Modeling of Polymer Clay Nanocomposite for a Multiscale Approach

The mechanical property enhancement of polymer reinforced with nano-thin clay platelets (of high aspect ratio) is associated with a high polymer-filler interfacial area per unit volume. The ideal case of fully separated (exfoliated) platelets is generally difficult to achieve in practice: a typical nanocomposite also contains multilayer stacks of intercalated platelets. Here we use numerical modelling to investigate how the platelet properties affect the overall mechanical properties. The configuration of platelets is modelled using a statistical interpretation of the Representative Volume Element (RVE) approach, in which an ensemble of "sample" heterogeneous material is generated (with periodic boundary conditions). A simple Monte Carlo algorithm is used to place non-intersecting platelets in the RVE according to a specified set of statistical distributions. The effective stiffness of the platelet-matrix system is determined by measuring the stress (using standard Finite Element analysis) produced as a result of applying a small deformation to the boundaries, and averaging over the entire statistical ensemble. In this work we determine the way in which the platelet properties (curvature, filling fraction, stiffness, aspect ratio) and the number of layers in the stack affect the overall stiffness enhancement of the nanocomposite. Thus, we bridge the gap between behaviour on the macroscopic scale with that on the scale of the nano-reinforcement, forming part of a multi-scale modelling framework.Comment: 39 pages, 19 figure

Modelling of polymer clay nanocomposites for a multiscale approach.

YesThe mechanical property enhancement of polymer reinforced with nano-thin clay platelets (of high aspect ratio) is associated with a high polymer-filler interfacial area per unit volume. The ideal case of fully separated (exfoliated) platelets is generally difficult to achieve in practice: a typical nanocomposite also contains multilayer stacks of intercalated platelets. Here we use numerical modelling to investigate how the platelet properties affect the overall mechanical properties. The configuration of platelets is modelled using a statistical interpretation of the Representative Volume Element (RVE) approach, in which an ensemble of "sample" heterogeneous material is generated (with periodic boundary conditions). A simple Monte Carlo algorithm is used to place non-intersecting platelets in the RVE according to a specified set of statistical distributions. The effective stiffness of the platelet-matrix system is determined by measuring the stress (using standard Finite Element analysis) produced as a result of applying a small deformation to the boundaries, and averaging over the entire statistical ensemble. In this work we determine the way in which the platelet properties (curvature, filling fraction, stiffness, aspect ratio) and the number of layers in the stack affect the overall stiffness enhancement of the nanocomposite. Thus, we bridge the gap between behaviour on the macroscopic scale with that on the scale of the nano-reinforcement, forming part of a multi-scale modelling framework

Multi Scale Modeling of The Elastic Properties of Polymer-Clay Nanocomposites

RÉSUMÉ Les Nanocomposites Polymères-Argiles (NPA) sont reconnus pour leur capacité à améliorer les propriétés mécaniques de polymères bruts, et ce, même dans le cas de faibles fractions volumiques de nano-argiles. Cette amélioration est attribuable aux rapports de forme élevés ainsi qu'aux propriétés mécaniques des nano-argiles. En outre, la zone d'interphase résultant d'une modification des chaînes de polymère à proximité des nano-argiles joue un rôle important dans la rigidité de NPA. Plusieurs approches analytiques existent pour la prédiction des propriétés élastiques de NPA, allant des modèles simplifiés en deux étapes aux modèles plus sophistiqués. Il n'existe toutefois aucune étude ayant déjà vérifié l'exactitude de ces modèles. Par ailleurs, les modèles numériques servant à évaluer leurs homologues analytiques sont encore loin de pouvoir modéliser la microstructure réelle de NPA. Par exemple, la majorité des modèles n'ont pas tenu compte de la microstructure tridimensionnelle de particules aléatoirement réparties, du rapport de forme élevé des nano-argiles, ou de l'intégration explicite de phases constitutives. Plus important encore, la plupart des études numériques ont été développées sans tenir compte du Volume Élémentaire Représentatif (VER) en raison du coût énorme de calculs imposé par ce dernier. Par conséquent, l'exactitude des résultats de référence ainsi obtenus est contestable. Le but principal de cette thèse était d’évaluer l'exactitude des modèles d'homogénéisation pour la prédiction de comportement mécanique de NPA. Dans un premier temps, la validité des modèles micromécaniques analytiques couramment utilisés pour la prédiction de propriétés élastiqués de NPA exfoliés a été évaluée à l'aide de simulations Éléments Finis (EF) tridimensionnelles. Une attention particulière a été accordée à l'interphase autour des nano-argiles. La stratégie de modélisation était une procédure en deux étapes se basant sur la notion de Particule Effective (PE). Dans cette approche de modélisation, les renforts multicouches ont été remplacés par des particules homogènes à effets équivalents. L'exactitude des modèles numériques dans des limites de tolérances prédéfinies était garantie grâce à la détermination du VER. Cette étude a révélé que la méthode de Mori-Tanaka est la plus fiable à utiliser parmi les modèles en deux étapes pour les valeurs typiques de paramètres de NPA exfoliés (contraste de module, rapport de forme et la fraction volumique). Les propriétés mécaniques de l'interphase ainsi que son épaisseur ont été estimées à partir d'une comparaison entre une étude paramétrique numérique et des résultats expérimentaux.----------ABSTRACT Polymer-Clay Nanocomposites (PCN) are known to improve the mechanical properties of bulk polymers, even for modest clay loadings. This enhancement is due to the High aspect ratio and mechanical properties of the nanoclay platelets. Additionally, the interphase zone created by altered polymer chains in the vicinity of the nanoclays plays an important reinforcing role. Several analytical approaches exist for predicting the elastic properties of PCN, ranging from simplified two-step models to more complex one-step methods. However, no thorough study has yet rigorously verified the accuracy of these models. On the other hand, the numerical models that are commonly used to evaluate the analytical models are still far from modeling the real PCN microstructure reported in the literature. For example, most of the models have failed to model the detailed 3D microstructure considering randomly positioned reinforcing particles, the large nanoclay aspect ratio and the explicit incorporation of the constituent phases. More significantly, most of numerical studies have been reported without a thorough determination of the appropriate Representative Volume Element (RVE) due its computational burden, resulting in benchmark results of questionable accuracy. The main purpose of this thesis was to evaluate the accuracy of homogenization models for predicting the mechanical behavior of nanoclay nanocomposites. First, the validity of commonly used analytical micromechanical models for the prediction of exfoliated PCN elastic properties was evaluated with the help of 3D Finite Element (FE) simulations. In particular, special attention was devoted to the interphase around the nanoclays. The modeling strategy was a two-step procedure relying on the Effective Particle (EP) concept, in which the multi-layer reinforcing stacks were replaced by homogenized particles. The accuracy of the numerical models was guaranteed, within a given tolerance, by rigorous determination of the RVE. It was found that the Mori-Tanaka model was the most reliable method to be used in two-step models for the possible ranges of modulus contrasts, aspect ratios and volume fractions typical of exfoliated PCN. The properties and the thickness of the interphase were estimated from comparison between a numerical parametric study and experimental results. The importance of incorporating the interphase for predicting the axial Young's modulus was highlighted. Second, the evaluation was extended to a wider class of models applicable to both intercalated and exfoliated morphologies

Dielectric mixtures -- electrical properties and modeling

In this paper, a review on dielectric mixtures and the importance of the numerical simulations of dielectric mixtures are presented. It stresses on the interfacial polarization observed in mixtures. It is shown that this polarization can yield different dielectric responses depending on the properties of the constituents and their concentrations. Open question on the subject are also introduced.Comment: 40 pages 12 figures, to be appear in IEEE Trans. on Dielectric

Modeling, Characterizing and Reconstructing Mesoscale Microstructural Evolution in Particulate Processing and Solid-State Sintering

abstract: In material science, microstructure plays a key role in determining properties, which further determine utility of the material. However, effectively measuring microstructure evolution in real time remains an challenge. To date, a wide range of advanced experimental techniques have been developed and applied to characterize material microstructure and structural evolution on different length and time scales. Most of these methods can only resolve 2D structural features within a narrow range of length scale and for a single or a series of snapshots. The currently available 3D microstructure characterization techniques are usually destructive and require slicing and polishing the samples each time a picture is taken. Simulation methods, on the other hand, are cheap, sample-free and versatile without the special necessity of taking care of the physical limitations, such as extreme temperature or pressure, which are prominent issues for experimental methods. Yet the majority of simulation methods are limited to specific circumstances, for example, first principle computation can only handle several thousands of atoms, molecular dynamics can only efficiently simulate a few seconds of evolution of a system with several millions particles, and finite element method can only be used in continuous medium, etc. Such limitations make these individual methods far from satisfaction to simulate macroscopic processes that a material sample undergoes up to experimental level accuracy. Therefore, it is highly desirable to develop a framework that integrate different simulation schemes from various scales to model complicated microstructure evolution and corresponding properties. Guided by such an objective, we have made our efforts towards incorporating a collection of simulation methods, including finite element method (FEM), cellular automata (CA), kinetic Monte Carlo (kMC), stochastic reconstruction method, Discrete Element Method (DEM), etc, to generate an integrated computational material engineering platform (ICMEP), which could enable us to effectively model microstructure evolution and use the simulated microstructure to do subsequent performance analysis. In this thesis, we will introduce some cases of building coupled modeling schemes and present the preliminary results in solid-state sintering. For example, we use coupled DEM and kinetic Monte Carlo method to simulate solid state sintering, and use coupled FEM and cellular automata method to model microstrucutre evolution during selective laser sintering of titanium alloy. Current results indicate that joining models from different length and time scales is fruitful in terms of understanding and describing microstructure evolution of a macroscopic physical process from various perspectives.Dissertation/ThesisDoctoral Dissertation Materials Science and Engineering 201

Methodological developments in electron spin resonance (ESR) low-temperature thermochronometry

Low-temperature thermochronometry provides a means of understanding the interaction between surface processes and underlying tectonics by quantifying the cooling histories of rocks. Electron spin resonance (ESR) thermochronometry works by determining the timing and rate at which electrons are trapped and thermally released in quartz in response to in situ ionizing radiation and rock cooling. This technique has great potential in reconstructing thermal histories of the upper ~ 2 km of the Earth's crust during the Quaternary. Its application, however, faces many challenges for methodological improvement since little work has been done on ESR thermochronometry after being first introduced in the late 1990s. Quantitative investigations of thermal histories by ESR thermochronometry rely on the determination of trap parameters of paramagnetic centres in quartz. This study has evaluated the activation energy and frequency factor of Al and Ti centres by analysing borehole samples with well-defined thermal histories and storage temperatures. Fergusons Hill-1 core is located at Otway Basin (Australia) where it is in a thermally steady state, while Eldzhurtinskiy Granite core is located in the Caucasus where it has experienced rapid cooling at a rate of ~ 520 degrees Celsius per million years. The best-fit parameters were determined by a first-order kinetic model which quantifies the irradiation-induced trapping and thermally-related detrapping processes. In heterogeneous rocks, numerical simulation is an ideal solution for accurate estimation of beta dose rate. Identification of mineral distribution is the basis for creating a model, and 2D mapping facilities are more effective than 3D X-ray computed tomography in this aspect. Thus, a 2D model "DosiVox-2D" was established for heterogeneous but isotropic samples, and verified by the comparison with the 3D model and infinite matrix dose method. The practical procedures were then investigated for applying 2D simulation on uniform and layered igneous rocks, including sample selection, mineral mapping, and estimation of radioelement concentrations. Thereafter, ESR thermochronometry was applied to Namche Barwa massif, the eastern Himalayan syntaxis. Samples were collected from a vertical transect to the south of the massif. ESR results, on one hand, have improved our understanding of the localised structural settings. On the other hand, the comparison of cooling history with the region adjacent to the north of the massif, has shed light on the domal development of Namche Barwa massif during Mid-late Pleistocene

Numerical modelling of crack propagation in quasi-brittle heterogeneous materials : a stochastic approach

Deformation and damage processes in brittle and quasi-brittle materials, such as rock and concrete, are strongly influenced by their heterogeneous nature, related to their formation processes. The presence of heterogeneities leads in fact to noticeable variation in material properties values: it is of extreme importance that a numerical model which aims to realistically, reliably reproduce with low computational effort deformation and damage processes is able to include the effect of laminations, micro-cracks, voids and other types of heterogeneities; this is even more important when a numerical models has to reproduce the propagation of fractures. This thesis presents the development of a numerical framework for the simulation of crack propagation in shale rocks and concrete which also looks at the optimisation problem in the sense of computational efficiency (defined as optimal computational time needed to obtain realistic and accurate results). The numerical framework for crack propagation developed in this thesis is a variational phase-field model based on a finite elements smeared approach, able to automatically and realistically capture crack initiation processes for a variety of loading conditions; this numerical framework is based on the relation between potential energy associated to body deformation and the energy released during fracture formation. Heterogeneity is considered in the model by means of a stochastic approach based on the assumption that some mechanical properties of heterogeneous brittle materials (such as fracture energy) follow a non-Gaussian Weibull distribution. To guarantee adequate convergence of the results, Monte Carlo Simulation (MCS) method has been used in combination with the developed stochastic methodology. A non-linear dimensionality reduction technique has been developed and incorporated in the algorithm to reduce the computational effort required for the generation of sample realisations. The methodology has been validated using experimental results from both laboratory tests on shale rocks and literature on fracture in concrete. Results show that the developed algorithm is capable of realistically reproducing the mechanical behaviour of the chosen case studies, showing an applicability to problems where cracks propagate in mode-I, mode-II and mixed-mode I and II, guaranteeing a fast generation of sampling realisations of realistic stochastic fields and convergence of results after a maximum of 130 MCS analyses. This methodology can be applied to materials with random spatially-distributed variations of mechanical properties and to those showing laminar natural formations

Fabrication, Characterization and Modeling of Functionally Graded Materials

In the past few decades, a number of theoretical and experimental studies for design, fabrication and performance analysis of solar panel systems (photovoltaic/thermal systems) have been documented. The existing literature shows that the use of solar energy provides a promising solution to alleviate the shortage of natural resources and the environmental pollution associated with electricity generation. A hybrid solar panel has been invented to integrate photovoltaic (PV) cells onto a substrate through a functionally graded material (FGM) with water tubes cast inside, through which water flow serves as both a heat sink and a solar heat collector. Due to the unique and graded material properties of FGMs, this novel design not only supplies efficient thermal harvest and electrical production, but also provides benefits such as structural integrity and material efficiency. In this work, a sedimentation method has been used to fabricate aluminum (Al) and high-density polyethylene (HDPE) FGMs. The size effect of aluminum powder on the material gradation along the depth direction is investigated. Aluminum powder or the mixture of Al and HDPE powder is thoroughly mixed and uniformly dispersed in ethanol and then subjected to sedimentation. During the sedimentation process, the concentration of Al and HDPE particles temporally and spatially changes in the depth direction due to the non-uniform motion of particles; this change further affects the effective viscosity of the suspension and thus changes the drag force of particles. A Stokes' law based model is developed to simulate the sedimentation process, demonstrate the effect of manufacturing parameters on sedimentation, and predict the graded microstructure of deposition in the depth direction. In order to improve the modeling for sedimentation behavior of particles, the Eshelby's equivalent inclusion method (EIM) is presented to determine the interaction between particles, which is not considered in a Stokes' law based model. This method is initially applied to study the case of one drop moving in a viscous fluid; the solution recovers the closed form classic solution when the drop is spherical. Moreover, this method is general and can be applied to the cases of different drop shapes and the interaction between multiple drops. The translation velocities of the drops depend on the relative position, the center-to-center distance of drops, the viscosity and size of drops. For the case of a pair of identical spherical drops, the present method using a linear approximation of the eigenstrain rate has provided a very close solution to the classic explicit solution. If a higher order of the polynomial form of the eigenstrain rate is used, one can expect a more accurate result. To meet the final goal of mass production of the aforementioned Al-HDPE FGM, a faster and more economical material manufacturing method is proposed through a vibration method. The particle segregation of larger aluminum particles embedded in the concentrated suspension of smaller high-density polyethylene is investigated under vibration with different frequencies and magnitudes. Altering experimental parameters including time and amplitude of vibration, the suspension exhibits different particle segregation patterns: uniform-like, graded and bi-layered. For material characterization, small cylinder films of Al-HDPE system FGM are obtained after the stages of dry, melt and solidification. Solar panel prototypes are fabricated and tested at different water flow rates and solar irradiation intensities. The temperature distribution in the solar panel is measured and simulated to evaluate the performance of the solar panel. Finite element simulation results are very consistent with the experimental data. The understanding of heat transfer in the hybrid solar panel prototypes gained through this study will provide a foundation for future solar panel design and optimization