Applicability of the Hartree-Fock (HF) based random phase approximation (RPA) with several Skyrme effective interactions to the description of the isoscalar giant monopole (ISGMR) and the isoscalar giant dipole resonance (ISGDR) in 90Zr, 116Sn, 144Sm and 208Pb nuclei has been investigated. The existing Skyrme interactions SL1, SkM*, SGII, Sly4 and Sk255 were used. Hartree-Fock description of the ground state properties of all nuclei of interest was obtained using these Skyrme interactions. Transition strength distributions for the ISGMR and the ISGDR in nuclei of interest were calculated using coordinate space representation for the RPA in the Green’s function formalism with discretized continuum. A method of projecting out the spurious state contribution from the transition strength distribution and the transition density of the ISGDR was employed to eliminate spurious state mixing, due to a not fully selfconsistent description of the particle-hole interaction within the RPA. Differential cross sections of 240 MeV alpha-particles inelastic scattering on all nuclei of interest were calculated using the folding model within the distorted wave Born approximation (DWBA). Optical potentials were obtained by folding HF ground state densities with a alpha-nucleon density dependent Gaussian interaction. Parameters of the interaction were obtained by fitting experimental angular distribution of alpha-nucleus elastic scattering. The inelastic differential cross sections were calculated using both collective and microscopic transition densities. Possible underestimations of the energy weighted sum rule for the case of the ISGDR are reported. An alternative description for the ISGDR in nuclei based on the Fermi liquid drop model (FLDM) with the collisional Fermi surface distortion was investigated. The FLDM dispersion relation was obtained from the linearized Landau-Vlasov equation. Centroid energies, E0 and E1, and widths, gamma-0 and gamma-1, of the ISGMR and ISGDR, respectively, were calculated as functions of the damping parameter using appropriate boundary conditions. Comparison of the theoretical ratios of the ISGDR and ISGMR centroid energies, E1/E0, to the experimental values resulted in a damping parameter equal to 0.5, however, systematic overestimation of energy of the ISGMR and ISGDR by 2.0-2.5 MeV was observed. The applicability of the HF-RPA to the description for the ISGDR in nuclei is confirmed.

Nonlinear time history analysis is increasingly being used in the design of tall steel structures, but member sizes still must be determined by a designer before an analysis can be performed. Often the distribution of story strength is still based on an assumed first mode response as determined from the Equivalent Lateral Force (ELF) procedure. For tall buckling restrained braced frames (BRBFs), two questions remain unanswered: what brace distribution will minimize total brace area, while satisfying story drift and ductility limits, and is the ELF procedure an effective approximation of that distribution? In order to investigate these issues, an optimization algorithm was incorporated into the OpenSees dynamic analysis platform. The resulting program uses a genetic algorithm to determine optimum designs that satisfy prescribed drift/ductility limits during nonlinear time history analyses. The computer program was used to investigate the optimized distribution of brace strength in BRBFs with different heights. The results of the study provide insight into efficient design of tall buildings in high seismic areas and evaluate the effectiveness of the ELF procedure.

MetPreg, a composite developed by Touchstone Research Laboratories (Tridelphia, WV), is an aluminum metal matrix composite reinforced by continuous NextelTM 610 alumina fibers. The question is, after processing, are the NextelTM fibers affected in any way that their strengthening contribution to the composite is reduced? From experimentation and statistical analysis, a strength distribution of pre-processed NextelTM 610 fibers is formed and an empirical correlation is developed relating strength to the observed flaw size on the failed single fibers. This correlation is then independently applied to flaw size information gathered from fibers on the fracture surface of MetPreg samples to develop a separate strength distribution of post-processed NextelTM 610 fibers. The pre- and post-processed distributions are compared to one another to determine the effect, if any, that composite processing has on the strength of NextelTM 610 fibers. The results indicate that the in-situ strength distribution of fibers was increased by composite processing. / Master of Science

An experimental method was further developed to quantify the anisotropy of multi-site fatigue crack initiation behaviors in high strength Al alloys by four-point bend fatigue testing under stress control. In this method, fatigue crack initiation sites (fatigue weak-links, FWLs) were measured on the sample surface at different cyclic stress levels. The FWL density in an alloy could be best described using a three-parameter Weibull function of stress, though other types of sigmoidal functions might also be used to quantify the relationship between FWL density and stress. The strength distribution of the FWLs was derived from the Weibull function determined by fitting the FWLs vs. stress curve experimentally obtained. As materials properties, the FWL density and strength distribution could be used to evaluate the fatigue crack nucleation behaviors of engineering alloys quantitatively and the alloy quality in terms of FWL density and strength distribution. In this work, the effects of environment, types of microstructural heterogeneities and loading direction on FWLs were all studied in detail in AA7075-T651, AA2026-T3511, and A713 Al alloys, etc. It was also found that FWLs should be quantified as a Weibull-type function of strain instead of stress, when the applied maximum cyclic stress exceeded the yield strength of the tested alloys. In this work, four-point bend fatigue tests were conducted on the L-T (Rolling-Transverse), L-S (Rolling-Short transverse) and T-S planes of an AA7075-T651 alloy plate, respectively, at room temperature, 20 Hz, R=0.1, in air. The FWL populations, measured on these surfaces, were a Weibull-type function of the applied maximum cyclic stress, from which FWL density and strength distribution could be determined. The alloy showed a significant anisotropy of FWLs with the weak-link density being 11 mm-2, 15 mm-2 and 4 mm-2 on the L-T, L-S and T-S planes, respectively. Fatigue cracks were predominantly initiated at Fe-containing particles on the L-T and L-S planes, but only at Si-bearing particles on the T-S plane, profoundly demonstrating that the pre-fractured Fe-containing particles were responsible for crack initiation on the L-T and L-S planes, since the pre-fracture of these particles due to extensive deformation in the L direction during the prior rolling operation could only promote crack initiation when the sample was cyclically stressed in the L direction on both the L-T and L-S planes. The fatigue strengths of the L-T, L-S and T-S planes of the AA7075 alloy were measured to be 243.6, 273.0 and 280.6 MPa, respectively. The differences in grain and particle structures between these planes were responsible for the anisotropy of fatigue strength and FWLs on these planes. Three types of fatigue cracks from particles, type-I: the micro-cracks in the particles could not propagate into the matrix, i.e., type-II: the micro-cracks were fully arrested soon after they propagated into the matrix, and type-III: the micro-cracks became long cracks, were observed in the AA7075-T651 alloy after fatigue testing. By cross-sectioning these three-types of particles using Focused Ion Beam (FIB), it was found that the thickness of the particles was the dominant factor controlling fatigue crack initiation at the particles, namely, the thicker a pre-fractured Fe-containing particle, the easier it became a type-III crack on the L-T and L-S planes. On the T-S plane, there were only types-I and III Si-bearing particles at which crack were initiated. The type-I particles were less than 6.5 μm in thickness and type-III particles were thicker than 8.3 μm. Cross-sectioning of these particles using FIB revealed that these particles all contained gas pores which promoted crack initiation at the particles because of higher stress concentration at the pores in connection with the particles. It was also found that fatigue cracks did not always follow the any specific crystallographic planes within each grain, based on the Electron Backscatter Diffraction (EBSD) measurement. Also, the grain orientation did not show a strong influence on crack initiation at particles which were located within the grains. The topography measurements with an Atomic Force Microscope (AFM) revealed that Fe-containing particles were protruded on the mechanically polished surface, while the Si-bearing particles were intruded on the surface, which was consistent with hardness measurements showing that Si-bearing particles were softer (4.030.92 GPa) than Fe-containing ones (8.9 0.87 GPa) in the alloy. To verify the 3-D effects of the pre-fractured particles on fatigue crack initiation in high strength Al alloys, rectangular micro-notches of three different types of dimensions were fabricated using FIB in the selected grains on the T-S planes of both AA2024-T351 and AA7075-T651 Al alloys, to mimic the three types of pre-fractured particles found in these alloys. Fatigue testing on these samples with the micro-notches verified that the wider and deeper the micro-notches, the easier fatigue cracks could be initiated at the notches. In the AA2024-T351 samples, cracks preferred to propagate along the {111} slip plane with the smallest twist angle and relatively large Schmid factor. These experimental data obtained in this work could pave a way to building a 3-D quantitative model for quantification of fatigue crack initiation behaviors by taking into account the driving force and resistance to short crack growth at the particles in the surface of these alloys.

A planing catamaran is a high-powered, twin-hull water craft that develops the lift which supports its weight, primarily through hydrodynamic water pressure. Presently, there is increasing demand to further develop the catamaran's planing and seakeeping characteristics so that it is more effectively applied in today's modern military and pleasure craft, and offshore industry supply vessels. Over the course of the past ten years, Vorus (1994,1996,1998,2000) has systematically conducted a series of research works on planing craft hydrodynamics. Based on Vorus' planing monohull theory, he has developed and implemented a first order nonlinear model for planing catamarans, embodied in the computer code CatSea. This model is currently applied in planing catamaran design. However, due to the greater complexity of the catamaran flow physics relative to the monohull, Vorus's (first order) catamaran model implemented some important approximations and simplifications which were not considered necessary in the monohull work. The research of this thesis is for relieving the initially implemented approximations in Vorus's first order planing catamaran theory, and further developing and extending the theory and application beyond that currently in use in CatSea. This has been achieved through a detailed theoretical analysis, algorithm development, and careful coding. The research result is a new, complete second order nonlinear hydrodynamic theory for planing catamarans. A detailed numerical comparison of the Vorus's first order nonlinear theory and the second order nonlinear theory developed here is carried out. The second order nonlinear theory and algorithms have been incorporated into a new catamaran design code (NewCat). A detailed mathematical formulation of the base first order CatSea theory, followed by the extended second order theory, is completely documented in this thesis.

In der vorliegenden Arbeit wird die Frage untersucht, ob effektive Eigenschaften von Verbunden auch nach dem Auftreten einer Dehnungslokalisierung aufgrund von entfestigendem Materialverhalten noch durch numerische Homogenisierungsmethoden berechnet werden können. Ihr Nutzen für diesen Anwendungsfall wird in der Literatur kritisch beurteilt. Aus diesem Grund werden hier systematisch alle Teilaufgaben betrachtet, die zu diesem Zweck gelöst werden müssen. Die erste dieser Aufgaben ist die Charakterisierung der einzelnen Verbundbestandteile. Zur Demonstration einer experimentell gestützten Charakterisierung wird ein glasfaserverstärktes Epoxidharz als Beispielmaterial gewählt. Neben der Beschreibung von Faser- und Matrixmaterial wird besonderes Augenmerk auf die Charakterisierung der Grenzschicht zwischen beiden gelegt. Die für die Glasfasern vorliegenden Festigkeitsmessungen entsprechen nicht der Kettenhypothese. Daher werden zahlreiche Verallgemeinerungen der Weibull-Verteilung untersucht, um störende Effekte zu erfassen. Schließlich werden Wahrscheinlichkeitsverteilungen hergeleitet, die Faserbrüche im Bereich der Einspannung einbeziehen. Die Messwerte können von diesen Verteilungen gut wiedergegeben werden. Zusätzlich macht ihre Anwendung das aufwändige Aussortieren und Wiederholen jener Experimente unnötig, bei denen der Faserbruch im Klemmbereich auftritt. Zur Modellierung der Grenzfläche wird ein Kohäsivzonengesetz entwickelt. Die Bestimmung seiner Parameter erfolgt anhand von Daten aus Pullout- und Einzelfaserfragmentierungsversuchen. Aus diesen ermittelte Festigkeiten und Energiefreisetzungsraten weisen eine sehr gute Übereinstimmung zwischen beiden Versuchen auf. Dabei erfolgt die Parameteridentifikation mithilfe von Finite-Elemente-Modellen anstatt der häufig genutzten vereinfachten analytischen Modelle, welche üblicherweise eine schlechtere Übereinstimmung erreichen. Sobald eine Dehnungslokalisierung auftritt, ist neben der Materialmodellierung auch das Homogenisierungsschema zu verallgemeinern. Zu diesem gehören die Generierung repräsentativer Volumenelemente, Randbedingungen (RB) und ein Mittelungsoperator. Anhand des aktuellen Standes der Literatur werden die Randbedingungen als ein signifikanter Schwachpunkt von Homogenisierungsverfahren erkannt. Daher erfolgt die Untersuchung periodischer RB, linearer Verschiebungsrandbedingungen und minimal kinematischer RB sowie zweier adaptiver RB, nämlich Lokalisierungspfad-ausgerichteter RB und generalisiert periodischer RB. Unter der Bezeichnung Tesselationsrandbedingungen wird ein weiterer Typ adaptiver RB vorgeschlagen. Zunächst erfolgt der Beweis, dass alle drei adaptiven RB die Hill-Mandel-Bedingung erfüllen. Des Weiteren wird mittels einer Modifikation der Hough-Transformation ein systematischer Fehler derselben bei der Bestimmung der Richtung von Lokalisierungszonen eliminiert. Schließlich werden die Eigenschaften aller Randbedingungen an verschiedenen Beispielen demonstriert. Dabei zeigt sich, dass nur Tesselationsrandbedingungen sowohl beliebige Richtungen von Lokalisierungszonen erlauben als auch fehlerhafte Lokalisierungen in Eckbereichen ausschließen. Zusammengefasst können in der Literatur geäußerte grundlegende Einschränkungen hinsichtlich der Anwendbarkeit numerischer Homogenisierungsverfahren beim Auftreten von Dehnungslokalisierungen aufgehoben werden. Homogenisierungsmethoden sind somit auch für entfestigendes Materialverhalten anwendbar. / The thesis at hand is concerned with the question if numerical homogenization schemes can be of use in deriving effective material properties of composite materials after the onset of strain localization due to strain softening. In this case, the usefulness of computational homogenization methods has been questioned in the literature. Hence, all the subtasks to be solved in order to provide a successful homogenization scheme are investigated herein. The first of those tasks is the characterization of the constituents, which form the composite. To allow for an experimentally based characterization an exemplary composite has to be chosen, which herein is a glass fiber reinforced epoxy. Hence the constituents to be characterized are the epoxy and the glass fibers. Furthermore, special attention is paid to the characterization of the interface between both materials. In case of the glass fibers, the measured strength values do not comply with the weakest link hypothesis. Numerous generalizations of the Weibull distribution are investigated, to account for interfering effects. Finally, distributions are derived, that incorporate the possibility of failure inside the clamped fiber length. Application of such a distribution may represent the measured data quite well. Additionally, it renders the cumbersome process of sorting out and repeating those tests unnecessary, where the fiber fails inside the clamps. Identifying the interface parameters of the proposed cohesive zone model relies on data from pullout and single fiber fragmentation tests. The agreement of both experiments in terms of interface strength and energy release rate is very good, where the parameters are identified by means of an evaluation based on finite element models. Also, the agreement achieved is much better than the one typically reached by an evaluation based on simplified analytical models. Beside the derivation of parameterized material models as an input, the homogenization scheme itself needs to be generalized after the onset of strain localization. In an assessment of the current state of the literature, prior to the generation of representative volume elements and the averaging operator, the boundary conditions (BC) are identified as a significant issue of such a homogenization scheme. Hence, periodic BC, linear displacement BC and minimal kinematic BC as well as two adaptive BC, namely percolation path aligned BC and generalized periodic BC are investigated. Furthermore, a third type of adaptive BC is proposed, which is called tesselation BC. Firstly, the three adaptive BC are proven to fulfill the Hill-Mandel condition. Secondly, by modifying the Hough transformation an unbiased criterion to determine the direction of the localization zone is given, which is necessary for adaptive BC. Thirdly, the properties of all the BC are demonstrated in several examples. These show that tesselation BC are the only type, that allows for arbitrary directions of localization zones, yet is totally unsusceptible to spurious localization zones in corners of representative volume elements. Altogether, fundamental objections, that have been raised in the literature against the application of homogenization in situations with strain localization, are rebutted in this thesis. Hence, the basic feasibility of homogenization schemes even in case of strain softening material behavior is shown.