An Experimental Study of a Nonlinear Viscoelastic Solid in Uniaxial Tension

1969 ◽  
Vol 36 (3) ◽  
pp. 558-564 ◽  
Author(s):  
W. G. Gottenberg ◽  
J. O. Bird ◽  
G. L. Agrawal
Keyword(s):  
Uniaxial Tension ◽  
Constitutive Relation ◽  
Simple Procedure ◽  
Constant Strain Rate ◽  
Integral Form ◽  
Multiple Integral ◽  
Kernel Functions ◽  
Load Response ◽  
Material Functions ◽  
Nonlinear Viscoelastic

The multiple integral form of the constitutive relation for nonlinear viscoelasticity is correlated with experimental results for the case of uniaxial tension of a polymeric material. Special forms of the kernel functions are assumed in which the arguments of these functions are taken in additive form. This permits the development of a simple procedure for determining the material functions from stress-relaxation tests. The resulting constitutive relation, for a particular material, is used to predict the load response to single and consecutive constant strain-rate programs and the results are compared with experimentally obtained data.

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.

scholarly journals Experimental Determination of Some Kernel Functions in the Multiple Integral Method for Nonlinear Creep of Polyvinyl Chloride

1971 ◽  
Vol 38 (1) ◽  
pp. 30-38 ◽  
Author(s):  
K. Onaran ◽  
W. N. Findley
Keyword(s):  
Polyvinyl Chloride ◽  
Viscoelastic Behavior ◽  
Multiple Integral ◽  
Kernel Functions ◽  
Product Form ◽  
Superposition Method ◽  
Nonlinear Creep ◽  
Nonlinear Viscoelastic ◽  
Nonlinear Viscoelastic Behavior ◽  
Accuracy Of Prediction

Kernel functions for mixed-time parameters in the multiple integral representation of the nonlinear viscoelastic behavior of polyvinyl chloride were determined from both two-step tension and two-step torsion creep experiments. First and second-order terms were used for tension and first and third-order terms were used for torsion to describe these kernel functions. Stepdown tests were needed for good accuracy of representation. Accuracy of prediction was good for stepdown but not stepup tests. The product form assumption for these kernel functions and the modified superposition method were also investigated. The latter gave the best overall predictability of the three methods, although the product form was nearly as satisfactory.

A Linear Compressibility Assumption for the Multiple Integral Representation of Nonlinear Creep of Polyurethane

1970 ◽  
Vol 37 (2) ◽  
pp. 441-448 ◽  
Author(s):  
K. G. Nolte ◽  
W. N. Findley
Keyword(s):  
Integral Representation ◽  
Multiple Integral ◽  
Kernel Functions ◽  
Nonlinear Creep ◽  
Volume Changes ◽  
Creep Tests ◽  
Third Order ◽  
Nonlinear Viscoelastic ◽  
Different Order ◽  
Order Kernel

The assumption that volume changes associated with creep of a nonlinear viscoelastic material are only linearly dependent on the stress history is incorporated into a third-order multiple integral representation. This assumption reduces the number of independent kernel functions in the representation from 12 to 7. The traces of these independent kernels may be determined from two tension, two torsion, and one combined tension and torsion creep tests. Experiments on polyurethane are well represented by this method. The time-dependence of the kernel functions is expressed by time raised to a power with the power differing for different-order kernel functions.

Constitutive modeling of strain-dependent bond breaking and healing kinetics of chemical polyampholyte (PA) gel

Soft Matter ◽  
2021 ◽  
Vol 17 (15) ◽  
pp. 4161-4169
Author(s):  
Sairam Pamulaparthi Venkata ◽  
Kunpeng Cui ◽  
Jingyi Guo ◽  
Alan T. Zehnder ◽  
Jian Ping Gong ◽  
...  
Keyword(s):  
Constitutive Model ◽  
Uniaxial Tension ◽  
Constitutive Modeling ◽  
Finite Strain ◽  
Bond Breaking ◽  
Nonlinear Viscoelastic ◽  
Viscoelastic Constitutive Model ◽  
Kinetics Of ◽  
Strain Dependent

A finite strain nonlinear viscoelastic constitutive model is used to study the uniaxial tension behaviour of a chemical polyampholyte (PA) gel.

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.

Modeling of Nonlinear Viscoelastic Creep of Polycarbonate

e-Polymers ◽  
2007 ◽  
Vol 7 (1) ◽  
Author(s):  
Wenbo Luo ◽  
Said Jazouli ◽  
Toan Vu-Khanh
Keyword(s):  
Creep Behavior ◽  
Room Temperature ◽  
Multiple Integral ◽  
Model Fit ◽  
Viscoelastic Creep ◽  
Commercial Grade ◽  
Nonlinear Viscoelastic ◽  
Schapery Model ◽  
Special Case ◽  
Better Than

AbstractThe creep behavior of a commercial grade polycarbonate was investigated in this study. 10 different constant stresses ranging from 8 MPa to 50 MPa were applied to the specimen, and the resultant creep strains were measured at room temperature. It was found that the creep could be modeled linearly below 15 MPa, and nonlinearly above 15 MPa. Different nonlinear viscoelastic models have been briefly reviewed and used to fit the test data. It is shown that the Findley model is a special case of the Schapery model, and both the Findley model and the simplified multiple integral representation are suitable for properly describing the creep behavior of the polycarbonate investigated in this paper; however, the Findley model fit the data better than the simplified multiple integral with three terms.

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.

Yield Surface and Complex Loading Path Simulation of a Duplex Stainless Steel Using a Bi-Phase Polycrystalline Model

2007 ◽  
Vol 567-568 ◽  
pp. 141-144 ◽  
Author(s):  
Pierre Evrard ◽  
Veronique Aubin ◽  
Suzanne Degallaix ◽  
Djimedo Kondo
Keyword(s):  
Stainless Steel ◽  
Uniaxial Tension ◽  
Compression Test ◽  
Plastic Anisotropy ◽  
Constant Strain Rate ◽  
Loading Path ◽  
Model Parameters ◽  
Proportional Loading ◽  
Loading Paths ◽  
Polycrystalline Model

In order to model the elasto-viscoplastic behaviour of an austenitic-ferritic stainless steel, the model initially developed by Cailletaud-Pilvin [1] [2] and used for modeling single-phase polycrystalline steel is extended in order to take into account the bi-phased character of a duplex steel. Two concentration laws and two local constitutive laws, based on the crystallographic slips and the dislocation densities, are thus simultaneously considered. The model parameters are identified by an inverse method. Simple tests among which tension test at constant strain rate and at different strain rates and uniaxial tension-compression test are used during the identification step. The predictive capabilities of the polycrystalline model are tested for non-proportional loading paths. It is shown that the model reproduces the over-hardening experimentally observed for this kind of loading paths. Then, yield surfaces are simulated during a uniaxial tension-compression test: it is shown that the distortion (i.e. plastic anisotropy induced by loading path) is correctly described.

Sign in / Sign up

Export Citation Format

Share Document