux massique. Cette méthode d'homogénéisation numérique a été implémentée dans un code aux éléments finis afin d'obtenir des résultats macro. Une validation de l'implentation est proposée pour des calculs en mecanique pure et en hydromécanique. / We present two different approaches to describe the hydromechanical behaviour of geomaterials. In the first approach the porous media is studied through an equivalent continuum media where the interaction between the fluide and solid phases caracterize the coupling behaviour at the macroscale.We take into account this approach to model experimental tests performed over a hollow cylinder sample of clay rock (Boom Clay), considered for nuclear waste storage. The experimental results clearly show that the mechanical behaviour of the material is strongly anisotropic. For this reason we chose an elasto-plastic model based on Drucker-Prager criterion where the elastic part is characterized by cross anisotropy.The numerical results of boundary value problem clearly show localised strains around the inner hollow section. In order to regularize the numerical problem we consider a second gradient local continuum media with an enriched kinematic where an internal lenght can be introduced making the results mesh independent. The uniqueness study is carried out showing that changing the temporal discretization of the problem leads to different solutions.In the second approach we study the hydromechanical behaviour of a porous media that it is characterised by the microstructure of the material. The microstructure taken into account is composed by elastic grains, cohesives interfaces and a network of fluid channels. Using a periodic media a numerical homogenization (square finite element method) is considered to compute mass flux, stress and density of the mixture. In this way a pure numerical constitutive law is built from the microstructure of the media. This method has been implemented into a finite element code (Lagamine, Université de Liège) to obtain results at the macroscale. A validation of this implementation is performed for a pure mechanical boundary value problem and for a hydromechanical one.