Dissertations / Theses on the topic 'Plastic-composite properties'

Wood plastic composites (WPCs) were made using matrices of recycled high-density polyethylene (rHDPE) and polypropylene (rPP) with sawdust (Pinus radiata) as filler. Corresponding WPCs were also made using virgin plastics (HDPE and PP) for comparison with the recycled plastic based composites. WPCs were made through melt compounding and hot-press moulding with varying formulations based on the plastic type (HDPE and PP), plastic form (recycled and virgin), wood flour content and addition of coupling agent. The dimensional stability and mechanical properties of WPCs were investigated. Durability performances of these WPCs were studied separately, by exposing to accelerated freeze-thaw (FT) cycles and ultraviolet (UV) radiation. The property degradation and colour changes of the weathered composites were also examined. Dimensional stability and flexural properties of WPCs were further investigated by incorporation of nanoclays in the composite formulation. To understand the changes in WPCs stability and durability performance, microstructure and thermal properties of the composites were examined. Two mathematical models were developed in this work, one model to simulate the moisture movement through the composites in long-term water immersion and the other model to predict the temperature profile in the composites during hot-press moulding. Both rHDPE and rPP matrix based composites exhibited excellent dimensional stability and mechanical properties, which were comparable to those made from virgin plastics. Incorporation of maleated polypropylene (MAPP) coupling agent in composite formulation improved the stability and the mechanical properties. The incorporation of 3 wt. % MAPP coupling agent to WPCs showed an increase in tensile strength by 60% and 35 %, respectively, for the rHDPE based and rPP based composites with 50 wt. % wood flour. Scanning electron microscopy (SEM) images of the fractured surfaces of WPCs confirmed that the MAPP coupling improved the interfacial bonding between the plastic and the wood filler for both series of composites. Long-term water immersion tests showed that the water transport mechanism within the WPCs follows the kinetics of Fickian diffusion. Dimensional stability and flexural properties of the WPC were degraded after 12 accelerated FT cycles as well as 2000 h of UV weathering for both recycled and virgin HDPE and PP based composites. However, the MAPP coupled composites had improved stability and flexural property degradation. The surface of the weathered composites experienced a colour change, which increased with the exposure time. The MAPP coupled composites exhibited less colour change as compared to non-coupled composites. Regarding the effect of the plastic type, the PP based composites experienced higher colour change than those based on HDPE. With weathering exposure, flexural strength and stiffness of the WPCs were decreased, but elongation at break was increased regardless of plastic type and wood flour content. MAPP coupled rPP and rHDPE based UV weathered WPCs lowered the degradation of stiffness by 50% and 75%, respectively compared to non-coupled WPCs. SEM images of the fractured surfaces of FT and UV weathered WPCs confirmed a decrease in the interfacial bonding between the wood flour and matrix. Thermal properties of weathered composites changed with weathering, but the extent of the changes depended on WPCs formulation and matrix type. From the experimental studies on nanoclay-filled rHDPE composites, it is found that stability, flexural properties of WPCs could be improved with an appropriate combination of coupling agent, and nanoclay contents processed by melt blending. Incorporation of 1-5 wt. % nanoclay in the maleated polyethylene (MAPE) coupled wood plastic composite improved the dimensional stability and flexural properties. The thermal properties changed with the addition of nanoclay and MAPE in WPCs. In this work, a hot press-moulding model was proposed based on the one-dimensional transient heat conduction to predict the temperature profile of the WPCs during hot pressing cycle. The results from this work clearly show that rHDPE and rPP can be successfully used to produce stable and strong WPCs, which properties and performances are similar to or comparable to composites made of wood and virgin plastics. Therefore, WPCs based on recycled PP and HDPE matrix could have potential to use as construction materials.

La présente étude fait suite à d’autres qui proposent une solution de récupération des déchets plastiques et de bois pour en faire un matériau de construction en composite bois-polymère. La particularité de ce travail de recherche est que la matrice thermoplastique utilisée est un ensemble de différents polymères pris dans des proportions bien définies. Les pourcentages considérés pour la matrice obtenue représentent les parts de déchets de polymères que l’on retrouve dans la ville de Cotonou (Bénin). Cette étude a consisté à fabriqué des échantillons de composite bois polymère CBP par extrusion, à les étudier à travers des tests physico-mécaniques et à les mettre en relation avec les échantillons fabriqués avec une méthode artisanale déjà existante. D’une part, nous avons étudié séparément la sciure de bois et la matrice thermoplastique en déterminant les constituants chimiques de la sciure de bois, et en effectuant une analyse physico-mécanique (analyse thermogravimétrique, test en flexion compression et traction, analyse du faciès de rupture au MEB) sur le renfort et la matrice. D’autre part nous avons évalué l’influence de l’ajout de 20%, 25%, 28% et 30% de sciure de bois sur les propriétés mécaniques (compression, flexion et traction). Les résultats obtenus révèlent que la sciure de bois se comporte comme un renfort lorsque l’échantillon est sollicité en compression et en flexion. La sciure de bois joue le rôle de charge lorsque les échantillons de CBP sont sollicités en traction. Par ailleurs, la sciure de bois améliore la rigidité des CBP en traction. Les résultats mécaniques obtenus par extrusion sont nettement meilleurs que ceux issus des méthodes de fabrication artisanale. Les analyses thermogravimétriques effectuées sur les échantillons de CBP issus de la méthode artisanale révèlent que lors de leur fabrication, ces échantillons sont soumis à des températures (supérieure à 300°C) qui entament la dégradation des polymères et de la sciure de bois dans les CBP<br>This study follow others that propose a solution for the recovery of plastic waste and wood to make it a construction material made of wood-polymer composite. The particularity of this research is that the thermoplastic matrix used is a set of different polymers taken in well-defined proportions. The percentages considered for the matrix obtained represent the proportion of polymer waste that can be found in the city of Cotonou (Benin Republic). This study consisted in making WPC polymer wood composite samples by extrusion, studying them through physico-mechanical tests and relating them to samples made with an already existing artisanal method. On the one hand, we studied separately the sawdust and the thermoplastic matrix by determining the chemical constituents of the sawdust, and by performing a physico-mechanical analysis (thermogravimetric analysis, compression and tensile bending test, facies analysis). SEM fracture) on the reinforcement and the matrix. On the other hand we evaluated the influence of the addition of 20%, 25%, 28% and 30% of sawdust on the mechanical properties (compression, bending and traction). The results show that sawdust behaves like a reinforcement when the sample is stressed in compression and bending. Sawdust acts as a load when WPC samples are stressed in tension. Sawdust also improves the rigidity of WPC in tension. The mechanical results obtained by extrusion are much better than those resulting from the artisanal methods. Thermogravimetric analyzes performed on WPC samples from the artisanal method reveal that during their manufacture, these samples are subjected to temperatures (above 300 ° C) that begin the degradation of polymers and sawdust in WPC

The purpose of the work is the determination of flexural properties for thebiocomposite Durapulp. The study includes laborative tests on Durapulp andreference materials, commonly used in the building sector. Stiffness and strength of Durapulp show that it has the potential as a replacement for conventional wood-based materials.

Two topics, i.e., the scale effects and the geodesics of random heterogeneous materials will be discussed in this work.<br>When the separation of scales in random media does not hold, the representative volume element (RVE) of deterministic continuum mechanics does not exist in the conventional sense, and new concepts and approaches are needed. This subject is discussed here in the context of microstructures of two types - planar random chessboards, and planar random inclusion-matrix composites -- with microscale behavior being elastic-plastic-hardening (power-law). The microstructure is assumed to be spatially homogeneous and ergodic. Principal issues under consideration are those of yield and incipient plastic flow of statistical volume elements (SVE) on mesoscales, and the scaling trend of SVE to the RVE response on macroscale. Indeed, the SVE responses under uniform displacement (or traction) boundary conditions bound from above (respectively, below) the RVE response, and we show via extensive simulations in plane stress that the larger is the mesoscale, the tighter are both bounds. However, the mesoscale flows under both kinds of loading do not, in general, display normality. Also, with the limitation imposed by currently available computational resources, we do not recover normality (or even a trend towards it) when studying the largest possible SVE domains.<br>The second topic is the geodesic (i.e., shortest path) character of strain fields occurring in elasto-plastic response of planar inclusion-matrix composites. The composites' spatially random morphology is created by generating the disk centers through a sequential inhibition process based on a poisson point field in plane. Both phases (inclusions and matrix) are elastic-plastic-hardening with the matrix being more compliant and weaker than the inclusions, and perfect bonding everywhere. A quantitative comparison of a response pattern obtained by computational micromechanics with that found only by mathematical morphology indicates that (i) the regions of plastic flow are very close to geodesics, and (ii) a purely geometric, and orders of magnitude more rapid than by computational mechanics assessment of these regions is possible.

Dans cette étude, les propriétés mécanique et la microstructure du polyéthylène à haute densité (PEHD)/ fibres de bois (Pinmaritime) ont été caractérisés. Le comportement en traction et en flexion 4 points de composites fibres de bois/polyéthylène(WPC) avec et sans additif a été étudié en utilisant des mesures de champs par stéréo-corrélation d’image numériques. Nousavons tout d’abord comparé les mesures de déformation longitudinale par stéréo-corrélation d’image à celles mesurées parextensométrie mécanique au cours d’un essai de traction simple uni-axial. Les valeurs de déformation macroscopiquemesurées sont comparables à celles obtenues par extensométrie mécanique classique. Quatre formulations ont été testées(avec ou sans l'additif et avec 10% ou 30% de bois) au travers des essais de traction et flexion 4 points en utilisant laméthode par stéréo-corrélation d’image. Nous avons pu ainsi corréler la visualisation combinée des images enregistrées parles caméras au comportement mécanique ainsi qu’aux modifications des surfaces des composites. Les résultats ont montréque les singularités au niveau de la surface des échantillons ainsi que la présence des fibres de bois (dans les proportionsutilisées durant nos essais) n’ont pas d’effets sur la qualité du composite. La stéréo corrélation d’images nous permet d’avoirune information précise sur le cisaillement tant d’un point de vue quantitatif que qualitatif. L’essai cyclique a été utilisé pouranalyser l’endommagement du composite. Les courbes en traction et flexion ont montré un comportement global non linéaire. Le module d’élasticité (MOE) est évalué par la tangente à l’origine d’un modèle de Maxwell-Binhgam ajusté paroptimisation sur les courbes expérimentales. Les cartographies fausses couleurs du champ de déformation du WPC ont étéprésentées. D’autre part, on a analysé le comportement endommageable et le degré d’hétérogénéité pour différentspourcentages de bois à l’aide des valeurs de l’écart type spatial du champ de déformation longitudinale. Par cette technique,nous avons également pu étudier les propriétés mécaniques en traction et en compression à partir d’un essai de flexion 4points. Le second objectif était d’améliorer la performance des liaisons entre les fibres de bois hydrophiles polaires et lamatrice plastique de PEHD hydrophobe non polaire. Pour cette raison, la fibre de bois a été traitée par anhydride maléique depolyéthylène (MAPE) (greffage par copolymérisation) et acétylée (greffage de chaine de carbone). Dans cette partie, nousavons étudié l’effet de MAPE ainsi que la longueur de la chaine de carbone greffée sur les propriétés mécaniques du WPC.Par ailleurs, nous avons pu observer et caractériser la morphologie à l’interface fibre de bois/HDPE du WPC greffé enutilisant un microscope électronique à balayage (MEB)<br>Firstly we have compared longitudinal strenght obtained by stereo correlation with mechanical extensometer forthe same tests. It is shown that macroscopic values of the longitudinal strain are closed to those measured bymechanical extensometers using standard mechanical tests. Four injected WPC formulations (with or withoutadditive and with 10% or 30% of wood) are consider. WPC surface particularities and wood fibers distributionon samples have no effect on WPC mechanical performances. Also 3D digital image correlation givesinformations on Tensile performances (from quality and quantity point of view). Cyclic tensile tests have beenperformed in order to analyse the damage of material. A non-linear behaviour is shown. The Modulus ofElasticity (MOE) is provided by a Maxwell-Bingham model fitted to the experimental tensile curves. Color mapsof the spatial strain distribution are commented. Moreover, the damage behaviour and the degree ofheterogeneity for several percentages of fibre wood-based WPC are analysed thanks to the spatial standarddeviation of the longitudinal strain field. With this technology it was possible to study of the mechanicalproperties in tensile and compression during four bending test. The second objective was to improve the linkbetween PEHD matrix and wood fibres because of the incompatibility between the polar hydrophilic wood fibresand the non-polar hydrophobic polyethylene. For this reason, the wood fibre was treated by maleic polyethyleneanhydride (MAPE) (grafting by copolymerization) and was acetylated (grafting of carbon chain). In this part, theeffect on the mechanical properties, of maleic anhydride modified polyethylene (MAPE) and of the length of thecarbon chain graft (CCG) between a (HDPE) matrix and wood fiber is studied. Furthermore, Scanning ElectronMicroscope (SEM) is used to characterize the morphology of the wood fibre / HDPE matrix interface forspecimens with carbon chain grafted

An inelastic material model for laminated composite plates and shells is formulated and incorporated into a finite element model that accounts for both geometric nonlinearity and transverse shear stresses. The elasto-plastic material behavior is incorporated using the flow theory of plasticity. In particular, the modified version of Hill's initial yield criterion is used in which anisotropic parameters of plasticity are introduced with isotropic strain hardening. The shear deformation is accounted for using an extension of the Sanders shell theory and the geometric nonlinearity is considered in the sense of the von Karman strains. A doubly curved isoparametric rectangular element is used to model the shell equations. The layered element approach is adopted for the treatment of plastic behavior through the thickness. A wide range of numerical examples is presented for both static and dynamic analysis to demonstrate the validity and efficiency of the present approach. The results for combined nonlinearity are also presented. The results for isotropic results are in good agreement with those available in the literature. The variety of results presented here based on realistic material properties of more commonly used advanced laminated composite plates and shells should serve as references for future investigations.<br>Ph. D.

It was found that a significant improvement of mechanical properties of CFRPs can be achieved by the adjustment of the matrix properties such as toughness and CF/matrix adhesion via the chemical modification, as well as the physical modification by a small amount of cheap and environment-friendly nano fibers. Based on investigation of fracture mechanisms at macro/micro scale, the effects of matrix properties and nano fiber on the mechanical properties of CFRP have been discussed. Subsequently, the relationship has been characterized by a numerical model to show how to modulate the parameters of the matrix properties to achieve excellent fatigue properties of CFRP.<br>博士(工学)<br>Doctor of Philosophy in Engineering<br>同志社大学<br>Doshisha University

Thesis (M.S.)--University of Wisconsin--Madison, 1999.<br>Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 110-113).

碩士<br>國立中興大學<br>森林學系所<br>99<br>The purpose of this study is to develop and manufacture wood plastic composite core plywood (WPCP) from wood particles (Pinus taiwanensis), different kinds of plastics (including vHDPE, rHDPE and rLDPE) and untreated/acetylated veneer (Pinus radiata) by one-step hot press molding. The effect of density, plastic and acetylated veneer on physicomechanicl properties of WPCP were evaluated by universl testing machine, color difference meter, stylus-type surface profilometer, gloss meter, attenuated total reflectance–Fourier transform infrared spectroscopy (ATR–FTIR) and X-ray density profiler, etc. Results revealed that, among WPCP with various densities, 800 kg/m3 of WPCP exhibited high performance on dimensional stability and mechanicl properties. In addition, the recycled HDPE based WPCP showed the similar physicomechanicl properties to the virgin HDPE based WPCP. On the other hand, the water absorption and the thickness swelling of WPCP with acetylated veneer were lower than those of untreated WPCP. As well as the surface tensile strength of WPCP increased with increasing the weight gain of acetylated veneer. Furthermore, the results of outdoor weathering demonstrated that not only the photostability, but also the MOE retention ratio and surface tensile strength of WPCP with acetylated veneer were significantly higher than those of WPCP with untreated veneer. Moreover, the rHDPE crystallinity of WPC was significantly increased, while the rHDPE crystallinity of WPCP was not significantly different during 64 days of outdoor weathering. Accordingly, it concludes that better dimensional stability, surface tensile strength and weathering properties could be achieved when the WPCP made by the acetylated veneer.

碩士<br>國立中興大學<br>森林學系所<br>100<br>In this study, Cryptomeria japonica (Sugi) and Fagus sylvatica (Beech) were heat treated during 2h by different temperatures (120–260oC) and gas atmosphere (air and nitrogen), and then heat treated particles and recycled high density polyethylene (rHDPE) were used as raw materials to manufacture wood-plastic composites (WPC). Effects of heat treatment on physicomechanical and thermal-properties of woods and WPC were evaluated by universal testing machine, dynamic mechanical analyzer, attenuated total refletcion–Fourier transform infrared spectroscopy (ATR–FTIR), X–ray diffractometer, 13C CP/MAS nuclear magnetic resonance spectrometer (13C CP/MAS NMR), and color difference meter. These results showed that the mass loss and dimensional shrinkage percentage of heat treated woods increased with increasing treated temperatures. As the results of soaking test, woods exhibited better dimensional stability and hydrophobic properties during heat treatment. As for mechanical properties, the modulus of rupture (MOR) of wood had significant decreased when heat treatment was performed at temperature exceed 200oC under air atmosphere. And then, the flexural properties of wood exhibited the worst at 260oC. For surface properties, the color of wood became darker during heat treatment, and the surface of heat treated wood was smoother. On the other hand, the crystallinity of heated wood increased due to the polysaccharides of amorphous region were degraded. In addition, lignin occurred thermal condensation and thermal cross-linking reaction at the same time according to NMR analysis. Furthermore, in this study, the combinations of ATR–FTIR and principle component analysis (PCA) is succeeded to discriminate different degrees of heat treated Sugi. Results from dynamic mechanical analyzer revealed that there was a high correlation between the storage modulus (E’) and treated temperatures. As an example of beech wood, there is no significant correlation between the natural log of decrease rate of storage modulus (E’D) and reciprocal absolute temperature when the heat treatment was performed at temperature below 160oC under a nitrogen atmosphere. However, a linear correlation between ln E’D and 1/K was observed (R2 = 0.995) when the temperature exceeded 160oC. Moreover, according to Arrhenius equation, the activation energy of beech wood under an air atmosphere was calculated as 141.3 kJ/mol which was lower than that of wood under a nitrogen atmosphere (150 kJ/mol). Results also showed that the water absorption and thickness swelling of WPC made by heat treated particles decreased with increasing treated temperature. Furthermore, the flexural properties and wood screw-holding strength of WPC had no significant difference between untreated and heat treated ones. However, internal bond strength of WPC were significantly increased after heat treatment, even though the treated temperature was 120oC, the internal bond strength of untreated and heat treated WPC were 1.5 MPa and 2.0 MPa, respectively. Accordingly, the result indicates that the compatibility and interfacial interaction between the wood particles and the polymeric matrix could be improved by heat treated process.

The study examined the properties of stalk and cob fibres from recombinant inbred corn lines and their parents, grown at two locations, in a polylactic acid (PLA) matrix. The objectives were to: determine fibre compositions; evaluate the effects of fibres on the functional properties of biocomposites and identify quantitative trait loci (QTLs) and gene markers for fibre performance in biocomposites. Significant Genotype*Location effects were observed. Composites had lower strength (impact, tensile, and flexural) but higher tensile/flexural modulus values than pure PLA. The latter were positively affected by cellulose and hemicellulose but negatively affected by free phenolic levels and 93 fibre QTLs and 62 composite markers were detected. This study identified fibre traits and markers for genes that may be important for the use of corn fibres in biocomposites.<br>Ontario BioCar Initiative Project funded by Ontario Ministry of Research and Innovation, Agriculture and Agri-Food Canada, The Natural Sciences and Engineering Research Council, The Ontario Ministry of Agriculture, Food and Rural Affairs (OMAFRA) and Ontario Public Sector

I have worked on many projects, but there are several things that they all had in common. First, nearly all projects involved searching for the structural parameters that governed the macroscopic properties of the polymers and composite materials. A second common denominator is that even though my work was performed in an “academic context”, the goals were targeted toward industrial needs. Lastly, the methods and procedures were similar; they were all based on experimental results obtained for various scales of measurement (see Fig. 1). Hence, multi-scale modeling was very useful and beneficial for these projects. The models developed (mainly numerical and sometimes analytical) were initially derived from experimental evidence and then validated and improved with further experimentation. The refined models provided an efficient means of: (i) optimizing the composites according to specific needs, (ii) better understanding the hierarchical relations between the different scales, (iii) controlling the micro or meso structure and thereby the macroscopic properties. This study of the relations between structure and properties was performed on a wide variety of physical properties and materials. However, the electric and dielectric properties of composites constituted the major- ity of it and will be presented in this report. The remaining property investigations provided supplemental but valuable information. This work often requires altering various conventional experimental techniques or using well-known techniques for new purposes. I also developed, when needed, several unconventional but necessary measurement techniques. This report contains two major parts which are separated according to the nature of the fillers: Part I : Conducting fillers. In the first part, the main interest both for application and fundamental point of view, is related to the changes in properties in the vicinity of the sharp percolation transition. After a brief introduction to the percolation theory, this part will be subdivided in three chapters: Chapter 1. presents a numerical method that correlates the mesostructure to the macroscopic electrical properties both in two and three dimensions. Chapter 2. will show that an external variable (the mechanical stress) may largely alter the microstruc- ture of the percolating network within composites as revealed the macroscopic conductivity. The understanding of the mesoscale changes will be based on the chemical structure of the polymer matrix. Chapter 3. is devoted to the description of a unique case in term of percolation behavior, which made possible the control of the phase arrangement within the composite and thereby the control of the macroscopic resistivity. p. 2 Multiscale relationships in polymer–based heterogeneous systems. . . Part II : Insulating fillers. In the second part, the main interest is to obtain good electrical insulators, i.e. that can withstand large electric fields. This part thus starts with a brief introduction to the common failure mechanisms, associated with the dielectric breakdown and is also divided in three chapters: Chapter 4. is devoted to the description of a numerical simulation of the relationships between mesostructure and dielectric breakdown. Chapter 5. reveals the influence of the processing conditions of a composite utilized in the industry on the microstructure and the quantitative consequences on breakdown properties. Chapter 6. presents the aging of these composites under “real word” conditions which will further be compared to accelerated aging performed in controlled conditions, in the laboratory. A comparison of the two aging situations will furnish a quantitative understanding of the relative influence of the chemical and physical contributions to the aging process. This report will then be concluded with a description of the current and future projects.

This thesis addresses issues related to the simulation and optimization of the injection molding of short fiber-reinforced plastics (SFRPs). The injection molding process is modeled by a two phase flow problem. The simulation of the two phase flow is accompanied by the solution of the Folgar-Tucker equation (FTE) for the simulation of the moments of fiber orientation densities. The FTE requires the solution of the so called 'closure problem'', i.e. the representation of the 4th order moments in terms of the 2nd order moments. In the absence of fiber-fiber interactions and isotropic initial fiber density, the FTE admits an analytical solution in terms of elliptic integrals. From these elliptic integrals, the closure problem can be solved by a simple numerical inversion. Part of this work derives approximate inverses and analytical inverses for special cases of fiber orientation densities. Furthermore a method is presented to generate rational functions for the computation of arbitrary moments in terms of the 2nd order closure parameters. Another part of this work treats the determination of effective material properties for SFRPs by the use of FFT-based homogenization methods. For these methods a novel discretization scheme, the 'staggered grid'' method, was developed and successfully tested. Furthermore the so called 'composite voxel'' approach was extended to nonlinear elasticity, which improves the approximation of material properties at the interfaces and allows the reduction of the model order by several magnitudes compared to classical approaches. Related the homogenization we investigate optimal experimental designs to robustly determine effective elastic properties of SFRPs with the least number of computer simulations. Finally we deal with the topology optimization of injection molded parts, by extending classical SIMP-based topology optimization with an approximate model for the fiber orientations. Along with the compliance minimization by topology optimization we also present a simple shape optimization method for compensation of part warpage for an black-box production process.:Acknowledgments v Abstract vii Chapter 1. Introduction 1 1.1 Motivation 1 1.2 Nomenclature 3 Chapter 2. Numerical simulation of SFRP injection molding 5 2.1 Introduction 5 2.2 Injection molding technology 5 2.3 Process simulation 6 2.4 Governing equations 8 2.5 Numerical implementation 18 2.6 Numerical examples 25 2.7 Conclusions and outlook 27 Chapter 3. Numerical and analytical methods for the exact closure of the Folgar-Tucker equation 35 3.1 Introduction 35 3.2 The ACG as solution of Jeffery's equation 35 3.3 The exact closure 36 3.4 Carlson-type elliptic integrals 37 3.5 Inversion of R_D-system 40 3.6 Moment tensors of the angular central Gaussian distribution on the n-sphere 49 3.7 Experimental evidence for ACG distribution hypothesis 54 3.8 Conclusions and outlook 60 Chapter 4. Homogenization of SFRP materials 63 4.1 Introduction 63 4.2 Microscopic and macroscopic model of SFRP materials 63 4.3 Effective linear elastic properties 65 4.4 The staggered grid method 68 4.5 Model order reduction by composite voxels 80 4.6 Optimal experimental design for parameter identification 93 Chapter 5. Optimization of parts produced by SFRP injection molding 103 5.1 Topology optimization 103 5.2 Warpage compensation 110 Chapter 6. Conclusions and perspectives 115 Appendix A. Appendix 117 A.1 Evaluation of R_D in Python 117 A.2 Approximate inverse for R_D in Python 117 A.3 Inversion of R_D using Newton's/Halley's method in Python 117 A.4 Inversion of R_D using fixed point method in Python 119 A.5 Moment computation using SymPy 120 A.6 Fiber collision test 122 A.7 OED calculation of the weighting matrix 123 A.8 OED Jacobian of objective and constraints 123 Appendix B. Theses 125 Bibliography 127<br>Diese Arbeit befasst sich mit Fragen der Simulation und Optimierung des Spritzgießens von kurzfaserverstärkten Kunststoffen (SFRPs). Der Spritzgussprozess wird durch ein Zweiphasen-Fließproblem modelliert. Die Simulation des Zweiphasenflusses wird von der Lösung der Folgar-Tucker-Gleichung (FTE) zur Simulation der Momente der Faserorientierungsdichten begleitet. Die FTE erfordert die Lösung des sogenannten 'Abschlussproblems'', d. h. die Darstellung der Momente 4. Ordnung in Form der Momente 2. Ordnung. In Abwesenheit von Faser-Faser-Wechselwirkungen und anfänglich isotroper Faserdichte lässt die FTE eine analytische Lösung durch elliptische Integrale zu. Aus diesen elliptischen Integralen kann das Abschlussproblem durch eine einfache numerische Inversion gelöst werden. Ein Teil dieser Arbeit leitet approximative Inverse und analytische Inverse für spezielle Fälle von Faserorientierungsdichten her. Weiterhin wird eine Methode vorgestellt, um rationale Funktionen für die Berechnung beliebiger Momente in Bezug auf die Abschlussparameter 2. Ordnung zu generieren. Ein weiterer Teil dieser Arbeit befasst sich mit der Bestimmung effektiver Materialeigenschaften für SFRPs durch FFT-basierte Homogenisierungsmethoden. Für diese Methoden wurde ein neuartiges Diskretisierungsschema 'staggerd grid'' entwickelt und erfolgreich getestet. Darüber hinaus wurde der sogenannte 'composite voxel''-Ansatz auf die nichtlineare Elastizität ausgedehnt, was die Approximation der Materialeigenschaften an den Grenzflächen verbessert und die Reduzierung der Modellordnung um mehrere Größenordnungen im Vergleich zu klassischen Ansätzen ermöglicht. Im Zusammenhang mit der Homogenisierung untersuchen wir optimale experimentelle Designs, um die effektiven elastischen Eigenschaften von SFRPs mit der geringsten Anzahl von Computersimulationen zuverlässig zu bestimmen. Schließlich beschäftigen wir uns mit der Topologieoptimierung von Spritzgussteilen, indem wir die klassische SIMP-basierte Topologieoptimierung um ein Näherungsmodell für die Faserorientierungen erweitern. Neben der Compliance-Minimierung durch Topologieoptimierung stellen wir eine einfache Formoptimierungsmethode zur Kompensation von Teileverzug für einen Black-Box-Produktionsprozess vor.:Acknowledgments v Abstract vii Chapter 1. Introduction 1 1.1 Motivation 1 1.2 Nomenclature 3 Chapter 2. Numerical simulation of SFRP injection molding 5 2.1 Introduction 5 2.2 Injection molding technology 5 2.3 Process simulation 6 2.4 Governing equations 8 2.5 Numerical implementation 18 2.6 Numerical examples 25 2.7 Conclusions and outlook 27 Chapter 3. Numerical and analytical methods for the exact closure of the Folgar-Tucker equation 35 3.1 Introduction 35 3.2 The ACG as solution of Jeffery's equation 35 3.3 The exact closure 36 3.4 Carlson-type elliptic integrals 37 3.5 Inversion of R_D-system 40 3.6 Moment tensors of the angular central Gaussian distribution on the n-sphere 49 3.7 Experimental evidence for ACG distribution hypothesis 54 3.8 Conclusions and outlook 60 Chapter 4. Homogenization of SFRP materials 63 4.1 Introduction 63 4.2 Microscopic and macroscopic model of SFRP materials 63 4.3 Effective linear elastic properties 65 4.4 The staggered grid method 68 4.5 Model order reduction by composite voxels 80 4.6 Optimal experimental design for parameter identification 93 Chapter 5. Optimization of parts produced by SFRP injection molding 103 5.1 Topology optimization 103 5.2 Warpage compensation 110 Chapter 6. Conclusions and perspectives 115 Appendix A. Appendix 117 A.1 Evaluation of R_D in Python 117 A.2 Approximate inverse for R_D in Python 117 A.3 Inversion of R_D using Newton's/Halley's method in Python 117 A.4 Inversion of R_D using fixed point method in Python 119 A.5 Moment computation using SymPy 120 A.6 Fiber collision test 122 A.7 OED calculation of the weighting matrix 123 A.8 OED Jacobian of objective and constraints 123 Appendix B. Theses 125 Bibliography 127