High Shear Strain Rates Research Articles

Correlating the rheological and mechanical response of polyurethane nanocomposites containing hyperbranched polymers

Cast polyurethane thermosets have been modified with randomly oriented exfoliated and intercalated montmorillonite clay using hyperbranched polymers (HBP) as reactive additives to promote dispersion of the clay platelets. The influence of the clay content on the stiffness of the nanocomposites is discussed in terms of simplified classical micromechanical models that allow correlations to be established between the properties of the final polyurethane and the limiting high strain rate shear viscosity of the HBP or HBP/polyethylene glycol nanocomposite precursors. Such models imply certain restrictions on the potential for mechanical reinforcement with unoriented platelets owing to crowding effects. Moreover, they appear unable to account simultaneously for the observed degrees of reinforcement in the glassy and the rubbery states, if currently accepted values for the stiffness of the MMT are assumed. Possible reasons for this are discussed.

Basal ice motion and deformation at the ice-sheet margin, West Greenland

AbstractMeasurements of basal ice deformation at the margin of Russell Glacier, West Greenland, have provided an opportunity to gain more insight into basal processes occurring near the margin. The basal ice layer comprises a debris-rich, heterogeneous stratified facies, overlain by a comparatively debris-poor dispersed facies. Ice velocities were obtained from anchors placed in both ice facies, at three sites under 5–15 m ice depth. Mean velocities ranged from 20 to 43 m a–1, and velocity gradients indicate high shear strain rates within the basal ice. Stick–slip motion and diurnal variations were observed during measurements at short (1–5 min) time intervals. Vertical gradients in horizontal ice velocity indicate two modes of deformation: (1) viscous deformation within the stratified ice facies, and (2) shear at the interface between the two basal ice facies. Deformation mode 1 may contribute to the folding and shear structures observed in the stratified facies. Deformation mode 2 may generate the stick–slip motion and be associated with the formation of debris bands. Active deformation close to the margin suggests that structures observed within the basal ice are only partially representative of processes occurring near the bed in areas away from the glacier margin.

The mechanical response of an A359/SiCp MMC and the A359 aluminum matrix to dynamic shearing deformations

Abstract : The mechanical response of a metal matrix composite to dynamic shearing deformations has been measured, using a new design of the thin-walled tubular specimen for the torsional Kolsky bar experiment that allows working with these difficult-to-machine materials. The advantages of using the new specimen design are as follows: (i) the thickness of the thin wall along the axial direction is very uniform; (ii) specimen machining is extremely simple; (iii) the cost of specimen machining is greatly reduced. The approach has been used to characterize the high shear strain rate (10(exp 3) s(exp -1)) behavior of an A359/SiC(sub p) composite and its corresponding A359 monolithic alloy with the torsion Kolsky bar. The experimental results show that the flow stress of the composite in shear increases in the presence of SiC particles, whereas the failure strain is reduced. The shear failure strain of both the A359/SiC(sub p) composite and the A359 monolithic alloy appear to increase with increasing strain rate. Previous observations have shown that particle develops during compressive deformations of this material. However, particle fracture is not a significant damage mode during the shearing deformations of the composite, and this is reflected in differences between the torsional and tension behaviors of the material.

Strain-rate-dependent rheology of partially molten rocks

Abstract Coupling or decoupling in the lithosphere is often related to the absence or the presence of a layer of partially molten rocks, although the rheology of such rocks remains unsolved. Theoretical arguments correlated with structural observations provide new insights into the rheology of partially molten rocks, namely migmatites and magma. These rocks are simplified to two-phase pseudo-fluids constituted of a quasi-solid matrix and a variable amount of melt. Previous experiments indicate that the matrix deforms plastically according to a power law. The melt is Newtonian and weakens at high shear strain rates. Because of the heterogeneous distribution of matrix and melt phases, their rheologies cannot be averaged to obtain the rock rheology. Four behaviours are identified. (i) At high stress and strain rates, the viscosity contrast between melt and matrix is lowest. Both phases can accommodate strain at a comparable rate, allowing migmatite and magma bodies to deform as quasi-solid units. (ii) At low strain rates, the viscosity contrast between melt and matrix is highest. Melt deforms and relaxes much faster than the matrix. The simultaneous coexistence of a weak and a strong phase is expressed in a 3D viscosity-strain rate-melt fraction diagram, in which a cusp-shaped surface represents viscosity. The cusp graphically shows that the viscosity of partially molten rocks may jump several orders of magnitude. These jumps, leading to sudden melt segregation, are temporally erratic. (iii) At low strain rates, strain partitioning may lead to internal instabilities and segregation between melt and restitic phases, as observed in the leucosome/melanosome separation. (iv) Cyclic processes follow hysteresis loops and trigger strain localization.

Crustal strain field in central japan, based on the wavelet analyzed GPS time-series data

In order to estimate the secular crustal deformation in central Japan, we adopted the wavelet technique to find and remove the data discontinuities associated with earthquakes and artificial errors, and also remove seasonal variations and white noises in the GPS time series data of daily co-ordinates obtained from the continuous GPS network, GEONET of GSI. The strain components were computed based on least-squares prediction method by using improved time series data. The motion velocities of GPS sites at uniform 7 km×7 km grids were interpolated by adopting the empirical covariance function and then differentiated with respect to space to estimate strain rates. The estimated strain field shows that there existed a compressive regime in the entire region. Higher maximum shear strain rates of about 0.2 microstrain/a are shown in and around the Izu and Boso peninsulas, and Tokyo Bay. Relatively high maximum shear strain rates are also shown in the southern Tohoku district and another notable area along the coast of the Japan Sea, which nearly corresponds to the Shinanogawa seismic zone.

Frictional‐viscous flow of phyllosilicate‐bearing fault rock: Microphysical model and implications for crustal strength profiles

It is widely believed that around the brittle‐ductile transition, crustal faults can be significantly weaker than predicted by conventional two‐mechanism brittle‐ductile strength envelopes. Factors contributing to this weakness include the polyphase nature of natural rocks, foliation development, and the action of fluid‐assisted processes such as pressure solution. Recently, ring shear experiments using halite/kaolinite mixtures as an analogue for phyllosilicate‐rich rocks for the first time showed frictional‐viscous behavior (i.e., both normal stress and strain rate sensitive behavior) involving the combined effects of pressure solution and phyllosilicates. This behavior was accompanied by the development of a mylonitic microstructure. A quantitative assessment of the implications of this for the strength of natural faults has hitherto been hampered by the absence of a microphysical model. In this paper, a microphysical model for shear deformation of foliated, phyllosilicate‐bearing fault rock by pressure solution‐accommodated sliding along phyllosilicate foliae is developed. The model predicts purely frictional behavior at low and high shear strain rates and frictional‐viscous behavior at intermediate shear strain rates. The mechanical data on wet halite + kaolinite gouge compare favorably with the model. When applied to crustal materials, the model predicts major weakening with respect to conventional brittle‐ductile strength envelopes, in particular, around the brittle‐ductile transition. The predicted strength profiles suggest that in numerical models of crustal deformation the strength of high‐strain regions could be approximated by an apparent friction coefficient of 0.25–0.35 down to depths of 15–20 km.

Ice‐stream‐related patterns of ice flow in the interior of northeast Greenland

Ice flow in the interior of the NE quadrant of the Greenland ice sheet is focused on the large ice stream draining the north side of the summit dome. The rapid ice flow in the stream is apparent in the surface features in the stream and at the margins, in the broad scale topography that drives ice flow, and in satellite‐derived ice motion information. The patterns of ice flow in the upper half of the stream are remarkable for their level of organization, simple geometry, and effects on local surface topography. The stream begins less than 100 km from the ice divide as a current 15 km wide and then broadens symmetrically downstream by the addition of ice from the sides to a width of more than 60 km. Elevation data and visible‐band imagery show that the stream has marginal troughs tens of meters deep in its upper reach which are coincident with regions of high shear strain rate. The topography of the margins and undulating surface of the stream is generated by the ice flow; the surface undulations in the stream are fixed in location and shape over the 5 year period from 1994 to 1999. The enhanced flow presents a challenge for researchers trying to understand the history of ice discharge from a significant area in the interior of the ice sheet.

Geodetic detection of active faults in S. California

A new analysis of velocities of geodetic markers straddling the San Andreas Fault System in southern California reveals that interseismic deformation is localized along a dozen sub‐parallel narrow belts of high shear strain rate that correlate well with active geologic fault segments and locally with concentrated zones of microseismicity. High shear strain rates (0.3–0.95 µstrain/year) are observed northward and southward of the San Andreas fault's big bend, whereas the big bend itself is characterized by a diffuse low magnitude shear strain rate. Dilatational deformation is diffuse and of relatively low magnitude (<0.2 µstrain/year), with the highest contraction rates occurring in the Ventura and Los Angeles basins. Because no prior assumptions were made regarding the geology, tectonics, or seismicity of the region, our analysis demonstrates that geodetic observations alone can be used to detect active fault segments.

Contemporary horizontal velocity and strain rate fields of the Pacific‐Australian plate boundary zone through New Zealand

We have inverted velocity solutions from nine geodetic networks distributed across New Zealand to derive present‐day continuous horizontal velocity and strain rate fields at the Earth's surface throughout the country. The nine networks contain a total of 362 Global Positioning System (GPS) stations that have been observed at least twice and at least a year apart between 1991 and 1998. The model velocity field is expanded as bicubic spline interpolation functions defined within a curvilinear grid that covers the country and extends into the assumed rigid Australian and Pacific plates to west and east. The inversion jointly minimizes the magnitudes of fitted strain rates and the misfit to the observed velocity data. The spline technique allows high spatial resolution of strain rate variations, especially in regions with spatially dense GPS data. Expansion of the model velocity field on the surface of a sphere allows arbitrarily large areas to be studied. Previously known aspects of New Zealand plate boundary deformation are highlighted with improved resolution, including back‐arc extension in the Taupo Volcanic Zone, rotation of the Hikurangi forearc away from this zone in the North Island, and a band of high shear strain rate under the Southern Alps to the southeast of the Alpine fault. Our results reveal several new features, including a region of enhanced shear straining apparently associated with strike‐slip faults in the southern North Island and a band of contractional straining subparallel and well east of the Alpine fault that is similar to features found in numerical and sandbox models of continental collision.

A new technique to characterize the fiber/matrix interphase properties under high strain rates

Dynamic interphase-loading apparatus (DILA) has been developed to directly characterize the fiber/matrix interphase properties of composites under high loading rates. This apparatus uses a micro-mechanical method (micro-indentation) that is based on the debonding of a fiber from the matrix at the interphase region. Displacement rates up to 3000 μm/s that cause deformation of the interphase under high shear strain rates were obtained using the fast expansion capability of piezoelectric actuators (PZT). Transient force and fiber displacement for a specific displacement rate is measured during the test. The data are reduced to apparent average interphase shear strength and energy absorbed during debonding and frictional sliding during the micro-debonding process. An E-glass-fiber/epoxy-amine interphase was tested under various loading rates to demonstrate the capability of the test apparatus. Test results showed that the strength and energy-absorbing capability of the E-glass/epoxy-amine interphase are sensitive to loading rate.

Perturbation analysis of high strain-rate shear localization in B.C.C. crystalline materials

A perturbation analysis has been used to obtain a detailed and fundamental understanding of the high strain-rate material mechanisms associated with material instabilities and adiabatic shear-band formation in single body-centered cubic (b.c.c.) crystals. The interrelated effects of wave number, shear-band orientation, strain hardening, strain-rate sensitivity, and thermal and geometrical softening on material instability and shear-strain localization have been investigated in terms of the competition between the softening and hardening mechanisms for nominal strain-rates from 100/s to 5000/s. A perturbed system of equations has been obtained, accounting for arbitrary crystal orientations, and since no approximations have been made for the magnitude of the strain-rate sensitivity parameter, all the roots associated with the stability of the perturbed equations can be obtained for physically representative deformations. Hence, a comprehensive characterization of material instabilities can be obtained beyond the initial instability point, and the strength of material instabilities can be then monitored throughout the deformation history to distinguish between material instabilities and shear-strain localization.

Modelling of anisotropic ice flow in Law Dome, East Antarctica

AbstractA model for ice flow in a polar ice sheet is presented. It is based on laboratory measurements of ice rheology, and includes the effect of anisotropic-flow enhancement in tertiary creep as the ice progresses through a range of stress regimes as it passes through the ice sheet. This flow model is applied to the transect from the summit of Law Dome, East Antarctica, to Gape Folger. In the upper layers of the ice sheet good agreement is found between the shear strain-rate profiles from the model and borehole-inclination measurements. Modifications of the simple model predictions for high shear strain rates in the lower layers of the ice cap are required in order to match the observed surface velocities. In these lower regions reductions in both the enhancement of shear flow and shear stress appear to be required, and this suggests that more attention needs to be given to the dynaimcs deep within ice sheets.

Friction Force, Contact Resistance, and Lubricant Shear Behavior at the Magnetic Head-Disk Interface During Starting

During the starting operation of magnetic rigid disks, a stiction phenomenon characterized by a high friction force may be encountered due to the smoothness of the contacting surfaces and the small thickness of the lubricant film. Since friction measurement using a force transducer yields a signal proportional to the slider displacement, the real friction force at the head-disk interface cannot be measured directly. In the present study, a dynamic data analysis scheme is developed to obtain the real friction force as a function of time based on the measured apparent friction force. Electric contact resistance measurements demonstrate that the transition from static to kinetic friction occurs before the apparent friction force reaches a maximum value. Assuming a constant acceleration of the disk, the relative slip velocity at the contact interface is obtained as a function of time. The relationship between the shear stress and shear strain rate for a relatively thick lubricant film is found to be approximately linear up to a critical value of the shear stress. Due to the extremely high shear strain rates, the maximum real friction force can be significantly greater than the maximum static friction force.

Comparison of damage accumulation measures in human cortical bone

Elastic modulus degradation, strength reduction, and energy dissipation have traditionally been the properties of choice to monitor the damage process in cortical bone. However, these properties only provide limited insight into the damage process given the complex mechanical nature of bone. In the current study, alternative measures of the damage process were investigated for machined human cortical bone specimens loaded under torsion. Seventy-two bone specimens from 6 human femurs were subjected to a series of torsional relaxation cycles in which damage was induced during a single relaxation cycle and the effects of damage on the elastic, yield, viscous, and failure properties were determined from pre- and post-damage relaxation cycles. The results revealed that degradation of all torsion properties exhibited a significant twist magnitude effect. However, the yield stress and strain, the relaxation rate, and the total relaxation exhibited 5–10 fold greater degradation than both strength and modulus, when residual strength tests were conducted at high shear strain rates. For the loading conditions examined in this study, the results indicated that the relaxation and yield properties of cortical bone are more sensitive to shear damage accumulation and better measures of the damage process than either strength or modulus. Further, the results reveal an important interaction between damage and the viscous behavior of bone which provides new insight into the effects of damage on bone mechanical properties.

High-Strain, High-Strain Rate Deformation, Shear Localization and Recrystallization in Tantalum

Des echantillons tubulaires en tantale, entoures par des cylindres a paroi epaisse ont subi une implosion de facon symetrique par la detonation d'un explosif place de facon co-axiale avec le cylindre en cuivre. La microstructure est constituee de : (i) dislocations et cellules de dislocations allongees; (ii) sous-grains; (iii) micrograins produits par recristallisation dynamique; (iv) grains generes par recristallisation statique dont la taille de grains a ete prevue par la cinetique conventionnelle de croissance des grains. Un mecanisme est propose pour l'evolution de la microstructure des cellules allongees, sous-grains, et micrograins. Une localisation de la deformation a l'echelle des grains a ete observee. La rupture ductile le long des bandes de cisaillement est due aux contraintes residuelles engendrees dans l'orifice interieur apres dechargement.

Deformation Fields Around A Fault Embedded In A Non-Linear Ductile Medium

SUMMARY The geological record of deformation is often characterized by a combination of discontinuous deformation, in which strain is concentrated in faults, and continuous deformation, in which strain is distributed through the material. Where slip occurs on a fault that terminates, the surrounding material is deformed. In the lower crust and in cases where large strains occur over long geological time-scales, it is appropriate to model the deformation using a viscous (probably non-linear viscous) rheology. We describe a method for practical finite-element solution of this problem using a dynamically self-consistent formulation for stress and displacement on a fault of arbitrary geometry; the accuracy of the method is tested by comparison with an analytical solution for the linear rheology. We describe here the instantaneous deformation fields around a mode II fault under both plane-strain and plane-stress conditions, and a range of rheological exponents n (where strain rate is proportional to deviatoric stress to the nth power). the distributions of stress and strain rate around the fault tip are controlled primarily by the rheological exponent n. A localized zone of high strain rate projects beyond the end of the fault if n is about 3 or greater, and the degree of localization of deformation increases with the value of n. the zone of high shear-strain rate can be defined in practical terms by considering (1) the region in which the creep velocity differs by more than 20 per cent from the velocity on the nearby external boundary and (2) the region in which the maximum shear-strain rate is greater than about twice the externally imposed shear-strain rate. For n= 1, the volumes so defined differ considerably, but for large values of n, the two definitions both describe the same narrow zone of deformation beyond the end of the fault. Evaluation of the Navier-Coulomb criterion for brittle failure of the medium surrounding the fault tip shows first that brittle failure is much more likely on the extensional side of the fault than the compressional side. It also shows that the volume of material subject to brittle failure decreases rapidly with increasing n because of the relatively weaker stress singularity. We analyse previously published displacement versus distance data for faults terminating in sedimentary rocks at 0.1 to 100 m length-scales under different tectonic conditions, in order to determine the rheological exponent n. These analyses result in n values between approximately 0.85 and 5 for the different faults, with error bounds on n typically pL 1. the variation in n values may result from differences in pressure, temperature and fluid conditions at the time of faulting. More importantly, the analysis demonstrates a new method for the determination of the effective rheological exponent under in situ geological conditions.

Properties of Zeolite- and Cornstarch-Based Electrorheological Fluids at High Shear Strain Rates

The mechanical and electrical properties of zeolite- and cornstarch-based ER fluids are explored using a concentric cylinder viscometer. With cylinder radius to gap size ratio on the order of 400, we achieved shear strain rates ranging from 3000 to 20,000 sec-1. Two different volume fractions of zeolite and cornstarch suspensions in silicone oil were tested at a constant temperature of 30°C. The shear stresses and electric resistivity of the fluids were computed from experimental measurements as functions of shear strain rate. Although the cornstarch ER fluids indicated anomalous behavior, the zeolite ER fluids were found to be more stable under high shear strain rates and electric fields and were characterized by a Bingham viscoplastic model-like behavior. Dynamic yield stress was increased in proportion to a power of the electric field. The higher the volume fraction of dispersions, the higher the yield stress. Plastic viscosity, as defined by the Bingham model, remained unchanged with the variation of elec tric field for a fixed volume fraction. This work was motivated by the need for applications to rotor-bearing control, where for usual bearings, the shear rate is much higher than the maxima of most of the published experimental results. Moreover, for high shear rates, the validity of the Bingham model was questioned by many authors without specific experimental justification, which is attempted here for two different kinds of dispersed particles.

High strain-rate shear response of polycarbonate and polymethyl methacrylate

The high strain rate response of polycarbonate (PC) and polymethyl methacrylate (PMMA) are measured using a split Hopkinson torsion bar for shear strain rates Ẏ from 500 s -1 to 2200 s -1 , and temperatures in the range —100°C to 200°C. The yield and fracture behaviours are compared with previous data and existing theories for Ẏ < I s -1 . We find that PC yields in accordance with the Eyring theory of viscous flow, for temperatures between the beta transition temperature T β ≈ — 100°C and the glass transition temperature T g = 147°C. At lower temperatures, T < T β , backbone chain motion becomes frozen and the shear yield stress is greater than the Eyring prediction. Strain softening is an essential feature of yield of PC at all strain rates employed. Poly methyl methacrylate fractures before yield in the high strain rate tests for T < 80°C, which is close to the glass transition temperature T g 120°C. It is found that the fracture stress for both materials obeys a thermal activation rate theory of Eyring type. Fracture is thought to be nucleation controlled, and is due to the initiation and break down of a craze at the fracture stress τ f . Examination of the fracture surfaces reveals that failure is by the nucleation and propagation of inclined mode I microcracks which link to form a stepped fracture surface. This reveals that failure is by tensile cracking and not by a thermal instability in the material. The process of shear localization is fundamentally different from that shown by steel and titanium alloys.

The Dynamic Response of Graphite Fiber-Epoxy Laminates at High Shear Strain Rates

The split Hopkinson bar was used to determine the stress, strain and strain rate response of woven graphite-epoxy laminates during high shear strain rate deformation. The specimens were oriented and tested in both interlaminar shear and in transverse shear at strain rates ranging from 6000 to 18000 sec-1. The results show that the strain rate effect in interlaminar shear is small. The fracture surface is characterized primarily by interfacial failure between the fibers and the matrix. In transverse shear, however, the strain rate effect is significant due to the greater role played by the resin matrix in the deformation process. In both cases, at the high strain rates imposed in this investigation, sparks were produced by the specimens during deformation. These are believed to be caused by the combustion of fragments resulting from the high rate deformation.

Flow Behavior of Basal Ice as Related to Modeling Considerations

Simple shear tests on the bottom 17 m of basal ice from Camp Century, Greenland, were carried out in order to study the flow behavior near the bottom of an ice sheet and its implications for ice-sheet modeling. The ice core was recovered in 1966. Our experimental results show that the basal ice tested, (which contained alternating bands of dirty and clean ice) has the highest strain-rate ever reported for polycrystalline ice under simple shear. The enhancement factors obtained are interpreted in terms of fabric, ageing, and impurity. Horizontal velocity profiles are calculated using data reported previously for Camp Century and Dye 3 stations. Various depth-age relationships are compared with these data. The higher than expected shear strain-rates measured on samples of near-bottom ice from Camp Century may very well exist at other locations. If such high shear strain-rates are more prevalent than presently thought, they could have an important bearing on ages calculated by physical or mathematical models of ice sheets.