Shear modulus of cohesionless soil: variation with stress and strain level

1992 ◽  
Vol 29 (1) ◽  
pp. 157-161 ◽  
Author(s):  
Martin Fahey
Keyword(s):  
Shear Stress ◽  
Shear Modulus ◽  
Shear Strain ◽  
Stress Level ◽  
Strain Curve ◽  
Strain Level ◽  
Cohesionless Soil ◽  
Backbone Curve ◽  
Stress Strain ◽  
Shear Stress Level

The value of the secant shear modulus (G) of sand measured in cyclic tests reduces as the amplitude of cycling increases. As a first approximation, it is assumed that the curve joining the extreme points of stress–strain (τ–γ) loops of different amplitudes (a so-called "backbone curve") is hyperbolic. The shear strength (τmax) of sand is directly proportional to the mean effective confining pressure (p′), whereas the maximum shear modulus (G0) is proportional to (p′)n, with n being between 0.4 and 0.5. Based on these assumptions, it is shown that at the same shear strain level, different G/G0 values should be expected at different p′ values. One of the features of a hyperbolic τ–γ curve is that there is a unique linear relationship between G/G0 and normalized shear stress level (defined as τ/τmax), independent of p′. Therefore, considering the normalized shear stress level rather than the shear strain level may be a more logical and unifying way of examining the variation in G/G0. Key words : shear modulus, hyperbolic stress–strain curve, pressuremeter test.

Influence of Compression upon the Shear Properties of Bonded Rubber Blocks

1980 ◽  
Vol 53 (5) ◽  
pp. 1133-1144 ◽  
Author(s):  
L. S. Porter ◽  
E. A. Meinecke
Keyword(s):  
Shear Stress ◽  
Shear Modulus ◽  
Simple Shear ◽  
Compressive Force ◽  
Strain Curve ◽  
Shear Loading ◽  
Total Force ◽  
Strain Response ◽  
Stress Strain ◽  
Spring Rate

Abstract Rubber has a stress-strain response to compression-shear loadings that is the same as its stress-strain response to simple shear loadings. However, its load-deflection response to the compression-shear loading is not the same as its simple shear response. In determining the stress-strain relationship of the compression-shear loading from the load-deflection responses, three factors must be considered. First, the compression of the sample gives a lower rubber thickness. After calculating the strain, the lower thickness will give a higher strain than the original thickness at an equal deflection. Second, the compression gives a larger surface area due to bulging of the rubber. The higher area would result in a lower stress than the original area at an equal load. Third, the force that is necessary to compress the rubber block is stored in the rubber. When the rubber is sheared, the shear vector of the compressive force aides in deflecting the rubber. Therefore, the shear force vector would be added to the recorded load to determine the total force needed to shear the rubber. The resulting shear stress would be higher than the shear stress calculated by using the recorded load in calculating the shear stress. With all three factors accounted for, the shear stress-strain of the rubber is the same for the compressed part as it is for the uncompressed part. Therefore, the rubber's shear modulus, the slope of the shear stress-strain curve, has not been affected by the superimposed compression and remains an inherent property of the rubber. When designing a part to be used in a compression-shear application, one can use the shear and compression moduli normally obtained for shear and compression applications. The compression modulus would be used for determining the compressive spring rate and the amount of force used in lowering the shear spring rate. The shear modulus would be used to determine the shear rate by taking into account the geometry changes and the force due to compression.

scholarly journals A Monotonic Smeared Truss Model to Predict the Envelope Shear Stress—Shear Strain Curve for Reinforced Concrete Panel Elements under Cyclic Shear

2021 ◽  
Vol 2 (1) ◽  
pp. 174-194
Author(s):  
Luís Bernardo ◽  
Saffana Sadieh
Keyword(s):  
Shear Stress ◽  
Reinforced Concrete ◽  
Shear Strain ◽  
Peak Load ◽  
Strain Curve ◽  
Fiber Reinforced Polymers ◽  
Shear Stresses ◽  
Cyclic Shear ◽  
Concrete Panels ◽  
Truss Model

In previous studies, a smeared truss model based on a refinement of the rotating-angle softened truss model (RA-STM) was proposed to predict the full response of structural concrete panel elements under in-plane monotonic loading. This model, called the “efficient RA-STM procedure”, was validated against the experimental results of reinforced and prestressed concrete panels, steel fiber concrete panels, and reinforced concrete panels externally strengthened with fiber-reinforced polymers. The model incorporates equilibrium and compatibility equations, as well as appropriate smeared constitutive laws of the materials. Besides, it incorporates an efficient algorithm for the calculation procedure to compute the solution points without using the classical trial-and-error technique, providing high numerical efficiency and stability. In this study, the efficient RA-STM procedure is adapted and checked against some experimental data related to reinforced concrete (RC) panels tested under in-plane cyclic shear until failure and found in the literature. Being a monotonic model, the predictions from the model are compared with the experimental envelopes of the hysteretic shear stress–shear strain loops. It is shown that the predictions for the shape (at least until the peak load is reached) and for key shear stresses (namely, cracking, yielding, and maximum shear stresses) of the envelope shear stress–shear strain curves are in reasonably good agreement with the experimental ones. From the obtained results, the efficient RA-STM procedure can be considered as a reliable model to predict some important features of the response of RC panels under cyclic shear, at least for a precheck analysis or predesign.

scholarly journals Prediction Models of Shear Parameters and Dynamic Creep Instability for Asphalt Mixture under Different High Temperatures

Polymers ◽  
2021 ◽  
Vol 13 (15) ◽  
pp. 2542
Author(s):  
Junxiu Lv ◽  
Xiaoyuan Zhang
Keyword(s):  
Shear Stress ◽  
Shear Strength ◽  
Stress Level ◽  
Prediction Models ◽  
Asphalt Mixture ◽  
Confining Pressure ◽  
Shear Strength Parameters ◽  
Dynamic Creep ◽  
Shear Stress Level ◽  
Creep Instability

This study mainly investigates the prediction models of shear parameters and dynamic creep instability for asphalt mixture under different high temperatures to reveal the instability mechanism of the rutting for asphalt pavement. Cohesive force c and internal friction angle φ in the shear strength parameters for asphalt mixture were obtained by the triaxial compressive strength test. Then, through analyzing the influence of different temperatures on parameters c and φ, the prediction models of shear strength parameters related to temperature were developed. Meanwhile, the corresponding forecast model related to confining pressure and shear strength parameters was obtained by simplifying the calculation method of shear stress level on the failure surface under cyclic loading. Thus, the relationship of shear stress level with temperature was established. Furthermore, the cyclic time FN of dynamic creep instability at 60 °C was obtained by the triaxial dynamic creep test, and the effects of confining pressure and shear stress level were considered. Results showed that FN decreases exponentially with the increase in stress levels under the same confining pressure and increases with the increase in confining pressure. The ratio between shear stress level and corresponding shear strength under the same confining pressure was introduced; thus, the relationship curve of FN with shear stress level can eliminate the effect of different confining pressures. The instability prediction model of FN for asphalt mixture was established using exponential model fitting analysis, and the rationality of the model was verified. Finally, the change rule of the parameters in the instability prediction model was investigated by further changing the temperature, and the instability forecast model in the range of high temperature for the same gradation mixture was established by the interpolation calculation.

Stress-Strain Curves for Oxygen-Free High Conductivity Copper at Shear Strain Rates of up to 103s-1

1970 ◽  
Vol 185 (1) ◽  
pp. 1149-1158 ◽  
Author(s):  
K. Bitans ◽  
P. W. Whitton
Keyword(s):  
Shear Strain ◽  
Testing Machine ◽  
Shear Bands ◽  
Strain Curve ◽  
Strain Rates ◽  
Adiabatic Shear Bands ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
The Given ◽  
Tubular Specimens

Shear stress-shear strain curves for o.f.h.c. copper at room temperature have been obtained at constant shear strain rates in the range 1 to 103s-1, using thin walled tubular specimens in a flywheel type torsion testing machine. Results show that, for a given value of strain, the stress decreases when the rate of strain is increased. Moreover, the elastic portion of the stress-strain curve tends to disappear as the rate of strain is increased. It is postulated that these effects are due to the formation of adiabatic shear bands in the material when the given rate of strain is impressed rapidly enough. A special feature of the design of the testing machine used is the rapid application of the chosen strain rate.

scholarly journals Characterization of the Dynamic Properties of Clay–Gravel Mixtures at Low Strain Level

2020 ◽  
Vol 12 (4) ◽  
pp. 1616 ◽  
Author(s):  
Xianwen Huang ◽  
Aizhao Zhou ◽  
Wei Wang ◽  
Pengming Jiang
Keyword(s):  
Shear Modulus ◽  
Shear Strain ◽  
Mechanical Performance ◽  
Dynamic Properties ◽  
Damping Ratio ◽  
Confining Pressure ◽  
Strain Level ◽  
Dynamic Shear Modulus ◽  
Dynamic Shear ◽  
Gravel Content

In order to support the dynamic design of subgrade filling engineering, an experiment on the dynamic shear modulus (G) and damping ratio (D) of clay–gravel mixtures (CGMs) was carried out. Forty-two groups of resonant column tests were conducted to explore the effects of gravel content (0%, 10%, 20%, 30%, 40%, 50%, and 60%, which was the mass ratio of gravel to clay), gravel shape (round and angular gravels), and confining pressure (100, 200, and 300 kPa) on the dynamic shear modulus, and damping ratio of CGMs under the same compacting power. The test results showed that, with the increase of gravel content, the maximum dynamic shear modulus of CGMs increases, the referent shear strain increases linearly, and the minimum and maximum damping ratios decrease gradually. In CGMs with round gravels, the maximum dynamic shear modulus and the maximum damping ratio are greater, and the referent shear strain and the minimum damping ratio are smaller, compared to those with angular gravels. With the increase of confining pressure, the maximum dynamic shear modulus and the referent shear strain increase nonlinearly, while the minimum and maximum damping ratios decrease nonlinearly. The predicting equation for the dynamic shear modulus and the damping ratio of CGMs when considering confining pressure, gravel content, and shape was established. The results of this research may put forward a solid foundation for engineering design considering low-strain-level mechanical performance.

About Relation Between Irradiation Hardening of Ferritic Steels and Ductile Fracture Toughness Decrease

2009 ◽  
Author(s):  
Jiri Novak
Keyword(s):  
Fracture Toughness ◽  
Temperature Dependence ◽  
Ductile Fracture ◽  
Stress Level ◽  
Deformation Theory ◽  
Strain Curve ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Irradiation Hardening ◽  
Ductile Fracture Toughness

We showed recently that temperature dependence of the ductile fracture toughness can be predicted on the base of two assumptions: 1) assumption of constant characteristic length, 2) assumption of proportionality between J-R curve slope and deformation work in unit volume, evaluated from zero to critical strain for initiation of deformation bands determined in plane strain geometry for material modeled by deformation theory of plasticity. Temperature dependence of ductile fracture toughness results simply from temperature dependence of the stress-strain curve. Irradiation hardening changes stress-strain behavior in a qualitatively different way: It is observed that irradiation hardening to certain yield stress level changes the stress-strain curve of the material in the same way as prestraining of the unirradiated material to the same flow stress level does. Equivalence of irradiation and prestraining concerns all key properties of deformation theory; namely the secant modulus should be taken from the stress-strain curve of unirradiated material. With exception of this specific feature, the task of finding relative fracture toughness decrease by irradiation is the same as prediction of relative decrease of fracture toughness by temperature change. In the frame of the corresponding theory, relative decrease of ductile fracture toughness expressed by J-R curve slope can be obtained from the stress-strain curve of unirradiated material and irradiation hardening level. Quantitative results are presented for the weld metals 72W and 73W, studied in the Fifth Irradiation Series in the Heavy-Section Steel Irradiation Program, and compared with experimental data.

Nonuniform Temperature Distribution in Adiabatic Shear Band Using Measured Shear Stress-Shear Strain Curve in Torsion of Thin-Walled Tube Aluminium Alloy Specimen and Gradient-Dependent Plasticity

2006 ◽  
Vol 519-521 ◽  
pp. 865-870 ◽  
Author(s):  
X.B. Wang
Keyword(s):  
Shear Stress ◽  
Strain Rate ◽  
Shear Strain ◽  
Temperature Rise ◽  
Strain Curve ◽  
Local Temperature ◽  
Dependent Plasticity ◽  
Peak Shear Stress ◽  
Nonlinear Shear ◽  
Shear Strain Curve

Gradient-dependent plasticity where a characteristic length is involved to consider the microstructural effect (interactions and interplaying among microstructures due to the heterogeneous texture) and the measured nonlinear shear stress-shear strain curves for different loading strain rates are used to calculate the distribution of local temperature rise in adiabatic shear band (ASB) for aluminum-lithium alloy specimen of thin-walled tube in dynamic torsion test. ASB is assumed to initiate just at peak shear stress in the specimen. The temperature rise in ASB is decomposed into the uniform temperature rise in strain-hardening stage and the nonuniform temperature rise in strain-softening stage. The former depends on the measured nonlinear shear stress-shear strain curve prior to the peak, the density, the work to heat conversion factor and the heat capacity. The latter is related to the softening branch of the measured nonlinear shear stress-shear strain curve, the internal length parameter and the physical parameters. For binary Al-Li alloy, the predicted maximum temperatures in ASB are 413K at strain rate of 2000s-1 and 433K at strain rate of 2600s-1. These peak temperatures are lower than the recrystallization and phase transformation temperatures. Higher loading strain rate results in higher pre-peak and post-peak temperature rises, steeper profile of local temperature and higher peak local temperature in ASB. These predictions qualitatively agree with the previously analytical solution for ductile metal exhibiting linear strain-softening behavior beyond the peak shear stress based on gradient-dependent plasticity.

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