A crack on the interface of piezo-electric bodies

Singularities of elastic and electric fields are investigated at the tip of a crack on the interface of two anisotropic piezo-electric media under various boundary conditions on the crack surfaces. The Griffith formulae are obtained for increments of energy functionals due to growth of the crack and the notion of the energy release matrix is introduced. Normalization conditions for bases of singular solution are proposed to adapt them to the energy, stress, and deformation fracture criteria. Connections between these bases are determined and additional properties of the deformation basis related to the notion of electric surface enthalpy are established.

Simulation on the process of fatigue crack initiation in a martensitic stainless steel

Die vorliegende Arbeit beschäftigt sich mit der Computersimulation des Rissinitiierungsprozesses für einen martensitischen Stahl, der der niederzyklischen Ermüdung unterworfen wurde. Wie auf der Probenoberfläche beobachtet wurde, sind die Initiierung und das frühe Wachstum dieser Mikrorisse in hohem Grade von der Mikrostruktur abhängig. Diese Tatsache wurde in mesoskopischen Schädigungsmodellen beschrieben, wobei die Körner als einzelne Kristalle mit anisotropem Materialverhalten modelliert wurden. Das repräsentative Volumenelement (RVE), das durch einen Voronoi-Zerlegung erzeugt wurde, wurde benutzt, um die Mikrostruktur des polykristallinen Materials zu simulieren. Spannungsverteilungen wurden mit Hilfe der Finiten-Elemente-Methode mit elastischen und elastoplastischen Materialeigenschaften analysiert. Dazu wurde die Simulation zunächst an zweidimensionalen Modellen durchgeführt. Ferner wurde ein vereinfachtes dreidimensionales RVE hinsichtlich des sowohl dreidimensionalen Gleitsystems als auch Spannungszustandes verwendet. Die kontinuierliche Rissinitiierung wurde simuliert, indem der Risspfad innerhalb jedes Kornes definiert wurde. Die Zyklenanzahl bis zur Rissinitiierung wurde auf Grundlage der Tanaka-Mura- und Chan-Gleichungen ermittelt. Die Simulation lässt auf die Flächendichten der einsegmentige Risse in Relation zur Zyklenanzahl schließen. Die Resultate wurden mit experimentellen Daten verglichen. Für alle Belastungsdehnungen sind die Simulationsergebnisse mit denen der experimentellen Daten vergleichbar.

Analytical Study of Light Propagation in Highly Nonlinear Media

The present dissertation is devoted to the construction of exact and approximate analytical solutions of the problem of light propagation in highly nonlinear media. It is demonstrated that for many experimental conditions, the problem can be studied under the geometrical optics approximation with a sufficient accuracy. Based on the renormalization group symmetry analysis, exact analytical solutions of the eikonal equations with a higher order refractive index are constructed. A new analytical approach to the construction of approximate solutions is suggested. Based on it, approximate solutions for various boundary conditions, nonlinear refractive indices and dimensions are constructed. Exact analytical expressions for the nonlinear self-focusing positions are deduced. On the basis of the obtained solutions a general rule for the single filament intensity is derived; it is demonstrated that the scaling law (the functional dependence of the self-focusing position on the peak beam intensity) is defined by a form of the nonlinear refractive index but not the beam shape at the boundary. Comparisons of the obtained solutions with results of experiments and numerical simulations are discussed.

Development of mechanical methods for cell-tray propagation and field transplanting of dwarf napiergrass (Pennisetum purpureum Schumach.)

Since dwarf napiergrass (Pennisetum purpureum Schumach.) must be propagated vegetatively due to lack of viable seeds, root splitting and stem cuttings are generally used to obtain true-to-type plant populations. These ordinary methods are laborious and costly, and are the greatest barriers for expanding the cultivation area of this crop. The objectives of this research were to develop nursery production of dwarf napiergrass in cell trays and to compare the efficiency of mechanical versus manual methods for cell-tray propagation and field transplanting. After defoliation of herbage either by a sickle (manually) or hand-mowing machine, every potential aerial tiller bud was cut to a single one for transplanting into cell trays as stem cuttings and placed in a glasshouse over winter. The following June, nursery plants were trimmed to a 25–cm length and transplanted in an experimental field (sandy soil) with 20,000 plants ha^(−1) either by shovel (manually) or Welsh onion planter. Labour time was recorded for each process. The manual defoliation of plants required 44% more labour time for preparing the stem cuttings (0.73 person-min. stemcutting^(−1)) compared to using hand-mowing machinery (0.51 person-min. stem-cutting^(−1)). In contrast, labour time for transplanting required an extra 0.30 person-min. m^(−2) (14%) using the machinery compared to manual transplanting, possibly due to the limited plot size for machinery operation. The transplanting method had no significant effect on plant establishment or plant growth, except for herbage yield 110 days after planting. Defoliation of herbage by machinery, production using a cell-tray nursery and mechanical transplanting reduced the labour intensity of dwarf napiergrass propagation.