Composite Rheology Research Articles

Sea levels and uplift rate from composite rheology in glacial isostatic adjustment modeling

Abstract Since laboratory experiments point to the existence of both diffusion creep and power-law creep at realistic mantle conditions, a composite rheology in which both mechanisms operate at the same time so that their strains are combined might be more realistic and has in the past been shown to provide a better fit to observations of glacial isostatic adjustment (GIA) than purely linear rheology ( Gasperini et al., 2004 , Dal Forno et al., 2005 ). To further investigate the effect of such rheology on sea level curves and uplift rate resulting from GIA, composite rheology is implemented in the coupled Laplace-finite element method for a 3D spherical self-gravitating Earth. We vary the pre-stress exponent (assumed to be derived from a uni-axial stress experiment) and the Newtonian viscosity for a homogeneous mantle. Composite rheology is found to have a statistically significant better fit with observed relative sea level data than linear rheology (diffusion creep only) and non-linear rheology (dislocation creep only). For the best-fitting composite rheology model it is shown that in the mantle below the former ice sheet margin, stress is high enough for power-law creep to become dominant during melting and shortly thereafter, causing the model to behave mostly in a non-linear way. It is found that composite rheology, with the parameters investigated in this paper, not only provides a better fit to sea level data than non-linear rheology but also slightly increases present-day uplift rate compared to non-linear rheology. This encourages application of composite rheology in GIA models that aim to improve knowledge of mantle rheology. Low uplift rates for composite rheology can be further increased by a large increase in ice thickness in North America at the expense of violating total melt-water constraints. A 1 or 2 ka delay in Laurentide glaciation and deglaciation increases uplift rates for all values of the pre-stress exponent investigated, while fit to a number of relative sea level observations in the Laurentide ice sheet is improved. Large increase in ice thickness disagrees with other observations (total melt constraints), therefore a delay in glaciation is a promising direction if global ice models are to be adjusted for a composite rheology.

Implications of post-perovskite transport properties for core–mantle dynamics

Recent evidence on perovskite to post-perovskite phase change in the lowermost mantle suggests that post-perovskite piles or lens should be present in the relatively cold downwelling areas, while the roots of the hot upwelling plumes consist of perovskite. Post-perovskite is often believed to be deformed predominantly by the dislocation creep and there are some hints that the activation parameters of the dislocation creep in post-perovskite induce lower viscosity than that of perovskite at the same pressure and temperature conditions. That can even result in a viscosity paradox in the lowermost mantle—viscosity in cold downwellings transformed to post-perovskite might be lower than the viscosity of warm perovskite plumes. Such a viscosity structure was indeed recently suggested by the geodynamical inversions of the geoid. Rheologically weak areas at the base of the subducted slabs may have important consequences for the slab deformation in the D ′ ′ . We investigate the dynamics of the cold slabs transformed to post-perovskite in the lowermost mantle by means of the simulations of thermal convection in a 2D Cartesian model of the lower mantle with composite rheology including diffusion creep and dislocation creep. Different creep parameters are used for the perovskite lower mantle and for the post-perovskite lens (or layer) respectively. While perovskite is considered to be deformed via linear diffusion creep, post-perovskite is modeled either as a constant viscosity material (with viscosity ranging from 10 20 Pa s to 10 23 Pa s) or it is deformed purely by the dislocation creep. The presence of the rheologically distinct post-perovskite not only strongly influences the slab deformation above the core–mantle boundary (CMB) but also results in different dynamic regimes of the CMB region (characterised by, e.g., the different length scales of the upwelling plumes) depending on the creep parameters of post-perovskite. Further, the presence of very low viscosity lens or a layer above the CMB strongly enhances the CMB heat flux in the cold slab areas. According to the amount of post-perovskite present in the D ′ ′ and the rheology of post-perovskite the heat flux across the CMB can vary considerably with time, which may have important implications for the core–mantle coupling and the character of the Earth’s geomagnetic field.

Long-wavelength character of subducted slabs in the lower mantle

The high resolution seismic tomography provides the detailed information about the fate of the subducted plates in the mantle. While the slab deformation in the transition zone is quite complex and differs among the individual subduction zones, it could be generally concluded that most slabs seem to penetrate into the lower mantle. The character of the fast seismic velocity anomalies, however, changes when the slabs cross the 670 km discontinuity. While in the upper mantle tomography resolves relatively narrow plate-like structures, in the lower mantle it rather indicates thick blobs of seismically fast material. Such thickening of the downgoing slabs is traditionally attributed to the effect of the viscosity increase in the lower mantle. Here we study the deformation of the slabs in the lower mantle in a viscous model with a non-linear composite rheology including the diffusion creep, the dislocation creep and a power-law stress limiter. We perform numerical simulations of the subduction process in a 2D Cartesian domain and concentrate especially on the effect of the change of the rheological parameters across the 670 km boundary on the slab deformation in the upper part of the lower mantle. The thickening or the buckling of the plate is indeed observed in the models with relatively low yield stress (0.1 GPa) of the stress-limiting mechanism and with a viscosity increase at the 670 km discontinuity. Further, we show that both the major mantle phase transitions and the strength of the crust layer have significant consequences for the creation of the buckling instabilities in the lower mantle.

Dispersion and rheology of carbon nanotubes in polymers

We review two generic mechanisms of dispersion of carbon nanotubes in a low-viscosity solvent or high-viscosity polymer, focusing on the neat nanotubes not surface-functionalized in any way. We give estimates of the van der Waals energies involved in nanotube aggregates and examine two main techniques: ultrasonication and shear mixing. For ultrasonic dispersion methods, the local mechanical energy applied to individual tubes is high and bundle separation is assured in the cavitation regime. We analyze and estimate the tube scission during ultrasonic cavitation and predict the characteristic nanotube length L lim below which scission does not occur. For shear-mixing, our analysis suggests that dispersion is possible in non-parallel bundled nanotube aggregates, in high-viscosity polymers, once a critical mixing time t* is reached. We then examine characteristic features of nanotube-polymer composite rheology and its aging/stability against re-aggregation. We show that at nanotube loading above overlap concentration the tubes form an elastic network in the matrix. Physical junctions of this network are strong and stable enough to provide a rubber-like elastic response with very slow relaxation.

Injection moulding simulation analysis of natural fiber composite window frame

Abstract Study of window frame fabrication by injection moulding process was carried out with the aid of Moldflow® software. Rice husk filled high-density polyethylene was used as the raw material. Solid and hollow designs (A001 and A002) were created to compare the pros and cons of each design. The investigations were carried out on flowing, packing, cooling and costing of injection moulded window frame. At the end of the analysis, the most feasible design was selected to be further undergone stress analysis according to BS EN 14608:2004 and BS EN 14609:2004. Eventually, the mechanical properties were classified according to BS EN 13115:2001. The actual processing conditions of rice husk composite were approximated to softwood at Cross-WLF viscosity model due to unavailability of rice husk plastic composite (RHPC) rheology property. RHPC melt is generally shear thinning, meanings that the viscosity decreases with increasing of shear rates. From the analysis, window frame with hollow design is preferable, since hollow design has advantage of filling, packing, and cooling properties. The hollow design also costs less than solid design of window frame. However, high injection pressure and clamping tonnage are unfavourable for hollow design. A002 hollow design was selected as the most feasible window frame to be fabricated. Stress analysis was done to classify the window frame. The analyses were carried out to determine racking and static torsion resistance. A002 window frame mechanical strength is classified as Class 2 according to BS EN 13115:2001.

Thermal cracking and the deep hydration of oceanic lithosphere: A key to the generation of plate tectonics?

The development of transient thermal stress in suboceanic mantle is investigated on the basis of two‐dimensional thermoviscoelastic models incorporating composite rheology appropriate for dry oceanic lithosphere. Thermal stress is shown to be sufficiently high to deeply fracture the coldest part of lithosphere, e.g., to the depth of at least ∼30 km (and possibly down to ∼50 km) in 100‐Ma‐old lithosphere. The release of thermal stress by tension cracking is limited to the vicinity of cracks, and the cascade crack system is suggested to be required given the finite fracture strength of mantle materials. Possible physical and chemical consequences of deep thermal cracking are also discussed. The rheological evolution of oceanic lithosphere is likely to be affected by thermal cracking and subsequent serpentinization, which introduces the localized zones of weakness in the otherwise stiffest part of lithosphere. This localized weakening may help to explain why plate tectonic convection, not stagnant lid convection, operates in Earth's mantle.

Modelling of mantle postglacial relaxation in axisymmetric geometry with a composite rheology and a glacial load interpolated by adjusted spherical harmonics analysis

Although studies on glacial isostatic adjustment usually assume a purely linear rheology, we have previously shown that mantle relaxation after the melting of Laurentide ice sheet is better described by a composite rheology including a non-linear term. This modelling is, however, based on axially symmetric geometry and glacial forcing derived from ICE-3G and suffers from a certain amount of arbitrariness in the definition of the ice load. In this work we apply adjusted spherical harmonics analysis to interpolate the ice thicknesses of ICE-3G and ICE-1 glaciological models. This filters out the non-axisymmetric components of the ice load by considering only the zonal terms in the spherical harmonics expansion. The resulting load function is used in finite-element simulation of postglacial rebound to compare composite versus purely linear rheology. Our results confirm that composite rheology can explain relative sea level (RSL) data in North America significantly better than a purely linear rheology. The performance of composite rheology suggests that in future investigations, it may be better to use this more physically realistic creep law for modelling mantle deformation induced by glacial forcing.

Use of an electron accelerator to produce nanopowders by evaporation of initial materials at atmospheric pressure

High-purity nanodispersed powders with extraordinary properties that can be used in various technologies (electronics, catalysis, ceramics, modification of composite rheology, and so on) can be produced by evaporation of various initial materials at atmospheric pressure. In particular, the authors succeeded in producing nanodispersed powders of oxides [including silicon dioxide and oxide (SiO2 and SiO) and magnesium (MgO), aluminum (Al2O3), and cuprous (Cu2O) oxides], metals [including tantalum (Ta), molybdenum (Mo), aluminum (Al), silver (Ag), and some others] in various atmospheres, semiconductors [including silicon (Si)], nitrides [including aluminum (AlN) and titanium (TiN) nitrides], and other materials. It is important for the developed production process that the main component of the setup (an industrial accelerator) is capable of creating high temperatures for evaporation of any refractory materials. The production process has high efficiency and productivity (reaching several kilograms of oxides per hour).

Granular flow in the marginal ice zone

The region of sea ice near the edge of the sea ice pack is known as the marginal ice zone (MIZ), and its dynamics are complicated by ocean wave interaction with the ice cover, strong gradients in the atmosphere and ocean and variations in sea ice rheology. This paper focuses on the role of sea ice rheology in determining the dynamics of the MIZ. Here, sea ice is treated as a granular material with a composite rheology describing collisional ice floe interaction and plastic interaction. The collisional component of sea ice rheology depends upon the granular temperature, a measure of the kinetic energy of flow fluctuations. A simplified model of the MIZ is introduced consisting of the along and across momentum balance of the sea ice and the balance equation of fluctuation kinetic energy. The steady solution of these equations is found to leading order using elementary methods. This reveals a concentrated region of rapid ice flow parallel to the ice edge, which is in accordance with field observations, and previously called the ice jet. Previous explanations of the ice jet relied upon the existence of ocean currents beneath the ice cover. We show that an ice jet results as a natural consequence of the granular nature of sea ice.

Linear or nonlinear rheology in the mantle: a 3D finite-element approach to postglacial rebound modeling

In a previous work, cast in axisymmetric flat geometry, we have shown that a realistic composite rheology (linear plus nonlinear) for the Earth’s mantle reproduces the postglacial isostatic readjustment of Laurentia significantly better than a purely linear one. In this work we address the same problem in a 3D flat geometry allowing to apply the ice load described by the ICE-3G deglaciation history without manipulations. Computation is numerically carried out through finite elements as the nonlinear formulation prevents the use of spectral methods. The goodness of fit is quantitatively tested by comparing observed and computed Relative Sea Level (RSL) data at 29 North American sites for the last 8 kyr. The mixed rheology model still shows a slightly but significantly better fit (in the statistical sense) than the linear model. © 2004 Elsevier Ltd. All rights reserved.

The anisotropic and rheological structure of the oceanic upper mantle from a simple model of plate shear

We have developed a channel flow model that dynamically couples plate motion and mantle stress with a composite rheology (diffusion creep and dislocation creep) to study the rheological and anisotropic structures of the oceanic upper mantle. A semi‐analytic approach is used to solve for mantle stress and viscosity, allowing fast calculations and exploration of a wide range of rheological parameters. Mantle stress in our model is due to shearing by a moving plate. By comparing mantle stress with a transition stress for dislocation creep, we identify regions where either diffusion creep or dislocation creep is active. Deformation by dislocation creep results in a mineral fabric that may be responsible for observed seismic anisotropy. Our study suggests that there is an important relation between plate motion, seismic anisotropy, mantle viscosity and transition stress. Using laboratory results for rheological parameters, we find that dislocation creep exists only in a layer at certain depths in the upper mantle. For a plate velocity of 10 cm yr−1, an asthenospheric viscosity of 1019 Pa s and an asthenospheric transition stress of 0.1 MPa, our model predicts a ∼200 km thick dislocation creep layer, which is broadly consistent with the observations of seismic anisotropy. For a plate velocity of 10 cm yr−1 and an asthenospheric transition stress of 0.1 MPa, the asthenospheric viscosity needs to be greater than 5 × 1018 Pa s to produce any dislocation creep deformation, and the asthenospheric viscosity needs to be larger for slower plate motion or larger transition stress. Slower plate motion leads to a thinner dislocation creep layer, which may partially explain the observed asymmetry in anisotropic structure in the East Pacific Rise.

Composite flow laws for crystalline materials with log-normally distributed grain size: theory and application to olivine

Conventional steady-state flow laws describing combined grain size insensitive dislocation creep and grain size sensitive diffusion creep incorporate grain size as a single (mean) value. However, rocks exhibit distributed grain size and variations in the shape of the distribution, such as its width, will accordingly affect rheological behavior. To evaluate this effect, we have derived composite dislocation–diffusion flow laws describing upper and lower bounds on the rate of deformation of materials showing a grain size distribution of the commonly observed log-normal type. The upper and lower bound flow laws obtained allow systematic investigation of the influence of the grain size distribution parameters, i.e. the median and standard deviation, on composite rheology. The results demonstrate major effects of distribution width as well as median value. Application to polycrystalline olivine, deforming by Coble creep and power law dislocation creep, reveals significant implications for interpreting deformation experiments and modeling flow in the Earth's mantle. The flow laws also provide an improved basis for modeling the deformation of rocks during geological processes in the crust and mantle.

Influence of grain size evolution on convective instability

Grain size, one of the most important microstructural properties of materials, evolves during creep deformation to minimize the free energy of polycrystalline aggregates. We apply a model of grain size evolution to the study of convective instability of cooling boundary layers. The grain size evolution model is coupled to a composite rheology where the deformation rate is the sum of that due to dislocation creep and grain size sensitive diffusion creep. The onset of convection is sensitive to grain growth rates and the initial grain size. The formation of convective instabilities is enhanced by stresses induced by plate motions; therefore small‐scale convection is more likely to occur beneath fast‐moving plates. In finite amplitude convection, grain size evolution leads to high viscosity in regions where convective stresses are low and can induce viscosity contrasts exceeding one order of magnitude. Such viscosity contrasts are sufficient to influence the dynamics of convection, often leading to domains which remain isolated from the well‐mixed convecting fluid. A composite viscosity including diffusion creep, which has a lower activation energy than dislocation creep, reduces the effective temperature dependence of viscosity.

Interaction between small‐scale mantle diapirs and a continental root

A possible mechanism for adding material to a continental root is by means of upwellings from the convecting mantle subject to pressure release partial melting. We present results of numerical modeling of the interaction of melting diapirs with continental roots in an Archean setting characterized by a mantle potential temperature of 1750°C in a two‐dimensional (2‐D) Cartesian geometry. In an extension of earlier work [de Smet et al., 2000b] we have investigated the influence of mantle rheology on the behavior of diapirs. We have in particular looked at the difference in behavior of diapirs using a composite rheology combining both grain size sensitive diffusion creep and dislocation creep mechanisms. We have used the grain size, here taken to be uniform, as a control parameter to obtain model cases with varying contribution from the two creep mechanisms. The diapirs in the composite rheology model rise much faster than they do in a purely Newtonian model. Observed diapiric ascent times from 230 km depth to the top of the ascent path at about 80 km depth are approximately 1 Myr for a Newtonian model (averaged 14 cm/yr) compared to about 50 thousand years for a composite rheology model (averaged 3 m/yr) with the same parameters for the Newtonian component. This clearly indicates the large impact of the dislocation creep component of the viscous deformation process. We have also investigated the effect of an increase in the viscosity due to dehydration during partial melting. This increase has a strong influence on the development of rising diapirs. The ascent velocity and lateral spreading of the diapirs at the end of their ascent are effectively reduced when a viscosity increase by a factor of 10 is applied, and the effect becomes stronger for larger factors. Average vertical velocities range from 1.4 cm/yr for a factor 10 to 2 mm/yr for a factor 200. The most striking result of the viscosity increase due to dehydration is the reduction of the ascent velocity, thereby stretching the characteristic timescale of the diapiric intrusion process to a value between 5 and 50 Myr for dehydration viscosity prefactor values of 10 and 200, respectively. In contrast with the strong difference between the Newtonian and the composite rheology models, small differences are found in the overall dynamics between the composite rheological models, characterized by different values of the uniform grain size. The composite rheological models exhibit self‐regulating behavior where substantial differences between the relative contributions of the two creep components result in very similar effective viscosities, due to a local dominance of dislocation creep at high stresses and corresponding similar flow dynamics. Stress levels and P,T paths in the modeling results are consistent with estimates obtained from Precambrian peridotite bodies which are interpreted to have originated from asthenospheric diapirism.

Rheological Modeling and Fracture of Hard Oxide Ceramics Modified by Ultra-Dispersed Diamond Nanoparticles

Fracture of Al-Al 2 O 3 -diamond-containing composite coating was investigated using rheological models for principal Hertzian contact of a sphere and a plate. The crystallographic and morphologic texture was characterized and the fracture resistance was measured using fracture mechanics. A rheological model of the composite coating was proposed and confirmed by in situ experiments. Examination of the composite coating showed a hardness value of 25 GPa (about 25% higher than for an alumina-based layer) and fracture resistance (about 50% higher than for a single oxide ceramic layer) as compared to prior alumina-based coatings on a soft substrate. Experiments revealed ultimate stresses and stress-strain modes of the coating. Diamond nanoparticles improved fracture resistance of an alumina-based layer. It is also thought that the composite coatings will have higher thermal conductivity and thermal shock resistance than alumina-based layers. Such physical characteristics suggest a number of possible commercial applications for the composite coatings, particularly for wear-resistant and related applications. The higher hardness and toughness of the coatings make them very attractive as substitutes for alumina-based and other ceramic-based composite coatings in these applications. composite rheology fracture stress indentation diamonds

The influence of rheological weakening and yield stress on the interaction of slabs with the 670 km discontinuity

Results of high resolution seismic tomography showing subducting slabs deflected in the transition zone and thickened in the lower mantle seem to call for slab material weaker than inferred from mineral physics deformation mechanisms. A possible mechanism suggested by several authors could be the weakening due to grain size reduction, which should occur in the cold portion of fast slabs after an exothermic phase transition at a depth of 400 km. Since the amount of weakening as well as the rate of subsequent strengthening due to the grain growth are not precisely known, we present here a parametric study of slab behavior in the transition zone and upper part of the lower mantle. We simulate a subducting slab in a two-dimensional (2-D) Cartesian box in the numerical model with composite rheology including diffusion creep, dislocation creep and a general stress limiting rheology approximating Peierl’s creep. We concentrate on two rheologic effects: the dynamic effect of slab weakening due to grain size reduction at the phase boundary and the effect of yield stress of stress limiting rheology. The effect of trench migration on slab deformation is also included in our study. Results show that the slab ability to penetrate into the lower mantle is not significantly affected by a trench retreat in the absence of grain size weakening. However, in case of a 4 cm/yr trench retreat, grain size weakening provides a viable mechanism to deflect the slab in the transition zone, provided that stress limiting deformation mechanism would limit the effective viscosity outside the areas of grain size weakening to about 1024 Pa s.

Effect of starch content on viscosity of starch‐filled poly(hydroxy ester ether) composites

AbstractThe effect of starch volume fraction on starch‐filled poly(hydroxy ester ether) (PHEE) biodegradable composites was analyzed using Mooney, Thomas, Maron & Pierce, and Frankel & Acrivos equations. Corn starch/PHEE materials were extruded using a twin‐screw extruder with starch volume fractions from 0.27 to 0.66. The starch was dried to a moisture content of 0.7% to minimize moisture effect on composite rheology. Dynamic frequency sweep measurements were carried out at 120°C and 1% strain. The equations of Maron & Pierce, Thomas, and Frankel & Acrivos can be used to describe the experimental data. It is found that the relative viscosity at the same shear stress increases with increasing shear stress. The possible existence of yield stress at high starch concentrations was examined using a Casson plot.

Localization of dislocation creep in the lower mantle: implications for the origin of seismic anisotropy

Recent seismological observations reveal the presence of seismic anisotropy in localized regions at the base of the mantle within an otherwise isotropic lower mantle. These regions can be placed in a tectonic context, corresponding to locations of paleosubduction and plume upwelling. This project works toward determining whether the observed seismic anisotropy may be explained by the development of a mineral fabric by lattice-preferred orientation (LPO). Numerical modeling is used to explore whether the conditions at the base of upwelling and downwelling regions are consistent with those required for fabric development. Specifically, we examine whether dislocation creep dominates these regions within a background mantle that flows primarily by diffusion creep. The key to our study is the use of a composite rheology that includes both mechanisms of diffusion and dislocation creep and is based on mineral physics experiments. Results show that it is possible to produce a localization of dislocation creep near slabs within a background mantle dominated by diffusion creep. In contrast, upwelling regions are characterized by a domination of diffusion creep. These results indicate that LPO may be the cause of lowermost mantle seismic anisotropy near paleoslabs, but other mechanisms such as shape-preferred orientation may be required to produce the anisotropy observed near upwellings.

Polymer and Composite Rheology

Polymer and Composite Rheology

Polymer and composite rheology, second edition [Book Review

Polymer and composite rheology, second edition [Book Review