On the initiation of boudinage and folding instabilities in layered elasto-visco-plastic solids - Insights from natural microstructures and numerical simulations

The present understanding of the initiation of boudinage and folding structures is based on viscosity contrasts and stress exponents, considering an intrinsically unstable state of the layer. The criterion of localization is believed to be prescribed by geometry-material interactions, which are often encountered in natural structures. An alternative localization phenomenon has been established for ductile materials, in which instability emerges for critical material parameters and loading rates from homogeneous conditions. In this thesis, conditions are sought under which this type of instability prevails and whether localization in geological materials necessarily requires a trigger by geometric imperfections. The relevance of critical deformation conditions, material parameters and the spatial configuration of instabilities are discussed in a geological context. In order to analyze boudinage geometries, a numerical eigenmode analysis is introduced. This method allows determining natural frequencies and wavelengths of a structure and inducing perturbations on these frequencies. In the subsequent coupled thermo-mechanical simulations, using a grain size evolution and end-member flow laws, localization emerges when material softening through grain size sensitive viscous creep sets in. Pinch-and-swell structures evolve along slip lines through a positive feedback between the matrix response and material bifurcations inside the layer, independent from the mesh-discretization length scale. Since boudinage and folding are considered to express the same general instability, both structures should arise independently of the sign of the loading conditions and for identical material parameters. To this end, the link between material to energy instabilities is approached by means of bifurcation analyses of the field equations and finite element simulations of the coupled system of equations. Boudinage and folding structures develop at the same critical energy threshold, where dissipative work by temperature-sensitive creep overcomes the diffusive capacity of the layer. This finding provides basis for a unified theory for strain localization in layered ductile materials. The numerical simulations are compared to natural pinch-and-swell microstructures, tracing the adaption of grain sizes, textures and creep mechanisms in calcite veins. The switch from dislocation to diffusion creep relates to strain-rate weakening, which is induced by dissipated heat from grain size reduction, and marks the onset of continuous necking. The time-dependent sequence uncovers multiple steady states at different time intervals. Microstructurally and mechanically stable conditions are finally expressed in the pinch-and-swell end members. The major outcome of this study is that boudinage and folding can be described as the same coupled energy-mechanical bifurcation, or as one critical energy attractor. This finding allows the derivation of critical deformation conditions and fundamental material parameters directly from localized structures in the field.

(Table 1) Chemical composition of oceanic phosphates and their selenium content

Selenium content of phosphate material from the ocean bottom ranges from 0.2 to 4.7 mg/kg. Phosphorites of various ages from the Atlantic and Pacific Oceans contain 1.0-2.4 mg/kg of selenium, phosphatized coproliths 0.7-1.2 mg/kg, fish bones 0.2-1,4 mg/kg, and bones of marine mammals 0.5-4.7 mg/kg. Recent diatom muds on the shelf of Namibia are considerably enriched in selenium (12.2-13.8 mg/kg) than phosphorites that form within them. Accumulation of selenium in phosphate material on the ocean bottom results from diagenetic reduction, causing it to be precipitated from liquid phase and to concentrate in organic components and sulfides.

(Table 2) Oxygen isotope composition of authigenic and detrital phosphates from ODL Leg 201 sites

Many (bio)geochemical processes that bring about changes in sediment chemistry normally begin at the sediment-water interface, continue at depth within the sediment column and may persist throughout the lifetime of sediments. Because of the differential reactivity of sedimentary phosphate phases in response to diagenesis, dissolution/precipitation and biological cycling, the oxygen isotope ratios of phosphate (d18OP) can carry a distinct signature of these processes, as well as inform on the origin of specific P phases. Here, we present results of sequential sediment extraction (SEDEX) analyses combined with d18OP measurements, aimed at characterizing authigenic and detrital phosphate phases in continental margin sediments from three sites (Sites 1227, 1228 and 1229) along the Peru Margin collected during ODP Leg 201. Our results show that the amount of P in different reservoirs varies significantly in the upper 50 m of the sediment column, but with a consistent pattern, for example, detrital P is highest in siliciclastic-rich layers. The d18OP values of authigenic phosphate vary between 20.2 per mil and 24.8 per mil and can be classified into at least two major groups: authigenic phosphate precipitated at/near the sediment-water interface in equilibrium with paleo-water oxygen isotope ratios (d18Ow) and temperature, and phosphate derived from hydrolysis of organic matter (Porg) with subsequent incomplete to complete re-equlibration and precipitated deeper in the sediments column. The d18OP values of detrital phosphate, which vary from 7.7-15.4 per mil, suggest two possible terrigenous sources and their mixtures in different proportions: phosphate from igneous/metamorphic rocks and phosphate precipitated in source regions in equilibrium with d18Ow of meteoric water. More importantly, original isotopic compositions of at least one phase of authigenic phosphates and all detrital phosphates are not altered by diagenesis and other biogeochemical changes within the sediment column. These findings help to understand the origin and provenance of P phases and paleoenvironmental conditions at/near the sediment-water interface, and to infer post-depositional activities within the sediment column.

Zirconium corrosion : a literature search /

"Metallurgy and Ceramics."

Unclassified U.S. Atomic Energy Commission reports on the metallurgy of zirconium and hafnium /

"TID-3508 Metallurgy and Ceramics."

Welding of thick plates of Bureau of Mines zirconium /

Work performed at the Battelle Memorial Institute, Columbus, Ohio.

Sequence in layered rocks; a study of features and structures useful for determining top and bottom order of succession in bedded and tabular rock bodies

Mode of access: Internet.

Effect of phosphates on water treatment : phosphates in Illinois surface waters /

"Final report for the period June 15, 1955 to September 15, 1957 for American Association of Soap and Glycerine Producers."

Effect of phosphates on water treatment : phase III. effects of phosphates on coagulation and sedimentation of turbid waters /

"Final report for the period June 15, 1955 to September 15, 1957 for American Association of Soap and Glycerine Producers."

The determination of hydrogen in uranium and zirconium by combustion methods /

"Contract AT-30-1-Gen-366."

Some empirical-theoretical considerations of uranium nitride in zirconium /

In this paper our method is critically examined to obtain a better understanding of the complexities of the system.

Zirconium : a bibliography of unclassified report literature.

This bibliography contains 225 annotated references to unclassified reports on zirconium. References are included to reports written prior to September 1955. Author, subject, and report number indexes are provided.