Deformation mechanisms in second-phase affected microstructures and their energy balance

Based on the relationship Zener parameter (Z=second-phase size/second-phase volume fraction) vs. calcite grain size (dg), second-phase controlled aggregates and microstructures that are weakly affected by second-phases are discriminated. The latter are characterized by large but constant grain sizes, high calcite grain boundary fractions and crystallographic preferred orientations (CPO), while calcite grain size and calcite grain boundary fraction decrease continuously and CPO weakens with decreasing Z in second-phase controlled microstructures. These observations suggest that second-phase controlled microstructures predominantly deform via granular flow because pinning of calcite grain boundaries reduces the efficiency of dynamic recrystallization favoring mass transfer processes and grain boundary sliding. In contrast, the balance of grain size reduction and growth by dynamic recrystallization maintains a steady state grain size in microstructures that are only weakly affected by second-phases promoting a predominance of dislocation creep. With increasing temperature, the relationship between Z and dg persists but the calcite grain size increases continuously. Based on microstructures, the energy of each modifying process is calculated and its relative contribution is compared with energies of the competing processes (surface energy, dragging energy, dynamic recrystallization energy). The steady state microstructures result from a temperature-dependent energy minimization procedure of the system.

The effect of dissolved magnesium on diffusion creep in calcite

We experimentally tested a series of synthetic calcite marbles with varying amounts of dissolved magnesium in a standard triaxial deformation machine at 300 MPa confining pressure, temperatures between 700 and 850°C, stresses between 2 and 100 MPa, and strain rates between 10−7 and 10−3 s−1. The samples were fabricated by hot isostatic pressing of a mixture of calcite and dolomite at 850°C and 300 MPa. The fabrication protocol resulted in a homogeneous, fine-grained high-magnesian calcite aggregate with minimal porosity and with magnesium contents between 0.07 and 0.17 mol% MgCO3. At stresses below 40 MPa the samples deformed with linear viscosity that depended inversely on grain size to the 3.26±0.51 power, suggesting that the mechanisms of deformation were some combination of grain boundary diffusion and grain boundary sliding. Because small grain sizes tended to occur in the high-magnesium calcite, the strength also appeared to vary inversely with magnesium content. However, the strength at constant grain size does not depend on the amount of dissolved magnesium, and thus, the impurity effect seems to be indirect. At stresses higher than 40 MPa, the aggregates become non-linearly viscous, a regime we interpret to be dislocation creep. The transition between the two regimes depends on grain size, as expected. The activation energy for diffusion creep is 200±30 kJ/mol and is quite similar to previous measurements in natural and synthetic marbles deformed at similar conditions with no added magnesium.

The influence of nano-scale second-phase particles on deformation of fine grained calcite mylonites

Grey and white carbonate mylonites were collected along thrust planes of the Helvetic Alps. They are characterised by very small grain sizes and non-random grain shape (SPO) and crystallographic preferred orientation (CPO). Presumably they deformed in the field of grain size sensitive flow by recrystallisation accommodated intracrystalline deformation in combination with granular flow. Both mylonites show a similar mean grain size, but in the grey mylonites the grain size range is larger, the grain shapes are more elongate and the dynamically recrystallised calcite grains are more often twinned. Grey mylonites have an oblique CPO, while the CPO in white mylonites is symmetric with respect to the shear plane. Combustion analysis and TEM investigations revealed that grey mylonites contain a higher amount of highly structured kerogens with particle sizes of a few tens of nanometers, which are finely dispersed at the grain boundaries. During deformation of the rock, nano-scale particles reduced the migration velocity of grain boundaries by Zener drag resulting in slower recrystallisation rates of the calcite aggregate. In the grey mylonites, more strain increments were accommodated by individual grains before they became refreshed by dynamic recrystallisation than in white mylonites, where grain boundary migration was less hindered and recrystallisation cycles were faster. Consequently, grey mylonites represent ‘deformation’ microfabrics while white mylonites are characterised by ‘recrystallisation’ microfabrics. Field geologists must utilise this different deformation behavior when applying the obliquity in CPO and SPO of the respective mylonites as reliable shear sense indicators.

A deformation model of flexible, high area-to-mass ratio debris under perturbations and validation method

A new type of space debris was recently discovered by Schildknecht in near -geosynchronous orbit (GEO). These objects were later identified as exhibiting properties associated with High Area-to-Mass ratio (HAMR) objects. According to their brightness magnitudes (light curve), high rotation rates and composition properties (albedo, amount of specular and diffuse reflection, colour, etc), it is thought that these objects are multilayer insulation (MLI). Observations have shown that this debris type is very sensitive to environmental disturbances, particularly solar radiation pressure, due to the fact that their shapes are easily deformed leading to changes in the Area-to-Mass ratio (AMR) over time. This thesis proposes a simple effective flexible model of the thin, deformable membrane with two different methods. Firstly, this debris is modelled with Finite Element Analysis (FEA) by using Bernoulli-Euler theory called “Bernoulli model”. The Bernoulli model is constructed with beam elements consisting 2 nodes and each node has six degrees of freedom (DoF). The mass of membrane is distributed in beam elements. Secondly, the debris based on multibody dynamics theory call “Multibody model” is modelled as a series of lump masses, connected through flexible joints, representing the flexibility of the membrane itself. The mass of the membrane, albeit low, is taken into account with lump masses in the joints. The dynamic equations for the masses, including the constraints defined by the connecting rigid rod, are derived using fundamental Newtonian mechanics. The physical properties of both flexible models required by the models (membrane density, reflectivity, composition, etc.), are assumed to be those of multilayer insulation. Both flexible membrane models are then propagated together with classical orbital and attitude equations of motion near GEO region to predict the orbital evolution under the perturbations of solar radiation pressure, Earth’s gravity field, luni-solar gravitational fields and self-shadowing effect. These results are then compared to two rigid body models (cannonball and flat rigid plate). In this investigation, when comparing with a rigid model, the evolutions of orbital elements of the flexible models indicate the difference of inclination and secular eccentricity evolutions, rapid irregular attitude motion and unstable cross-section area due to a deformation over time. Then, the Monte Carlo simulations by varying initial attitude dynamics and deformed angle are investigated and compared with rigid models over 100 days. As the results of the simulations, the different initial conditions provide unique orbital motions, which is significantly different in term of orbital motions of both rigid models. Furthermore, this thesis presents a methodology to determine the material dynamic properties of thin membranes and validates the deformation of the multibody model with real MLI materials. Experiments are performed in a high vacuum chamber (10-4 mbar) replicating space environment. A thin membrane is hinged at one end but free at the other. The free motion experiment, the first experiment, is a free vibration test to determine the damping coefficient and natural frequency of the thin membrane. In this test, the membrane is allowed to fall freely in the chamber with the motion tracked and captured through high velocity video frames. A Kalman filter technique is implemented in the tracking algorithm to reduce noise and increase the tracking accuracy of the oscillating motion. The forced motion experiment, the last test, is performed to determine the deformation characteristics of the object. A high power spotlight (500-2000W) is used to illuminate the MLI and the displacements are measured by means of a high resolution laser sensor. Finite Element Analysis (FEA) and multibody dynamics of the experimental setups are used for the validation of the flexible model by comparing with the experimental results of displacements and natural frequencies.

Regular homomorphisms of minimal sets

The classification of minimal sets is a central theme in abstract topological dynamics. Recently this work has been strengthened and extended by consideration of homomorphisms. Background material is presented in Chapter I. Given a flow on a compact Hausdorff space, the action extends naturally to the space of closed subsets, taken with the Hausdorff topology. These hyperspaces are discussed and used to give a new characterization of almost periodic homomorphisms. Regular minimal sets may be described as minimal subsets of enveloping semigroups. Regular homomorphisms are defined in Chapter II by extending this notion to homomorphisms with minimal range. Several characterizations are obtained. In Chapter III, some additional results on homomorphisms are obtained by relativizing enveloping semigroup notions. In Veech's paper on point distal flows, hyperspaces are used to associate an almost one-to-one homomorphism with a given homomorphism of metric minimal sets. In Chapter IV, a non-metric generalization of this construction is studied in detail using the new notion of a highly proximal homomorphism. An abstract characterization is obtained, involving only the abstract properties of homomorphisms. A strengthened version of the Veech Structure Theorem for point distal flows is proved. In Chapter V, the work in the earlier chapters is applied to the study of homomorphisms for which the almost periodic elements of the associated hyperspace are all finite. In the metric case, this is equivalent to having at least one fiber finite. Strong results are obtained by first assuming regularity, and then assuming that the relative proximal relation is closed as well.