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 long-term mechanical integrity of non-reinforced PEEK-OPTIMA polymer for demanding spinal applications: experimental and finite-element analysis

Polyetheretherketone (PEEK) is a novel polymer with potential advantages for its use in demanding orthopaedic applications (e.g. intervertebral cages). However, the influence of a physiological environment on the mechanical stability of PEEK has not been reported. Furthermore, the suitability of the polymer for use in highly stressed spinal implants such as intervertebral cages has not been investigated. Therefore, a combined experimental and analytical study was performed to address these open questions. A quasi-static mechanical compression test was performed to compare the initial mechanical properties of PEEK-OPTIMA polymer in a dry, room-temperature and in an aqueous, 37 degrees C environment (n=10 per group). The creep behaviour of cylindrical PEEK polymer specimens (n=6) was measured in a simulated physiological environment at an applied stress level of 10 MPa for a loading duration of 2000 hours (12 weeks). To compare the biomechanical performance of different intervertebral cage types made from PEEK and titanium under complex loading conditions, a three-dimensional finite element model of a functional spinal unit was created. The elastic modulus of PEEK polymer specimens in a physiological environment was 1.8% lower than that of specimens tested at dry, room temperature conditions (P<0.001). The results from the creep test showed an average creep strain of less than 0.1% after 2000 hours of loading. The finite element analysis demonstrated high strain and stress concentrations at the bone/implant interface, emphasizing the importance of cage geometry for load distribution. The stress and strain maxima in the implants were well below the material strength limits of PEEK. In summary, the experimental results verified the mechanical stability of the PEEK-OPTIMA polymer in a simulated physiological environment, and over extended loading periods. Finite element analysis supported the use of PEEK-OPTIMA for load-bearing intervertebral implants.

From transient to steady state deformation and grain size: A thermodynamic approach using elasto-visco-plastic numerical modeling

Numerical simulation experiments give insight into the evolving energy partitioning during high-strain torsion experiments of calcite. Our numerical experiments are designed to derive a generic macroscopic grain size sensitive flow law capable of describing the full evolution from the transient regime to steady state. The transient regime is crucial for understanding the importance of micro structural processes that may lead to strain localization phenomena in deforming materials. This is particularly important in geological and geodynamic applications where the phenomenon of strain localization happens outside the time frame that can be observed under controlled laboratory conditions. Ourmethod is based on an extension of the paleowattmeter approach to the transient regime. We add an empirical hardening law using the Ramberg-Osgood approximation and assess the experiments by an evolution test function of stored over dissipated energy (lambda factor). Parameter studies of, strain hardening, dislocation creep parameter, strain rates, temperature, and lambda factor as well asmesh sensitivity are presented to explore the sensitivity of the newly derived transient/steady state flow law. Our analysis can be seen as one of the first steps in a hybrid computational-laboratory-field modeling workflow. The analysis could be improved through independent verifications by thermographic analysis in physical laboratory experiments to independently assess lambda factor evolution under laboratory conditions.

Geomorphic coupling between hillslopes and channels in the Swiss Alps

The coupling relationships between hillslope and channel network are fundamental for the understanding of mountainous landscapes' evolution. Here, we applied dendrogeomorphic methods to identify the hillslope–channel relationship and the sediment transfer dynamics within an alpine catchment, at the highest possible resolution. The Schimbrig catchment is located in the central Swiss Alps and can be divided into two distinct geomorphic sectors. To the east, the Schimbrig earth flow is the largest sediment source of the basin, while to the west, the Rossloch channel network is affected by numerous shallow landslides responsible for the supply of sediment from hillslopes to channels. To understand the connectivity between hillslopes and channels and between sources and sink, trees were sampled along the main Rossloch stream, on the Schimbrig earth flow and on the Rossloch depositional area. Geomorphic observations and dendrogeomophic results indicate different mechanisms of sediment production, transfer and deposition between upper and lower segments of the channel network. In the source areas (upper part of the Rossloch channel system), sediment is delivered to the channel network through slow movements of the ground, typical of earth flow, shallow landslides and soil creep. Contrariwise, in the depositional area (lower part of the channel network), the mechanisms of sediment transfer are mainly due to torrential activity, floods and debris flows. Tree analysis allowed the reconstruction of periods of high activity during the last century for the entire catchment. The collected dataset presents a very high temporal resolution but we encountered some limitations in establishing the source-to-sink connectivity at the catchment-wide scale. Despite these uncertainties, for decennial timescales the results suggest a direct coupling between hillslopes and neighbouring channels in the Rossloch channel network, and a de-coupling between sediment sources and sink farther downstream, with connections possible only during extraordinary events.

Water versus ice: The competing roles of modern climate and Pleistocene glacial erosion in the Central Alps of Switzerland

Recent studies have identified relationships between landscape form, erosion and climate in regions of landscape rejuvenation, associated with increased denudation. Most of these landscapes are located in non-glaciated mountain ranges and are characterized by transient geomorphic features. The landscapes of the Swiss Alps are likewise in a transient geomorphic state as seen by multiple knickzones. In this mountain belt, the transient state has been related to erosional effects during the Late Glacial Maximum (LGM). Here, we focus on the catchment scale and categorize hillslopes based on erosional mechanisms, landscape form and landcover. We then explore relationships of these variables to precipitation and extent of LGM glaciers to disentangle modern versus palaeo controls on the modern shape of the Alpine landscape. We find that in grasslands, the downslope flux of material mainly involves unconsolidated material through hillslope creep, testifying a transport-limited erosional regime. Alternatively, strength-limited hillslopes, where erosion is driven by bedrock failure, are covered by forests and/or expose bedrock, and they display oversteepened hillslopes and channels. There, hillslope gradients and relief are more closely correlated with LGM ice occurrence than with precipitation or the erodibility of the underlying bedrock. We relate the spatial occurrence of the transport- and strength-limited process domains to the erosive effects of LGM glaciers. In particular, strength-limited, rock dominated basins are situated above the equilibrium line altitude (ELA) of the LGM, reflecting the ability of glaciers to scour the landscape beyond threshold slope conditions. In contrast, transport-limited, soil-mantled landscapes are common below the ELA. Hillslopes covered by forests occupy the elevations around the ELA and are constrained by the tree line. We conclude that the current erosional forces at work in the Central Alps are still responding to LGM glaciation, and that the modern climate has not yet impacted on the modern landscape.

Three-dimensional Vortex Structures on Heated Micro-lattice in a Gas

This paper addresses the microscale heat transfer problem from heated lattice to the gas. A micro-device for enhanced heat transfer is presented and numerically investigated. Thermal creep induces 3-D vortex structures in the vicinity of the lattice. The gas flow is in the slip flow regime (Knudsen number Kn⩽0.1Kn⩽0.1). The simulations are performed using slip flow Navier–Stokes equations with boundary condition formulations proposed by Maxwell and Smoluchowski. In this study the wire thicknesses and distances of the heated lattice are varied. The surface geometrical properties alter significantly heat flux through the surface.

Experimental, theoretical and numerical investigation of the nonlinear micromechanical properties of bone

Aging societies suffer from an increasing incidence of bone fractures. Bone strength depends on the amount of mineral measured by clinical densitometry, but also on the micromechanical properties of the bone hierarchical organization. A good understanding has been reached for elastic properties on several length scales, but up to now there is a lack of reliable postyield data on the lower length scales. In order to be able to describe the behavior of bone at the microscale, an anisotropic elastic-viscoplastic damage model was developed using an eccentric generalized Hill criterion and nonlinear isotropic hardening. The model was implemented as a user subroutine in Abaqus and verified using single element tests. A FE simulation of microindentation in lamellar bone was finally performed show-ing that the new constitutive model can capture the main characteristics of the indentation response of bone. As the generalized Hill criterion is limited to elliptical and cylindrical yield surfaces and the correct shape for bone is not known, a new yield surface was developed that takes any convex quadratic shape. The main advantage is that in the case of material identification the shape of the yield surface does not have to be anticipated but a minimization results in the optimal shape among all convex quadrics. The generality of the formulation was demonstrated by showing its degeneration to classical yield surfaces. Also, existing yield criteria for bone at multiple length scales were converted to the quadric formulation. Then, a computational study to determine the influence of yield surface shape and damage on the in-dentation response of bone using spherical and conical tips was performed. The constitutive model was adapted to the quadric criterion and yield surface shape and critical damage were varied. They were shown to have a major impact on the indentation curves. Their influence on indentation modulus, hardness, their ratio as well as the elastic to total work ratio were found to be very well described by multilinear regressions for both tip shapes. For conical tips, indentation depth was not a significant fac-tor, while for spherical tips damage was insignificant. All inverse methods based on microindentation suffer from a lack of uniqueness of the found material properties in the case of nonlinear material behavior. Therefore, monotonic and cyclic micropillar com-pression tests in a scanning electron microscope allowing a straightforward interpretation comple-mented by microindentation and macroscopic uniaxial compression tests were performed on dry ovine bone to identify modulus, yield stress, plastic deformation, damage accumulation and failure mecha-nisms. While the elastic properties were highly consistent, the postyield deformation and failure mech-anisms differed between the two length scales. A majority of the micropillars showed a ductile behavior with strain hardening until failure by localization in a slip plane, while the macroscopic samples failed in a quasi-brittle fashion with microcracks coalescing into macroscopic failure surfaces. In agreement with a proposed rheological model, these experiments illustrate a transition from a ductile mechanical behavior of bone at the microscale to a quasi-brittle response driven by the growth of preexisting cracks along interfaces or in the vicinity of pores at the macroscale. Subsequently, a study was undertaken to quantify the topological variability of indentations in bone and examine its relationship with mechanical properties. Indentations were performed in dry human and ovine bone in axial and transverse directions and their topography measured by AFM. Statistical shape modeling of the residual imprint allowed to define a mean shape and describe the variability with 21 principal components related to imprint depth, surface curvature and roughness. The indentation profile of bone was highly consistent and free of any pile up. A few of the topological parameters, in particular depth, showed significant correlations to variations in mechanical properties, but the cor-relations were not very strong or consistent. We could thus verify that bone is rather homogeneous in its micromechanical properties and that indentation results are not strongly influenced by small de-viations from the ideal case. As the uniaxial properties measured by micropillar compression are in conflict with the current literature on bone indentation, another dissipative mechanism has to be present. The elastic-viscoplastic damage model was therefore extended to viscoelasticity. The viscoelastic properties were identified from macroscopic experiments, while the quasistatic postelastic properties were extracted from micropillar data. It was found that viscoelasticity governed by macroscale properties has very little influence on the indentation curve and results in a clear underestimation of the creep deformation. Adding viscoplasticity leads to increased creep, but hardness is still highly overestimated. It was possible to obtain a reasonable fit with experimental indentation curves for both Berkovich and spherical indenta-tion when abandoning the assumption of shear strength being governed by an isotropy condition. These results remain to be verified by independent tests probing the micromechanical strength prop-erties in tension and shear. In conclusion, in this thesis several tools were developed to describe the complex behavior of bone on the microscale and experiments were performed to identify its material properties. Micropillar com-pression highlighted a size effect in bone due to the presence of preexisting cracks and pores or inter-faces like cement lines. It was possible to get a reasonable fit between experimental indentation curves using different tips and simulations using the constitutive model and uniaxial properties measured by micropillar compression. Additional experimental work is necessary to identify the exact nature of the size effect and the mechanical role of interfaces in bone. Deciphering the micromechanical behavior of lamellar bone and its evolution with age, disease and treatment and its failure mechanisms on several length scales will help preventing fractures in the elderly in the future.

Modeling episodic fluid-release events in the ductile carbonates of the Glarus thrust

The exposed Glarus thrust displays midcrustal deformation with tens of kilometers of displacement on an ultrathin layer, the principal slip zone (PSZ). Geological observations indicate that this structure resulted from repeated stick-slip events in the presence of highly overpressured fluids. Here we show that the major characteristics of the Glarus thrust movement (localization, periodicity, and evidence of pressurized fluids) can be reconciled by the coupling of two processes, namely, shear heating and fluid release by carbonate decomposition. During this coupling, slow ductile creep deformation raises the temperature through shear heating and ultimately activates the chemical decomposition of carbonates. The subsequent release of highly overpressurized fluids forms and lubricates the PSZ, allowing a ductile fault to move tens of kilometers on millimeter-thick bands in episodic stick-slip events. This model identifies carbonate decomposition as a key process for motion on the Glarus thrust and explains the source of overpressured fluids accessing the PSZ.

Small quantity but large effect — How minor phases control strain localization in upper mantle shear zones

Low viscosity domains such as localized shear zones exert an important control on the geodynamics of the uppermost mantle. Grain size reduction and subsequent strain localization related to a switch from dislocation to diffusion creep is one mechanism to form low viscosity domains. To sustain strain localization, the grain size of mantle minerals needs to be kept small over geological timescales. One way to keep olivine grain sizes small is by pinning of mobile grain boundaries during grain growth by other minerals (second phases). Detailed microstructural studies based on natural samples from three shear zones formed at different geodynamic settings, allowed the derivation of the olivine grain-size dependence on the second-phase content. The polymineralic olivine grain-size evolution with increasing strain is similar in the three shear zones. If the second phases are to pin the mobile olivine grain boundary the phases need to be well mixed before grain growth. We suggest that melt-rock and metamorphic reactions are crucial for the initial phase mixing in mantle rocks. With ongoing deformation and increasing strain, grain boundary sliding combined with mass transfer processes and nucleation of grains promotes phase mixing resulting in fine-grained polymineralic mixtures that deform by diffusion creep. Strain localization due to the presence of volumetrically minor minerals in polymineralic mantle rocks is only important at high strain deformation (ultramylonites) at low temperatures (<~800°C). At smaller strain and stress conditions and/or higher temperatures other parameters like overall energy available to deform a given rock volume, the inheritance of mechanical anisotropies or the presence of water or melts needs to be considered to explain strain localization in the upper mantle.

Terrestrial Radar Interferometric Measurement of Hillslope Deformation and Atmospheric Disturbances in the Illgraben Debris-Flow Catchment, Switzerland

We describe a method for rapid identification and precise quantification of slope deformation using a portable radar interferometer. A rockslide with creep-like behavior was identified in the rugged and inaccessible headwaters of the Illgraben debris-flow catchment, located in the Central Swiss Alps. The estimated volume of the moving rock mass was approximately 0.5 x 10(6) m(3) with a maximum daily (3-D) displacement rate of 3 mm. Fast scene acquisition in the order of 6 s/scene led to uniquely precise mapping of spatial and temporal variability of atmospheric phase delay. Observations led to a simple qualitative model for prediction of atmospheric disturbances using a simple model for solar radiation, which can be used for advanced campaign planning for short observation periods (hours to days).

Atomistic Modeling of Effect of Mg on Oxygen Vacancy Diffusion in α-Alumina

Oxygen diffusion plays an important role in grain growth and densification during the sintering of alumina ceramics and governs high-temperature processes such as creep. The atomistic mechanism for oxygen diffusion in alumina is, however, still debated; atomistic calculations not being able to match experimentally determined activation energies for oxygen vacancy diffusion. These calculations are, however, usually performed for perfectly pure crystals, whereas virtually every experimental alumina sample contains a significant fraction of impurity/dopants ions. In this study, we use atomistic defect cluster and nudged elastic band (NEB) calculations to model the effect of Mg impurities/dopants on defect binding energies and migration barriers. We find that oxygen vacancies can form energetically favorable clusters with Mg, which reduces the number of mobile species and leads to an additional 1.5 eV energy barrier for the detachment of a single vacancy from Mg. The migration barriers of diffusive jumps change such that an enhanced concentration of oxygen vacancies is expected around Mg ions. Mg impurities were also found to cause destabilization of certain vacancy configurations as well as enhanced vacancy–vacancy interaction.

Redistribution of particles across the nucleus of comet 67P/Churyumov-Gerasimenko

Context. We present an investigation of the surface properties of areas on the nucleus of comet 67P/Churyumov-Gerasimenko. Aims. We aim to show that transport of material from one part of the cometary nucleus to another is a significant mechanism that influences the appearance of the nucleus and the surface thermal properties. Methods. We used data from the OSIRIS imaging system onboard the Rosetta spacecraft to identify surface features on the nucleus that can be produced by various transport mechanisms. We used simple calculations based on previous works to establish the plausibility of dust transport from one part of the nucleus to another. Results. We show by observation and modeling that "airfall" as a consequence of non-escaping large particles emitted from the neck region of the nucleus is a plausible explanation for the smooth thin deposits in the northern hemisphere of the nucleus. The consequences are also discussed. We also present observations of aeolian ripples and ventifacts. We show by numerical modeling that a type of saltation is plausible even under the rarified gas densities seen at the surface of the nucleus. However, interparticle cohesive forces present difficulties for this model, and an alternative mechanism for the initiation of reptation and creep may result from the airfall mechanism. The requirements on gas density and other parameters of this alternative make it a more attractive explanation for the observations. The uncertainties and implications are discussed.

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.

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.