Experiments on Strain Rate History and Temperature Effects During the Plastic Deformation of Close-Packed Metals

1978 ◽  
Vol 45 (1) ◽  
pp. 60-66 ◽  
Author(s):  
P. E. Senseny ◽  
J. Duffy ◽  
R. H. Hawley
Keyword(s):  
Flow Stress ◽  
Strain Rate ◽  
Constant Strain Rate ◽  
Strain Rates ◽  
Stress Strain ◽  
Pure Zinc ◽  
Polycrystalline Metals ◽  
Commercially Pure ◽  
The Difference ◽  
Incremental Strain

A study is presented on the influence of strain rate and strain rate history on the flow stress of several metals. Experiments were performed on specimens of four polycrystalline metals: 1100-0 aluminum, OFHC copper, AZ31 B magnesium, and commercially pure zinc. The experiments involve, the use of a modified Kolsky bar to increase abruptly the imposed strain rate, initially 2 × 10−4 s−1, by a factor of more than 106. Tests were performed at selected temperatures in the range T ≤ (1/2)Tm. The results include complete stress-strain curves for deformation at constant strain rates as well as for deformation involving a sharp increment in strain rate. The difference in flow stress at a given value of strain for stress-strain curves obtained at constant but different strain rates provides one measure of the influence of strain rate on the flow stress. However, the results of the incremental strain rate experiments show that both strain rate and strain rate history contribute to this difference in flow stress. Hence, interpretation of both the incremental and the constant strain rate tests offers a means for distinguishing between the effects of strain rate as opposed to those of differences in strain rate history.

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

2005 ◽  
Vol 297-300 ◽  
pp. 905-911 ◽  
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.

scholarly journals Constant Strain-Rate Tensile Testing of Natural Snow

1980 ◽  
Vol 26 (94) ◽  
pp. 519 ◽  
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.

One-Dimensional Dynamic Compressive Behavior of EPDM Rubber

2003 ◽  
Vol 125 (3) ◽  
pp. 294-301 ◽  
Author(s):  
B. Song ◽  
W. Chen
Keyword(s):  
Strain Rate ◽  
High Speed ◽  
Dynamic Stress ◽  
Split Hopkinson Pressure Bar ◽  
Constant Strain Rate ◽  
Strain Rates ◽  
Hopkinson Pressure Bar ◽  
Stress Strain ◽  
Epdm Rubber ◽  
One Dimensional

Dynamic compressive stress-strain curves at various strain rates of an Ethylene-Propylene-Diene Monomer Copolymer (EPDM) rubber have been determined with a modified split Hopkinson pressure bar (SHPB). The use of a pulse-shaping technique ensures that the specimen deforms at a nearly constant strain rate under dynamically equilibrated stress. The validity of the experiments was monitored by a high-speed digital camera for specimen edge deformation, and by piezoelectric force transducers for dynamic stress equilibrium. The resulting dynamic stress-strain curves for the EPDM indicate that the material is sensitive to strain rates and that the strain-rate sensitivity depends on the value of strain. Based on a strain energy function theory, a one-dimensional dynamic constitutive equation for this rubber was modified to describe the high strain-rate experimental results within the ranges of strain and strain rates presented in this paper.

The Influence of Microstructure on Superplastic Behaviours of γ-TiAl Alloys

1998 ◽  
Vol 552 ◽  
Author(s):  
J. Sun ◽  
J. S. Wu ◽  
G. X. Hu ◽  
Y. H. He ◽  
B. Y. Huang
Keyword(s):  
Flow Stress ◽  
Strain Rate ◽  
Strain Rate Sensitivity ◽  
Superplastic Deformation ◽  
Rate Sensitivity ◽  
Strain Rates ◽  
Maximum Elongation ◽  
Tial Alloys ◽  
Different Temperatures ◽  
Incremental Strain

ABSTRACTIn this work, superplastic behaviours in Ti-33A1–3Cr-0.5Mo (wt%) γ-TiAl alloys with two different initial microstructures of near gamma (NG) and duplex (DM) structure were investigated with respect to the effect of testing temperatures and strain rates. At 1050°C and a strain rate of 8×10–5 S–1, a maximum elongation of 570% was observed for NG-TiAl and a maximum elongation of 467% for DM-TiAl. The relations of flow stress and strain rate sensitivity vs. strain rates at different temperatures were also determined by incremental strain rate tests. The results showed that the value of strain rate sensitivity is higher and the flow stress is lower for NG than those for DM at the same condition. The microstructural evolution during superplastic deformation was examined and correlated to the mechanical properties for these two alloys. The influence of microstructure on the superplastic behaviours of γ-TiAl alloys, and possible superplastic deformation mechanisms were finally discussed.

scholarly journals Constant Strain-Rate Tensile Testing of Natural Snow

1980 ◽  
Vol 26 (94) ◽  
pp. 519-519
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

AbstractIn 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.

Establishment of Flow Stress Model of EW75 Alloy

2013 ◽  
Vol 423-426 ◽  
pp. 241-246
Author(s):  
Ming Long Ma ◽  
Kui Zhang
Keyword(s):  
Mathematical Model ◽  
Flow Stress ◽  
Magnesium Alloy ◽  
Strain Rate ◽  
Strain Rate Range ◽  
Strain Rates ◽  
Stress Strain ◽  
Deformation Degree ◽  
Maximum Deformation ◽  
The Mathematical Model

The behavior evolvement of Mg-7.22Gd-4.84Y-1.26Nd-0.58Zr (EW75) magnesium alloy during the hot deformation process was discussed. The flow stress behavior of magnesium alloy over the strain rate range 0.002s-1to 2s-1and the temperature range 623K to 773K had been researched on Gleeble-1500D hot simulator under the maximum deformation degree 60%. A mathematical model was established to predict the stress-strain curves of this alloy during deformation. The experimental results showed that the stress-strain curves were obviously affected by the strain rates and deformation temperatures. The mathematical model could predict the stress-strain curves when the strain rates were under 0.2-1, but there was significant error in some of stress-strain curves when the strain-rate was 2-1by the reason of deformation temperature rising.

Nonlinear Viscoelastic Response of Amorphous Elastomers to Constant Strain Rates

1963 ◽  
Vol 36 (3) ◽  
pp. 682-696 ◽  
Author(s):  
Thor L. Smith
Keyword(s):  
Strain Rate ◽  
Constant Strain Rate ◽  
Relaxation Modulus ◽  
Nonlinear Effects ◽  
Published Data ◽  
Strain Rates ◽  
Stress Strain ◽  
Linear Viscoelastic Material ◽  
Wide Range ◽  
Strain Data

Abstract Tensile stress-strain curves determined at constant strain rates are nonlinear because relaxation of stress generally occurs during a test and also because of inherent nonlinear effects. To develop a method for determining the conditions under which time and nonlinear effects are separable, consideration was first given to a linear viscoelastic material. It was shown that stress-strain curves determined at different strain rates superpose to yield a single curve on a plot of log σ(ε, t)/ε vs. log t, where σ(ε, t) is the stress, a function of the strain ε and the time t; by definition t equals ε/ε where ε is the strain rate. The quantity σ(ε, t)/ε was called the constant-strain rate modulus F(t) which is related exactly to the stress-relaxation modulus E(t) by the equation E(t)=F(t)(1+m) where m=d log F(t)/d log t. For amorphous elastomers tested in tensions over a wide range of strain, it was proposed that stress-strain curves determined at constant strain rates can be represented by F(t)=g(ε)σ(ε,t)/ε where g(ε) is a function only of strain and approaches unity as the strain goes to zero. To test this equation, an analysis was made of stress-strain curves of an SBR gum vulcanizate measured to rupture at numerous strain rates at 10 temperatures between −42.8 and 93.3° C. From − 34.4 to 93.3° C, g (ε) was found to be independent of both time and temperature, but at −42.8° C for strains greater than about unity, g(ε) was found to be different. The functional form of g(ε) was compared with that predicted by three different analytical expressions for representing stress-strain data. To show further the advantages of F(t) for representing stress-strain data determined at different strain rates and temperatures, previously published data on the NBS polyisobutylene were presented on a plot of log F(t)298/T vs. log t/aT. From the composite curve, E(t) was calculated and found to be in close agreement with published data.

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.

Hot Deformation Behavior and Microstructure of 6069 Aluminum Alloy

2014 ◽  
Vol 788 ◽  
pp. 201-207 ◽  
Author(s):  
Hui Zhong Li ◽  
Jun Jiang ◽  
Min Deng ◽  
Xiao Peng Liang ◽  
Jie Ouyang
Keyword(s):  
Aluminum Alloy ◽  
Steady State ◽  
Flow Stress ◽  
Strain Rate ◽  
Deformation Behavior ◽  
Deformation Temperature ◽  
Constant Strain Rate ◽  
Strain Rates ◽  
Steady State Flow ◽  
State Flow

The deformation behavior and microstructure of 6069 aluminum alloy have been studied by isothermal compression at temperature ranging from 300°C to 450°C on Gleeble-1500 machine at strain rates from 0.01 to 10s-1. The results show that the deformation temperature and strain rate is essential to the flow characteristic, and the main deformation mechanism for 6069 aluminum alloy is dynamic recovery at low strain rates. The dynamic recrystallization take place at the strain rates of 10s-1 and deformation temperature ranges of 300~350°C. At constant strain rate, the flow stress and steady-state flow stress decrease with deformation temperature increasing. While at constant temperature, the flow stress and steady-state flow stress increase with increasing strain rate. The processing map at the strain of 0.7 is obtained and the map exhibits two safe deformation domains (300~350°C at 1~10s-1 and 380~450°C at 0.01~0.3s-1).

scholarly journals Effects of Cu Addition on Mechanical Behaviour, Microstructural Evolution and Anti-Corrosion Performance of TiAl-Based Intermetallic Alloy under Different Strain Rates

Materials ◽  
2021 ◽  
Vol 14 (17) ◽  
pp. 5056
Author(s):  
Cheng-Hsien Kuo ◽  
Tao-Hsing Chen ◽  
Ting-Yang Zeng
Keyword(s):  
Flow Stress ◽  
Strain Rate ◽  
Fracture Strain ◽  
Split Hopkinson Pressure Bar ◽  
Constant Strain Rate ◽  
Rate Sensitivity ◽  
Strain Rates ◽  
Phase Content ◽  
Corrosion Performance ◽  
Hopkinson Pressure Bar

TiAl-based intermetallic alloys are prepared with Cu concentrations of 3–5 at.% (atomic ratio). The mechanical properties and microstructural characteristics of the alloys are investigated under static and dynamic loading conditions using a material testing system (MTS) and split-Hopkinson Pressure Bar (SHPB), respectively. The electrochemical properties of the various alloys are then tested in Ringer’s solution. It is shown that the level of Cu addition significantly affects both the flow stress and the ductility of the samples. For Cu contents of 3 and 4 at.%, respectively, the flow stress and strain rate sensitivity increase at higher strain rates. Furthermore, for a constant strain rate, a Cu content of 4 at.% leads to an increased fracture strain. However, for the sample with the highest Cu addition of 5 at.%, the flow stress and fracture strain both decrease. The X-ray diffraction (XRD) patterns and optical microscopy (OM) images reveal that the lower ductility is due to the formation of a greater quantity of γ phase in the binary TiAl alloy system. Among all the specimens, that with a Cu addition of 4 at.% has the best anti-corrosion performance. Overall, the results indicate that the favourable properties of the TiAlCu4 sample stem mainly from the low γ phase content of the microstructure and the high α2 phase content.

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