scholarly journals A Modified Fractional Maxwell Numerical Model for Constitutive Equation of Mn-Cu Damping Alloy

Materials ◽  
2020 ◽  
Vol 13 (9) ◽  
pp. 2020
Author(s):  
Baoquan Mao ◽  
Rui Zhu ◽  
Zhiqian Wang ◽  
Yuying Yang ◽  
Xiaoping Han ◽  
...  
Keyword(s):  
Constitutive Equation ◽  
Strain Rate ◽  
Constitutive Relation ◽  
Constant Strain Rate ◽  
Strain Curve ◽  
Maxwell Model ◽  
Nonlinear Viscoelastic ◽  
Fractional Maxwell Model ◽  
Hysteretic Characteristics ◽  
Nonlinear Elastic

To better describe its constitutive relation, we need a new constitutive equation for an important nonlinear elastic material, Mn-Cu damping alloy. In this work, we studied the nonlinear and hysteretic characteristics of the stress-strain curve of the M2052 alloy with the uniaxial cyclic tensile test with constant strain rate. The strain rate and amplitude correlations of M2052 resembled those of nonlinear viscoelastic material. Therefore, we created a new constitutive equation for the M2052 damping alloy by modifying the fractional Maxwell model, and we used the genetic algorithm to carry out numerical fitting with MATLAB. By comparing with the experimental data, we confirmed that the new constitutive equation could accurately depict the nonlinear constitutive relation and hysteretic property of the damping alloy. Taken together, this new constitutive equation for Mn-Cu damping alloy based on the fractional Maxwell model can serve as an effective tool for further studies of the constitutive relation of the Mn-Cu damping alloys.

Viscoplastic Constitutive Equation of High-Density Polyethylene

2007 ◽  
Vol 340-341 ◽  
pp. 1097-1102 ◽  
Author(s):  
Yukio Sanomura ◽  
Mamoru Mizuno
Keyword(s):  
Constitutive Equation ◽  
Strain Rate ◽  
High Density Polyethylene ◽  
Kinematic Hardening ◽  
Constant Strain Rate ◽  
Strain Curve ◽  
High Density ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Creep Theory

A viscoplastic constitutive equation based on the kinematic hardening creep theory of Malinin-Khadjinsky and the nonlinear kinematic hardening rule of Armstrong-Frederick is formulated to describe the inelastic behavior of high-density polyethylene under various loading. The gentle progress of back stress by the introduction of loading surface in the viscoplastic strain space and smaller material constant under unloading can be expressed. Material constants are identified by various stress-strain curves under compression at constant strain rate and creep curves under compression at constant stress. The viscoplastic model can describe stress-strain curve under compression with change in strain rate and shear stress-strain curve including unloading. The model can qualitatively describe stress-strain curves under compression with changed strain rate including unloading, but it is quantitatively insufficient.

Some Implications of a Nonlinear Viscoelastic Constitutive Theory Regarding Interrelationships Between Creep and Strength Behavior of Ice at Failure

1989 ◽  
Vol 111 (2) ◽  
pp. 144-148 ◽  
Author(s):  
B. D. Harper
Keyword(s):  
Strain Rate ◽  
Constant Strain Rate ◽  
Nonlinear Viscoelastic ◽  
Uniaxial Creep ◽  
Strength Behavior ◽  
Minimum Strain Rate ◽  
Strength Constant ◽  
Viscoelastic Constitutive Model ◽  
Stress And Strain Rate ◽  
Special Case

This study explores several possibilities for a correspondence in the behavior of ice at failure during uniaxial creep (constant stress) and strength (constant strain rate) experiments. The usual notion of failure in ice is employed (i.e., the occurrence of a minimum strain rate during a creep test and a peak or maximum stress during a strength test), and the behavior at failure is discussed in terms of a recently proposed nonlinear viscoelastic constitutive model for ice. It is demonstrated that no correspondence between creep and strength data can be expected in general; however, several approximate interrelationships do occur for the experimentally motivated special case of a constant (independent of stress and strain rate) failure strain.

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.

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.

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.

Refined Modeling of Projectile Impact Onto Submerged Structure

2008 ◽  
Author(s):  
Justin Onisoru ◽  
Ovidiu Coman ◽  
Paul Wilson ◽  
George Thomas
Keyword(s):  
Strain Rate ◽  
Structural Integrity ◽  
Initial Conditions ◽  
Safety Issue ◽  
Constant Strain Rate ◽  
Strain Curve ◽  
Material Behavior ◽  
Spent Fuel ◽  
The Impact

Structural integrity of spent fuel racks is a critical safety issue in nuclear power stations. The standard approach of evaluating the effects of an impact projectile on a submerged structure, which constitute the start point of the current study, involves three main steps: determination of the conditions just prior to the impact (that are considered as initial conditions for the analysis), setting the mechanism of transferring energy from the projectile to the target structure, and determining how that energy is absorbed by the impacted structure. Usually, the dynamics of the projectile are ideally considered, the influence of the fluid presence is restricted to the determination of the impact velocity and strain rate dependency is limited to choosing a true stress vs. strain curve corresponding to some constant strain rate. Starting from the standard engineering approach, the authors have refined the model considering more realistic dynamics of the projectile, extending the influence of the fluid to the entire analysis and using a more accurate strain rate dependant material behavior. Explicit Finite Element analyses are used in order to incorporate the desired effects.

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.

The influence of strain rate and pulp properties on the stress-strain curve and relaxation rate of wet paper

TAPPI Journal ◽  
2015 ◽  
Vol 14 (8) ◽  
pp. 515-524 ◽  
Author(s):  
JARMO KOUKO ◽  
ELIAS RETULAINEN
Keyword(s):  
Strain Rate ◽  
Relaxation Rate ◽  
Kraft Pulp ◽  
Constant Strain Rate ◽  
Strain Curve ◽  
Paper Machine ◽  
Initial Tension ◽  
Wet Strength ◽  
Tensile Stiffness ◽  
Solids Content

Sufficient tension of the wet web is crucial for paper machine runnability. As profitability pressures have been increasing, the potential to improve runnability is of interest. The runnability of wet paper is especially important for paper machines running at high speeds, making paper at lower grammage, and using large amounts of filler or recovered paper. The typical location of web breaks depends on the paper grade and paper machine. A break typically takes place when the paper is wet and a fast draw is applied to the web. Because information on wet paper is scarce, especially information on the effect of strain rate on the tensile properties, we investigated the effects of strain rate on the tension-strain curve and relaxation of wet paper and how they depend on pulp type, refining, solids content, and fines. Higher strain rate leads to higher tensile strength, tensile stiffness, and relaxation rate. The initial wet strength and stiffness of the studied pulps, bleached softwood kraft pulp and bleached hardwood kraft pulp, were increased by increasing the solids content, fines, wet pressing, and refining. At a constant strain rate and constant strain, the tension at a certain moment depended strongly on the initial tension and thus on the tensile stiffness.

A Uniaxial Nonlinear Viscoelastic Constitutive Relation for Ice

1986 ◽  
Vol 108 (2) ◽  
pp. 156-160 ◽  
Author(s):  
B. D. Harper
Keyword(s):  
Strain Rate ◽  
Constant Strain Rate ◽  
Constitutive Theory ◽  
Uniaxial Deformation ◽  
Explicit Dependence ◽  
Deformation And Failure ◽  
Nonlinear Viscoelastic ◽  
Defect Growth ◽  
Special Cases ◽  
Strength Constant

The present paper concerns the description of uniaxial deformation and failure of ice in uniaxial compression in terms of a nonlinear viscoelastic constitutive theory. The constitutive model incorporates explicit dependence upon micro-structural defect growth and assumes the form of a so-called modified superposition integral contaiing a linear kernel which depends only upon time. This last feature will greatly simplify the task of experimentally characterizing the various material properties which appear in the theory. The existence of correspondence principles for the model will also facilitate the solution of practical boundary value problems. Predictions based upon this model will be shown to agree qualitatively with experimental results for creep (constant stress) and strength (constant strain-rate) tests on ice. In addition, specific empirically deduced relationships between stress, strain, strain-rate and time at certain critical points in these standard tests will be shown to result directly from the constitutive theory as special cases.

Study on Hot Deformation Behavior of a New Titanium Alloy

2014 ◽  
Vol 644-650 ◽  
pp. 4872-4875
Author(s):  
Qun Hui Zheng ◽  
Ke Lu Wang ◽  
Shi Qiang Lu
Keyword(s):  
Titanium Alloy ◽  
Strain Rate ◽  
Hot Deformation ◽  
Constant Strain Rate ◽  
Strain Curve ◽  
Constitutive Relationship ◽  
Alloy Sample ◽  
Two Phase ◽  
Data Points ◽  
Gleeble 3500

Two-phase titanium alloy sample which initial microstructure is equiaxed have been tested by the Gleeble-3500 thermo-analogue machine with the isothermal and constant strain rate, the constitutive relationship of the titanium alloy was constructed by analyzing true stress-strain curve under different hot deformation conditions and considering the effect of the strain rate, deformation temperature and strain on flow stress synthetically. Error analysis shows that the constructed constitutive relationship has good accuracy, in the range of 900 ~ 1150 °C the error is less than 10% of the data points are accounted for 97.4% of all data points, can conform the requirements of plastic processing.

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