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The master thesis is focused on analysis of stress field in the vicinity of stress concentration of stainless steel IPE beam loaded in tree point bending. Theoretical part includes introduction to fracture mechanics with basic terms, principles and variables used to describe fatigue behaviour of material. It concludes teoretical grounds of fracture tests which are future focus of the thesis, methodes used by numerical softwares and methodes used to obtain numerical results. Practical part includes comparision between two and three dimensional numerical models in three point bending, IPE model with different crack front shapes and plastic zone size. Numerical modelling was processed in Ansys Mechanical APDL. Thesis also involves results of experimental testing evaluated using numerical model.

[pt] Materiais feitos com microestruturas arquitetadas possuem propriedades mecânicas ajustáveis e podem ser usados na obtenção de estruturas leves e, ao mesmo tempo, com máxima rigidez. Em estruturas celulares formadas por rede de treliças, por exemplo, pode-se variar o tipo de topologia e porosidade de modo que o material seja eficientemente distribuído no domínio de projeto. Devido às geometrias complexas destas estruturas, projetá-las usando ferramentas de desenho assistido por computador é uma tarefa desafiadora. Neste trabalho, foi desenvolvida uma modelagem paramétrica no programa Rhinoceros usando a extensão Grasshopper para auxiliar na construção de modelos de sólidos celulares com estrutura interna treliçada de densidade variável. A modelagem paramétrica desenvolvida permite definir a topologia e o diâmetro das barras das treliças que simplificam em muito a geração de modelos de sólidos porosos. Modelos de microestrutura foram gerados e fabricados em poliamida 12 por meio de sinterização seletiva a laser para avaliar se é viável imprimir as treliças a partir dos parâmetros estabelecidos. O problema de uma viga biapoiada com carga concentrada no centro foi resolvido utilizando-se o método de otimização topológica e o campo de densidades foi usado para geração do modelo de densidade variável. Considerando a mesma massa final dos modelos otimizados, modelos com densidade constante foram gerados e fabricados juntamente com os modelos de densidade variável. Foram realizadas análises experimentais por meio de ensaios de flexão em três pontos e os resultados mostram que a solução usando densidade variável tem um grande aumento da rigidez quando comparadas com as soluções com densidade uniforme. / [en] Materials made with architected microstructures present tunable mechanical properties and can be used to obtain light structures and, at the same time, with maximum stiffness. In lattice structures, for example, the type of topology and porosity can be varied so that the material is efficiently distributed in the design domain. Due to the complex geometries of these structures, designing them using computer-aided design tools is a challenging task. In this work, a parametric modeling was developed in the Rhinoceros program using the Grasshopper extension to assist in the construction of models of lattice structures with varying truss diameters. The developed parametric modeling allows defining the topology and the diameter of the truss bars, which greatly simplifies the generation of models of porous solids. Microstructure models were generated and manufactured in polyamide 12 through selective laser sintering to assess whether it is feasible to print the trusses from the established parameters. The problem of a simply supported beam with a concentrated load at the center was solved using the topology optimization method and the density field was used to generate the variable density model. Considering the same final mass of the optimized models, models with constant density were generated and manufactured together with the models with variable density. Experimental analyzes were carried out using three-point bending tests and the results show that the solution using variable density has a large increase in stiffness when compared to solutions with uniform density.

Ph. D. (Department of Chemical Engineering, Faculty of Engineering and Technology), Vaal University of Technology. / Investment casting process is the most suitable technique for producing high quality castings which are dimensionally accurate with excellent surface finish and complex in nature. Recently with the ever-changing manufacturing landscape, the process has been increasingly used to produce components for the medical, aerospace and sports industry. The present study looked at three investigative scenarios in the development of a pattern material for investment casting process: (i) the development of wax/ethyl vinyl acetate (EVA) and wax/linear low-density polyethylene (LLDPE) blends as the carrier vehicle materials for the development of pattern material for investment casting; (ii) the development of wax/EVA/polymethyl methacrylate (PMMA) based investment casting pattern and lastly (iii) the development of wax/LLDPE/PMMA based investment casting pattern material. The first part of the studies elucidates the effects in terms of the thermal, mechanical, surface and rheological properties when paraffin wax in blended with poly EVA and LLDPE. The developments involved the extrusion of seven formulations for EVA and also LLDPE using a twin-screw extrusion compounder. The paraffin wax weight percent investigated ranged from 33% to 87% thus encompassing both low and high wax loading ratios. The thermal properties of the developed binary blends were characterized via thermogravimetric analysis (TGA) and differential scanning calorimetry (DSC). The mechanical properties were characterized using three-point bending test. The thermo-mechanical and rheological properties were determined using thermomechanical analysis (TMA) and a rheometer respectively. A scanning electron microscope (SEM) was used to study the surface texture of the extruded blends. The thermal properties indicated that the thermal stability of paraffin wax is improved when it is blended with both EVA and LLDPE. DSC curves showed two endothermic melting peaks and two exothermic crystallisation peaks. In the case of wax/EVA blends, there was no distinct peak showing the independent melting of neat wax and EVA. The peak at a temperature of 50 – 72 °C corresponds to the melting of the wax/EVA blend. In the case of wax/LLDPE blends, the peak at 50 -66 °C corresponds to the melting of wax whereas the large peak at 112 - 125°C corresponds to the melting of the LLDPE. Wax/EVA and wax/LLDPE had improved mechanical properties as compared to that of neat wax. The rheological properties of both the EVA based and LLDPE based blends indicated that the viscosity of the blends increased as compared to that of neat wax. SEM confirmed that EVA alters the wax crystal habit at higher concentrations. In the case of wax/LLDPE blends, at 20-30 % wax content, a heterogeneous surface was observed, indicating the immiscibility of the paraffin wax within the LLDPE matrix. At a high wax content, there was agglomeration of wax. LLDPE allows amorphous structure of wax to disperse easily between the chains. The second part of the studies focussed on the wax/EVA filled with poly (methyl methacrylate) (PMMA) microbeads. TGA behaviour on the pyrolysis of wax/EVA/PMMA showed that the compounds volatilise readily with virtually no residue remaining above 500 °C. The DSC curves indicated that, the incorporation of PMMA reduced the crystallinity of wax/EVA blend. A distinct endothermic peak and another small peak was observed in all the formulations. The mechanical properties of wax/EVA/PMMA improved significantly. The methylene group present in both wax and EVA combined to form a blend with enhanced mechanical properties whereas the PMMA microbeads improved the needle penetration hardness. The melt viscosity of wax/EVA/PMMA increased as the EVA and/or the PMMA content is increased. The rheological experimental data fitted with the data predicted using the modified Krieger and Dougherty expression. The maximum attainable volume fraction of suspended PMMA particles was at max = 0.81. The SEM micrograph of wax/EVA/PMMA revealed a near perfect spherical nature for the filler particles in the wax/EVA polymer matrix. It further shows that the PMMA microbeads were weakly bonded and well distributed in the wax/EVA matrix. The third part of the studies focussed on the wax/LLDPE filled with Poly (methyl methacrylate) (PMMA) microbeads. The incorporation of LLDPE and PMMA into paraffin wax had a strong influence on the thermal properties, tensile properties, flow properties and its morphology. The TGA analysis showed that there was a slight observable decrease in the melting onset temperatures when the wax content was increased. From the DSC curves, the corresponding values of onset temperatures observed are between melting and crystallization temperature of neat paraffin wax and neat LLDPE. The short chains of the paraffin wax and the fragments formed by scission of wax chain have sufficient energy to escape from the matrix at lower temperatures. The slight decrease in peak temperatures associated with melting and crystallization could be attributed to the decrease in the average lamellar thickness of the blends. The tensile properties by three-point bending tests indicated an increase in the stress with an increase in the LLDPE content. This can be attributed to the formation of paraffin wax crystals in the amorphous phase of the blend which may influence the chain mobility. Since the paraffin wax used for this study had a low viscosity as compared to LLDPE, both LLDPE or PMMA had an influence on the viscosities of the blends. The data obtained from the experiments fitted with the data predicted obtained from the modified Krieger and Dougherty expression. The maximum attainable volume fraction of suspended PMMA particles was at max = 0.74. Similar observation with that of wax/EVA/PMMA was made in terms of the morphology of the wax/LLDPE/PMMA blends. The excellent thermal stabilities, the superior mechanical strength of wax/EVA/PMMA and wax/LLDPE/PMMA and the flow properties with relatively high EVA and also with high PMMA loadings, open new opportunities for EVA and LLDPE based pattern material for in investment casting process. It is worth pursuing further comprehensive studies since it offers a strong potential for realizing further technological improvement in the field of investment casting and rapid prototyping technologies.

In dieser Dissertation werden Aspekte von superkonformen Quantenfeldtheorien untersucht, die für die sogenannte AdS/CFT Korrespondenz relevant sind. Die AdS/CFT Korrespondenz beschreibt eine Dualität zwischen Stringtheorien im Anti-de Sitter Raum und superkonformen Quantenfeldtheorien im Minkowskiraum. In diesem Kontext wurde die sog. Wilsonschleifen / Amplituden Dualität entdeckt, die die Übereinstimmung von n-Gluon MHV Amplituden und n-seitigen polygonalen Wilsonschleifen in der N=4 supersymmetrischen Yang-Mills (SYM) Theorie beschreibt. Im ersten Teil dieser Dissertation wird die Wilsonschleifenseite einer solchen möglichen Dualität in der N=6 superkonformen Chern-Simons (ABJM) Theorie untersucht. Das Hauptergebnis dieser Untersuchungen ist, dass der Erwartungswert der n-seitigen polygonalen Wilsonschleifen auf Einschleifenebene verschwindet, während er auf Zweischleifenebene in seiner funktionalen Form identisch zu der analogen Wilsonschleife in N=4 SYM auf Einschleifenniveau ist. Außerdem wird eine anomale konforme Wardidentität für Wilsonschleifen in Chern-Simons Theorie berechnet. Zudem werden die damit im Zusammenhang stehenden Entwicklungen für Amplituden und Korrelatoren in der ABJM Theorie diskutiert. Im zweiten Teil dieser Dissertation werden Dreipunktfunktionen von zwei geschützten Operatoren und einem Twist-Zwei Operator mit beleibigem Spin j in der N=4 SYM Theorie berechnet. Dafür werden die Indizes des Spin j Operators auf den Lichtkegel projiziert und der Korrelator wird in einem Grenzfall untersucht in dem der Impuls der bei dem Spin j Operator einfließt verschwindet. Dieser Grenzfall vereinfacht die perturbative Berechnung erheblich, da alle Dreipunktdiagramme effektiv auf Zweipunktdiagramme reduziert werden und die Abhängigkeit der Mischungsmatrix auf Einschleifenebene herausfällt. Das Ergebnis stimmt mit der Analyse der Operatorproduktentwicklung von Vierpunktfunktionen geschützter Operatoren von Dolan und Osborn aus dem Jahre 2004 überein. / In this thesis aspects of superconformal field theories that are of interest in the so-called AdS/CFT correspondence are investivated. The AdS/CFT correspondence states a duality between string theories living on Anti-de Sitter space and superconformal quantum field theories in Minkowski space. In the context of the AdS/CFT correspondence the so-called Wilson loop / amplitude duality was discovered, stating the equality of the finite parts of n-gluon MHV amplitudes and n-sided lightlike polygonal Wilson loops in N=4 supersymmetric Yang-Mills (SYM) theory. It is the subject of the first part of this thesis to investigate the Wilson loop side of a possible similar duality in N=6 superconformal Chern-Simons matter (ABJM) theory. The main result is, that the expectation value of n-sided lightlike polygonal Wilson loops vanishes at one-loop order and at two-loop order is identical in its functional form to the Wilson loop in N=4 SYM theory at one-loop order. Furthermore, an anomalous conformal Ward identity for Wilson loops in Chern-Simons theory is derived. Related developments and symmetries of amplitudes and correlators in ABJM theory are discussed as well. In the second part of this thesis we calculate three-point functions of two protected operators and one twist-two operator with arbitrary even spin j in N =4 SYM theory. In order to carry out the calculations, the indices of the spin j operator are projected to the light-cone and the correlator is evaluated in a soft-limit where the momentum coming in at the spin j operator becomes zero. This limit largely simplifies the perturbative calculation, since all three-point diagrams effectively reduce to two-point diagrams and the dependence on the one-loop mixing matrix drops out completely. The result is in agreement with the analysis of the operator product expansion of four-point functions of half-BPS operators by Dolan and Osborn in 2004.

Es wird ein einfacher Berechnungsansatz für ein Baukastensystem aus Kastenprofilen verschiedener Querschnittsabmessungen erarbeitet. Diese Profile bestehen aus WVC (Wood Veneer Composites, Holzfurnierlagenverbundwerkstoffen). Der Ansatz bildet den statischen Lastfall und das Ermüdungsverhalten unter schwellende Dreipunktbiegung ab. Am Beispiel eines ausgewählten Strukturbauteils aus handelsüblichen Birkensperrholz wird der Berechnungsansatz konkretisiert und durch Versuche evaluiert. Aufbauend auf dem Kraft-Verformungsverhalten der analysierten Einzelbauteile und der kapillarporösen Struktur des Holzes wird bei dem Berechnungsansatz auf eine Analyse der Spannungen verzichtet. Stattdessen wird als Berechnungskriterium die kritische Normaldehnung in der Randfaser der Strukturbauteile genutzt. Weiterhin wird eine Methode vorgestellt um mittels niederzyklischen Ermüdungsversuchs (LCF, ca. 1e+03 Lastwechsel) den „Knickpunkt“ der Zeitfestigkeitslinie eines einstufigen Ermüdungsversuchs bei hohen Lastspielzahlen (HCF, 1e+06 bis 1e+07 Lastwechsel) für diese Strukturbauteile zu bestimmen. / It was developed a simple approach for the calculation of a modular construction system for box sections (profile structures) of different cross-sectional dimensions. These profile structures consists of WVC (Wood Veneer Composites). The approach maps the static load case and the fatigue behavior under pulsating three-point bending. By using a structural component made from commercial birch plywood, the calculation approach is specified and verified. Based on the force-deformation behavior of the analyzed single components in connection with the capillary-porous structure of the wood, the calculation approach dispense on an analysis of the tensions. Instead, a criterion, which calculates the critical normal strain in the outer fibers of the structural components, is used. Furthermore, a method of a low-cycle fatigue test (LCF, abbr. 1e+03 cycles) is presented. This method detects the “knee point" of the fatigue limit line for the profiles. That point is usually determined by the use of a high-cycle fatigue tests (HCF, 1e+06 until 1e+07 cycles).

Ce projet de thèse se situe dans le cadre de l'étude de la fiabilité prédictive de nouveaux concepts d'assemblages microélectroniques de type « system in package » SiP. L'objectif est de développer une méthodologie de fiabilité prédictive adaptée aux nouveaux concepts d'assemblage qui permet d'optimiser et de prédire les performances dès la phase de conception. Elle est ensuite appliquée sur des projets concrets. Cette méthodologie de fiabilité prédictive fait intervenir des études expérimentales, des simulations thermomécaniques et des analyses statistiques pour traiter les données et évaluer la fiabilité et les risques de défaillance. L'utilisation d'outils de simulation des composants électroniques est bien adaptée pour aider à l'évaluation des zones les plus fragiles, la mise en place des règles de conception et la détermination des paramètres les plus influents avec une réduction du temps de mise en marché d'un produit fiable et une optimisation des performances. Les études réalisées sur le silicium avec deux tests : bille sur anneau et test trois points montrent que le rodage et l'épaisseur ont une influence sur la variation de la contrainte et la déflexion du silicium à la rupture. Avec le test trois points, le déclenchement des fissures est lié à la qualité de sciage et de rodage. Cependant avec le test bille sur anneau, seule la qualité de surface influence le déclenchement des fissures. Le test bille sur anneau est bien adapté pour évaluer la qualité de surface du silicium. Avec les techniques chimiques de réduction de contraintes, comme la gravure humide et plasma, la résistance à la rupture a été considérablement améliorée. Ces tests de rupture sur le silicium ont permis de caractériser la rupture du silicium sous une contrainte de flexion et de compléter les résultats de simulation. Ces travaux démontrent, le besoin et l'utilité du prototypage virtuel des composants électroniques et de l'utilisation d'une méthodologie prédictive dans l'évaluation de la fiabilité en l’appliquant sur des composants réels. / This thesis project is a study of the predictive reliability of new microelectronic package concepts such as "system in package" SiP. The objective is to develop a reliable predictive methodology adapted to the new assembly concepts to optimize and to predict the performance at the design phase. Then, the methodology is applied to concrete projects. This methodology of predictive reliability involves the use of experimental studies, thermomechanical simulations and statistical analysis to process the data and assess the reliability and risks of failure. The use of simulation tools for electronic components is well suited to assist in the evaluation of the most fragile areas, the setting up of design rules and the determination of the most influential parameters with a reduction in the setup time market for a reliable and optimized performance. Studies on silicon strength are conducted with two tests: ball on ring test and on three-point bend test show that the grinding and the thickness influence the variation of the stress and deflection of the silicon at break. With the three points bend test, the onset of crack is linked to defects in sawing and grinding zone. However, with the ball on ring test, only the surface quality influences the initiation of cracks. The ball on ring test is well suited for evaluating the quality of the silicon surface. Chemical techniques of stress release, such as wet etching and plasma etching, improve significantly the strength of silicon samples. These tests on silicon dies are used to characterize the breakdown of silicon under bending test and to complete the simulation results. We have demonstrated in this work, the need and the usefulness of the virtual prototyping of electronic components and the use of a predictive methodology in assessing reliability.

The diploma thesis is focused on the evaluation of mechanical fracture parameters of concrete after exposure to high temperatures. In the introductory theoretical part general principles of fracture mechanics with the concentration on a linear elastic fracture mechanics and non-linear fracture models for the concrete are summarized. The meaning of the three-point bending fracture test used for determination of fracture parameters is also explained. Further the influence of high temperatures on the partial components of concrete and general modeling of temperature loading is described. The practical part is concerned with the evaluation of fire experiments on the concrete panels including numerical simulations using GiD and ATENA software. The evaluation of data obtained from the three-point bending test carried out on specimens with initial stress concentrator taken from concrete panels is a main part of the diploma thesis. The values of modulus of elasticity, effective fracture toughness, work of fracture and fracture energy are determined from the measured F–d and F–CMOD diagrams after their proper corrections in the GTDiPS application. The evaluation of the selected mechanical fracture parameters was performed by StiCrack software using effective crack model and work of fracture method and DKFM_BUT software using the double-K fracture model. Finally, the attention is paid to the analysis of the obtained data.

Es wird ein einfacher Berechnungsansatz für ein Baukastensystem aus Kastenprofilen verschiedener Querschnittsabmessungen erarbeitet. Diese Profile bestehen aus WVC (Wood Veneer Composites, Holzfurnierlagenverbundwerkstoffen). Der Ansatz bildet den statischen Lastfall und das Ermüdungsverhalten unter schwellende Dreipunktbiegung ab. Am Beispiel eines ausgewählten Strukturbauteils aus handelsüblichen Birkensperrholz wird der Berechnungsansatz konkretisiert und durch Versuche evaluiert. Aufbauend auf dem Kraft-Verformungsverhalten der analysierten Einzelbauteile und der kapillarporösen Struktur des Holzes wird bei dem Berechnungsansatz auf eine Analyse der Spannungen verzichtet. Stattdessen wird als Berechnungskriterium die kritische Normaldehnung in der Randfaser der Strukturbauteile genutzt. Weiterhin wird eine Methode vorgestellt um mittels niederzyklischen Ermüdungsversuchs (LCF, ca. 1e+03 Lastwechsel) den „Knickpunkt“ der Zeitfestigkeitslinie eines einstufigen Ermüdungsversuchs bei hohen Lastspielzahlen (HCF, 1e+06 bis 1e+07 Lastwechsel) für diese Strukturbauteile zu bestimmen. / It was developed a simple approach for the calculation of a modular construction system for box sections (profile structures) of different cross-sectional dimensions. These profile structures consists of WVC (Wood Veneer Composites). The approach maps the static load case and the fatigue behavior under pulsating three-point bending. By using a structural component made from commercial birch plywood, the calculation approach is specified and verified. Based on the force-deformation behavior of the analyzed single components in connection with the capillary-porous structure of the wood, the calculation approach dispense on an analysis of the tensions. Instead, a criterion, which calculates the critical normal strain in the outer fibers of the structural components, is used. Furthermore, a method of a low-cycle fatigue test (LCF, abbr. 1e+03 cycles) is presented. This method detects the “knee point" of the fatigue limit line for the profiles. That point is usually determined by the use of a high-cycle fatigue tests (HCF, 1e+06 until 1e+07 cycles).

The purpose of dissertation is the analysis of the calculation of fracture parameters using Double-K fracture model for quasi-brittle specimens with the stress concentrator loaded by three-point bending or wedge splitting. To calculation of these parameters was used the developed DKFM_BUT software in Microsoft Excel application with using of Visual Basic programming language. Furthermore, the adequate shape functions and compliance functions were introduced for the selected wedge splitting test configurations. Main part of this dissertation is the series of comprehensively implemented and evaluated fracture experiments on specimens from advanced building materials, while the attention was paid to the analysis of experimental data. Finally, the selected results obtained using mentioned software support were presented and discussed.