Ni-base superalloys are widely used in hot sections of gas turbine engines due to the high resistance to fatigue and creep at elevated temperatures. Due to the demands for improved performance and efficiency in applications of the superalloys, new and improved higher temperature alloy systems are being developed. Constitutive relations for these materials need to be formulated accordingly to predict behavior of cracks at notches in components under cyclic loading with peak dwell periods representative of gas turbine engine disk materials. Since properties are affected by microstructure at various length scales ranging from 10 nm tertiary γ' precipitates to 5-30 μm grains, hierarchical multiscale modeling is essential to address behavior at the component level. The goal of this work is to develop a framework for hierarchical multiscale modeling network that features linkage of several fine scale models to incorporate relevant microstructure attributes into the framework to improve the predictability of the constitutive model. This hierarchy of models is being developed in a collaborative research program with the Ohio State University. The fine scale models include the phase field model which addresses dislocation dissociation in the γ matrix and γ' precipitate phases, and the critical stresses from the model are used as inputs to a grain scale crystal plasticity model in a bottom-up fashion. The crystal plasticity model incorporates microstructure attributes by homogenization. A major task of the present work is to link the crystal plasticity model, informed by the phase field model, to the macroscale model and calibrate models in a top-down fashion to experimental data for a range of microstructures of the improved alloy system by implementing a hierarchical optimization scheme with a parameter clustering strategy. Another key part of the strategy to be developed in this thesis is the incorporation of polycrystal plasticity simulations to model a large range of virtual microstructures that have not been experimentally realized (processed), which append the experimentally available microstructures. Simulations of cyclic responses with dwell periods for this range of virtual (and limited experimental) polycrystalline microstructures will be used to (i) provide additional data to optimize parameter fitting for a microstructure-insensitive macroscopic internal state variable (ISV) model with thermal recovery and rate dependence relevant to the temperatures of interest, and (ii) provide input to train an artificial neural network that will associate the macroscopic ISV model parameters with microstructure attributes for this material. Such microstructure sensitive macroscopic models can then be employed in component level finite element studies to model cyclic behavior with dwell times at smooth and cracked notched specimens.

Polymer clay nanocomposites have been a popular area of materials research since they were first introduced in the 1990s. The inclusion of clays into many different host polymers has been shown to improve the properties of matrix polymers in a number of ways including increased mechanical strength, thermal stability and improved barrier properties while keeping the composite light weight and transparent. Although there is a great deal of published work on the preparation and property measurements of polymer clay nanocomposites, there is no model to design a nanocomposite with a given set of properties for a specific end-use. While it is important to know the structure property relationships of materials, the understanding of how nanocomposites reach their final forms and properties is equally important. A thorough understanding of processing effects on the final structure of polymer clay nanocomposites is still missing. With this perspective, this thesis addresses building structure-processing relationships of polymer clay nanocomposites by analyzing multiaxial deformation behavior using in-situ x-ray scattering techniques. This thesis can be divided into two distinct parts. The first part concerns the design of the in-situ multiaxial deformation device (IMDD) used to create the deformation conditions that polymers go through during processing such as blow molding and thermoforming. The device was designed to overcome several concerns with in situ measurement by maintaining constant sample to detector distance, minimizing the material between the incident beam and the detectors, as well as exposing the same point on the sample throughout deformation. A new design to create biaxial deformation, termed in-situ biaxial deformation device (IBDD), is also introduced in this part of the thesis.. In addition, a new heating unit, attached to IBDD, is designed for higher temperature studies, up to 150°C, to imitate industrial processing conditions more closely. The second part of the thesis addresses the effect of strain, strain rate, and temperature as well as the amount of clay on the polymer morphology evolution during multiaxial deformation.. Two different polymer/clay systems were studied: poly(ethylene)/clay and poly(propylene)/clay. It was observed that the morphological evolution of polyethylene and polypropylene is affected by the existence of clay platelets as well as the deformation temperature and the strain rate. Martensitic transformation of orthorhombic polyethylene crystals into monoclinic crystal form was observed under strain but is hindered in the presence of clay nanoplatelets. The morphology evolution of poly(propylene) crystal structure during multiaxial deformation was more subtle where the most stable α-crystalline form went through strain induced melting. This was more noticeable in the nanocomposites with clays up to 5 wt%. It was also noted that the thickness of the interlamellar amorphous region increased with increasing strain at room temperature due to the elongation of the amorphous chains. The increase in the amorphous layer thickness is slightly higher for the poly(ethylene)/clay nanocomposites compared to neat poly(ethylene) while the increase in the lamellar long spacing is slightly higher for the neat poly(propylene) compared to poly(propylene)/clay nanocomposites. The rate of change in the characteristic repeat distance in both poly(ethylene) and poly(propylene) systems is higher at faster strain rates, at room temperature, where it remained constant during higher temperature deformations. Time dependent recovery after deformation studies have shown that poly(ethylene)/clay system reverts back to its initial configuration. The recovery in the amorphous chains was however observed to take longer in the clay added poly(ethylene)s. Crystalline relaxation was observed to happen almost instantly in the poly(ethylene)/clay system. On the other hand, amorphous chains in the poly(propylene)/clay system did not revert back to the initial configuration in the period of time that the recovery observations were performed while the crystalline configuration recovered back almost fully in the given time.

Uranium (U) exhibits a high temperature body-centered cubic (b.c.c.) allotrope that is often stabilized by alloying with transition metals such as Zr, Mo, and Nb for technological applications. One such application involves U-Zr as nuclear fuel, where radiation damage and diffusion (processes heavily dependent on point defects) are of vital importance. Metallic nuclear fuels swell under fission conditions, creating fission product gases such as helium, xenon and krypton. Several systems of U are examined within a density functional theory framework utilizing projector augmented wave pseudopotentials. Two separate generalized gradient approximations of the exchange-correlation are used to calculate defect properties and are compared. The bulk modulus, the lattice constant, and the Birch-Murnaghan equation of state for the defect free b.c.c. uranium allotrope are calculated. Defect parameters calculated include energies of formation of vacancies in the α and γ allotropes, as well as self-interstitials, Zr, He, Xe and Kr interstitial and substitutional defects. The results for vacancies agree very well with experimental and previous computational studies. The most probable self-interstitial site in γ-U is the <110> dumbbell and the most probable defect location for dilute Zr in γ-U is the substitutional site. The most likely position for Xe and Kr atoms in uranium is the substitutional site. Helium atoms are likely to be found in a wide variety of defect positions due to the comparable formation energies of all defect configurations analyzed.

High voltage power transformers are designed to withstand a variety of overvoltages and short circuit forces. Occurrence of these events in a power system is natural, inevitable, and one of the main causes of transformer failure. Therefore, an early and reliable detection of an incipient fault is paramount. To this end, diagnostic testing and condition monitoring, not only enables power utilities in early detection of incipient fault-like conditions, but also is a practical way of optimizing existing assets, lowering operating costs, scheduling maintenance, preventing unplanned outages, etc. and consequently improve efficiency. Over the years, many monitoring and diagnostic methods have evolved. In par- ticular, low voltage impulse and frequency response analysis or transfer function approaches have emerged as useful tools in detecting winding deformations. Literature study reveals that although much has been acclaimed about these methods, advancement in interpretation of acquired data must be rigorously pursued, to facilitate a more meaningful assessment. As a matter of fact, diagnosis (which means interpretation of monitored data) has at-the-most been confined to a mere comparison of two subsequently acquired data sets. This philosophy certainly needs to be improved, to realize the true potential of monitoring/diagnostic tools. Achieving this goal calls for newer impetus. It is natural that there will arise many problems while achieving this goal and they will have to be resolved. Keeping these aspects in mind, the objective of this thesis was aimed at developing Solutions to two specific topics that are closely related to and concern the transformer winding, namely, * An efficient solution to the generalized model of a transformer winding, with no particular limitation on the size of network and number of windings, no restriction on circuit topology and terminal condition, etc. * Propose a method to locate the position, quantum and type of change (i.e. deformation) a model winding undergoes, based on terminal measurements. Details of these approaches are presented in this thesis, which is divided into two parts. 1. A comprehensive analysis of the behaviour of a transformer winding under impulse excitation and its interaction with adjacent windings was until now severely limited, due to the simplifying assumptions imposed (by the existing approaches), like neglecting interaction with neighbouring windings, Ignoring loss, considering only a few sections, etc. thereby rendering the computed results less accurate. A solution considering all these aspects often times results in a very large-sized circuit that needs to be solved. Although circuit simulation software afford iterative solutions, a direct estimation of poles and zeros of any desired network function is not possible. In the first part of the thesis, a novel and closed-form (i.e. analytical) solution based on state space analysis is proposed. It is shown, how the renders the entire computation to be purely numeric. Thus, time-consuming symbolic manipulations are avoided. With this feature, there is practically no limit on the size of network and no restriction on circuit topologies that can be considered. So, virtually any number of windings of a transformer can be considered, permitting a comprehensive analysis of winding behaviour and its interactions. Further, the formulation also permits computation of poles and zeros of any desired network function (e.g. transfer admittance), response to any excitation (e.g. neutral current, transferred surge), estimation of voltage distribution, etc. with little extra effort. Hence, it would be apppropriate to term the proposed method as a \Generalized" solution. For the sole purpose of demonstration, a large-sized network (representing a two-winding transformer with 250 sections/winding) was solved and required only 700 seconds. This shows the time-efficiency achieved, and also that it is free from issues like numerical instability, convergence problems, etc. encountered in some of the existing methods. 2. Detection of mechanical deformation in transformer windings can be achieved with a fair degree of sensitivity using frequency response methods. However, a major challenge that has remained elusive is ascertaining the \extent of damage" and likewise \its location along the winding". It is needless to say that finding these answers is crucial. Ideally, a diagnosis tool is expected to be endowed with powers to answer these questions. Therefore, it is desirable to explore alternative ways of harnessing these embedded features, if any. This was the next motivation. Obviously, a direct solution to this problem on an actual transformer winding is far too complex. Hence, in this preliminary effort a solution was attempted considering a model winding. However, care was taken to incorporate other winding-related nuances as far as practicable. The method was formulated based on quantities measured at the terminals. In the second part of the thesis, a novel algorithm is proposed for determining the location, extent and type of changes intrroduced in a model winding, based on terminal measurements. It employs the well-known properties of driving-point functions and adopts an iterative circuit synthesis approach. From knowledge of the measured short-circuit and open-circuit natural frequencies, and some relevant winding design data, an equivalent circuit was synthesized (called reference circuit). Next, changes were introduced at different locations in the model winding and natural frequencies measured again. Corresponding to every new set of measured natural frequencies, a fresh circuit was synthesized (with topology remaining unchanged). A comparison of these circuits with the reference circuit revealed that a mapping could be established between changes introduced in the model winding and those predicted by the synthesized circuits. Initially, the underlying principle is discussed, and thereafter, the experimental results are presented for both continuous-disc and interleaved winding representations. The case studies involved examples wherein changes in the model winding were made to elements connected to a single tap, two physically different tap positions, multiple changes to different elements, and so on. In all cases, the positions of all the `changes' were reasonably well locatable, and so was the `type of change'. The results were very encouraging. In summary, localization of changes based on terminal measurements, is shown to be a possibility. Lastly, it is conjectured that these findings could be of some assistance in addressing the ultimate task of locating mechanical deformations in actual transformer windings.

Thesis (doctoral)--Westfälische Wilhelms-Universität Münster, 2003. / "Dezember 2003"--P. [2] of cover. Includes bibliographical references (p. 132-139). Also available via the World Wide Web.

Thesis (Ph. D.)--University of Washington, 2001. / Vita. Includes bibliographical references (p. 104-108).

Eine einfache Darstellung der Grundgleichungen für 'Große Deformationen' und Herleitung eines geeigneten Fehlerschätzers für die adaptive FEM.

In this paper we continue the considerations of [5] (CSC/09-05). A numerical study for the parameter identification problem with linear elastic material and large deformations is presented. We discuss the numerical implementation in MATLAB and illustrate some results for a 2D test problem.

A curved nonlinear finite element is developed in this work to observe the behavior of slender arches which undergo large deformations. The derivation of the strain equation is based upon the assumption that cross sections of the undeformed state remain undeformed and plane, but not necessarily normal to the centroidal axis during deformation. It is also assumed that the strain will be small and the rotations will be finite. The in-plane bending and the buckling modes for arches with fixed end and hinged end supports are analyzed. Deep circular arches and deep arches with arbitrary geometry of the centroidal axis are studied. Vertical concentrated loads, uniformly distributed loads, a combination of concentrated and distributed loads, and nonsymmetrical loads are considered. The governing differential equations are differentiated with respect to time to give a system of rate equations. Using these equations, the original nonlinear differential equations are solved using the Runge-Kutta scheme with Simpson's coefficients. If the solution drifts, a Newton-Raphson iteration scheme is used to return the solution to the equilibrium path.

Darbe pasiūlyta tempiamojo betono įtempių - deformacijų priklausomybė trumpalaikio ir ilgalaikio apkrovimo atveju. Pasiūlyta priklausomybė gauta, taikant EC2 momentų–kreivių priklausomybių apskaičiavimo metodiką. Atlikta lenkiamųjų gelžbetoninių elementų įtempių ir deformacijų priklausomybių analizė. Apžvelgti tokių elementų deformacijų skaičiavimo metodai ir matematiniai modeliai, apžvelgti paskelbti literatūros šaltiniai, susijusę su lenkiamųjų gelžbetoninių elementų deformacijomis. Skaitinio eksperimento pagalba sudaryta lenkiamųjų gelžbetoninių elementų duomenų imtis, išnagrinėta trumpalaike ir ilgalaike apkrova veikiami lenkiamieji gelžbetoniniai elementai, deformacijos ir jas lemiantys faktoriai, atlikta jų analizė. Taikant VGTU tiltų ir specialiųjų statinių katedroje pasiūlytą sluoksnių metodą iš skaitinių eksperimentų gautų momentų-kreivių diagramų gautos supleišėjusio tempiamojo betono įtempių-deformacijų priklausomybės. Parinkti pagrindiniai teorinės diagramos parametrai, priklausomai nuo betono klasės, armavimo procento bei valkšnumo koeficiento. Gautoji priklausomybė pritaikyta gelžbetoninių sijų kreivių apskaičiavimui sluoksnių metodu. Gautieji rezultatai palyginti su empirinėmis EC2 normų prikalsumybėmis gautais rezultatais. Palyginamoji gautų skaičiavimo rezultatų analizė parodė gerą abiem metodais gautų rezultatų atitikimą. Gautoji priklausomybė gali būti pritaikyta netiesiniuose skaičiavimuose, taikant baigtinių elementų metodą. / The paper suggests tension concrete stress-strain dependence of the short-term and long-term case-load of the EC2 method. Bending reinforced concrete elements of stress and strain dependence are analyzed. Presented overview of such elements deformation calculation methods and mathematical models, highlight the relevance literature review, relating to bending reinforced concrete elements. Collected bending reinforced concrete elements (numerical experiments) data, examined short-term and long term effects of load to bended reinforced concrete elements, deformations and the determining factors, performed their analysis. For the purposed of VGTU bridges and special structures department’s constitutive model from the numerical experiments obtained moment-curvature relationships derived the charts of cracked pulling concrete stress-strain dependence. Choose the basic theoretical parameters of the relationships, depending on the class of concrete, reinforcement rates, and creep coefficient. The calculation results are compared with the experimental beam data. Performed calculation results of the analysis showed quite accurate results with the derived dependencies.