Small-strain Shear Research Articles

Effect of The Shape of Cyclic Loading on Damping Ratio at Small Strains

A series of 69 cyclic tests was conducted to study the damping properties of two reconstituted sands and three laboratory-made clays at small cyclic shear strain amplitudes γ c ~ 0.001-0.04%. A recently developed constant-volume equivalent-undrained direct simple shear device for small-strain testing was employed. The specific effect of the shape of cyclic strain-time history on the equivalent viscous damping ratio, λ, was investigated. The results show that λ can be significantly affected by the shape of the cyclic strain-time history because of the viscous nature of soil material response and the associated effects of creep and relaxation. As the shape of the cyclic strain-time history is changed from triangular to sinusoidal, and further from trapezoidal to square, λ at small strains may increase by a factor of two or more. The test results show that this effect was largest for clays, smaller for silty sand and negligible for clean sand.

Three-dimensional residual strain in midanterior canine left ventricle

All previous studies of residual strain in the ventricular wall have been based on one- or two-dimensional measurements. Transmural distributions of three-dimensional (3-D) residual strains were measured by biplane radiography of columns of lead beads implanted in the midanterior free wall of the canine left ventricle (LV). 3-D bead coordinates were reconstructed with the isolated arrested LV in the zero-pressure state and again after local residual stress had been relieved by excising a transmural block of tissue. Nonhomogeneous 3-D residual strains were computed by finite element analysis. Mean +/- SD (n = 8) circumferential residual strain indicated that the intact unloaded myocardium was prestretched at the epicardium (0.07 +/- 0.06) and compressed in the subendocardium (-0.04 +/- 0.05). Small but significant longitudinal shortening and torsional shear residual strains were also measured. Residual fiber strain was tensile at the epicardium (0.05 +/- 0.06) and compressive in the subendocardium (-0.01 +/- 0.04), with residual extension and shortening, respectively, along structural axes parallel and perpendicular to the laminar myocardial sheets. Relatively small residual shear strains with respect to the myofiber sheets suggest that prestretching in the plane of the myocardial laminae may be a primary mechanism of residual stress in the LV.

Damping Force Characteristics of High-Damping Rubber Damper in Small Shear Strain Regions.

In this study we discuss the applicability of a high-damping rubber damper, which is composed of micro-networks and viscous material, as the damping device in microvibration-isolation devices or tables. For those purposes, damping force characteristcs of the high-damping rubber damper were measured using a new measuring device. We could estimate damping force characteristics to a shear displacement amplitude of 2.5×10-6m, and this high-damping rubber damper was found to have energy-absorption capacity in the regions of very small shear displacement amplitude. Also, the damping force characteristics of a viscous shear damper using silicone oil, which is the most popular damper for vibration-isolation devices, were measured. On comparing the damping force characteristics, our high damping rubber damper was found to have a larger energy absorption ability than the viscous shear damper. Furthermore, the rubber dampers were installed to the vibration isolation table which can mainly isolate microvibrations in horizontal direction. Through microvibrationisolation tests it was confirmed that this high damping rubber could be applied to microvibrationisolation devices.

Molecular theory of the yield behavior of a polymer gel: Application to gelatin

A microscopic model for the endpoint separation dependent scission rate of a polymer connection in a network is developed. The predicted dissociation rate is proportional to the exponential of the bond force, which is in line with experiments. This atomistic description is thereupon incorporated in a mesoscopic theory to describe strain hardening and failure of physical gels. The resulting theory has been analyzed by a new numerical algorithm, which is some 100 to 1000 times faster than the algorithm described in the literature. We applied this theory to gelatin. To arrive at the correct nonlinear rheologic behavior of the gel, the non-Gaussian nature of the polymer endpoint distribution has to be taken into account. There are four important physical quantities that describe the nonlinear rheology of gelatin. For relatively small shear strain (0<γ<1), stress increases nonlinearly with strain when a gel is deformed (strain hardening). The strain at which the gel ruptures (the yield strain γy) increases quite slowly with shear rate: γy∝γ̇0.05. When experiments are carried out at different shear rate, we find a linear correlation between yield stress and yield strain. Finally it is observed that the yield strain decreases with increasing strain hardening. These four observations are all covered by the theory up to quantitative accuracy. The interpretation that comes forward from this work is that the nonlinearity of the stress–strain curve for γ<1 is correlated to the strain at which the gel yields. The reason for this correlation is that both effects are dominated by a non-Hookean force–distance relationship of the polymer connections. On the one hand side, this function directly causes the upturn of the stress–strain curve. On the other hand, the rate by which polymer connections break is proportional to the exponential of this force. Therefore a nonlinear force–distance relationship leads both to a nonlinear stress–strain relation and to an early and sudden yield behavior.

Primary creep and anelastic behaviour of aluminium at low strains and temperatures below 0·45 Tm

AbstractUsing highly sensitive equipmentfor the measurement of small shear strains up to 1·5 × 10−4 and their variation with time, the form of the primary creep curves for aluminium at low stresses has been determined. The extent and rate of recovery of these strains has also been measured to establish the pattern of anelastic behaviour, and best fit equations are presented. A unique activation enthalpy could not be identified for anelastic recovery, but a value for the activation enthalpy comparable with grain boundary or dislocation pipe diffusion was derived from primary creep when the strain exceeded 10−5. The ratio of the anelastic recovery strain to the forward creep strain decreased logarithmically with time over most of its range, but reached a limiting value that was dependent on the forward creep strain.MST/3265

Nonlinear viscoelastic response of carbon black reinforced rubber derived from moderately large deformations in torsion

The response of Butyl rubber loaded with carbon black is investigated experimentally, by subjecting it to a finite twist. The experimental set-up and the measurement procedure are described. The material shows a highly nonlinear behaviour for relatively small shear strains. Constitutive relations corresponding to the data are derived from a theory based on a nonlinear tensorial generalization of a three-parameter model. The sample stiffness and normal force for a cylindrical sample subjected to simple torsion are derived for the quasistatic case. To explain the marked drop in stiffness of the material beyond the linear range, a damage and rehealing model is introduced. It consists basically of an evolution equation for the model parameters. With the theory proposed here the measured response for torque and normal force corresponding to a given deformation history can be confirmed satisfactorily.

Stress‐History‐Based Model for Ge of Cohesionless soils

An empirical, stress‐history‐based model for the small strain (or elastic) shear modulus Ge of cohesionless soils has been developed. Various sands were tested in an 18 cm diameter oedometer equipped with lateral‐stress measuring capabilities and bender elements for propagating and recording elastic waves through the specimens. While previous efforts have found Ge scaling with approximately the 1/2 power of confining stress (n=0.5), the present work shows n on virgin loading n1 ranging from 0.39 to 0.72. Furthermore, n1 was shown to be related to the maximum dimensionless stiffness coefficient for 1‐D strain (S1Dmax). The values of n on unloading and reloading nu displayed a much narrower range than nl. The average value of nu was 0.38, a value much closer to the theoretical n=1/3 for perfect spheres. This is attributed to the smaller changes in number and quality of intergranular contacts during unloading and reloading than during virgin compression. The developed model for Ge includes overconsolidation ...

Settlement of Compacted Clay in a Cyclic Direct Simple Shear Device

Abstract The results of 36 cyclic strain-controlled direct simple shear tests on a low-plasticity compacted clay are presented and analyzed. The tests were conducted in a Marshall Silver-type device, which utilizes the Norwegian Geotechnical Institute (NGI) type of short cylinder specimen confined in a wire-reinforced rubber membrane. Three degrees of compaction achieved by the modified compaction test are encompassed: (1) below the optimum moisture content, (2) at the optimum, and (3) above the optimum. All specimens were sheared under the same vertical consolidation stress. In each test the cyclic shear strain amplitude, γc, was controlled, i.e., the cyclic tests were strain controlled. The range of γc was between 0.008 and 4.6%. The test results show a very consistent behavior of the clay at all three moisture contents. At small cyclic shear strains below γc ≅ 0.1%, the stress-strain behavior is slightly nonlinear, i.e., close to linearly elastic, and the vertical settlement is negligible. In some tests such nondestructive behavior was recorded up to γc ≅ 0.2%, showing that for the clay tested, the volumetric threshold shear strain, γtv, ranges between 0.1 and 0.2%. At γc larger than γtv the cyclic stress-strain behavior becomes nonlinear and a continuous settlement with the number of cycles, N, occurs. The results do not show a clear relation between the rate of settlement with N and the degree of the compaction and moisture content. For different moisture contents, similar settlements were obtained for given γc and N. The study also shows how to arrange the specimen setup and measuring system to eliminate the effect of the simple shear apparatus compliance. In such an arrangement very small shear strains can be applied and successfully measured.

Geotechnical Parameters Used for Design of Coastal Structures on Cohesive Seabed

For the prediction of the stability or settlement of the sea floor or any structure founded on it we should determine the kind of parameters to solve each problem. If we restrict our considerations to cohesive sediments, then the soil constants used for the design of coastal structures on them are classified into the two categories during and after cyclic loading, each depending on the magnitude of cyclically induced excess pore pressures and shear strains. Each cateogry is also sub-divided into the ranges of small and large shear strains, respectively. In this paper, comments are made on both the degradation of deformation modulus during cyclic loading which is regarded as in the category of small strains and the changes in deformation and strength after cyclic loading, as pertaining to the category of large strain for cohesive soils.

A Method for Evaluating Membrane Compliance and System Compliance in Undrained Cyclic Shear Tests

ABSTRACT A method for evaluating system compliance and membrane compliance is proposed. Only changes in pore pressure and axial stress due to undrained cyclic loading at small shear strain amplitude are necessary to evaluate the value of system compliance ratio C r . Pore pressure coefficient JB-value is also necessary to calculate the value of membrane compliance ratio CRM. These parameters can be obtained by nondestructive tests before destructive tests with large strain amplitude on soil specimens. The proposed method is applied to both reconstituted and undisturbed specimens. The test results imply that: (1) For reconstituted specimens, the values of normalized membrane penetration S calculated by CRM indicate satisfactory consistency with other investigators’ results. Therefore the values of CRM can be successfully estimated by the proposed method. (2) A treatment for minimizing the unevenness of lateral surface of undisturbed specimens, has an effect of reducing the value of CRM. (3) For undisturbed samples tested in this study, the values of C r calculated by the method gave a consistent explanation of differences in pore pressure response characteristics of the specimens from the view of influence of the lateral surface treatment.

Stiffness and Penetration Resistance of Sands versus State Parameter

Normalized small strain Young and shear moduli of pluvially deposited predominantly silica Ticino sand are well correlated against the state parameter as defined by Been and Jefferies. The same holds true for normalized cone resistance measured during the calibration chamber tests performed on the same test sand. It is shown that also parameters obtained from other kinds of penetration tests are correlatable against the state parameter of a sand. These findings might indicate a way to rationalize the correlations between penetration resistances and stiffness of sands being the latter referred to the preyield behavior of a sand.

Control of intergranular fatigue cracking by slip homogeneity in copper: II. Effect of loading mode: Liang, F.-L. and Laird, C. Mater. Sci. Eng. A Sept. 1989 A117, (1–2), 103–113

The effect of local strain state on twinning behavior during compression of AZ31 magnesium alloy was investigated, making use of a micro-grid method to correlate the local strain tensor with observations of twinning using electron backscatter diffraction (EBSD) measurements. Eight prism samples were used to get deformation zones subjected to different strain states. The strain distribution across the whole sample surface was measured with the micro-grid method and the results show that the local strain states exhibit much variation, with zones subjected to large shear strain as well as zones subjected to little shear strain. Samples were compressed at room temperature and detailed EBSD measurements were taken in two zones, where one zone was subject to only small shear strains and the other was subject to large shear strains. Twin variant selection was then analyzed with respect to both stress-based (Schmid factor) and strain-based criteria. The former was found to provide the best explanation for the observed pattern of twinning.

Micromechanical model to predict sand Densification by Cyclic Straining

It has been observed that the application of cyclic shear loading to a dry sand and other cohesionless soils results in a progressive volume reduction and a relative density increase. Although this densification is larger and takes place faster in loose sands, it occurs in both loose and dense soils, and is caused by the tendency of any sand to contract under a small shear strain. A micromechanical statistical model was developed by the writers to interpret and compute the compaction of such a dry granular soil subjected to a strain‐controlled cyclic simple‐shear test. The method postulates that an important role is played in the compaction phenomenon by the spatial statistical distribution of porosity within the soil specimen. Numerical simulations of densification are presented using the proposed model, which are in excellent agreement with observed sand compaction in actual cyclic simple‐shear tests. These simulations provide new insight into the densification process, and especially on the significanc...

Residual Stresses in Unidirectional Al2O3 Fiber/Silicate Glass Composites by X-ray Diffraction

AbstractUnidirectional continuous fiber composites fabricated from 20 μm diameter α-AI2O3 fibers (duPont FP) and 5 different silicate glass matrices (Corning 9013 and 7740, Owns Illinois N51A and Schott 8229 and 8228) were examined for residual strain and stress in the fibers using x-ray diffraction and the results compared with the predictions of two simple residual stress models. The glasses were chosen to have thermal expansion coefficients ranging from 1.3 to 10.2 x 10-6 /°C, compared with 7.2 x 10-6 /°C for the fiber, so as to produce a range of residual stresses. The magnitudes of the measured normal strains and stresses increased with increasing fiber/matrix thermal expansion mismatch in the order expected except for the sample containing Corning glass 7740 which showed extensive microcracking. Small shear strains were also detected in most of the samples due to the fibers not lying precisely along the presumed uniaxial direction. Agreement with the models was qualitative only but revealed that the residual stresses in the samples containing Corning 7740 and Schott 8229 glasses were substantially less than expected, possibly due to microcracking and/or fiber degradation.

Studies on the steady-shear behavior of electrorheological suspensions

The structures of nonaqueous suspensions subjected to electrical fields and continuous shear are described. Based on observations that particle strands and columns formed upon application of an electric field behave as elastic solids for small shear strains but yield above a critical strain, models for the yield stress and continuous-shear response of these electrorheological (ER) suspensions are developed. Comparison of model calculations with experimental results indicates that the yield stress is dominated by the work required to overcome electrically induced interparticle forces.

Structural changes in polyethyleneterephthalate films on rolling

The effect of small compressions and shear strains during rolling on the properties and structural changes in PETP films is studied. The modifying rolling effect is shown to produce a change in the character of the subsequent deformation of films below T g. In particular, below 50°C the rolled films are strained without necking and crazing.

Induced and inherent anisotropy in sand

Data from an extensive series of drained tests on dense sand in a directional shear cell have been used to explore the interaction of inherent and induced anisotropy. The essential link between previous strain and induced anisotropy has been demonstrated. This link is shown to hold regardless of any inherent anisotropy or previous cyclic rotation of principal stress directions. In dense sand a small permanent shear strain of the order of 0·5% leads to significant induced anisotropy. Induced anisotropy is shown as causing very large directional variations in stiffness of sand and associated capability for porewater pressure generation. The underlying causes of inherent and induced anisotropy are discussed and related to the widely recognized persistence of inherent anisotropy which frequently controls peak shear resistance. Possible methods for predicting the effects of anisotropy are briefly discussed. Des données obtenues à partir d'une série grande d'essais drainés effectués sur du sable dense dans une cellule de cisaillement directionnel ont été employées pour étudier l'interaction entre l'anisotropie inhérente et induite. On a démontré que le lien essentiel prouvé entre la déformation précédente et l'anisotropie induite reste valable indépendamment de l'anisotropie inhérente ou de la rotation cyclique précédente des directions principales de contrainte. Dans du sable dense une petite déformation de cisaillement permanente de l'ordre de 0, 5% produit une anisotropie induite importante. On indique comment l'anisotropie induite provoque de très grandes variations différentielles dans la rigidité du sable et la capacité associée pour générer la pression de l'eau interstitielle. Les raisons profondes de l'anisotropie inhérente et induite sont discutées et reliées à la persistance connue de l'anisotropie inhérente qui régit fréquemment la résistance maximale au cisaillement. L'article discute brièvement des methods possibles pour prévoir les effets de l'anisotropie.

Measurement of complex shear modulus of marine carbonate sand and coral rock by very small amplitude torsional resonant column apparatus

The complex shear modulus of marine carbonate sand and coral rock has been mechanically measured for shear strain amplitudes as low as 10−8. A high precision torsional resonant column apparatus, equipped with the latest electronic instrumentation, was used to determine both the shear modulus and attenuation at various shear strain amplitudes and several stress conditions of prepared marine carbonate sand and coral rock specimens. The influence of test parameters such as confining effective stress and stress anisotropy was studied to simulate actual field states of stress. Vibrational wave amplitude was also varied in order to determine its effect on the dynamic properties of these commonly occurring marine sediments and to compare them with values found in the literature. The frequency range covered was from 50–500 Hz. The geoaeoustic data obtained at small shear strain amplitude are of special significance in acoustic wave propagation in the ocean with strong bottom interaction. [Work supported by ONR, Code 425UA.]

The Poynting-Swift effect in relation to initial and post-yield deformation

The material behaviour predicted by the constitutive equation of a general elastic material is considered in relation to the combined extension and torsion of a thin-walled tube and a solid rod. This state of combined stressing is considered in relation to material behaviour at small strains, and at finite strains in the context of initial yield and the Poynting-Swift effect. A composite yield condition has been postulated on general grounds which, over a given range of application, is identical to the von Mises yield criterion, or some modified form of it, and over the remaining range of application takes the form of a 12-sided, linear, piece-wise continuous yield condition. The theory is applied to the classical combined-stress experiments of Taylor and Quinney[3], using a total deformation-type constitutive equation. It is shown that the proposed yield condition when combined with the new constitutive equation, is in full agreement with the useable experimental data obtainable from these particular combined-stress measurements. The available studies of the Poynting-Swift effect are shown to be in general accord with the proposed yield function and total deformation type constitutive equation. In particular, for sufficiently small shear strains it has been shown that simple torsion of both a thin-walled tube and a solid rod is characterised by an axial elongation which is proportional to the square of the twist. It is also shown that the available experimental results are in quantitative agreement with the predictions of the proposed constitutive equation.

A Unified Approach To The Modelling of Liquefaction And Cyclic Mobility Of Sands

In this paper the problem of liquefaction of sand under either monotonic or cyclic loading is tackled from the point of view of continuum mechanics. It is shown that a suitable constitutive model may explain, in a phenomenological sense, the generation of pore pressure in an undrained test either when the load is monotonically increased to failure or when sand is cyclically sheared at constant stress or strain amplitudes. It is demonstrated that in the former case liquefaction of loose samples amy be described if a convenient set of constitutive parameters is chosen. It is also shown that liquefaction under cyclic loading may occur even for very dense sands, and that the essential features revealed by experiments, such as progressive pore pressure build-up accompanied by small shear strains followed by a sudden pore pressure increase with large strains, are correctly modelled by the theory. The constitutive model employed is a combination of a classical elastoplastic constitutive law, which proved to be successful in modelling the behaviour of sand under monotonic loading, and of a law allowing for hysteresis, which applies to loading processes within the yield locus, especially conceived to interpret the behaviour of soils under cyclic loading. (Author/TRRL)