Evolution of the rheological and microstructural properties of olivine aggregates during dislocation creep under hydrous conditions
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A source-sink model of the generation of plate tectonics from non-Newtonian mantle flow
A model of mantle convection which generates plate tectonics requires strain rate- or stress-dependent rheology in order to produce strong platelike flows with weak margins as well as strike-slip deformation and plate spin (i.e., toroidal motion). Here, we employ a simple model of source-sink driven surface flow to determine the form of such a rheology that is appropriate for Earth's present-day plate motions. In this model, lithospheric motion is treated as shallow layer flow driven by sources and sinks which correspond to spreading centers and subduction zones, respectively. Two plate motion models are used to derive the source sink field. As originally implied in the simpler Cartesian version of this model, the classical power law rheologies do not generate platelike flows as well as the hypothetical Whitehead-Gans stick-slip rheology (which incorporates a simple self-lubrication mechanism). None of the fluid rheologies examined, however, produce more than approximately 60% of the original maximum shear. For either plate model, the viscosity fields produced by the power law rheologies are diffuse, and the viscosity lows over strike-slip shear zones or pseudo-margins are not as small as over the prescribed convergent-divergent margins. In contrast, the stick-slip rheology generates very platelike viscosity fields, with sharp gradients at the plate boundaries, and margins with almost uniformly low viscosity. Power law rheologies with high viscosity contrasts, however, lead to almost equally favorable comparisons, though these also yield the least platelike viscosity fields. This implies that the magnitude of toroidal flow and platelike strength distributions are not necessarily related and thus may present independent constraints on the determination of a self-consistent plate-mantle rheology.
Bercovici, David↗
Chain Dynamics in Magnetorheological Suspensions
Magnetorheological (MR) suspensions are composed of colloidal particles which acquire dipole moments when subjected to an external magnetic field. At sufficient field strengths and concentrations, the dipolar particles rapidly aggregate to form long chains. Subsequent lateral cross-linking of the dipolar chains is responsible for a rapid liquid-to-solid-like rheological transition. The unique, magnetically-activated rheological properties of MR suspensions make them ideal for interfacing mechanical systems to electronic controls. Additionally, the ability to experimentally probe colloidal suspensions interacting through tunable anisotropic potentials is of fundamental interest. Our current experimental work has focused on understanding the fluctuations of dipolar chains. It has been proposed by Halsey and Toor (HT) that the strong Landau-Peierls thermal fluctuations of dipolar chains could be responsible for long-range attractions between chains. Such interactions will govern the long-time relaxation of MR suspensions. We have synthesized monodisperse neutrally buoyant MR suspensions by density matching stabilized ferrofluid emulsion droplets with D2O. This allows us to probe the dynamics of the dipolar chains using light scattering without gravitational, interfacial, and polydispersity effects to resolve the short-wavelength dynamics of the dipolar chains. We used diffusing wave spectroscopy to measure these dynamics. The particle displacements at short times that show an independence to the field strength, but at long times exhibit a constrained, sub-diffusive motion that slows as the dipole strength is increased. The experiments are in good qualitative agreement with Brownian dynamics simulations of dipolar chains. Although there have been several important and detailed studies of the structure and interactions in MR suspensions, there has not been conclusive evidence that supports or contradicts the HT model prediction that long-range interactions exist between fluctuating chains of dipolar particles. Resolving this issue would contribute greatly to the understanding of these interesting and important materials. We have begun to test the predictions of the HT model by both examining the dynamics of individual chains and by measuring the forces between dipolar chains directly to accurately and quantitatively assess the interactions that they experience. To do so, we employ optical trapping techniques and video-microscopy to manipulate and observe our samples on the microscopic level. With these techniques, it is possible to observe chains that are fluctuating freely in three-dimensions, independent of interfacial effects. More importantly, we are able to controllably observe the interactions of two chains at various separations to measure the force-distance profile. The techniques also allow us to study the mechanical properties of individual chains and chain clusters. Our work to this point has focused on reversibly-formed dipolar chains due to field induced dipoles where the combination of this chaining, the dipolar forces, and the hydrodynamic interactions that dictate the rheology of the suspensions. One can envision, however, many situations where optical, electronic, or rheological behavior may be optimized with magneto-responsive anisotropic particles. Chains of polarizable particles may have the best properties as they can coil and flex in the absence of a field and stiffen and orient when a field is applied. We have recently demonstrated a synthesis of stable, permanent paramagnetic chains by both covalently and physically linking paramagnetic colloidal particles. The method employed allows us to create monodisperse chains of controlled length. We observed the stability, field-alignment, and rigidity of this new class of materials. The chains may exhibit unique rheological properties in an applied magnetic field over isotropic suspensions of paramagnetic particles. They are also useful rheological models as bead-spring systems. These chains form the basis for our current experiments with optical traps.
Gast, A. P.↗
Simulating the Formation of Lunar Floor-Fracture Craters Using Elastoviscoplastic Relaxation
Lunar floor-fracture craters formed during the height of mare basalt emplacement. Due to a general temporal and spatial relation with the maria, these craters, numbering some 200, may be diagnostic of the thermal structure of the crust during this time. As the name suggests, these craters exhibit brittle failure, generally limited to the central floor region. That, and a shallower depth than fresh lunar craters, has led to two main theories as to their formation: laccolith emplacement under the crater and viscous relaxation. The implications of each model for the state of the Moon's crust during this time are quite different, so the viability of each model must be checked. Laccolith emplacement has been treated elsewhere. However, previous attempts to study the relaxation of the craters have assumed only a uniform, Newtonian viscous response of the near surface to the topographic driving forces, and simply postulated that the fractures resulted from tensile stresses associated with floor uplift. Here, we use a more sophisticated rheological model that includes not only non-Newtonian viscous behavior (i.e., the viscosity is stress-dependent), but also incorporates elastic behavior and a plastic component to the rheology to directly simulate the formation of the floor fractures. The results of our simulations show that while elastoviscoplastic relaxation is potentially viable for larger floor-fracture craters, it is not viable for craters with diameters < or = 60 km, the size of the majority of floor-fracture craters. We employ the finite element method, a numerical technique well suited for boundary-value problems, via the commercially available MARC software package. To test the viability of topographic relaxation, our goal is to prepare the simulations as to maximize the amount of relaxation. We take advantage of the natural axisymmetry of craters, simulating one radial plane. Initial shapes are based on data for fresh craters from Pike. To simplify implementation, a fourth order polynomial is used for the basin, while a third order inverse function is used for the rim. This form closely approximates the long-wavelength behavior of complex craters, while ignoring higher-frequency topography, save the rim. This approximation is appropriate because crater relaxation is strongly controlled by long-wavelength topography. Loading is accomplished assuming a uniform gravity field (1.62 m/s-square) and a uniform density of 2900 kg/cubic m. The initial stress state is set to be hydrostatic, with an additional pressure term to account for any overlying topography. This additional pressure term is tapered exponentially with depth. While the simulations quickly settle on a preferred stress state, and while the final solution is fairly insensitive to the choice of the e-folding depth of the taper, selecting an e-folding depth close to the diameter of the crater sets the initial stress state near the preferred state. We assume a diuranally averaged surface temperature of -20 C, and allow temperature to increase with depth at a rate of 50 K//km. Assuming a thermal conductivity of 2 W/in/K, this gradient translates to a heat flow of 100mW/square m, an extremely high value for the Moon. Temperature, of course, will not increase without bound. To maximize relaxation, we allow our temperature profile to increase linearly until it reaches the solidus (assumed to be 1200C) at a depth of 24.4 km, at which point it is kept constant. The presence of melt will drop the bulk viscosity; however, we have no rheological control for partial melts. Therefore, we make no attempt to simulate this situation. Elastoviscoplastic rheological model. In general, geologic materials can behave in three main ways: elastically, viscously (via solid-state creep), and brittly (plasticity is a continuum approach to simulate this phenomenon). We combine these three deformation mechanisms in an extended Maxwell solid, where the total strain can be broken down into a simple summation of the elastic, creep, and plastic strains. In relaxation phenomena in general, the system takes advantage of any means possible to eliminate deviatoric stresses by relaxing away the topography. Previous analyses have only modeled the viscous response. Comparatively, the elastic response in our model can augment the relaxation, to a point. This effect decreases as the elastic response becomes stiffer; indeed, in the limit of infinite elastic Young's modulus (and with no plasticity), the solution converges on the purely viscous solution. Igneous rocks common to the lunar near-surface have Young's modulii in the range of 10-100 GPa. To maximize relaxation, we use a Young's modulus of 10 GPa. (There is negligible sensitivity to the other elastic modulus, the Poisson's ratio; we use 0.25.) For the viscous response, we use a flow law for steady-state creep in thoroughly dried Columbia diabase, because the high plagioclase (about 70 vol%) and orthopyroxene (about 17 vol%) content is similar to the composition of the lunar highland crust as described by remote sensing and sample studies: noritic anorthosite. This flow law is highly non-Newtonian, i.e., the viscosity is highly stress dependent. That, and the variability with temperature, stands in strong contrast to previous examinations of lunar floor-fracture crater relaxation. To model discrete, brittle faulting, we assume "Byerlee's rule," a standard geodynamical technique. We implement this "rule" with an-angle of internal friction of about 40 deg, and a higher-than-normal cohesion of about 3.2 MPa (to approximate the breaking of unfractured rock). The actual behavior of geologic materials is more complex than in our rheological model, so the uncertainties in the plasticity do not represent the state-of-the-art error. Additional information is contained in the original.
Dombard, A. J.↗
Anelastic response of the earth to a dip slip earthquake
The deformation induced by a vertical dip slip earthquake is examined using a variety of rheologic models. In this way the complications of dipping faults are avoided, and the phenomenon of transient peripheral warping is clearly revealed. A thrust fault dipping at 30 deg is investigated, and the important effects of dip and the existence of a slab on the asymmetry of strain pulses propagated into the overthrust and subducted lithosphere are demonstrated. One of the signal results of the study is the essential similarity of the strain patterns for Newtonian and non-Newtonian flow laws: the two rheologies give nearly identical strain field geometries. The principal difference between the two, which is readily observable, is in their time evolution. Relaxation in non-Newtonian rheologies tends to be initially fast, then slow at times that are late in comparison with relaxation in a Newtonian rheology. The possibility of simply recalling the time dependence of a Newtonian solution to obtain an approximate solution to a non-Newtonian problem is demonstrated.
Melosh, H. J.↗
The relationship between plate velocity and trench viscosity in Newtonian and power-law subduction calculations
The relationship between oceanic trench viscosity and oceanic plate velocity is studied using a Newtonian rheology by varying the viscosity at the trench. The plate velocity is a function of the trench viscosity for fixed Rayleigh number and plate/slab viscosity. Slab velocities for non-Newtonian rheology calculations are significantly different from slab velocities from Newtonian rheology calculations at the same effective Rayleigh number. Both models give reasonable strain rates for the slab when compared with estimates of seismic strain rate. Non-Newtonian rheology eliminates the need for imposed weak zones and provides a self-consistent fluid dynamical mechanism for subduction in numerical convection models.
King, Scott D.↗
Convective Instability in Ice I: Application to Callisto and Ganymede
Laboratory experiments measuring ice rheology suggest that it deforms under the influence of several nonNewtonian creep mechanisms, where the viscosity depends on both strain rate and temperature [Goldsby & Kohlstedt, 2001]. Whether or not a fluid with a purely temperature-dependent viscosity convects can be determined by comparing the Rayleigh number of the system to the critical Rayleigh number (Racr), which depends on rheological, thermal, and physical parameters of the fluid layer. However, in a nonNewtonian fluid where viscosity depends on the strain rate (i.e. velocity), convection can only occur if a temperature or velocity perturbation is issued to the system to lower the viscosity and permit fluid motions. Therefore, whether convection occurs in an ice I layer depends on initial conditions, in addition to rheological, thermal, and physical properties of the layer. We show new results for a scaling between the critical Rayleigh number and perturbation amplitude for grain boundary sliding rheology. This scaling can be used to determine the conditions required to initiate convection in the ice I shell of a generic icy satellite. We use this scaling to judge the convective instability of Ganymede and Callisto's ice shells in the absence of tidal dissipation.
Barr, A. C.↗
Predictive Modeling of Fast-Curing Thermosets in Nozzle-Based Extrusion
This work presents an approach to modeling the dynamic spreading and curing behavior of thermosets in nozzle-based extrusions. Thermosets cover a wide range of materials, some of which permit low-temperature processing with subsequent high-temperature and high-strength working properties. Extruding thermosets may overcome the limited working temperatures and strengths of conventional thermoplastic materials used in additive manufacturing. This project aims to produce technology for the fabrication of thermoset-based structures leveraging advances made in nozzle-based extrusion, such as fused deposition modeling (FDM), material jetting, and direct writing. Understanding the synergistic interactions between spreading and fast curing of extruded thermosetting materials will provide essential insights for applications that require accurate dimensional controls, such as additive manufacturing [1], [2] and centrifugal coating/forming [3]. Two types of thermally curing thermosets -- one being a soft silicone (Ecoflex 0050) and the other being a toughened epoxy (G/Flex) -- served as the test materials in this work to obtain models for cure kinetics and viscosity. The developed models align with extensive measurements made with differential scanning calorimetry (DSC) and rheology. DSC monitors the change in the heat of reaction, which reflects the rate and degree of cure at different crosslinking stages. Rheology measures the change in complex viscosity, shear moduli, yield stress, and other properties dictated by chemical composition. By combining DSC and rheological measurements, it is possible to establish a set of models profiling the cure kinetics and chemorheology without prior knowledge of chemical composition, which is usually necessary for sophisticated mechanistic modeling. In this work, we conducted both isothermal and dynamic measurements with both DSC and rheology. With the developed models, numerical simulations yielded predictions of diameter and height of droplets, along with width and height of extruded lines cured at varied temperatures. Experimental results carried out on a goniometric platform and a nozzle-based 3D printer showed agreement with the numerical simulations. Finally, this presentation will show how the models are adaptable to the planning of tool paths and designs in additive manufacturing.
Xie, Jingjin↗
Mechanics of couple-stress fluid coatings
The formal development of a theory of viscoelastic surface fluids with bending resistance - their kinematics, dynamics, and rheology are discussed. It is relevant to the mechanics of fluid drops and jets coated by a thin layer of immiscible fluid with rather general rheology. This approach unifies the hydrodynamics of two-dimensional fluids with the mechanics of an elastic shell in the spirit of a Cosserat continuum. There are three distinct facets to the formulation of surface continuum mechanics. Outlined are the important ideas and results associated with each: the kinematics of evolving surface geometries, the conservation laws governing the mechanics of surface continua, and the rheological equations of state governing the surface stress and moment tensors.
Waxman, A. M.↗
Surface Structures of Hawaiian Lavas
Surface and internal lava structures can be valid indicators of lava viscosity and rheology, provided that care is taken to identify and eliminate structures which are strain-rate-dependent. Here, a spectrum of types among Hawaiian basaltic flows is found ranging from pahoehoe to a'a, that are interpreted as marking a progression in lava viscosity and a change in rheology. The most fluid type in this spectrum is normal pahoehoe that has a smooth but commonly wrinkled or folded (ropy) surface. The next type, distinctly more viscous and probably non-Newtonian in rheology, is spiny pahoehoe which is characterized by a spinose surface and an absence of ropy structures. Preliminary studies on the long lavas of Mauna Loa indicated, perhaps surprisingly, that there is no clear-cut correlation of lava length with type in this spectrum of lavas, indicating that viscosity/yield strength of the basaltic lavas per se are not the primary controls determining flow length. Flowage of the lava through lava tubes, while it may help to account for the long flow distance of some lavas, is not a generally applicable explanation for long flow length.
Rowland, S. K.↗
Characterization of Polyimide Matrix Resins and Prepregs
Graphite/polyimide composite materials are attractive candidates for a wide range of aerospace applications. They have many of the virtues of graphite/epoxies, i.e., high specific strengths and stiffness, and also outstanding thermal/oxidative stability. Yet they are not widely used in the aerospace industry due to problems of procesability. By their nature, modern addition polyimide (PI) resins and prepregs are more complex than epoxies; the key to processing lies in characterizing and understanding the materials. Chemical and rheological characterizations are carried out on several addition polyimide resins and graphite reinforced prepregs, including those based on PMR-15, LARC 160 (AP 22), LARC 160 (Curithane 103) and V378A. The use of a high range torque transducer with a Rheometrics mechanical spectrometer allows rheological data to be generated on prepreg materials as well as neat resins. The use of prepreg samples instead of neat resins eliminates the need for preimidization of the samples and the data correlates well with processing behavior found in the shop. Rheological characterization of the resins and prepregs finds significant differences not readily detected by conventional chemical characterization techniques.
Maximovich, M. G.↗
Constitutive modelling of lubricants in concentrated contacts at high slide to roll ratios
A constitutive lubricant friction model for rolling/sliding concentrated contacts such as gears and cams was developed, based upon the Johnson and Tevaarwerk fluid rheology model developed earlier. The friction model reported herein differs from the earlier rheological models in that very large slide to roll ratios can now be accommodated by modifying the thermal response of the model. Also the elastic response of the fluid has been omitted from the model, thereby making it much simpler for use in the high slide to roll contacts. The effects of this simplification are very minimal on the outcome of the predicted friction losses (less than 1%). In essence then the lubricant friction model developed for the high slide to roll ratios treats the fluid in the concentrated contact as consisting of a nonlinear viscous element that is pressure, temperature, and strain rate dependent in its shear response. The fluid rheological constants required for the prediction of the friction losses at different contact conditions are obtained by traction measurements on several of the currently used gear lubricants. An example calculation, using this model and the fluid parameters obtained from the experiments, shows that it correctly predicts trends and magnitude of gear mesh losses measured elsewhere for the same fluids tested here.
Tevaarwerk, J. L.↗
Excitation of the earth's rotational axis by recent glacial discharges
The effects of present-day glacial discharges and the growth of the Antarctic ice sheet on exciting the earth's rotational axis are studied. Glacial forcing could cause a maximum change in J2 of about one-third of the observed amount, for the Maxwell rheology and for Burgers' body models with a long-term, lower-mantle viscosity greater than about 10 to the 23rd P. For transient rheologies the amount of excitation due to glacial melting decreases. Polar wander is not much excited by recent glacial melting for the various types of rheologies examined.
Gasperini, P.↗
Time-dependent convection with non-Newtonian viscosity
A numerical model of bottom-heated, two-dimensional convection in boxes of aspect ratios 2.5 and 4.0 was used to study the differences in time-dependent convection between Newtonian and stress-dependent viscosity. The onset of time dependence due to boundary layer instability is found at approximately the same effective Rayleigh number for both rheologies. However, with increasing Rayleigh number, the temporal and spatial fluctuations in the flow field become much more pronounced with non-Newtonian rheology; also, the tendency for breakup of long cells into smaller ones is stronger. The presence of stress-dependent rheology can cause long-wavelength lateral viscosity variations up to an order of magnitude; this result could have strong implications for the interpretation of mantle viscosity from postglacial rebound.
Christensen, Ulrich R.↗
Hydro-isostatic deflection and tectonic tilting in the central Andes: Initial results of a GPS survey of Lake Minchin shorelines
Sufficiently large lake loads provide a means of probing rheological stratification of the crust and upper mantle. Lake Minchin was the largest of the late Pleistocene pluvial lakes in the central Andes. Prominent shorelines, which formed during temporary still-stands in the climatically driven lake level history, preserve records of lateral variations in subsequent net vertical motions. At its maximum extent the lake was 140 m deep and spanned 400 km N-S and 200 km E-R. The load of surficial water contained in Lake Minchin was sufficient to depress the crust and underlying mantle by 20-40 m, depending on the subjacent rheology. Any other differential vertical motions will also be recorded as departures from horizontality of the shorelines. We recently conducted a survey of shoreline elevations of Lake Minchin with the express intent of monitoring the hydro-isostatic deflection and tectonic tilting. Using real-time differential Global Positioning System (GPS), we measured topographic profiles across suites of shorelines at 15 widely separated locations throughout the basin. Horizontal and vertical accuracies attained are roughly 30 and 70 cm, respectively. Geomorphic evidence suggests that the highest shoreline was occupied only briefly (probably less than 200 years) and radiocarbon dates on gastropod shells found in association with the shore deposits constrain the age to roughly 17 kyr. The basin-side pattern of elevations of the highest shoreline is composed of two distinct signals: (27 +/- 1) m of hydro-isostatic deflection due to the lake load, and a planar tilt with east and north components of (6.8 +/- 0.4) 10(exp -5) and 9-5.3 +/- 0.3) 10(exp -5). This rate of tilting is too high to be plausibly attributed to steady tectonism, and presumably reflects some unresolved combination of tectonism plus the effects of oceanic and lacustrine loads on a laterally heterogeneous substrate. The history of lake level fluctuations is still inadequately known to allow detailed inferences of crust and mantle rheology. However, it is already clear that the effective elastic plate thickness is closer to 40 km than the 60-70 km crustal thickness in the central Andes and the effective viscosity is less than 5 10(exp 20) Pa s.
Bills, Bruce G.↗
A spectral formalism for computing three-dimensional deformations due to surface loads. 2: Present-day glacial isostatic adjustment
Using a spherically symmetric, self-gravitating, linear viscoelastic Earth model, we predict present-day three-dimensional surface deformation rates and baseline evolutions arising as a consequence of the late Pleistocene glacial cycles. In general, we use realistic models for the space-time geometry of the final late Pleistocene deglaciation event and incorporate a gravitationally self-consistent ocean meltwater redistribution. The predictions of horizontal velocity presented differ significantly, in both their amplitude and their spatial variation, from those presented in earlier analysis of others which adopted simplified models of both the late Pleistocene ice history and the Earth rheology. An important characteristic of our predicted velocity fields is that the melting of the Laurentide ice sheet over Canada is capable of contributing appreciably to the adjustment in Europe. The sensitivity of the predictions to variations in mantle rheology is investigated by considering a number of different Earth models, and by computing appropriate Frechet kernels. These calculations suggest that the sensitivity of the deformations to the Earth's rheology is significant and strongly dependent on the location of the site relative to the ancient ice sheet. The effects on the predictions of three-dimensional deformation rates of altering the ice history or adopting approximate models for the ocean meltwater redistribution have also been considered and found to be important (the former especially so). Finally, for a suite of Earth models we provide predictions of the velocity of a number of baselines in North America and Europe. We find that, in general, both radial and tangential motions contribute significantly to baseline length changes, and that these contributions are a strong function of the Earth model. We have, furthermore, found a set of Earth models which, together with the ICE-3G deglaciation chronology, produce predictions of baseline length changes that are consistent with very long baseline interferometry measurements of baselines within Europe.
Mitrovica, J. X.↗
Foam Optics and Mechanics
The Foam Optics and Mechanics (FOAM) project will exploit the microgravity environment to more accurately measure the rheological and optical characteristics of wet aqueous foams. Using both rheology and laser light scattering diagnostics, the goal is to quantify the unusual elastic character of foams in terms of their underlying microscopic structure and dynamics. Of particular interest is determining how the elastic character vanishes, i.e., how the foam 'melts' into a simple viscous liquid, as a function of both increasing liquid content and increasing shear strain rate. The unusual elastic character of foams will be quantified macroscopically by measurement of the shear stress as a function of shear strain rate and of time following a step strain. Such data will be analyzed in terms of a yield stress, shear moduli, and dynamical time scales. Microscopic information about bubble packing and rearrangement dynamics, from which the macroscopic non-Newtonian properties ultimately arise, will be obtained non-invasively by multiple-light scattering: diffuse transmission spectroscopy (DTS) and diffusing wave spectroscopy (DWS). Quantitative trends with materials parameters, most importantly average bubble size and liquid content, will be sought in order to elucidate the fundamental connection between the microscopic structure and dynamics and the macroscopic rheology.
Durian, Douglas J.↗
Numerical Simulations of Non-Newtonian Convection in Ice: Application to Europa
Numerical simulations of solid state convection in Europa's ice shell have so far been limited to consideration of Newtonian flow laws, where the viscosity of ice is strongly dependent upon temperature, predicting that a stagnant lid should form at the top (10-40%) of a convecting ice shell. Such large thicknesses seem to contradict estimates of the effective elastic thickness of Europa s ice shell during its geologically active period. Recent laboratory experiments characterize the rheology of ice as the sum of contributions from several temperature and strain rate-dependent creep mechanisms. We present the results of numerical simulations of convection within Europa s ice shell using the finite-element model Citcom, applying the non-Newtonian rheology of grain boundry sliding. Our calculations suggest a shallower brittle/ductile transition and larger interior convective velocities compared to Newtonian rheology. The flow field is time-dependent, with small, localized upwellings and downwellings at the thermal boundary layers that have minimal topographic expression at the surface.
Barr, A. C.↗