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.

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 Evolution of specimen strain rate in split Hopkinson bar test

2019 ◽  
Vol 233 (13) ◽  
pp. 4667-4687 ◽  
Author(s):  
Hyunho Shin ◽  
Jong-Bong Kim
Keyword(s):  
Strain Rate ◽  
Rate Equation ◽  
Constant Strain Rate ◽  
Strain Curve ◽  
Hopkinson Bar ◽  
Stress Strain ◽  
Split Hopkinson Bar ◽  
Specimen Diameter ◽  
Strain And Strain Rate ◽  
Split Hopkinson

The specimen strain rate in the split Hopkinson bar (SHB) test has been formulated based on a one-dimensional assumption. The strain rate is found to be controlled by the stress and strain of the deforming specimen, geometry (the length and diameter) of specimen, impedance of bar, and impact velocity. The specimen strain rate evolves as a result of the competition between the rate-increasing and rate-decreasing factors. Unless the two factors are balanced, the specimen strain rate generally varies (decreases or increases) with strain (specimen deformation), which is the physical origin of the varying nature of the specimen strain rate in the SHB test. According to the formulated strain rate equation, the curves of stress–strain and strain rate–strain are mutually correlated. Based on the correlation of these curves, the strain rate equation is verified through a numerical simulation and experiment. The formulated equation can be used as a tool for verifying the measured strain rate–strain curve simultaneously with the measured stress–strain curve. A practical method for predicting the specimen strain rate before carrying out the SHB test has also been presented. The method simultaneously solves the formulated strain rate equation and a reasonably estimated constitutive equation of specimen to generate the anticipated curves of strain rate–strain and stress–strain in the SHB test. An Excel® program to solve the two equations is provided. The strain rate equation also indicates that the increase in specimen stress during deformation (e.g., work hardening) plays a role in decreasing the slope of the strain rate–strain curve in the plastic regime. However, according to the strain rate equation, the slope of the strain rate–strain curve in the plastic deformation regime can be tailored by controlling the specimen diameter. Two practical methods for determining the specimen diameter to achieve a nearly constant strain rate are presented.

Influence of strain rate on the stress-strain curve in the range of Lüders strain

1996 ◽  
Vol 67 (11) ◽  
pp. 495-500 ◽  
Author(s):  
Essam El-Magd ◽  
Herbert Scholles ◽  
Herbert Weisshaupt
Keyword(s):  
Strain Rate ◽  
Strain Curve ◽  
Stress Strain Curve ◽  
Stress Strain

High Strain Rate Test of a Steel Plate under Blast Loading from High Explosive

2013 ◽  
Vol 767 ◽  
pp. 144-149 ◽  
Author(s):  
Tei Saburi ◽  
Shiro Kubota ◽  
Yuji Wada ◽  
Tatsuya Kumaki ◽  
Masatake Yoshida
Keyword(s):  
Strain Rate ◽  
Dynamic Stress ◽  
Steel Plate ◽  
High Strain ◽  
Strain Curve ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Time Deformation ◽  
Rate Test ◽  
High Strain Rate Test

In this study, a high strain rate test method of a steel plate under blast loading from high explosive was designed and was conducted by a combined experimental/numerical approach to facilitate the estimation process for the dynamic stress-strain curve under practical strain rate conditions. The steel plate was subjected to a blast load, which was generated by Composition C4 explosive and the dynamic deformation of the plate was observed with a high-speed video camera. Time-deformation relations were acquired by image analysis. A numerical simulation for the dynamic behaviors of the plate identical to the experimental condition was conducted using a coupling analysis of finite element method (FEM) and discrete particle method (DPM). Explosives were modeled by discrete particles and the steel plate and other materials were modeled by finite element. The blast load on the plate was described fluid-structure interaction (FSI) between DPM and FEM. As inverse analysis scheme to estimate dynamic stress-strain curve, an evaluation using a quasistatic data was conducted. In addition, two types of approximations for stress-strain curve were assumed and optimized by least square method. One is a 2-piece approximation, and was optimized by least squares method using a yield stress and a tangent modulus as parameters. The other is a continuous piecewise linear approximation, in which a stress-strain curve was divided into some segments based on experimental time-deformation relation, and was sequentially optimized using youngs modulus or yield stress as parameter. The results showed that the piecewise approximation can gives reasonably agreement with SS curve obtained from the experiment.

Predictive Stress-Strain Models for High Strength Concrete Subjected to Uniaxial Compression

2014 ◽  
Vol 567 ◽  
pp. 476-481
Author(s):  
Nasir Shafiq ◽  
Tehmina Ayub ◽  
Muhd Fadhil Nuruddin
Keyword(s):  
Predictive Models ◽  
High Strength Concrete ◽  
Cement Content ◽  
Strain Curve ◽  
High Strength ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Strength Concrete ◽  
Strain Behavior ◽  
Four Cylinders

To date, various predictive models for high strength concrete (HSC) have been proposed that are capable of generating complete stress-strain curves. These models were validated for HSC prepared with and without silica fume. In this paper, an investigation on these predictive models has been presented by applying them on two different series of HSC. The first series of HSC was prepared by utilizing 100% cement content, while second series was prepared by utilizing 90% cement and 10% Metakaolin. The compressive strength of the concrete was ranged from 71-87 MPa. For each series of HSC, total four cylinders of the size 100×200mm were cast to obtain the stress-strain curves at 28 days.It has been found that the pattern of the stress-strain curve of each cylinder among four cylinders of each series was different from other, in spite of preparing from the similar batch. When predictive models were applied to these cylinders using their test data then it was found that all models more or less deficient to accurately predict the stress-strain behavior.

Stress-Strain Behavior of an Aluminum Alloy Under Transient Strain-Rates

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
Y. W. Kwon ◽  
Y. Esmaeili ◽  
C. M. Park
Keyword(s):  
Aluminum Alloy ◽  
Strain Rate ◽  
Fracture Strain ◽  
Strain Curve ◽  
Strain Rates ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Single Strain ◽  
Transient Strain ◽  
Strain Rate Loading

Because most structures are subjected to transient strain-rate loading, an experimental study was conducted to investigate the stress-strain behaviors of an aluminum alloy undergoing varying strain-rate loading. To this end, uniaxial tensile loading was applied to coupons of dog-bone shape such that each coupon underwent two or three different strain-rates, i.e., one rate after another. As a basis, a series of single-strain-rate tests was also conducted with strain-rates of 0.1–10.0 s−1. When the material experienced multistrain-rate loading, the stress-strain curves were significantly different from any single-strain-rate stress-strain curve. The strain-rate history affected the stress-strain curves under multistrain-rate loading. As a result, some simple averaging of single-strain-rate curves did not predict the actual multistrain-rate stress-strain curve properly. Furthermore, the fracture strain under multistrain-rate loading was significantly different from that under any single-strain-rate case. Depending on the applied strain-rates and their sequences, the former was much greater or less than the latter. A technique was proposed based on the residual plastic strain and plastic energy density in order to predict the fracture strain under multistrain-rate loading. The predicted fracture strains generally agreed well with the experimental data. Another observation that was made was that the unloading stress-strain curve was not affected by the previous strain-rate history.

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.

A Probabilistic Methodology for Random Stress-Strain Curves

1991 ◽  
Author(s):  
H. R. Millwater ◽  
S. V. Harren ◽  
B. H. Thacker
Keyword(s):  
Finite Element Analysis ◽  
Numerical Evaluation ◽  
General Procedure ◽  
Strain Curve ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Element Analysis ◽  
Strain Behavior ◽  
Engineering Parameters ◽  
Analysis System

Abstract This paper presents a methodology for analyzing structures with random stress-strain behavior. Uncertainties in the stress-strain curve of a structure are simulated by letting a small number of engineering parameters which describe the stress-strain curve be random. Certain constraints are imposed on the engineering parameters in order to have a physically realizable material. A general procedure to handle correlation among the stress-strain parameters has also been developed. This methodology has been integrated into the NESSUS (Numerical Evaluation of Stochastic Structures Under Stress) probabilistic structural analysis system. With this system, probabilistic finite element analysis of structures with random stress-strain behavior can be analyzed in an accurate, automated fashion. An example problem is presented to demonstrate the capabilities of the code. The problem analyzed is that of a pressure vessel fabricated with a material exhibiting random stress-strain behavior.

Experimental Equipment Research on Uniaxial Compression Stress-Strain Curve of Concrete

2010 ◽  
Vol 163-167 ◽  
pp. 1333-1338
Author(s):  
Hai Bin Chen ◽  
You Po Su ◽  
Yu Min Zhang ◽  
Li Na Wang
Keyword(s):  
Structural Analysis ◽  
Strain Rate ◽  
Uniaxial Compression ◽  
Theoretical Basis ◽  
Indirect Method ◽  
Strain Curve ◽  
Experimental Equipment ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Loading System

The constitutive relation of concrete under uniaxial compression is the essential theoretical basis for structural analysis of concrete. Because of lack of sufficient stiffness for ordinarily tester, stable falling branch of stress-strain curve cannot be obtained. The common methods to increase rigidity of loading system include direct and indirect method. The condition of realizing the stress-strain complete curve for concrete uniaxial compression is derived. A set of stiffness experimental equipment is designed by using the indirect method, which has the advantages of simple, dependable and strong adaptability. Experiment shows that stress-strain complete curve of uniaxial compression under different strain rate could be achieved by using this equipment and electro-hydraulic loading system of MTS co. ltd. It will lay foundation for putting forward the stress-strain curve equation of uniaxial tension and compression under considering the effect of strain rate. It can provide theoretical basis for structural analysis of concrete.

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