The analysis presented in this thesis provides a methodology for grouted bolts design, based on empirical and analytical methods. Hence, the main objectives of this thesis are to offer practical means for better characterisation of poor to very poor rock masses, to better predict support pressure, and to develop an elasto-plastic analytical model for design of grouted bolts in tunnels excavated in such rock masses. To improve the applicability of the GSI (Geological Strength Index) in poor to very poor rock masses, using Broken Domain Structure (BSTR), Structure Rating (SR), and Intact Core Recovery (ICR), some modifications have been offered, resulting in the Modified-GSI. Applying rock-load height concept and Modified-GSI, an approach to estimate support pressure has been developed. The main advantage of this approach is its applicability in squeezing ground and anisotropic stress conditions. Numerical modelling was carried out in order to adjust the proposed support pressure equation. Considering convergence reduction approach, an elasto-plastic model based on the latest version of Hoek- Brown failure criterion has been developed for a more effective and practical grouted bolt design. The link between empirical approach and elasto-plastic solution makes it possible to reach more realistic and appropriate bolting pattern design. In this way, the need for the redesign procedure in the convergence reduction approach is eliminated. The results of the proposed elastic-plastic solution have been compared with a numerical model using FLAC2D, and a reasonable agreement was observed. The practical application of the developed methodology is depicted by an analysis of a case study in Turkey.

The purpose of this study is to investigate the plastic deformation behavior of a round bar at the roll-gap during the rolling process of a three-roll planetary mill. The analysis is carried out with the aid of a finite element program MARC adopting the large deformation - large strain theory and the updated lagrangian formulation (ULF). A mesh rezoning procedure is also adopted to improve the uncontrollable running error of elements turning inside out. The mesh system of the whole bar billet is created by using three-dimensional brick elements, and the three-dimensional elastic-plastic finite element model in MARC is chosen to perform the simulations of three-roll planetary rolling processes. The simulation examples consist of three groups. Firstly, three different friction coefficients are adopted to investigate the rolling process. Secondly, totally five different offset angles are used during the simulation of the rolling process. Finally, five different profiles of the roller are used to study the simulation of the rolling process. The successfully obtained numerical results, including equivalent von-Mises stress and plastic strain distributions, rolling force, rolling moment, billet speeds at the entrance and exit planes of the roll-gap are useful in designing the pass schedules of the three-roll planetary rolling processes.

Rapid development and stiff competition in material related industries such as the automotive, demand very high precision in end products in very quick time. The transformation of raw material into an intricate-shaped final product involves various intermediate steps like design, material selection, manufacturing processes, etc. In all these steps, an in-depth understanding of material behavior plays an important role. The available traditional methods such as trial-and-error, especially in the case of die design, become highly inefficient in terms of time and money. This, there is a growing interest in simulation of the final product in order to predict different parameters which are important in design and manufacturing. Currently available simulation techniques are based on existing theories of plasticity or large deformation. These theories have been developed over several decades and many theoretical and practical issues have been debated over the years. Though the theories have great utility in understanding and solving some practical problems, there are ranges of applications for which no acceptable models are available. Most of these theories are either materials or process-specific with oversimplified real physical situations using assumptions and empirical relations. Development of field equations from first principles to stimulate elasto-plastic deformation is one such, still a subject of on-going discussion. Materials and composites exhibit hysteresis even at very low stresses, i.e., inelasticity is always present under all types of loading. This observation shows that the representing constitutive relation cannot treat the elastic and plastic deformations separately. The deformation is due to changes in size and shape, and studies with varying strain rates show considerable material sensitivity to the rate of deformation. Therefore, a generalized field equation is developed from first principles in the Eulerian coordinate system using material resistance to changes in size and shape, and their rates. The formulation uses a unified approach representing continuous effect of elastic and plastic strains and strain rates. The field equation involves eight material parameters, viz. bulk modulus, shear modulus, material shear velocity, material bulk viscosity, and four more constants associated with activation points related to deviatoric and volumetric strains and plastic strain rates. The elastic moduli, bulk and shear, are constants, and so also the material viscosities, while plastic stain rates are functions of elastic strain rates. The field equation redces to Cauchy’s equation in the solid limit and Navier-Stokes equation in the fluid limit. Simple experimental measurements are suggested to obtain the numerical values of the material parameters. Uniaxial tension tests are carried out on commercially available mild steel and aluminium alloy at different strain rates to quantify any variations in the values of material parameters during large deformation. Experimental results and the classical understanding of material deformation reveal the constant nature of elastic moduli during large deformation and, from fluids, the viscosities seem to remain constant. Around the yield region, materials experience a sharp increase in absorbed energy which is modeled to represent the plastic strain rates. The variations and contributions from elastic and plastic strains, both volumetric and deviatoric, and the corresponding stresses are observed. The effects of strain rate on plastic stress and energy absorbed are investigated. The model is checked for different materials and loading conditions to ascertain the proposed changes to earlier theories. Available experimental data in the literature are used for this purpose. The analysis shows that, though the overall stress-strain relations of different materials look similar, their internal responses differ. The internal response of a material depends on various microstructural factors, like alloying elements, impurities, etc. The present model is able to capture those internal differences between various materials. Numerical solution of different plasticity problems have to be undertaken to ascertain the applicability, generality, realism, accuracy and feasibility of the model.

Ce travail de thèse se situe dans le contexte de l'évaluation du comportement permanent des enrobés bitumineux. L'objectif est de proposer un modèle mécanique pour les déformations permanentes des matériaux bitumineux et de l'appliquer à la prédiction du phénomène d'orniérage des chaussées. Dans un premier temps, un modèle tridimensionnel de viscoplasticité à plusieurs mécanismes et plusieurs critères est proposé. Ce modèle résulte du couplage d'un critère quadratique particularisé avec un critère de type Drucker-Prager linéaire. Il est capable de prendre en compte un certain nombre d'aspects du comportement mécanique des matériaux bitumineux, parmi lesquelles les déformations permanentes sous sollicitations cycliques. La validation de ce modèle s'effectue par la simulation de quelques essais de fluage cycliques. Dans un deuxième temps, une approche améliorée est proposée en présentant un modèle monosurfacique multi-mécanisme. Le nouveau modèle permet de simuler non seulement les sollicitations cycliques mais aussi les chargements monotones de fluage statique. Quelques validations sont présentées et montrent les capacités et la pertinence de ce modèle. Finalement, ce modèle est appliqué aux calculs de l'onriérage de chaussées bitumineuses à travers son implémentation au sein du module ORNI du code de calcul CESAR-LCPC.

Elasto-plastic shock waves in high-velocity compaction of spherical metal particles are the focus of this thesis which consists of four papers (A-D). The compaction process is modeled by a discrete element method while using elastic and plastic loading, elastic unloading and adhesion at contacts. Paper A investigates the dynamic compaction of a one-dimensional chain of homogenous particles. The development of the elasto-plastic shock waves, its propagation and influence on the compaction process are examined. Simulations yield information on the contact behavior, velocity of the particle and its deformation during dynamic compaction. Effects of changing loading parameters on the compaction process are also discussed. Paper B addresses the non-homogeneity in a chain having; particles of different sizes and materials, voids between the particles and particles with/without adhesion between them. Simulations show transmission and reflection of elasto-plastic shock wave during compaction process. The particle deformation during incident and reflected shocks and particle velocity fluctuations due to voids between particles are simulated. The effects of adhesion on particles separation during unloading stage are also discussed. Paper C develops a simulation model for a high-velocity compaction process with auxiliary pistons, known as relaxation assists, in a compaction assembly. The simulation results reveals that the relaxation assists offer; smooth compaction during loading stage, prevention of  the particle separation during unloading stage and conversion of  higher kinetic energy of hammer into particles deformation.  Furthermore, the influence of various loading elements on compaction process is investigates. These results support the findings of experimental work. Paper D further extends the one-dimensional case of Paper A and B into two-dimensional assembly of particles while adding friction between particles and between particles and container walls. Three particular cases are investigated including closely packed hexagonal, loosely packed random and a non-homogenous assembly of particles of various sizes and materials. Consistent with the one-dimensional case, primary interest is the linking of particle deformation with the elasto-plastic shock wave propagation. Simulations yield information on particle deformation during shock propagation and change in overall particles compaction with the velocity of the hammer. The force exerted by particles on the container walls and rearrangement of the loosely packed particles during dynamic loading are also investigated. Finally, the effects of presence of friction and adhesion on both overall particles deformation and compaction process are simulated. / QC 20110311

Zr-2.5Nb is currently used for pressure tubes in the CANDU (CANada Deuterium Uranium) reactor. A complete understanding of the deformation mechanism of Zr-2.5Nb is important if we are to accurately predict the in-reactor performance of pressure tubes and guarantee normal operation of the reactors. This thesis is a first step in gaining such an understanding; the deformation mechanism of ZrNb alloys at room temperature has been evaluated through studying the effect of texture and microstructure on deformation. In-situ neutron diffraction was used to monitor the evolution of the lattice strain of individual grain families along both the loading and Poisson’s directions and to track the development of interphase and intergranular strains during deformation. The following experiments were carried out with data interpreted using elasto-plastic modeling techniques: 1) Compression tests of a 100%Zr material at room temperature. 2) Tension and compression tests of hot rolled Zr-2.5Nb plate material. 3) Compression of annealed Zr-2.5Nb. 4) Cyclic loading of the hot rolled Zr-2.5Nb. 5) Compression tests of ZrNb alloys with different Nb and oxygen contents. The experimental results were interpreted using a combination of finite element (FE) and elasto-plastic self-consistent (EPSC) models. The phase properties and phase interactions well represented by the FE model, the EPSC model successfully captured the evolution of intergranular constraint during deformation and provided reasonable estimates of the critical resolved shear stress and hardening parameters of different slip systems under different conditions. The consistency of the material parameters obtained by the EPSC model allows the deformation mechanism at room temperature and the effect of textures and microstructures of ZrNb alloys to be understood. This work provides useful information towards manufacturing of Zr-2.5Nb components and helps in producing ideal microstructures and material properties for pressure tubes. Also it is helpful in guiding the development of new materials for the next generation of nuclear reactors. Furthermore, the large data set obtained from this study can be used in evaluation and improving current and future polycrystalline deformation models. / Thesis (Ph.D, Mechanical and Materials Engineering) -- Queen's University, 2008-09-05 13:51:30.42

The internal combustion engine is still at the heart of the vast majority of vehicles manufactured worldwide today. For these applications reciprocating pistons are typically employed to convert the pressures generated by internal combustion into mechanical work required by the vehicle. Of the energy supplied to the engine as a whole approximately 17% is lost by means of mechanical friction. The piston ring - liner and piston skirt - liner conjunctions contribute approximately 30% of the overall friction losses in almost equal proportions. It is, therefore, important to note that reduction in piston assembly friction would have a significant effect on the fuel consumption and, therefore, performance of engines manufactured today. In order to reduce the effect of friction it is of critical importance that the model and predictions made alongside the design of engine components accurately represent the real incycle conditions encountered in practice. Much of the published research to date has excluded the effects of global thermo-elastic distortions on the lubrication of the piston skirt. In cases where this effect has been studied, it has been for relatively low engine speeds or loads on relatively stiff conjunctions. In motorsport applications the expected component lifespans are much shorter than in the usual OEM production vehicles. Reduction in component mass, particularly in reciprocating components has been at the centre of these recent gains. The effect of mass reduction coupled with the increased BMEP observed in high performance engines emphasises the importance of underlying mechanisms of lubrication. This thesis develops the modelling methodology for piston skirt-cylinder liner conjunction for the motorsport and high performance engine applications. It presents a multi-body, multiscale approach to the prediction of the lubrication conditions of the skirt-liner conjunction, incorporating realistic measured boundary conditions. It highlights the effect of inertial loading observed at high speeds in such applications. Using the methodology developed in this work, future improvements in friction may be accurately predicted though the use of the modular boundary and component contributions used throughout. Crucially though, the models created have been scrutinised and verified using instantaneous ultrasonic film thickness measurements non-invasively from the conjunction. One of the key findings of the thesis is that the component stiffness profiles have a significant effect on the dynamics of the piston assembly. The shape of the conjunction at a given instant, and thus the contact condition, is largely governed by the interaction between the themo-mechanical distortion of the contiguous solids, as well as changes in lubricant characteristic responses. The iso-viscous elastic mechanism of lubrication has been identified as being the dominant mechanism of lubrication.

Neste trabalho é apresentado a modelagem mecânica e numérica de um escoamento elastoviscoplástico tixotrópico, em termos dos campos de velocidade, pressão, tensão e parâmetro de estrutura. A discretização numérica é feita pelo Método de Elementos Finitos Estabilizado, também conhecido como Galerkin Mínimos Quadrados (GMQ), através de elementos quadrangulares bilineares. O clássico problema da cavidade é utilizado nas simulações, a fim de comparar a formulação e o código utilizados com os resultados conhecidos na literatura. Além disso, apresenta-se o estudo de materiais elasto-viscoplástico tixotrópico em uma contração abrupta na escala 4:1, utilizando a formulação descrita e uma nova função viscosidade para fluidos viscoplásticos, denominada função Viscoplástica Harmônica (VPH). Resultados envolvendo a função VPH são introduzidos e discutidos pela primeira vez nesta tese e apresenta um ótimo ajuste de curva, quando comparada com outras funções disponíveis na literatura. Além da fácil implementação, essa função também apresenta um platô para as altas e baixas viscosidades que são fisicamente realistas, visto que não é possível uma viscosidade infinita ou nula. O menor tempo computacional é também uma característica perceptível nas simulações usando a nova função viscoplástica, isso é um atributo do seu equacionamento que não depende de um termo exponencial, como outros modelos. O estudo de qualidade de malha também é apresentado a fim de garantir a escolha do domínio discreto adequado. Apesar do uso de elementos de ordem inferior, o método GMQ mostrou-se estável na aproximação numérica de todos os problemas dispostos, garantindo até mesmo a análise sobre os efeitos da cinemática, da elasticidade e da tixotropia no escoamento dos fluidos dentro da contração abrupta. / In this work the mechanical and numerical modeling of a thixotropic elasto-viscoplastic flow in terms of the velocity, pressure, stress and structure parameter is presented. Numerical discretization is done by the Stabilized Finite Element Method, also known as Galerkin Least Squares (GLS), through bilinear quadrangular elements. The classical liddriven cavity problem is used in the simulations in order to compare the formulation and code used with the results in the literature. In addition, the study of elasto-viscoplastic thixotropic materials in a 4:1 abrupt contraction using the described formulation and a new viscosity function for viscoplastic fluids, called the Harmonic Viscoplastic Function (HVP), is presented. Results involving the HVP function are introduced and discussed for the first time in this thesis and present a better curve fit when compared to other functions available in the literature. Besides to easy implementation, this function also features a plateau for high and low viscosities that are physically realistic, since infinite or zero viscosity is not possible. The shortest computational time is also a perceptible feature in the simulations using the new viscoplastic function, this is an attribute of its equation that does not depend on an exponential term like other models. The mesh quality study is also presented in order to ensure the choice of the appropriate discrete domain. Despite the use of lower-order elements, the GLS method proved to be stable in the numerical approximation of all the problems, guaranteeing even the analysis of the effects of kinematics, elasticity and thixotropy on fluid flow within the abrupt contraction.

A maioria dos líquidos encontrados na natureza são não newtonianos e o estudo do seu comportamento reológico tem uma importância significante em diferentes áreas da engenharia. Entre eles, existe uma classe de fluidos que exibem pequena deformação aparente quando sujeitos a um nível de tensões inferior a uma tensão limite de escoamento, referido como comportamento viscoplástico. Nesta classe de materiais, alguns apresentam também comportamento elástico quando submetidos a baixas taxas de cisalhamento. A presente Tese tem como objetivo o estudo numérico de escoamentos bidimensionais em regime permanente de fluidos elasto-viscoplásticos através de uma expansão-contração planar. O modelo mecânico é definido pelas equações de conservação de massa e de balanço de momentum acopladas ao modelo elasto-viscoplástico proposto nesta Tese. Esta modelagem é aproximada por um método de elementos finitos multi-campos estabilizado baseado na metodologia de Galerkin mínimos-quadrados que possui como variáveis primais os campos de tensão extra polimérica, velocidade e pressão. As condições de compatibilidade entre os sub-espaços de elementos finitos para tensão extra-velocidade e velocidade-pressão são violadas, permitindo assim a utilização de interpolações de igual ordem. O método estabilizado foi implementado no código de elementos finitos para fluidos não newtonianos em desenvolvimento no Laboratório de Mecânica dos Fluidos Aplicada e Computacional (LAMAC) da Universidade Federal do Rio Grande do Sul. Nesta Tese é adotada uma metodologia alternativa para a definição das zonas rígidas do escoamento como sendo a posição onde a taxa de cisalhamento é igual a um valor dado pela relação de parâmetros reológicos do fluido, especificamente a tensão limite de escoamento e a viscosidade newtoniana para baixas taxas de cisalhamento. Nas simulações numéricas realizadas, o tempo de relaxação adimensional, o número de salto, o coeficiente power-law, a vazão adimensional e a massa específica adimensional são variados de forma a avaliar de que modo influenciam na dinâmica de escoamentos elastoviscoplásticos. Os resultados obtidos estão qualitativamente de acordo com a literatura, atestando a estabilidade da formulação empregada. / Non-Newtonian fluids are the majority of liquids found in nature and the study of their rheological behavior has a significant importance on different areas of engineering. Among them, there is a class of materials that exhibits little apparent deformation when subjected to a stress level behind an yield stress, referenced as viscoplastic material. In this class of materials, some fluids also exhibit elastic behavior at low shear rates. The present work aimed to a numerical study of two-dimensional steady state laminar flows of elasto-viscoplastic fluids through a planar expansion-contraction cavity. The mechanical model was defined by the mass conservation and momentum balance equations coupled to the elasto-viscoplastic model porposed in this work. This modeling has been approximated by a stabilized multi-field finite element method based on the Galerkin least-squares methodology, having as primal variables the elastic extra-stress component, velocity and pressure fields. In this way, the compatibility conditions between the extra-stress-velocity and pressure-velocity (Babuška- Brezzi condition) finite element subspaces are violated, allowing to use equal-order finite element interpolations. The stabilized method has been implemented in the finite element code for non-Newtonian fluids under development at the Laboratory of Applied and Computational Fluid Mechanics (LAMAC) of the Federal University of Rio Grande do Sul. An alternative methodology is adopted to define the yield surface as the position where the strain rate is equal to a value given by the relation of the rheological parameters of the fluid, namely the yield stress and the viscosity at low shear rates. In the performed numerical simulations, the non-dimensional relaxation time, the jump number, the power-law coefficient, the non-dimensional flow rate, and the non-dimensional density are varied in order to evaluate their influence on the elasto-viscoplastic fluid dynamics. All results found are in qualitatively accordance with the affine literature, and attesting the good stability features of the formulation.

A maioria dos líquidos encontrados na natureza são não newtonianos e o estudo do seu comportamento reológico tem uma importância significante em diferentes áreas da engenharia. Entre eles, existe uma classe de fluidos que exibem pequena deformação aparente quando sujeitos a um nível de tensões inferior a uma tensão limite de escoamento, referido como comportamento viscoplástico. Nesta classe de materiais, alguns apresentam também comportamento elástico quando submetidos a baixas taxas de cisalhamento. A presente Tese tem como objetivo o estudo numérico de escoamentos bidimensionais em regime permanente de fluidos elasto-viscoplásticos através de uma expansão-contração planar. O modelo mecânico é definido pelas equações de conservação de massa e de balanço de momentum acopladas ao modelo elasto-viscoplástico proposto nesta Tese. Esta modelagem é aproximada por um método de elementos finitos multi-campos estabilizado baseado na metodologia de Galerkin mínimos-quadrados que possui como variáveis primais os campos de tensão extra polimérica, velocidade e pressão. As condições de compatibilidade entre os sub-espaços de elementos finitos para tensão extra-velocidade e velocidade-pressão são violadas, permitindo assim a utilização de interpolações de igual ordem. O método estabilizado foi implementado no código de elementos finitos para fluidos não newtonianos em desenvolvimento no Laboratório de Mecânica dos Fluidos Aplicada e Computacional (LAMAC) da Universidade Federal do Rio Grande do Sul. Nesta Tese é adotada uma metodologia alternativa para a definição das zonas rígidas do escoamento como sendo a posição onde a taxa de cisalhamento é igual a um valor dado pela relação de parâmetros reológicos do fluido, especificamente a tensão limite de escoamento e a viscosidade newtoniana para baixas taxas de cisalhamento. Nas simulações numéricas realizadas, o tempo de relaxação adimensional, o número de salto, o coeficiente power-law, a vazão adimensional e a massa específica adimensional são variados de forma a avaliar de que modo influenciam na dinâmica de escoamentos elastoviscoplásticos. Os resultados obtidos estão qualitativamente de acordo com a literatura, atestando a estabilidade da formulação empregada. / Non-Newtonian fluids are the majority of liquids found in nature and the study of their rheological behavior has a significant importance on different areas of engineering. Among them, there is a class of materials that exhibits little apparent deformation when subjected to a stress level behind an yield stress, referenced as viscoplastic material. In this class of materials, some fluids also exhibit elastic behavior at low shear rates. The present work aimed to a numerical study of two-dimensional steady state laminar flows of elasto-viscoplastic fluids through a planar expansion-contraction cavity. The mechanical model was defined by the mass conservation and momentum balance equations coupled to the elasto-viscoplastic model porposed in this work. This modeling has been approximated by a stabilized multi-field finite element method based on the Galerkin least-squares methodology, having as primal variables the elastic extra-stress component, velocity and pressure fields. In this way, the compatibility conditions between the extra-stress-velocity and pressure-velocity (Babuška- Brezzi condition) finite element subspaces are violated, allowing to use equal-order finite element interpolations. The stabilized method has been implemented in the finite element code for non-Newtonian fluids under development at the Laboratory of Applied and Computational Fluid Mechanics (LAMAC) of the Federal University of Rio Grande do Sul. An alternative methodology is adopted to define the yield surface as the position where the strain rate is equal to a value given by the relation of the rheological parameters of the fluid, namely the yield stress and the viscosity at low shear rates. In the performed numerical simulations, the non-dimensional relaxation time, the jump number, the power-law coefficient, the non-dimensional flow rate, and the non-dimensional density are varied in order to evaluate their influence on the elasto-viscoplastic fluid dynamics. All results found are in qualitatively accordance with the affine literature, and attesting the good stability features of the formulation.