Small Strain Rates Research Articles

Strain Rate Dependency of Cohesive Soils in Consolidation Settlement

ABSTRACT It has been revealed from the long term consolidation test that the e-logp relation is linearly shifted with decrease in the strain rate in logarithm scale. The minimum strain rate measured by the conventional long term consolidation test is at most in the order of 10-9s-1. Question arises whether such a shift of the e-logp relation continues at even the infinite small strain rate, for example, smaller than 10-9s-1. To investigate the strain rate dependency of cohesive soil, the relaxation test was carried out for Osaka Pleistocene clays. It may be considered that in relaxation test, recoverable strain decreases due to decrease in acting pressure, and the irrecoverable strain equally increases, because the total strain remains constant. In this paper, assuming that the isotaches model can be applied to the irrecoverable strain, the strain rate dependency at very small strain rate was obtained from a series of relaxation tests. In this investigation the “strain rate dependency ratio” (SRDR) is defined as the ratio of the stress in the same e or e under the objective strain rate, based on the strain rate of 3.3×10-6s-1. It is revealed that the SRDR at infinite small strain rate is about 0.7.

Material Strengthening Mechanisms and Their Contribution to Size Effect in Micro-Cutting

The specific cutting energy in machining is known to increase nonlinearly with decrease in uncut chip thickness. It has been reported in the literature that this phenomenon is dependent on several factors such as material strengthening, ploughing due to finite edge radius, and material separation effects. This paper examines the material strengthening effect where the material strength increases nonlinearly as the uncut chip thickness is reduced to a few microns. This increase in strength has been attributed in the past to various factors such as strain rate, strain gradient, and temperature effects. Given that the increase in material strength can occur due to many factors, it is important to understand the contributions of each factor to the increase in specific cutting energy and the conditions under which they are dominant. This paper analyzes two material strengthening factors, (i) the contribution of the decrease in the secondary deformation zone cutting temperature and (ii) strain gradient strengthening, and their relative contributions to the increase in specific cutting energy as the uncut chip thickness is reduced. Finite element (FE)-based orthogonal cutting simulations are performed with Aluminum 5083-H116, a work material with a small strain rate hardening exponent, thus minimizing strain rate effects. Suitable cutting conditions are identified under which the temperature and strain gradient effects are dominant. Orthogonal cutting experiments are used to validate the model in terms of cutting forces. The simulation results are then analyzed to identify the contributions of the material strengthening factors to the size effect in specific cutting energy.

The influence of chemical mechanisms on PDF calculations of nonpremixed piloted jet flames

Seven different chemical mechanisms for methane are used in PDF model calculations of the Barlow and Frank flames D, E, and F in order to investigate the ability of these mechanisms to represent the local extinction, reignition, and other chemical phenomena observed in these nonpremixed piloted jet flames. The mechanisms studied range from a 5-step reduced mechanism to the GRI3.0 mechanism which involves 53 species. As in several other recent studies, we use the PDF method based on the joint probability density function of velocity, turbulence frequency, and composition. Extensive tests are performed to ensure the numerical accuracy of the calculations, to relate them to previous calculations based on the same model, and to reexamine the sensitivity of the calculations (especially of flame F) to uncertainties in the pilot temperature and the treatment of radiation. As has been observed in other studies of laminar and turbulent nonpremixed flames, we find that the GRI3.0 mechanism overpredicts the levels of NO, typically by a factor of 2. Apart from this, the GRI3.0 and GRI2.11 mechanisms yield comparably good agreement with the experimental data for all three flames, including the level of local extinction and the conditional means of major and other minor species. Two augmented reduce mechanism (ARM1 and ARM2) based on GRI2.11 and containing 16 and 19 species are slightly less accurate; while the 5-step reduced mechanism and two C 1 skeletal mechanisms containing 16 species display significant inaccuracies. An examination of the autoignition and laminar-flame behavior of the different mechanisms confirms (with some exceptions) expected trends: there is an association between long ignition delay times, small extinction strain rates, and high levels of local extinction. This study again demonstrates the ability of the joint PDF method to represent accurately the strong turbulence–chemistry interactions in these flames, and it clarifies the necessary level of description of the chemical kinetics.

Roller Extrusion of a Ceramic Paste

The roller extrusion of a stiff model ceramic paste has been studied experimentally using a fully instrumented roller apparatus that allows simultaneous measurement of roller separation, separating force, torque, and roll surface pressure. The paste exhibited no noticeable wall slip and little expansion, detaching from the rollers shortly downstream of the nip. Data collected over reduction ratios of 0.92−0.15 and speeds of 1.5−30 rpm (7.9−160 mm s-1) showed consistent trends when plotted against reduction ratio. A small strain rate dependence was observed, which was consistent with the rheological parameters obtained from the Benbow−Bridgwater characterization approach that models the material as a yield strength material. The data were also compared with the results from three models for rolling based on the plasticity approach: an upper bound model, a lower bound model, and a hot metal rolling model originally presented by Orowan. The experimental and predicted results showed good agreement for the latter model, and it was then extended to incorporate a simple strain rate dependency based on the Benbow−Bridgwater characterization approach. These results indicate that this characterization approach can be used to predict or gauge the rolling performance of such soft-solid materials.

Device with a self-aligned microgap for studying microscale flows

With the increasing interest in pressure-driven liquid flows in confined geometries, there emerges a need for the development of suitable devices for microrheological studies. The standard rheometry with macrogaps, however, has inherent disadvantages in adapting itself into a microscale version. On the other hand, compliance-based apparatuses are inappropriate for high-shear flows because of their extremely low load capacity and small allowable strain and strain rate. In this article, a self-aligned device that involves a pair of parallel disks with the bottom one fixed and the top one floated is presented. A concentrated load is applied at the center of the floating plate, for adjusting the gap size and centering the top plate. The applied load is balanced by the upward force inside the liquid film resulting from viscous flow. Due to the complete axisymmetry in terms of the geometry and the stress field, the top plate will be self-aligned in reference to the bottom plate. The self-alignment mechanism and the design principle of the device were verified using experiments with water as a testing liquid.

Heterogeneous crustal deformation along the central-northern Itoigawa-Shizuoka Tectonic Line Fault system, Central Japan

We investigated the crustal deformation around the northern Itoigawa-Shizuoka Tectonic Line Fault Zone by continuous observation with a dense GPS array. The observation revealed concentrated deformation around the East Matsumoto-Basin Fault while the more active Gofukuji Fault has smaller strain rate. By examining the physical meanings of geodetic strain rate and the geological slip rate data, we estimate a larger seismic potential around the Gofukuji Fault. The deep slip model proposed for the strain concentration around the Omachi area was not validated. Inelastic deformation may play an important role as a cause of strain concentration.

Roll waves in mud

The stability of a viscoplastic fluid film falling down an inclined plane is explored, with the aim of determining the critical Reynolds number for the onset of roll waves. The Herschel–Bulkley constitutive law is adopted and the fluid is assumed two-dimensional and incompressible. The linear stability problem is described for an equilibrium in the form of a uniform sheet flow, when perturbed by introducing an infinitesimal stress perturbation. This flow is stable for very high Reynolds numbers because the rigid plug riding atop the fluid layer cannot be deformed and the free surface remains flat. If the flow is perturbed by allowing arbitrarily small strain rates, on the other hand, the plug is immediately replaced by a weakly yielded ‘pseudo-plug’ that can deform and reshape the free surface. This situation is modelled by lubrication theory at zero Reynolds number, and it is shown how the fluid exhibits free-surface instabilities at order-one Reynolds numbers. Simpler models based on vertical averages of the fluid equations are evaluated, and one particular model is identified that correctly predicts the onset of instability. That model is used to describe nonlinear roll waves.

Elliptic instability in a Rankine vortex with axial flow

The elliptic instability of a Rankine vortex with axial flow subject to a weak strain field perpendicular to its axis is analyzed by asymptotic methods in the limit of small strain rate. General unstable modes associated with resonant Kelvin modes of arbitrary azimuthal wavenumbers are considered. Both the effects of axial flow and viscosity are analyzed in details.

Convergence vs. retreat in Southern Tyrrhenian Sea: Insights from kinematics

The Tyrrhenian Sea is an extensional basin opened by trench retreat and back‐arc extension during subduction of the Calabrian slab in the last 10–12 My. Subduction is still active beneath the SEmost part of the Tyrrhenian Sea, as testified by seismicity down to 500 km depth. By analyzing seismicity and geodetic data, together with recent tomographic images, we define the present‐day situation. An evident ∼N‐S compressional regime prevails in the Tyrrhenian region west of the Aeolian archipelago, while east of them a NNW‐SSE extension is documented by focal mechanisms and GPS data, with a much smaller strain rate with respect to the past. The transition between these two domains is accommodated by a N‐S discontinuity zone which runs from Aeolian Islands to Mt. Etna with an extensional to strike‐slip deformation.

Numerical modelling and experimental verification of blown film processing

A non-isothermal viscoelastic Kelvin model was developed to simulate the film blowing process. The predictions made by the Kelvin model for processing characteristics, such as bubble diameter, film thickness and strain rate profiles were compared to predictions from the non-isothermal Newtonian model and actual experimental film blowing data of polypropylene (PP). Reasonable agreement was found between the non-isothermal Newtonian model and experimentally observed bubble characteristics. However, by incorporating the elasticity of the polymer elasticity, using the Kelvin model, predictions were found to significantly improve. The reasonably good agreement between the theoretical predictions from the non-isothermal Kelvin model and actual experimental data may be due to the relatively small Hencky strains and strain rates used in the film blowing conditions in this work. Temperature was found to be the most critical parameter which influenced the film blowing characteristics of PP. A correct estimate of the relaxation time of the polymer is particularly important in giving a reasonably accurate fit with the experimentally observed processing behaviour of the polymer. Experimentally observed bubble stability measurements indicated that the stable operating window for PP increased up to a frost line height of 210 mm beyond which the stability decreased.

Influence of micro-inhomogeneity of plastic deformation in metals on their strength

A simplified model of metal behavior is developed accounting for inhomogeneous (on micro-level) plastic deformation and used for explanation of strength decrease at high stain rates, that follows from experiments on impact indentation. According to this model an increase of plastic strain rate leads to increased influence of micro-inhomogeneity of plastic flow on strength (decrease of strength). Such influence is insignificant at small plastic strain and low strain rate.

Effect of carbon content on plastic flow behaviour of plain carbon steels at elevated temperature

In the present study the effect of carbon composition on the hot flow behaviour of two different plain carbon steels is analysed. For this purpose the constitutive equations describing the stress–strain (σ–ϵ) relationships at a given strain rate ϵ and temperature T were determined for each steel. Uniaxial hot compression tests were performed to characterise the mechanical behaviour of the alloys. It was observed that irrespective of the test conditions, the low carbon steel displayed similar flow stresses to the high carbon steel. Comparison of the characteristic parameters of the constitutive equations describing the high temperature flow behaviour of these steels, together with values reported in the literature enabled determination of the effect of carbon content on flow behaviour. It has been found that flow stresses can be rationalised as a balance between work hardening and softening processes (basically dynamic recovery). At high temperatures and small strain rates, the high carbon steel showed lower hardening rates and slower dynamic recovery kinetics than the low carbon steel. In contrast, at low temperatures and large strain rates, the high carbon steel displayed higher hardening rates and recovery rates than the low carbon steel.

Rheometer for equibiaxial and planar elongations of polymer melts

In a new rheometer for polymer melts equibiaxial and planar elongations were performed at 150 °C with a low and a high density polyethylene (LDPE and HDPE, respectively), and equibiaxial elongations at 170 °C with a commercial polystsyrene (PS); for simple elongations a previously described rheometer was used. Each sample is clamped by metal belts that introduce the elongation and measure the forces that act upon each clamp. The samples are small and are supported by inert gas. By particle tracking and video recording the deformation history and the test performance are determined. The resulting elongational viscosities μi(t) (i=u, e, p for the different elongational modes) are newly defined such that at small strain rates they are equal to the linear viscoelastic shear viscosity, η°(t). The ratio μi/η° represents the nonlinear behavior: μi/η°>1 means strain hardening and μi/η°<1 strain softening. Hardening occurs in simple and in planar elongation in the flow direction, more for LDPE than for HDPE and is...

RETRACTED: Is the plastic flow uniformly distributed below the seismogenic region?

We compared the cutoff depth of seismicity in and around the Nojima fault broken by the 1995 Kobe earthquake occurring in intraplate Japan with the brittle–ductile transition depth of the widely accepted strength profile model of the crust. We successfully determined the temperature profile from borehole measurements, since almost the same geothermal gradients were observed at two boreholes located about 4 km apart from each other, and the thermal conductivity and heat production were also measured by taking numerous core samples. We found that the cutoff depth was much deeper than the transition depth under the assumption that wet granite is deformed at a strain rate of 3×10−15 s−1. This small strain rate implies, however, that plastic flow is uniformly distributed below the seismogenic region. When the strain rate is assumed to be greater than 10−13 s−1, the cutoff depth can be attributed to the transition depth. This suggests that deformation is localized in a narrow fault zone below the seismogenic region, even in the intraplate region.

The influence of temperature on the small-strain viscous deformation mechanics of snow: a comparison with polycrystalline ice

AbstractGlen’s law is commonly used to model the viscous deformation of polycrystalline ice. It is a power law that relates stress to viscous strain rate and contains three material parameters: n, a power-law exponent, Q, an activation energy, and A0, a material constant. Because polycrystalline ice is the constituent material of snow, it is to be expected that the viscous deformation mechanics of snow are related to the viscous behaviour of polycrystalline ice, especially under small strains and low strain rates when kinematic effects in the ice matrix like bond breakage, bond formation and grain sliding are of secondary importance. Based on 64 deformation-controlled compression tests on fine-grained snow in the density range 200–430kg m–3 and temperature range T = –20 to –2°C, we show that Glen’s law—with material parameters similar to those for polycrystalline ice—can be applied to model the viscous deformation of high-density snow However, the values of the ice material parameters are valid for densities above a relatively low density of 400 kg m–3; they are not valid for snow with densities below 360 kg m–3. We present the variation of n, Q and A for snow as a function of density and temperature. A possible explanation for this behaviour is that the ice grains in low-density snow are less constrained. Therefore, deformation mechanisms, such as grain-boundary sliding, increase in overall importance, leading to smaller n values and higher activation energies, Q. Although the material behaviour of low-density snow can be accurately modelled using a power law, the power-law parameters depart substantially from those of polycrystalline ice. The large variation of n and Q with temperature and density underscores the difficulty of predicting snow avalanches.

Is the plastic flow uniformly distributed below the seismogenic region?

The cut-off depth of seismicity in and around the Nojima fault broken by the 1995 Kobe earthquake occurring in the intraplate Japan was compared with a brittle-ductile transition depth of the widely-accepted strength profile model of the crust. It was found that the cut-off depth is much deeper than the transition depth under the assumption that wet granite is deformed at a strain rate of 10−15/s. Such a small strain rate implies that the plastic flow is uniformly distributed below the seismogenic region. When the strain rate is assumed to be greater than 10−13, the cut-off depth can be attributed to the transition depth. This suggests that deformation is localized in a narrow fault zone below the seismogenic region even in the intraplate region.

The structure of an unstable circular vortex in a background straining flow

The formation of compound vortices from a ‘shielded’ vortex monopole embedded in a two-dimensional background straining flow is studied numerically. The computations are performed in plane polar coordinates using an infinite radial domain Navier–Stokes solver. The straining flow excites an azimuthal instability, leading to vortex tripole formation in the case of small strain rates. For larger strain rates, tripole formation proceeds briefly before the structure is destroyed by the dominant background straining flow.

On stretch-affected pulsating instability in rich hydrogen/air flames: asymptotic analysis and computation

Effects of stretch on the pulsating instability of rich hydrogen/air premixed flames, which are characterized by large Lewis numbers, were analytically and computationally investigated via the negatively stretched inwardly propagating spherical flame (IPF) and the positively stretched counterflow flame (CFF). Analytical results yield explicit criteria for the onset of pulsation, and show that positive stretch promotes pulsation while negative stretch retards it. Computational results for the IPF show that the flame initially propagates at the laminar flame speed when the flame radius is large. Oscillation subsequently develops, and is then amplified, damped, and eventually suppressed when the flame is still sufficiently far away from the center. Thus negative stretch tends to suppress the occurrence of pulsating instability, and thereby extend the flammable range of rich hydrogen/air flames beyond that of their unstretched, planar counterpart. Furthermore, the pulsating propagation is quasi-steady in that it is independent of the initial state. Computational results for the CFF show that oscillation is initiated at an equivalence ratio much smaller than the one-dimensional rich threshold, and that the critical strain rate leading to pulsation is smaller than the corresponding static extinction limit. Furthermore, similar to the one-dimensional, unstretched cases, with progressive increase in the strain rate for a sufficiently rich mixture, the pulsation mode changes from that of monochromatic, to period doubling, and to permanent extinction. The pulsating flames are also quasi-steady in nature in that the period of oscillation is larger than the characteristic flame time. As such, the unsteady flame cannot recover once the instantaneous flame temperature is reduced below the corresponding steady-state extinction temperature. Because pulsating extinction occurs at a smaller strain rate than the steady extinction limit, the flame extinguishes in the pulsating instead of the steadily propagating mode, and the flammable range is accordingly narrowed. Finally, the numerically calculated critical states at which the IPF and the CFF respectively lose stability are predicted well by using the analytically derived transition criteria and global flame parameters.

Three-dimensional finite element analysis of single-lap adhesive joints under impact loads

This paper deals with the stress wave propagation and stress distribution in single-lap adhesive joints subjected to impact tensile loads with small strain rate. The stress wave propagations and stress distributions in single-lap joints have been analyzed using an elastic three-dimensional finite-element method (DYNA3D). An impact load was applied to the single-lap adhesive joint by dropping a weight. One end of one of the adherends in the single-lap adhesive joint was fixed and the other adherend to which a bar was connected was impacted by the weight. The effects of Young's modulus of the adherends, the overlap length, the adhesive thickness and the adherend thickness on the stress wave propagations and stress distributions at the interfaces have been examined. It was found that the maximum stress occurred near the edge of the interface and that it increased with an increase of Young's modulus of the adherends. It was also seen that the maximum stress increased as the overlap length, the adhesive thickness and the adherend thickness decreased. In addition, strain response of single-lap adhesive joints subjected to impact tensile loads was measured using strain gauges. Fairly good agreements were observed between the numerical and experimental results.

Three-dimensional finite element analysis of single-lap adhesive joints subjected to impact bending moments

This paper deals with the stress wave propagations and stress distributions in single-lap adhesive joints subjected to impact bending moments with small strain rate. The elastic stress wave propagation and the stress distribution in single-lap adhesive joints of similar adherends subjected to impact bending moments are analyzed using three-dimensional finite-element method (FEM). A three-point impact bending moment is applied to the joint by dropping a weight. FEM code employed is DYNA3D. The effects of Young's modulus of the adherends, the lap length, the adherend thickness and the adhesive thickness on the stress wave propagation at the interfaces are examined. It is found that the maximum value of the maximum principal stress, σ1, appears at the interface between the adhesive and the upper surface of upper adherend which is impacted. The maximum stress, σ1, increases as Young's modulus of adherends, the lap length and the adhered thickness increase. It is also found that the maximum stress, σ1 increases with decreasing adhesive thickness. In addition, experiments were carried out to measure the strain response of single-lap joints subjected to impact bending moments using strain gauges. A fairy good agreement was observed between the numerical and experimental results.