published_or_final_version / Mechanical Engineering / Doctoral / Doctor of Philosophy

A dissertation submitted to the Faculty of Engineering and the Built Environment, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Master of Science in Engineering Johannesburg, 11 October 2016 / Refractory lining failure of damaged magnesia bricks and used alumina bricks was investigated by XRF, XRD, SEM-EDS analysis and computational thermochemistry (phase diagrams). In addition, the effect of oxygen partial pressure towards the refractory lining and alkali sulphate ratio were also determined. The presence of low melting phases of KCl, (Na, K) Cl, K2SO4 and CaSO4 compromised the refractoriness of the magnesia bricks because they are liquid at temperatures below clinkerisation temperature (1450 °C). Sodium oxide and potassium oxide in the kiln feed and chlorine and sulphur in the kiln gas atmosphere migrated into the magnesia brick and react to form KCl, (Na, K) Cl and K2SO4. Components of the magnesia brick, CaO reacted with the excess sulphur in the kiln gas atmosphere forming CaSO4. The presence of these impurity phases indicated that the magnesia bricks suffered chemical attack. Potassium and part of components of high-alumina brick reacted to form K2 (MgSi5O12) impurity phase. Phase diagram predictions indicated that the presence of sodium at any given concentration automatically results in liquid formation in the high alumina brick. This confirms that the chemical attack is also the cause of the failure of the high alumina brick. The analysis of the microstructures of both unused and damaged magnesia bricks revealed that the fracture was predominantly intergranular whereas, in high alumina brick, the fracture was transgranular. The absence of evidence of micro-cracks in both magnesia and alumina bricks rules out thermal shock as a failure mechanism. The absence of clinker species and phases in the examined magnesia and alumina bricks indicated that corrosion by clinker diffusion was absent. The partial pressure of oxygen is low (1.333×10−4 atm), it indicates the stability of Fe3O4 and Mn3O4 and therefore does not favour the oxidation of Fe3O4 to formation of Fe2O3 and Mn3O4 to formation of Mn2O3. The values of alkali sulphate ratio indicated that the kiln operating conditions were favourable for chemical attack to occur. / MT2017

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All materials are heterogeneous at various scales of observation. The influence of material heterogeneity on nonuniform response and microstructure evolution can have profound impact on continuum thermomechanical response at macroscopic "engineering" scales. In many cases, it is necessary to treat this behavior as a multiscale process. This research developed a hierarchical multiscale approach for modeling microstructure evolution. A theoretical framework for the hierarchical homogenization of inelastic response of heterogeneous materials was developed with a special focus on scale invariance principles needed to assure physical consistency across scales. Within this multiscale framework, the second gradient is used as a nonlocal kinematic link between the response of a material point at the coarse scale and the response of a neighborhood of material points at the fine scale. Kinematic consistency between two scales results in specific requirements for constraints on the fluctuation field. A multiscale internal state variable (ISV) constitutive theory is developed that is couched in the coarse scale intermediate configuration and from which an important new concept in scale transitions emerges, namely scale invariance of dissipation. At the fine scale, the material is treated using finite element models of statistical volume elements of microstructure. The coarse scale is treated using a mixed-field finite element approach. The coarse scale constitutive equations are implemented in a finite deformation hyperelastic inelastic integration scheme developed for second gradient constitutive models. An example problem based on an idealized porous microstructure is presented to illustrate the approach and highlight its predictive utility. This example and a few variations are explored to address the boundary-value-problem dependent nature of length scale parameters employed in nonlocal continuum theories. Finally, strategies for developing meaningful kinematic ISVs, free energy functions, and the associated evolution kinetics are presented. These strategies are centered on the goal of accurately representing the energy stored and dissipated during irreversible processes.

Polymer nanocomposites (PNCs) have gained significant interest because they have outstanding performance that allows cost reduction, weight reduction, and product improvement. This research study focuses on the manufacture and characterization of PNCs in order to explore their potential in automotive applications. More specifically, polypropylene (PP) nanocomposites reinforced with xGnP and nanokaolin were fabricated by manufacturing methods that optimize their performances. Exfoliated graphite nanoplatelets (xGnP) are promising nanofillers that are cost effective and multifunctional with superior mechanical, thermo-mechanical and electrical properties. Nanokaolin is a newly introduced natural mineral mind in Georgia that has not been studied as of now. PNCs reinforced with these two nanofillers were characterized in terms of mechanical, thermo-mechanical, and various other properties, and then compared to talc- reinforced PP composites, which are the current state of the art for rear bumpers used by Honda Motor. Characterization results indicated that xGnP had better performance than talc and nanokaolin. Furthermore, the addition of xGnP introduces electrical conductivity in the PNCs, leading to more potential uses for PNCs in automotive applications such as the ability to be electrostatic painted. In order to fabricate PNCs with a desired conductivity value, there is need for a design tool that can predict electrical conductivity. Existing electrical conductivity models were examined in terms of model characteristics and parameters, and model predictions were compared to the experimental data. The percolation threshold is the most important parameter in these models, but it is difficult to determine experimentally, that is why a correlation between thermo-mechanical properties and electrical conductivity is also investigated in this study.

Under consideration is the finite-size scaling of two thermomechanical responses of random heterogeneous materials. Stochastic mechanics is applied here to the modeling of heterogeneous materials in order to construct the constitutive relations. Such relations (e.g. Hooke's Law in elasticity or Fourier's Law in heat transfer) are well-established under spatial homogeneity assumption of continuum mechanics, where the Representative Volume Element (RVE) is the fundamental concept. The key question is what is the size L of RVE? According to the separation of scales assumption, L must be bounded according to d<L<<LMacro where d is the microscale (or average size of heterogeneity), and LMacro is the macroscale of a continuum mechanics problem. Statistically, for spatially ergodic heterogeneous materials, when the mesoscale is equal to or bigger than the scale of the RVE, the elements of the material can be considered homogenized. In order to attain the said homogenization, two conditions must be satisfied: (a) the microstructure's statistics must be spatially homogeneous and ergodic; and (b) the material's effective constitutive response must be the same under uniform boundary conditions of essential (Dirichlet) and natural (Neumann) types. / In the first part of this work, the finite-size scaling trend to RVE of the Darcy law for Stokesian flow is studied for the case of random porous media, without invoking any periodic structure assumptions, but only assuming the microstructure's statistics to be spatially homogeneous and ergodic. By analogy to the existing methodology in thermomechanics of solid random media, the Hill-Mandel condition for the Darcy flow velocity and pressure gradient fields was first formulated. Under uniform essential and natural boundary conditions, two variational principles are developed based on minimum potential energy and complementary energy. Then, the partitioning method was applied, leading to scale dependent hierarchies on effective (RVE level) permeability. The proof shows that the ensemble average of permeability has an upper bound under essential boundary conditions and a lower bound under uniform natural boundary conditions. / To quantitatively assess the scaling convergence towards the RVE, these hierarchical trends were numerically obtained for various porosities of random disk systems, where the disk centers were generated by a planar Poisson process with inhibition. Overall, the results showed that the higher the density of random disks---or, equivalently, the narrower the micro-channels in the system---the smaller the size of RVE pertaining to the Darcy law. / In the second part of this work, the finite-size scaling of effective thermoelastic properties of random microstructures were considered from Statistical to Representative Volume Element (RVE). Similarly, under the assumption that the microstructure's statistics are spatially homogeneous and ergodic, the SVE is set-up on a mesoscale, i.e. any scale finite relative to the microstructural length scale. The Hill condition generalized to thermoelasticity dictates uniform essential and natural boundary conditions, which, with the help of two variational principles, led to scale dependent hierarchies of mesoscale bounds on effective (RVE level) properties: thermal expansion strain coefficient and stress coefficient, effective stiffness, and specific heats. Due to the presence of a non-quadratic term in the energy formulas, the mesoscale bounds for the thermal expansion are more complicated than those for the stiffness tensor and the heat capacity. To quantitatively assess the scaling trend towards the RVE, the hierarchies are computed for a planar matrix-inclusion composite, with inclusions (of circular disk shape) located at points of a planar, hard-core Poisson point field. Overall, while the RVE is attained exactly on scales infinitely large relative to microscale, depending on the microstructural parameters, the random fluctuations in the SVE response become very weak on scales an order of magnitude larger than the microscale, thus already approximating the RVE. / Based on the above studies, further work on homogenization of heterogeneous materials is outlined at the end of the thesis. / Keywords: Representative Volume Element (RVE), heterogeneous media, permeability, thermal expansion, mesoscale, microstructure.

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Les mousses minérales sont des matériaux alvéolaires utilisables en isolation thermique répartie. L’objectif de ces travaux de recherche est de développer, à partir d’une suspension très concentrée de liants hydrauliques, des mousses légères présentant de bonnes performances mécaniques et thermiques. L’introduction de tensioactif est nécessaire à la formation des mousses minérales. Six molécules tensioactives sont sélectionnées dans cette étude. Leurs capacités à réduire la tension de surface et à stabiliser une mousse aqueuse sont évaluées. Deux groupes de tensioactifs sont distingués sur la base de différents critères : tension de surface, CMC, stabilité de la mousse. Les suspensions minérales concentrées sont des fluides à seuil. L’étude du comportement de bulles formées dans de tels fluides est réalisée à l’aide d’un fluide à seuil modèle transparent, le Carbopol®, et d’un système d’injection à pression contrôlée. Le seuil de mise en écoulement affecte les conditions de formation, de croissance, de stabilité et d’évolution de la forme des bulles en modifiant la distribution des pressions au voisinage de la bulle. L’étude permet de proposer une équation de Laplace modifiée prenant en compte l’influence de la sphéricité et du seuil de cisaillement. L’introduction du tensioactif affecte les conditions de contact entre bulles et permet de contrôler le risque de coalescence. En cas de rupture de membrane, la présence du seuil de cisaillement conduit à une géométrie particulière des bulles coalescées. Les liants minéraux choisis sont un sulfate de calcium anhydre particulièrement réactif, un ciment Portland et un ciment prompt. La formulation des suspensions découle d’un critère de fluidité. La pâte fraîche est caractérisée par un seuil de cisaillement faible. Sa masse volumique apparente dépend de la nature et du dosage en tensioactif. Les mousses minérales sont générées à partir d’une composition identique. Deux méthodes de moussage traditionnelles : malaxage simple et mousse préformée et une méthode alternative : la méthode dissociée, sont exploitées. Les meilleures performances thermomécaniques des mousses durcies sont obtenues avec la méthode dissociée, méthode spécifique au laboratoire et peu énergivore. Un groupe de tensioactifs permet d’obtenir des mousses peu denses satisfaisant simultanément aux critères de performances thermomécaniques fixés. Pour ces tensioactifs, un dosage caractéristique est identifié permettant une optimisation des performances mécaniques. Des visualisations réalisées au MEB révèlent des modifications sensibles de la structure cristalline fonction du tensioactif employé et de son dosage. Les structures les plus fines et homogènes sont les plus résistantes. Les performances des mousses et leur structure porale sont donc liées. Pour analyser quantitativement la structure porale, les distributions alvéolaires surfaciques sont construites puis comparées aux distributions alvéolaires volumiques obtenues par tomographie. Une méthode analytique de passage 2D/3D est créée en s’appuyant sur les principes de la stéréologie. Un coefficient de correction est proposé pour tenir compte de la représentativité de la surface étudiée. La maîtrise de toutes les étapes de fabrication des mousses minérales ainsi que la compréhension des phénomènes physiques intervenant tout au long de la production d’une mousse (de la suspension minérale jusqu’à la mousse durcie) permettent d’obtenir des produits satisfaisant les objectifs fixés : légèreté, isolation et caractère porteur. / Mineral foams are cellular materials usable as thermal insulation solution. The purpose of these PhD researches is to develop lightweight foams with good thermal and mechanical performances realized from highly concentrated mineral suspension. Surfactant addition is required for foaming. Six surfactants molecules are selected. Their abilities to reduce surface tension and to stabilize aqueous foam are evaluated. Two surfactants groups are detected based on different criteria: surface tension, CMC and aqueous foam stability. Concentrated mineral suspensions are yield stress fluids. The study of bubbles behavior in such fluids is performed with a transparent yield stress fluid, Carbopol® and an injection device with controlled pressure. Yield stress impacts bubbles creation, growth, stability and shape by changing local pressure distribution in the fluid nearby bubble. The study proposes a revised Laplace law depending on yield stress and bubble sphericity. Contact conditions between bubbles are influenced by surfactant addition allowing to control coalescence phenomena. In case of inter-bubbles membrane breakage, presence of yield stress leads to particular geometry of the coalesced bubbles. Mineral binders selected are a highly reactive anhydrous calcium sulfate, ordinary Portland and prompt cements. Mineral suspension formulations arise from expected fluidity criterion. Fresh paste is characterized by a low yield stress. Its bulk density depends on surfactant nature and content. Mineral foams are created with same composition. Two traditional foaming methods: mix-foaming and pre-foaming and an alternative one, the dissociated method are employed. Best thermo-mechanical performances are achieved with the dissociated method, a specific method of the laboratory. A surfactant group leads to lightweight foams which simultaneously fulfills both thermal and mechanical targeted objectives. For these surfactants a characteristic content is found leading to optimized mechanical performances. Visualizations performed with SEM reveal sensitive crystalline structure modifications depending on surfactant nature and content. Thinner and more homogeneous structures are associated with the best mechanical performances which demonstrates the existing link between the porous structure and mineral foams mechanical performances. To quantitatively evaluate porous structure, surface bubble-size distributions are built and then compared to volume bubble-size distributions obtained by tomography analysis. An analytic method linking 2D and 3D distributions is created based on stereology principles. A correction coefficient is proposed to take into account the analyzed representative surface. By controlling all production steps and associated physical phenomena during mineral foams production (from mineral suspension to solid foams), products satisfying all targeted objectives are realized: lightness, insulation and load-bearing ability.

In this thesis, the thermomechanical approach with internal variables has been thoroughly analyzed. This approach is based on the combination of thermodynamic principles and continuum mechanics. Therefore it reflects the physical essence of constitutive behavior of materials. Based on this approach, a one-dimensional constitutive model for the two-way shape memory effect and a one-dimensional constitutive model for piezoceramics have been developed, respectively. In modeling the two-way shape memory effect, a residual stress σ_re is introduced as a controlling parameter for the two-way shape memory effect. A further refinement of the transformation kinetics expression for two-way shape memory is derived. It is demonstrated that the material parameters required by this model can be calculated or measured using a standard materials testing apparatus. A numerical study is conducted and the effectiveness of this model is verified. In the constitutive modeling of piezoceramics, a new internal state variable is introduced to relate the macroscopic behavior of a piezoceramic with its micro-properties. A phenomenological formulation of polarization reversal is proposed, and then a fully-coupled thermo-electro-mechanical model is developed. It is shown that the theory developed can describe the electromechanical behavior of piezoceramics well. / Master of Science