Small-strain behavior of frozen sand in triaxial compression

1995 ◽  
Vol 32 (3) ◽  
pp. 428-451 ◽  
Author(s):  
Glen R. Andersen ◽  
Christopher W. Swan ◽  
Charles C. Ladd ◽  
John T. Germaine
Keyword(s):  
High Pressure ◽  
Strain Rate ◽  
Yield Stress ◽  
Axial Strain ◽  
Triaxial Compression ◽  
Strain Curve ◽  
Confining Pressure ◽  
Stress Strain ◽  
Strain Behavior ◽  
Frozen Sand

The stress–strain behavior of frozen Manchester fine sand has been measured in a high-pressure low-temperature triaxial compression testing system developed for this purpose. This system incorporates DC servomotor technology, lubricated end platens, and on-specimen axial strain devices. A parametric study has investigated the effects of changes in strain rate, confining pressure, sand density, and temperature on behavior for very small strains (0.001%) to very large (> 20%) axial strains. This paper presents constitutive behavior for strain levels up to 1%. On-specimen axial strain measurements enabled the identification of a distinct upper yield stress (knee on the stress–strain curve) and a study of the behavior in this region with a degree of precision not previously reported in the literature. The Young's modulus is independent of strain rate and temperature, increases slightly with sand density in a manner consistent with Counto's model for composite materials, and decreases slightly with confining pressure. In contrast, the upper yield stress is independent of sand density, slightly dependent on confining pressure (considered a second order effect), but is strongly dependent on strain rate and temperature in a fashion similar to that for polycrystalline ice. Key words : frozen sand, high-pressure triaxial compression, strain rate, temperature, modulus, yield stress.

Understanding Dynamic Recrystallization Behavior through a Delay Differential Equation Approach

2007 ◽  
Vol 558-559 ◽  
pp. 441-448 ◽  
Author(s):  
Jong K. Lee
Keyword(s):  
Differential Equation ◽  
Strain Rate ◽  
Critical Strain ◽  
Strain Curve ◽  
Single Peak ◽  
Strain Rates ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Strain Behavior ◽  
Delay Differential

During hot working, deformation of metals such as copper or austenitic steels involves features of both diffusional flow and dislocation motion. As such, the true stress-true strain relationship depends on the strain rate. At low strain rates (or high temperatures), the stress-strain curve displays an oscillatory behavior with multiple peaks. As the strain rate increases (or as the temperature is reduced), the number of peaks on the stress-strain curve decreases, and at high strain rates, the stress rises to a single peak before settling at a steady-state value. It is understood that dynamic recovery is responsible for the stress-strain behavior with zero or a single peak, whereas dynamic recrystallization causes the oscillatory nature. In the past, most predictive models are based on either modified Johnson-Mehl-Avrami kinetic equations or probabilistic approaches. In this work, a delay differential equation is utilized for modeling such a stress-strain behavior. The approach takes into account for a delay time due to diffusion, which is expressed as the critical strain for nucleation for recrystallization. The solution shows that the oscillatory nature depends on the ratio of the critical strain for nucleation to the critical strain for completion for recrystallization. As the strain ratio increases, the stress-strain curve changes from a monotonic rise to a single peak, then to a multiple peak behavior. The model also predicts transient flow curves resulting from strain rate changes.

scholarly journals Investigation of the Mechanical Properties of St. Lawrence River Ice

1971 ◽  
Vol 8 (2) ◽  
pp. 163-169 ◽  
Author(s):  
L. W. Gold ◽  
A. S. Krausz
Keyword(s):  
Mechanical Properties ◽  
Strain Rate ◽  
Yield Stress ◽  
Power Law ◽  
River Ice ◽  
Stress Strain ◽  
Strain Behavior ◽  
Brittle Transition ◽  
Ductile To Brittle Transition ◽  
St Lawrence River

Observations are reported on the stress–strain behavior at −9.5 ± 0.5 °C of four types of ice obtained from the St. Lawrence River. The ice was subject to nominal rates of strain covering the range 2.1 × 10−5 min−1 to 5.8 × 10−2 min−1. A ductile-to-brittle transition was observed for strain rate of about 10−2 min−1. In the ductile range the four types had an upper yield stress that increased with strain rate according to a power law.

scholarly journals Experimental Study on the Permeability of Weakly Cemented Rock under Different Stress States in Triaxial Compression Tests

Geofluids ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Gangwei Fan ◽  
Mingwei Chen ◽  
Dongsheng Zhang ◽  
Zhen Wang ◽  
Shizhong Zhang ◽  
...  
Keyword(s):  
Underground Mining ◽  
Axial Strain ◽  
Triaxial Compression ◽  
Confining Pressure ◽  
Initial Permeability ◽  
Compression Tests ◽  
Mining Operations ◽  
Stress Strain ◽  
Loading And Unloading ◽  
Stress States

Mudstone and shaly coarse sandstone samples of Jurassic units in northwestern China were collected to study the seepage mechanism of weakly cemented rock affected by underground mining operations. Samples were studied using seepage experiments under triaxial compression considering two processes: complete stress-strain and postpeak loading and unloading. The results show that permeability variations closely correspond to deviatoric stress-axial strain during the process of complete stress-strain. The initial permeability is 7 times its minimum, contrasting with lesser differentials of initial, peak, and residual permeability. The magnitude of permeability ranges from 10−17 to 10−19 m2, representing a stable water-resisting property, and is 1 to 2 orders lower in mudstone than that in shaly coarse sandstone, indicating that the water-resisting property of the mudstone is much better than that of the shaly coarse sandstone. Permeability is negatively correlated with the confining pressure. In response to this pressure, the permeability change in mudstone is faster than that in shaly coarse sandstone during the process of postpeak loading and unloading. Weakly cemented rock has lower permeability according to the comparison with congeneric ordinary rocks. This distinction is more remarkable in terms of the initial permeability. Analyses based on scanning electron microscope (SEM) observations and mineral composition indicate that the samples are rich in clay minerals such as montmorillonite and kaolin, whose inherent properties of hydroexpansiveness and hydrosliming can be considered the dominant factors contributing to the seepage properties of weakly cemented rock with low permeability.

Strain-Rate Effects on Constitutive Behavior of Sn3.8-Ag0.7-Cu Lead-Free Solder

2009 ◽  
Author(s):  
Kok Ee Tan ◽  
John H. L. Pang
Keyword(s):  
Strain Rate ◽  
Yield Stress ◽  
Strain Curve ◽  
Tensile Tests ◽  
Lead Free ◽  
Indentation Hardness ◽  
Strain Rates ◽  
Test Results ◽  
Stress Strain Curve ◽  
Stress Strain

In this paper, the strain-rate dependent mechanical properties and stress-strain curve behavior of Sn3.8Ag0.7Cu (SAC387) solder is presented for a range of strain-rates at room temperature. The apparent elastic modulus, yield stress properties and stress-strain curve equation of the solder material is needed to facilitate finite element modeling work. Tensile tests on dog-bone shaped bulk solder specimens were conducted using a non-contact video extensometer system. Constant strain-rate uni-axial tensile tests were conducted over the strain-rates of 0.001, 0.01, 0.1 and 1 (s−1) at 25°C. The effects of strain-rate on the stress-strain behavior for lead-free Sn3.8Ag0.7Cu solder are presented. The tensile yield stress results were compared to equivalent yield stress values derived from nano-indentation hardness test results. Constitutive models based on the Ramberg-Osgood model and the Cowper-Symond model were fitted for the tensile test results to describe the elastic-plastic behavior of solder deformation behavior.

scholarly journals Study on Damage Statistical Constitutive Model of Triaxial Compression of Acid-Etched Rock under Coupling Effect of Temperature and Confining Pressure

Materials ◽  
2021 ◽  
Vol 14 (23) ◽  
pp. 7414
Author(s):  
Youliang Chen ◽  
Peng Xiao ◽  
Xi Du ◽  
Suran Wang ◽  
Zhoulin Wang ◽  
...  
Keyword(s):  
Constitutive Model ◽  
Coupling Effect ◽  
Triaxial Compression ◽  
Strain Curve ◽  
Confining Pressure ◽  
Effect Of Temperature ◽  
Acid Etching ◽  
Model Parameters ◽  
Stress Strain Curve ◽  
Stress Strain

Based on Lemaitre’s strain equivalence hypothesis theory, it is assumed that the strength of acid-etching rock microelements under the coupling effect of temperature and confining pressure follows the Weibull distribution. Under the hypothesis that micro-element damage meets the D-P criterion and based on continuum damage mechanics and statistical theory, chemical damage variables, thermal damage variables and mechanical damage variables were introduced in the construction of damage evolution equations and constitutive models for acid-etching rocks considering the coupled effects of temperature and confining pressure. The required model parameters were obtained by theoretical derivation, and the model was verified based on the triaxial compression test data of granite. Comparing the experimental stress-strain curve with the theoretical stress-strain curve, the results show that they were in good agreement. By selecting reasonable model parameters, the damage statistical constitutive model can accurately reflect the stress-strain curve characteristics of rock in the process of triaxial compression. The comparison between the experimental and theoretical results also verifies the reasonableness and reliability of the model. This model provides a new rock damage statistical constitutive equation for the study of rock mechanics and its application in engineering, and has certain reference significance for rock underground engineering.

Molecular dynamics simulations of the effect of temperature and strain rate on the plastic deformation of body centred cubic iron nanowires

2021 ◽  
pp. 1-19
Author(s):  
Qian Wu ◽  
Yong Wang ◽  
Tao Han ◽  
Hongtao Wang ◽  
Laihui Han ◽  
...  
Keyword(s):  
Molecular Dynamics ◽  
Plastic Deformation ◽  
Strain Rate ◽  
Yield Stress ◽  
Young’S Modulus ◽  
Young's Modulus ◽  
Strain Curve ◽  
Dislocation Slip ◽  
Stress Strain Curve ◽  
Stress Strain

Abstract The tensile tests of BCC Fe nanowires were simulated through molecular dynamics methods. The temperature and strain rate effects on the mechanical properties as well as the orientation-dependent plastic deformation mechanism were analyzed. For [001]-oriented BCC Fe nanowires, as the temperature increased, the yield stress and Young's modulus decreased. While the yield stress and Young's modulus increased as the strain rate increased. With the increase of temperature, when the temperature was less than 400 K, the twin propagation stress decreased dramatically, and then tended to reach a saturation value at higher temperatures. Under different temperatures and strain rates, the [001]-oriented Fe nanowires all deformed by twinning. The oscillation stage in the stress-strain curve corresponds to the process from the nucleation of the twin to the reorientation of the nanowire. For [110]-oriented Fe nanowires, the plastic deformation is dominated by dislocation slip. The independent events such as the nucleation, slip, and annihilation of dislocations are the causes of the unsteady fluctuations in the stress-strain curve. The Fe nanowires eventually undergo shear damage along the dominant slip surface.

scholarly journals Triaxial tests on snow at low strain rate. Part II. Constitutive behaviour

2003 ◽  
Vol 49 (164) ◽  
pp. 91-101 ◽  
Author(s):  
Carlo Scapozza ◽  
Perry Bartelt
Keyword(s):  
Strain Rate ◽  
Yield Stress ◽  
Power Law ◽  
Triaxial Compression ◽  
Confining Pressure ◽  
Triaxial Tests ◽  
Constitutive Behaviour ◽  
Fine Grained ◽  
Polycrystalline Ice ◽  
Confining Pressures

AbstractFine-grained, dry snow with a density range of 190–435 kg m−3 was tested in triaxial compression at −12°C with confining pressures varying between 0 and 40 kPa. The tests were strain-rate controlled, with strain rates ranging between 7.4 × 10−7 s−1 and 6.6 × 10−5 s−1. The analysis of the test results revealed that the relationship between yield stress and viscous strain rate is best given by a power law, similar to polycrystalline ice. However, the power-law exponent n is a function of density and varies between 1.8 (low-density snow, ρ < 200 kg m−3) and 3.6 (high-density snow, ρ > 320 kg m−3). The tests also showed that lower-density snow displays a significant non-linear stress–strain response before yielding. Two further aspects of the constitutive behaviour of snow were identified: (1) the strainrate independence of the post-yield work-hardening behaviour in compression and (2) the independence of the axial yield stress in relation to the confining pressure. The experimental observations are discussed with respect to the mechanical properties of polycrystalline ice, which is the constituent material of the load-bearing ice skeleton.

Dynamic Constitutive Equations and Behaviour of Brass at High Strain Rates

1995 ◽  
Vol 209 (4) ◽  
pp. 287-293 ◽  
Author(s):  
L-Y Li ◽  
T C K Molyneaux
Keyword(s):  
Flow Stress ◽  
Strain Rate ◽  
Yield Stress ◽  
Constitutive Equations ◽  
High Strain ◽  
Strain Curve ◽  
Strain Rates ◽  
Stress Strain Curve ◽  
High Strain Rates ◽  
Stress Strain

This paper presents an experimental study of the mechanical properties of brass at high strain rates. The brass tested is the copperzinc alpha-beta and beta two-phase alloy in the cold-worked state. Experiments were conducted using an extended tension split Hopkinson bar apparatus. It is found that, at lower strain rates, the stress-strain curve is smooth, exhibiting no well-defined yield stress, but at higher strain rates the stress-strain curve not only shows a well-defined yield stress but also displays a very pronounced drop in stress at yield. The flow stress is found to increase with increasing strain rate, but the increase is more significant for the yield stress than for the flow stress, showing that the yield stress is more sensitive to the strain rate than the flow stress away from the yield point. Based on the experimental results, empirical strain-rate-dependent constitutive equations are recommended. The suggested constitutive equations provide a reasonable estimate of the strain-rate-sensitive behaviour of materials.

scholarly journals A New Rock Brittleness Evaluation Method Based on the Complete Stress-Strain Curve

Lithosphere ◽  
2021 ◽  
Vol 2021 (Special 4) ◽  
Author(s):  
Chenyang Liu ◽  
Lizhi Du ◽  
Xiaopei Zhang ◽  
Yong Wang ◽  
Xinmin Hu ◽  
...  
Keyword(s):  
Stress Drop ◽  
Evaluation Method ◽  
Triaxial Compression ◽  
Strain Curve ◽  
Confining Pressure ◽  
Brittleness Index ◽  
Peak Strain ◽  
Stress Strain ◽  
Rock Brittleness ◽  
Drop Rate

Abstract Brittleness is a crucial parameter of rock mass and the key indicator in rock engineerings, such as rockburst prediction, tunnelling machine borehole drilling, and hydraulic fracturing. To solve the problem of using present brittleness indexes, the existing rock brittleness indexes were firstly summarised in this paper. Then, a brittleness index (BL), which considers the ratio of stress drop rate and stress increase rate and the peak stress, was proposed. This new index has the advantage of simplifying the acquisition of key parameters and avoiding dimensional problems, as well as taking the complete stress-strain curves into account. While applying the BL, the peak strain is used to describe the difficulty of brittle failure before the peak point, and the ratio of stress drop to strain increase can reflect the stress drop rate without dimension problem. In order to verify the applicability of BL, through the PFC2D, the microparameters and confining pressure were changed to model different types of rock numerical specimens and different stress condition. The results show that the BL can well reflect and classify the brittleness characteristics of different rock types and characterise the constraint of confining pressure on rock brittleness. Moreover, the influence of microparameter on macroparameter was studied. In order to further verify the reliability of the brittleness index (BL), this study conducted uniaxial and triaxial compression tests (30 MPa) on marble, sandstone, limestone, and granite under different confining pressure.

The Dynamic Stress-Strain Behavior in Torsion of 1100-0 Aluminum Subjected to a Sharp Increase in Strain Rate

1972 ◽  
Vol 39 (4) ◽  
pp. 939-945 ◽  
Author(s):  
R. A. Frantz ◽  
J. Duffy
Keyword(s):  
Strain Rate ◽  
Strain Curve ◽  
Initial Response ◽  
Material Behavior ◽  
High Rate ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Strain Behavior ◽  
Split Hopkinson ◽  
Explosive Charges

A modification of the torsional split Hopkinson bar is described which superimposes a high rate of shear strain on a slower “static” rate. The static rate of 5 × 10−5 sec−1 is increased to 850 sec−1 at a predetermined value of plastic strain by the detonation of small explosive charges; the rise time of the strain-rate increment is about 10 microsec. During deformation at the dynamic rate, direct measurement is made of the excess stress above the maximum static stress attained. Results for 1100-O aluminum show that the initial response to the strain rate increment is elastic, followed by yielding behavior reminiscent in appearance to an upper yield point. The incremental stress-strain curve always lies beneath the stress-strain curve obtained entirely at the higher strain rate but approaches it asymptotically with increasing strain. It is concluded that the material behavior is a function of strain, strain rate, and strain rate history.

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