Investigation of the stress-strain rate curve at low strain rates for superplastic Zn22%Al alloy

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.

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A Strain Rate-Dependent Damage Evolution Model for Concrete Based on Experimental Results

Advances in Civil Engineering ◽

10.1155/2021/6643263 ◽

2021 ◽

Vol 2021 ◽

pp. 1-8

Author(s):

Bin Xu ◽

Xiaoyan Lei ◽

P. Wang ◽

Hui Song

Keyword(s):

Strain Rate ◽

Uniaxial Compression ◽

Damage Evolution ◽

Damage Model ◽

Evolution Model ◽

Experimental Results ◽

Strain Rates ◽

Compression Tests ◽

Stress Strain ◽

Actual Damage

There are various definitions of damage variables from the existing damage models. The calculated damage value by the current methods still could not well correspond to the actual damage value. Therefore, it is necessary to establish a damage evolution model corresponding to the actual damage evolution. In this paper, a strain rate-sensitive isotropic damage model for plain concrete is proposed to describe its nonlinear behavior. Cyclic uniaxial compression tests were conducted on concrete samples at three strain rates of 10−3s−1, 10−4s−1, and 10−5s−1, respectively, and ultrasonic wave measurements were made at specified strain values during the loading progress. A damage variable was defined using the secant and initial moduli, and concrete damage evolution was then studied using the experimental results of the cyclic uniaxial compression tests conducted at the different strain rates. A viscoelastic stress-strain relationship, which considered the proposed damage evolution model, was presented according to the principles of irreversible thermodynamics. The model results agreed well with the experiment and indicated that the proposed damage evolution model can accurately characterize the development of macroscopic mechanical weakening of concrete. A damage-coupled viscoelastic constitutive relationship of concrete was recommended. It was concluded that the model could not only characterize the stress-strain response of materials under one-dimensional compressive load but also truly reflect the degradation law of the macromechanical properties of materials. The proposed damage model will advance the understanding of the failure process of concrete materials.

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Tensile Stress-Strain Curves Modeling of Four Kinds of Solders with Temperature and Rate Dependence

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.297-300.905 ◽

2005 ◽

Vol 297-300 ◽

pp. 905-911 ◽

Cited By ~ 2

Author(s):

Xu Chen ◽

Li Zhang ◽

Masao Sakane ◽

Haruo Nose

Keyword(s):

Tensile Stress ◽

Constitutive Model ◽

Strain Rate ◽

Constant Strain Rate ◽

Tensile Tests ◽

Strain Rate Range ◽

Rate Dependence ◽

Strain Rates ◽

Stress Strain ◽

Rate Range

A series of tensile tests at constant strain rate were conducted on tin-lead based solders with different Sn content under wide ranges of temperatures and strain rates. It was shown that the stress-strain relationships had strong temperature- and strain rate- dependence. The parameters of Anand model for four solders were determined. The four solders were 60Sn-40Pb, 40Sn-60Pb, 10Sn-90Pb and 5Sn-95Pb. Anand constitutive model was employed to simulate the stress-strain behaviors of the solders for the temperature range from 313K to 398K and the strain rate range from 0.001%sP -1 P to 2%sP -1 P. The results showed that Anand model can adequately predict the rate- and temperature- related constitutive behaviors at all test temperatures and strain rates.

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A Dynamic Mechanical Analysis of T2 Copper at High Strain Rates

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.812.38 ◽

2019 ◽

Vol 812 ◽

pp. 38-44

Author(s):

Shuai Chen ◽

Wen Bin Li ◽

Xiao Ming Wang ◽

Wen Jin Yao

Keyword(s):

Yield Strength ◽

Strain Rate ◽

High Strain ◽

Split Hopkinson Pressure Bar ◽

Pure Copper ◽

Dislocation Slip ◽

Strain Rates ◽

High Strain Rates ◽

Stress Strain ◽

Shpb Test

This work compares the pure copper (T2 copper)’s stress-strain relationship at different strain rates in the uni-axial tension test and Split Hopkinson Pressure Bar (SHPB) test. Small samples were utilized in the high strain rate SHPB test in which the accuracy was modified by numerical simulation. The experimental results showed that the T2 copper’s yield strength at high strain rates largely outweighed the quasi static yield strength. The flow stress in the stress-strain curves at different strain rates appeared to be divergent and increased with the increase in strain rates, showing great strain strengthening and strain rate hardening effects. Metallographic observation showed that the microstructure of T2 copper changed from equiaxed grains to twins and the interaction between the dislocation slip zone grain boundary and twins promoted the super plasticity distortion in T2 copper.

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Constant Strain-Rate Tensile Testing of Natural Snow

Journal of Glaciology ◽

10.1017/s0022143000011138 ◽

1980 ◽

Vol 26 (94) ◽

pp. 519 ◽

Cited By ~ 3

Author(s):

H. Singh ◽

F.W. Smith

Keyword(s):

Strain Rate ◽

Strain Gage ◽

Constant Strain Rate ◽

Strain Curve ◽

Strain Rates ◽

Strain Gages ◽

Compression Tests ◽

Snow Sample ◽

Stress Strain ◽

Natural Snow

Abstract In conducting tension and compression tests on snow samples, strains and strain-rates are usually determined from the displacements of the ends of the samples. In this work, a strain-gage which mounts directly onto the snow sample during testing, was developed and was found to give accurate and direct measurements of strain and strain-rates. A commercially available 0-28 pF variable capacitor was modified to perform the required strain measurements. It is a polished metallic plunger sliding inside a metal-coated glass tube. The plunger and tube were each soldered to the end of a spring-steel wire arm. To the other end of these arms were soldered to 10 mm square pads made of thin brass shim stock. The whole device weighs 2.5 g and the low coefficient of friction in the capacitor resulted in a very low actuation force. To mount the strain gage, the pads are wetted and frozen onto the snow sample. A high degree of sensitivity was achieved through the use of “phase-lock-loop” electronic circuitry. The capacitance change caused by the strain in the sample, changes the frequency of output signal from an oscillator and thus causes the change in output from the system. In the locked state, to which the system is constantly driven by a feed-back loop, the system output is almost ripple free. The strain gages were calibrated in the field in order to take into account the effects of very low field temperatures. The calibration curves were almost linear over the travel of 15 mm, the maximum limit. The sensitivity of the system is 4 mV per strain unit, but this could be increased by an order of magnitude by minor adjustments in the circuit. Constant strain-rate tensile tests were performed on natural snow at Berthoud Pass, Colorado, U.S.A., in the density range of 140-290 kg m-3. Four strain gages were mounted onto the samples to sense any non-uniform deformation which otherwise would have gone unnoticed or caused scatter in the data. The average indication of these gages was used to construct stress—strain curves for various types of snow at different strain-rates. The effect of strain-rate on the behavior of snow was studied. “Ratcheting” in the stress-strain curve in the region where the snow becomes plastic was observed first by Kinosita in his compression tests. A similar phenomenon was observed in these tension tests. It was found that directly measured strain is quite different from that which would be calculated from sample end movement. Strain softening was not observed in these tests up to total strains of 8%. The strain-rate effects found were comparable to the results of other investigators.

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Experimental Estimation of Strain Rate during FSW of Al-Alloy Using Plane-Strain Compression

Materials Science Forum ◽

10.4028/www.scientific.net/msf.580-582.299 ◽

2008 ◽

Vol 580-582 ◽

pp. 299-302 ◽

Cited By ~ 3

Author(s):

Kunitaka Masaki ◽

Yutaka S. Sato ◽

Masakatsu Maeda ◽

Hiroyuki Kokawa

Keyword(s):

Strain Rate ◽

Plane Strain ◽

Travel Speed ◽

Plane Strain Compression ◽

Stir Zone ◽

Grain Structure ◽

Al Alloy ◽

Strain Rates ◽

Friction Stir ◽

Grain Structures

Friction stir welding (FSW) makes the stir zone with fine recrystallized grain structure. The recrystallized grains would be formed through dynamic recrystallization at high temperatures and high strain-rate. The present study experimentally simulated the dynamically recrystallized microstructure of a friction stir welded Al alloy 1050 produced at 600 rpm rotation and 100 mm/min travel speed, using combination of the plane-strain compression at various strain rates and the subsequent cooling along the cooling cycle of FSW. The equiaxed grain structures similar to the microstructure of the stir zone were produced at strain rates between 0.1 and 32 s-1; the grain size decreased with increasing strain rate. Strain rate during the FSW could be estimated to be about 1.8 s-1. The present study suggests that plane-strain compression test can simulate the recrystallized grain structure of the friction stir welds.

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Stress-Strain Equations for Some Near-Eutectic Tin-Lead Solders

Journal of Engineering Materials and Technology ◽

10.1115/1.2904128 ◽

1991 ◽

Vol 113 (4) ◽

pp. 475-484 ◽

Cited By ~ 13

Author(s):

K. P. Jen ◽

J. N. Majerus

Keyword(s):

Strain Rate ◽

Printed Circuit Boards ◽

Volume Fraction ◽

Total Error ◽

Tensile Tests ◽

Elastic Behavior ◽

Plastic Behavior ◽

Strain Rates ◽

Stress Strain ◽

Engineering Strain

This paper presents the evaluation of the stress-strain behavior, as a function of strain-rate, for three tin-lead solders at room temperature. This behavior is critically needed for reliability analysis of printed circuit boards (PCB) since handbooks list minimal mechanical properties for the eutectic solder used in PCBs. Furthermore, most handbook data are for stable eutectic microstructure whereas PCB solder has a metastable microstructure. All three materials were purchased as “eutectics.” However, chemical analysis, volume fraction determination, and microhardness tests show some major variations between the three materials. Two of the materials have a eutectic composition, and one does not. The true stress-strain equations of one eutectic and the one noneutectic material are determined from compressive tests at engineering strain-rates between 0.0002/s and 0.2/s. The second eutectic material is evaluated using tensile tests with strain-rates between 0.00017/s and 0.042/s. The materials appear to exhibit linear elastic behavior only at extremely small strains, i.e., less than 0.0005. However, this “elastic” behavior showed considerable variation, and depended upon the strain rate. In both tension and compression the eutectic alloy exhibits nonlinear plastic behavior, i.e., strain-softening followed by strain-hardening, which depends upon the strain rate. A quadratic equation σy = σy(ε˚/ε˚0) + A(ε˚/ε˚0)ε + B(ε˚/ε˚0)ε2 fit to the data gives correlation coefficients R2 > 0.91. The coefficients σy(ε˚/ε˚0), A(ε˚/ε˚0), B(ε˚/ε˚0) are fitted functions of the normalized engineering strain rate ε˚/ε˚0. Replicated experiments are used at each strain-rate so that a measure of the statistical variation could be estimated. Measures of error associated with the regression analysis are also obtained so that an estimate of the total error in the stress-strain relations can be made.

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Dynamic Constitutive Model of Ultra-High Molecular Weight Polyethylene (UHMWPE): Considering the Temperature and Strain Rate Effects

Polymers ◽

10.3390/polym12071561 ◽

2020 ◽

Vol 12 (7) ◽

pp. 1561 ◽

Cited By ~ 1

Author(s):

Kebin Zhang ◽

Wenbin Li ◽

Yu Zheng ◽

Wenjin Yao ◽

Changfang Zhao

Keyword(s):

Mechanical Properties ◽

Constitutive Model ◽

Strain Rate ◽

Split Hopkinson Pressure Bar ◽

Plastic Material ◽

Strain Rates ◽

Hopkinson Pressure Bar ◽

Ballistic Performance ◽

Stress Strain ◽

Different Temperatures

The temperature and strain rate significantly affect the ballistic performance of UHMWPE, but the deformation of UHMWPE under thermo-mechanical coupling has been rarely studied. To investigate the influences of the temperature and the strain rate on the mechanical properties of UHMWPE, a Split Hopkinson Pressure Bar (SHPB) apparatus was used to conduct uniaxial compression experiments on UHMWPE. The stress–strain curves of UHMWPE were obtained at temperatures of 20–100 °C and strain rates of 1300–4300 s−1. Based on the experimental results, the UHMWPE belongs to viscoelastic–plastic material, and a hardening effect occurs once UHMWPE enters the plastic zone. By comparing the stress–strain curves at different temperatures and strain rates, it was found that UHMWPE exhibits strain rate strengthening and temperature softening effects. By modifying the Sherwood–Frost model, a constitutive model was established to describe the dynamic mechanical properties of UHMWPE at different temperatures. The results calculated using the constitutive model were in good agreement with the experimental data. This study provides a reference for the design of UHMWPE as a ballistic-resistant material.

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High Strain-Rate Compressive Behavior and Constitutive Modeling of Selected Polymers Using Modified Ramberg-Osgood Equation

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.566.80 ◽

2014 ◽

Vol 566 ◽

pp. 80-85

Author(s):

Kenji Nakai ◽

Takashi Yokoyama

Keyword(s):

High Strain Rate ◽

Strain Rate ◽

Compressive Stress ◽

Constitutive Modeling ◽

High Strain ◽

Strain Rates ◽

Stress Strain ◽

Strain Behavior ◽

Least Squares Fit ◽

Wide Range

The present paper is concerned with constitutive modeling of the compressive stress-strain behavior of selected polymers at strain rates from 10-3 to 103/s using a modified Ramberg-Osgood equation. High strain-rate compressive stress-strain curves up to strains of nearly 0.08 for four different commercially available extruded polymers were determined on the standard split Hopkinson pressure bar (SHPB). The low and intermediate strain-rate compressive stress-strain relations were measured in an Instron testing machine. Six parameters in the modified Ramberg-Osgood equation were determined by fitting to the experimental stress-strain data using a least-squares fit. It was shown that the monotonic compressive stress-strain behavior over a wide range of strain rates can successfully be described by the modified Ramberg-Osgood constitutive model. The limitations of the model were discussed.

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Time and Temperature Dependence of the Ultimate Properties of an SBR Rubber at Constant Elongations

Rubber Chemistry and Technology ◽

10.5254/1.3540259 ◽

1961 ◽

Vol 34 (3) ◽

pp. 897-909

Author(s):

Thor L. Smith ◽

Paul J. Stedry

Keyword(s):

Tensile Strength ◽

Strain Rate ◽

Temperature Dependence ◽

Rate Dependence ◽

Strain Rates ◽

Type Specimens ◽

Stress Strain ◽

Ultimate Elongation ◽

Tensile Tester ◽

Ultimate Properties

Abstract A study was made previously of the temperature and strain rate dependence of the stress at break (tensile strength) and the ultimate elongation of an unfilled SBR rubber. In that study, stress-strain curves to the point of rupture were measured with an Instron tensile tester on ring type specimens at 14 temperatures between −67.8° and 93.3° C, and at 11 strain rates between 0.158×10−3 and 0.158 sec−1 at most temperatures. The tensile strength was found to increase with both increasing strain rate and decreasing temperature. At all temperatures above −34.4° C, the ultimate elongation was likewise found to increase with increasing strain rate and decreasing temperature but at lower temperatures the opposite dependence on rate was observed; at −34.4° C, the ultimate elongation passed through a maximum with increasing rate.

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