A State Variable Modeling of Plasticity and Necking Under Uniaxial Tension

1992 ◽  
Vol 114 (4) ◽  
pp. 378-383 ◽  
Author(s):  
G. Ferron ◽  
H. Karmaoui Idrissi ◽  
A. Zeghloul
Keyword(s):  
Strain Rate ◽  
Uniaxial Tension ◽  
Plastic Flow ◽  
Constitutive Equations ◽  
Growth Process ◽  
Constant Strain Rate ◽  
Uniaxial Tensile ◽  
Long Wavelength ◽  
State Variable ◽  
Diffusion Controlled

Constitutive equations based on a state variable modeling of the thermo-viscoplastic behavior of metals are discussed, and incorporated in an exact, long-wavelength analysis of the neck-growth process in uniaxial tension. The general formalism is specialized to the case of f.c.c. metals in the range of intragranular, diffusion controlled plastic flow. The model is shown to provide a consistent account of aluminum behavior both under constant strain-rate and creep. Calculated uniaxial tensile ductilities and rupture lives in creep are also compared with experiments.

Elasto-viscoplastic constitutive equations for the description of glassy polymers behavior at constant strain rate

2006 ◽  
Vol 129 (1) ◽  
pp. 29-35 ◽  
Author(s):  
Fahmi Zaïri ◽  
Moussa Naït-Abdelaziz ◽  
Krzysztof Woznica ◽  
Jean-Michel Gloaguen
Keyword(s):  
Constitutive Equations ◽  
Constant Strain Rate ◽  
Tensile Tests ◽  
Glassy Polymers ◽  
Uniaxial Tensile ◽  
Model Parameters ◽  
Strain Rates ◽  
State Variable ◽  
Rubber Toughened ◽  
Compressive Tests

In this study, a modelization of the viscoplastic behavior of amorphous polymers is proposed, from an approach originally developed for metal behavior at high temperature, in which state variable constitutive equations have been modified. A procedure for the identification of model parameters is developed through the use of experimental data from both uniaxial compressive tests extracted from the literature and uniaxial tensile tests performed in this study across a variety of strain rates. The numerical algorithm shows that the predictions of this model well describe qualitatively and quantitatively the intrinsic softening immediately after yielding and the subsequent progressive orientational hardening corresponding to the response of two polymers, amorphous polyethylene terephthalate and rubber toughened polymethyl methacrylate.

Strain-rate dependence of hardening and softening in compression of a bulk-metallic glass

2007 ◽  
Vol 22 (10) ◽  
pp. 2655-2658 ◽  
Author(s):  
W.H. Jiang ◽  
F.X. Liu ◽  
F. Jiang ◽  
K.Q. Qiu ◽  
H. Choo ◽  
...  
Keyword(s):  
Flow Stress ◽  
Metallic Glass ◽  
Strain Rate ◽  
Bulk Metallic Glass ◽  
Plastic Flow ◽  
Shear Banding ◽  
Constant Strain Rate ◽  
Rate Dependence ◽  
Strain Rate Dependence ◽  
Plastic Flow Stress

We investigated the effect of strain rate on the plastic-flow stress of a Zr-based bulk-metallic glass in quasistatic compression. The results indicate that the plastic-flow stress is dependent on the strain rate: an increase in the strain rate leads to a decrease in the plastic-flow stress, and vice versa. However, simply loading, unloading, and reloading at a constant strain rate do not change the plastic-flow stress. This strain-rate dependence of the plastic-flow stress may be related to shear-banding operations.

scholarly journals Influence of Deformation Controlled Strain Rate on Tensile and Compression Behaviour of Magnesium and Steel Wire

2017 ◽  
Vol 892 ◽  
pp. 89-96 ◽  
Author(s):  
Thorsten Henseler ◽  
Madlen Ullmann ◽  
Grzegorz Korpala ◽  
Klaudia Klimaszewska ◽  
Rudolf Kawalla ◽  
...  
Keyword(s):  
Strain Rate ◽  
Elevated Temperatures ◽  
Steel Wire ◽  
Testing Machine ◽  
Constant Strain Rate ◽  
Strain Curve ◽  
Compression Testing ◽  
Uniaxial Tensile ◽  
Flow Curves ◽  
The Difference

This article demonstrates the difference in the flow curves of an AZ31 magnesium alloy and S235JR structural steel wire caused by non-linear strain rates during uniaxial tensile and compression testing at elevated temperatures. Throughout tensile deformation, the traverse velocity of the testing machine has to be adapted according to the current elongation of the specimen, thus accelerating, to ensure a constant strain rate during the admission of the stress-strain curve. The equivalent is necessary during compression testing, where the traverse velocity of the testing machine needs to decelerate ensuring a constant strain rate. Nevertheless, tensile and compression tests are performed with constant traverse velocity, which lead to divergent flow curves in comparison to deformation controlled traverse velocities. The results of the research show the difference in flow behaviour of magnesium and steel wire, when the temperature and strain rate are varied in conjunction with constant and deformation controlled traverse velocities.

Theoretical Deduction of Constitutive Equations with Variational Parameters during Superplastic Tension

2014 ◽  
Vol 941-944 ◽  
pp. 1509-1512
Author(s):  
Zhi Ping Guan ◽  
Xiao Fang Guan ◽  
Yu Quan Song
Keyword(s):  
Strain Rate ◽  
Test Data ◽  
Constitutive Equations ◽  
Constant Strain Rate ◽  
Rate Sensitivity ◽  
State Equation ◽  
Sensitivity Index ◽  
Tensile Tester ◽  
Strain Rate Sensitivity Index ◽  
Superplastic Tension

In this article, firstly, the strain hardening index and the strain rate sensitivity index were deducted from the general state equation and the mechanical meaning of the two indexes were correspondingly depicted, and then constitutive equations, where both/either of the two indexes appear as constants, were theoretically deducted from the same state equation. Secondly, constitutive equations where both/either of the two indexes present as variables were put forward by numerical simulation. Next, constitutive equations were built, where mechanical variables are replaced by test data obtained on an electronic universal tensile tester with the capacity to carry out a true constant strain rate path. Finally, based on the test data of Zn-5%Al during superplastic tension, it is proved that the theoretical results in this article are valid.

Inelastic Bending of Beams Under Time-Varying Moments—A State Variable Approach

1979 ◽  
Vol 101 (4) ◽  
pp. 305-310 ◽  
Author(s):  
K. J. Chang ◽  
R. Lance ◽  
S. Mukherjee
Keyword(s):  
Strain Rate ◽  
Strain Rate Sensitivity ◽  
Constitutive Equations ◽  
Inelastic Deformation ◽  
Rate Sensitivity ◽  
Time Varying ◽  
Deformation History ◽  
State Variable ◽  
Variable Approach ◽  
Bending Of Beams

The inelastic response of a beam to several time-varying moments is presented in this paper. The constitutive equations used to describe the beam material are due to Hart. This is one of several state variable theories of inelastic deformation that have been proposed recently. Hart’s equations have been previously shown to accurately predict the response of uniaxial specimens to time-varying loads. It is seen from this paper that Hart’s theory is able to qualitatively simulate various phenomena in creep and plasticity such as the effect of previous deformation history, stress redistribution, yielding, strain recovery, material hardening and strain rate sensitivity in this case of bending of a beam. The computational scheme used to integrate the equations is very efficient.

In-reactor uniaxial tensile testing of pure copper at a constant strain rate at 90 °C

2003 ◽  
Vol 320 (3) ◽  
pp. 299-304 ◽  
Author(s):  
B.N. Singh ◽  
S. Tähtinen ◽  
P. Moilanen ◽  
P. Jacquet ◽  
J. Dekeyser
Keyword(s):  
Strain Rate ◽  
Tensile Testing ◽  
Pure Copper ◽  
Constant Strain Rate ◽  
Uniaxial Tensile ◽  
Uniaxial Tensile Testing

Viscoplastic Constitutive Equations for Copper With Strain Rate History and Temperature Effects

1978 ◽  
Vol 100 (4) ◽  
pp. 388-394 ◽  
Author(s):  
S. R. Bodner ◽  
A. Merzer
Keyword(s):  
Strain Rate ◽  
Constitutive Equations ◽  
Internal State ◽  
Rate Sensitivity ◽  
Experimental Program ◽  
Internal State Variable ◽  
Plastic Working ◽  
State Variable ◽  
History Effects ◽  
Good Agreement

Elastic-viscoplastic constitutive equations based on a single internal state variable which is a function of plastic work are used to calculate the response of copper to a six decade change of strain rate over a range of temperatures. Calculations were performed for the conditions of an experimental program on copper by Senseny, Duffy, and Hawley, namely, temperatures ranging from 77°K to 523°K and strain rate jumps from 2 × 10−4sec−1 to 3 × 102sec−1 at three strain levels. The computed results are in good agreement with the experiments and show similar strain rate and strain rate history effects. Relations are obtained for the temperature dependence of certain parameters in the equations which indicate correspondence between plastic working and temperature and between strain rate sensitivity and temperature.

The effect of strain rate on the plastic flow characteristics of steel and aluminium sheet

1966 ◽  
Vol 1 (5) ◽  
pp. 439-446 ◽  
Author(s):  
A N Bramley ◽  
P B Mellor
Keyword(s):  
Strain Rate ◽  
Uniaxial Tension ◽  
Plastic Flow ◽  
Work Hardening ◽  
Sheet Steel ◽  
Flow Characteristics ◽  
Strain Rates ◽  
Plastic Strains ◽  
Aluminium Sheet

Work-hardening characteristics for sheet steel and aluminium have been obtained experimentally over a range of strain rates from 10−4 to 102/s. Use of the diaphragm test enables work-hardening characteristics to be obtained to much higher plastic strains than is possible in uniaxial tension. Results for killed steel show that the slope of the work-hardening characteristics decreases with increase in strain rate. Tentative extrapolation of the results suggests that if similar tests could be carried out at a strain rate of 104 then the work hardening characteristic would be that of an ideally plastic solid. In the case of aluminium the above phenomenon is not so marked and it is not possible to make even a tentative extrapolation to higher strain rates.

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