Adiabatic shear localization: occurrence, theories, and applications

Smaller Deborah number inducing more serrated plastic flow of metallic glass

Spherical nano-indentations of Cu46Zr54 bulk metallic glass (BMG) model systems were performed using molecular dynamics (MD) computer simulations, focusing specifically on the physical origin of serrated plastic flow. The results demonstrate that there is a direct correlation between macroscopic flow serration and underlying irreversible rearrangement of atoms, which is strongly dependent on the loading (strain) rate and the temperature. The serrated plastic flow is, therefore, determined by the magnitude of such irreversible rearrangement that is inhomogeneous temporally. A dimensionless Deborah number is introduced to characterize the effects of strain rate and temperature on serrations. Our simulations are shown to compare favorably with the available experimental observations.

A universal Biot number determining the susceptibility of ceramics to quenching

A universal Biot number of ceramics, which not only determines the susceptibility of the ceramics to quenching but also indicates the duration that the ceramics fail during thermal shock, is theoretically obtained. The present analysis shows that the thermal shock failure of the ceramics with a Biot number greater than this universal value is a very rapid process that just occurs in the initial regime of the heat conduction of the ceramics. This universal Biot number provides a guide to the selection of the ceramics applying to the thermostructural engineering including thermal shock.

Estimation of the number of purse-seiner sets on tuna associated with dolphins in the Eastern Pacific Ocean during 1959-1980

ENGLISH: Annual estimates of the number of purse-seine sets made on tunas associated with dolphins are needed to estimate the total number of dolphins killed incidentally by the eastern Pacific tuna fishery. The most complete source of data, the Inter-American Tropical Tuna Commission's logbook data base, was used in this study. In the logbook data base, most sets are identified as being either associated with dolphins or not associated with dolphins. Some sets are not identified in this respect. However, the number of these unidentified sets which were associated with dolphins have been estimated by stratifying the logbook data according to whether or not any tuna were caught, whether or not the nearest identified set was associated with dolphins, and the distance to the nearest identified set. Most of the unidentified sets fell in strata characterized by a proportion of sets on tuna associated with dolphins that was lower than the overall unstratified proportion. Landings data were used to estimate the number of sets on tunas associated with dolphins from fishing trips not included in the logbook data base. SPANISH: Se necesitan las estimaciones anuales de la cantidad de lances realizados sobre atunes asociados con delfines para calcular todo el número de delfines muertos accidentalmente en la pesca atunera del Pacífico oriental. Se empleó en este estudio la fuente más completa-los datos de la Comisión Interamericana del Atún Tropical, proveniente de los cuadernos de bitácora. En éstos, la mayoría de los lances han sido identificados ya sea como asociados o no asociados con delfines. Algunos de los lances no han sido identificados a este respecto. Sin embargo, se ha estimado el número de estos lances asociados con delfines que no se habían identificado, al estratificar los datos de bitácora de acuerdo a si se había o no capturado atún, a si el lance identificado más próximo era o no un lance asociado con delfines y al averiguar la distancia del lance identificado más cercano. La mayoría de los lances sin identificar se colocan en los estratos caracterizados por una proporción de lances sobre atunes asociados con delfines, inferior a la proporción general sin estratificar. Se usaron los datos de los desembarques para calcular la cantidad de lances sobre atunes asociados con delfines en viajes pesqueros que no fueron incluídos en la base de los datos de bitácora. (PDF contains 73 pages.)

Generalized modal identification of linear and nonlinear dynamic systems

This dissertation is concerned with the problem of determining the dynamic characteristics of complicated engineering systems and structures from the measurements made during dynamic tests or natural excitations. Particular attention is given to the identification and modeling of the behavior of structural dynamic systems in the nonlinear hysteretic response regime. Once a model for the system has been identified, it is intended to use this model to assess the condition of the system and to predict the response to future excitations.

A new identification methodology based upon a generalization of the method of modal identification for multi-degree-of-freedom dynaimcal systems subjected to base motion is developed. The situation considered herein is that in which only the base input and the response of a small number of degrees-of-freedom of the system are measured. In this method, called the generalized modal identification method, the response is separated into "modes" which are analogous to those of a linear system. Both parametric and nonparametric models can be employed to extract the unknown nature, hysteretic or nonhysteretic, of the generalized restoring force for each mode.

In this study, a simple four-term nonparametric model is used first to provide a nonhysteretic estimate of the nonlinear stiffness and energy dissipation behavior. To extract the hysteretic nature of nonlinear systems, a two-parameter distributed element model is then employed. This model exploits the results of the nonparametric identification as an initial estimate for the model parameters. This approach greatly improves the convergence of the subsequent optimization process.

The capability of the new method is verified using simulated response data from a three-degree-of-freedom system. The new method is also applied to the analysis of response data obtained from the U.S.-Japan cooperative pseudo-dynamic test of a full-scale six-story steel-frame structure.

The new system identification method described has been found to be both accurate and computationally efficient. It is believed that it will provide a useful tool for the analysis of structural response data.

Non-linear dispersive waves with a small dissipation

The general theory of Whitham for slowly-varying non-linear wavetrains is extended to the case where some of the defining partial differential equations cannot be put into conservation form. Typical examples are considered in plasma dynamics and water waves in which the lack of a conservation form is due to dissipation; an additional non-conservative element, the presence of an external force, is treated for the plasma dynamics example. Certain numerical solutions of the water waves problem (the Korteweg-de Vries equation with dissipation) are considered and compared with perturbation expansions about the linearized solution; it is found that the first correction term in the perturbation expansion is an excellent qualitative indicator of the deviation of the dissipative decay rate from linearity.

A method for deriving necessary and sufficient conditions for the existence of a general uniform wavetrain solution is presented and illustrated in the plasma dynamics problem. Peaking of the plasma wave is demonstrated, and it is shown that the necessary and sufficient existence conditions are essentially equivalent to the statement that no wave may have an amplitude larger than the peaked wave.

A new type of fully non-linear stability criterion is developed for the plasma uniform wavetrain. It is shown explicitly that this wavetrain is stable in the near-linear limit. The nature of this new type of stability is discussed.

Steady shock solutions are also considered. By a quite general method, it is demonstrated that the plasma equations studied here have no steady shock solutions whatsoever. A special type of steady shock is proposed, in which a uniform wavetrain joins across a jump discontinuity to a constant state. Such shocks may indeed exist for the Korteweg-de Vries equation, but are barred from the plasma problem because entropy would decrease across the shock front.

Finally, a way of including the Landau damping mechanism in the plasma equations is given. It involves putting in a dissipation term of convolution integral form, and parallels a similar approach of Whitham in water wave theory. An important application of this would be towards resolving long-standing difficulties about the "collisionless" shock.

Fracture of materials undergoing solid-solid phase transformation

A large number of technologically important materials undergo solid-solid phase transformations. Examples range from ferroelectrics (transducers and memory devices), zirconia (Thermal Barrier Coatings) to nickel superalloys and (lithium) iron phosphate (Li-ion batteries). These transformations involve a change in the crystal structure either through diffusion of species or local rearrangement of atoms. This change of crystal structure leads to a macroscopic change of shape or volume or both and results in internal stresses during the transformation. In certain situations this stress field gives rise to cracks (tin, iron phosphate etc.) which continue to propagate as the transformation front traverses the material. In other materials the transformation modifies the stress field around cracks and effects crack growth behavior (zirconia, ferroelectrics). These observations serve as our motivation to study cracks in solids undergoing phase transformations. Understanding these effects will help in improving the mechanical reliability of the devices employing these materials.

In this thesis we present work on two problems concerning the interplay between cracks and phase transformations. First, we consider the directional growth of a set of parallel edge cracks due to a solid-solid transformation. We conclude from our analysis that phase transformations can lead to formation of parallel edge cracks when the transformation strain satisfies certain conditions and the resulting cracks grow all the way till their tips cross over the phase boundary. Moreover the cracks continue to grow as the phase boundary traverses into the interior of the body at a uniform spacing without any instabilities. There exists an optimal value for the spacing between the cracks. We ascertain these conclusion by performing numerical simulations using finite elements.

Second, we model the effect of the semiconducting nature and dopants on cracks in ferroelectric perovskite materials, particularly barium titanate. Traditional approaches to model fracture in these materials have treated them as insulators. In reality, they are wide bandgap semiconductors with oxygen vacancies and trace impurities acting as dopants. We incorporate the space charge arising due the semiconducting effect and dopant ionization in a phase field model for the ferroelectric. We derive the governing equations by invoking the dissipation inequality over a ferroelectric domain containing a crack. This approach also yields the driving force acting on the crack. Our phase field simulations of polarization domain evolution around a crack show the accumulation of electronic charge on the crack surface making it more permeable than was previously believed so, as seen in recent experiments. We also discuss the effect the space charge has on domain formation and the crack driving force.