Correlation of Large Longitudinal Deformations with Different Strain Histories

1967 ◽  
Vol 40 (2) ◽  
pp. 506-516 ◽  
Author(s):  
L. J. Zapas ◽  
T. Craft
Keyword(s):  
Stress Relaxation ◽  
Single Step ◽  
Strain History ◽  
Simple Extension ◽  
Stress Strain ◽  
Fluid Equation ◽  
Elastic Fluid ◽  
Strain Behavior ◽  
Elastomeric Materials ◽  
Single Integral

Abstract In 1963 Bernstein, Kearsley, and Zapas1 presented a theory of an elastic fluid which gave the correct stress-relaxation response for a large variety of elastomeric materials, including vulcanized rubbers. A principle attractiveness of this theory is its relative simplicity; with a single integral in time, it describes the stress-strain behavior for all types of deformation histories. In the case of simple extension, it predicts the behavior in any uniaxial strain history from the results of single step stress-relaxation experiments which cover the same range of extension and time. We designed a series of experiments to check the validity of this theory and found, as is shown in this paper, excellent agreement with experiment in all cases. We are aware that experiments cannot prove a theory. From our results, however, we feel strongly that a single integral expression with a nonlinear integrand such as the BKZ elastic fluid equation is sufficient to describe the stress-strain behavior of elastomeric materials.

scholarly journals A Simplified Method for Elastic-Plastic-Creep Structural Analysis

1985 ◽  
Vol 107 (1) ◽  
pp. 231-237 ◽  
Author(s):  
A. Kaufman
Keyword(s):  
Finite Element ◽  
Stress Relaxation ◽  
Kinematic Hardening ◽  
Nonlinear Finite Element ◽  
Strain History ◽  
Stress Strain ◽  
Element Analysis ◽  
Inelastic Analysis ◽  
Simplified Method ◽  
Time Required

A simplified inelastic analysis computer program (ANSYMP) was developed for predicting the stress-strain history at the critical location of a thermomechanically cycled structure from an elastic solution. The program uses an iterative and incremental procedure to estimate the plastic strains from the material stress-strain properties and a plasticity hardening model. Creep effects can be calculated on the basis of stress relaxation at constant strain, creep at constant stress or a combination of stress relaxation and creep accumulation. The simplified method was exercised on a number of problems involving uniaxial and multiaxial loading, isothermal and nonisothermal conditions, dwell times at various points in the cycles, different materials, and kinematic hardening. Good agreement was found between these analytical results and nonlinear finite element solutions for these problems. The simplified analysis program used less than 1 percent of the CPU time required for a nonlinear finite element analysis.

Tensile Stress—Strain and Stress Relaxation Behavior of Raw Elastomers Using a High Speed Tester

1974 ◽  
Vol 47 (2) ◽  
pp. 307-317 ◽  
Author(s):  
H. H. Bowerman ◽  
E. A. Collins ◽  
N. Nakajima
Keyword(s):  
Stress Relaxation ◽  
High Speed ◽  
Strain Rates ◽  
Time Behavior ◽  
Stress Strain ◽  
Strain Behavior ◽  
Relaxation Measurements ◽  
Ultimate Properties ◽  
Short Time ◽  
Acrylonitrile Copolymers

Abstract A high-speed, tensile-testing device was used to determine the stress—strain behavior of uncompounded butadiene—acrylonitrile copolymers over a range of temperatures and deformation rates. The strain rates were varied from 267 to 26,700 per cent/sec and the temperature was varied from 25 to 97° C. The high-speed tester was also used for stress—relaxation measurements by applying the strain nearly instantly in conformity with theoretical requirements in order to obtain the short time behavior. The WLF equation was obtained from the stress—relaxation data and then used to reduce the ultimate properties to one temperature over four decades of the strain rates. The ultimate properties could be represented by a failure envelope similar to those obtained for vulcanizates.

Departures of the Elastic Behavior of Rubbers in Simple Extension from the Kinetic Theory

1955 ◽  
Vol 28 (1) ◽  
pp. 24-35 ◽  
Author(s):  
S. M. Gumbrell ◽  
L. Mullins ◽  
R. S. Rivlin
Keyword(s):  
Kinetic Theory ◽  
Volume Fraction ◽  
Single Parameter ◽  
Elastic Behavior ◽  
Simple Extension ◽  
Stress Strain ◽  
Equilibrium Stress ◽  
Strain Behavior

Abstract It is shown that the equilibrium stress-strain behavior of highly swollen rubber vulcanizates in simple extension agrees with the predictions of the kinetic theory. The departures from these predictions which are found in dry or lightly swollen rubbers have been investigated, and it is shown that they can be described in terms of a single parameter C2. The magnitude of this parameter is large in dry rubbers, and decreases to zero at high degrees of swelling ; this decrease occurs linearly with decrease in the volume fraction of rubber. The value of C2 is found to be independent of the nature of the rubber polymer, of the degree of vulcanization, and of the nature of the swelling liquid. The possible significance of this parameter is discussed in light of these observations.

Theoretical Model for the Elastic Behavior of Filler-Reinforced Vulcanized Rubbers

1957 ◽  
Vol 30 (2) ◽  
pp. 555-571 ◽  
Author(s):  
L. Mullins ◽  
N. R. Tobin
Keyword(s):  
Elastic Properties ◽  
Tensile Tests ◽  
Elastic Behavior ◽  
Simple Extension ◽  
Stress Strain ◽  
Empirical Relationships ◽  
Equilibrium Stress ◽  
Strain Behavior ◽  
Strain Data ◽  
Limited Applicability

Abstract One of the more important advances in rubber science during the past twenty years has been the development of quantitative theories describing the elastic properties of pure-gum vulcanized rubbers. As a result it is now possible to account for their equilibrium stress-strain behavior with considerable success. There is, however, no adequate theory to describe the elastic properties of filler-reinforced rubber vulcanizates and the work described herein is an attempt to provide a basis for such a theory. When a reinforcing filler is added to rubber it produces a large increase in the stiffness of the vulcanizate. This increase is reduced and may be substantially destroyed by deformation. Numerous attempts have been made to describe the increase of stiffness resulting from the introduction of fillers and relationships describing the dependence of the modulus on the concentration and particle shape of the filler have been developed. However, these do not take into account the softening which results from previous deformation and thus have limited applicability. Recently Blanchard and Parkinson have attempted to develop empirical relationships to describe the elastic properties in simple extension of reinforced rubber vulcanizates after they have been previously deformed. They started with the appropriate stress-strain relationships from the classical kinetic theory and introduced two curve-fitting parameters to describe stress-strain data obtained in conventional tensile tests on a Goodbrand machine. In this way they were able to fit the course of the stress-strain data obtained after previous extension at extensions less than those previously applied and to describe the dependence of the parameters on previous deformation. Unfortunately, the significance of the parameters is obscure.

Applicability of Neuber’s Rule to the Analysis of Stress and Strain Concentration Under Creep Conditions

1998 ◽  
Vol 120 (3) ◽  
pp. 224-229 ◽  
Author(s):  
G. Ha¨rkega˚rd ◽  
S. So̸rbo̸
Keyword(s):  
Stress Relaxation ◽  
Elastic Response ◽  
Strain History ◽  
Stress And Strain ◽  
Stress Strain ◽  
Strain Concentration ◽  
Long Time ◽  
Concentration Factors ◽  
Neuber's Rule ◽  
Good Agreement

A differential form of Neuber’s rule, originally proposed by M. Chaudonneret, has been formulated for a generic viscoplastic notch problem, making extensive use of suitably normalised stress, strain and time. It has been shown that the stress-strain history at the root of a notch in a viscoplastic body can be determined directly from the elastic response, provided far-field viscoplastic strains can be neglected. Neuber’s rule has also been applied to the more general cases of stress and strain concentration at notches under (i) nominal creep conditions (constant nominal stress) and (ii) stress relaxation (constant nominal strain). Predictions are in good agreement with results from finite element analyses. Stress and strain concentration factors have been observed to approach stationary values after long-time loading. The stationary stress concentration factor under stress relaxation falls below that under nominal creep conditions.

scholarly journals Slipping in Stress Relaxation in Shear Estimated by Damping and Stress- Strain Behavior of Polyisobutylene

2017 ◽  
Vol 66 (1) ◽  
pp. 13-17
Author(s):  
Katsuyuki YOSHIKAWA ◽  
Fei TENG ◽  
Jun-ichi HORINAKA ◽  
Toshikazu TAKIGAWA
Keyword(s):  
Stress Relaxation ◽  
Stress Strain ◽  
Strain Behavior

The Effect of Overshooting the Target Strain on Estimating Viscoelastic Properties From Stress Relaxation Experiments

2004 ◽  
Vol 126 (6) ◽  
pp. 844-848 ◽  
Author(s):  
Jonathan A. Gimbel ◽  
Joseph J. Sarver ◽  
Louis J. Soslowsky
Keyword(s):  
Stress Relaxation ◽  
Single Step ◽  
Strain History ◽  
Estimation Of Parameters ◽  
Ramp Rate ◽  
Relaxation Experiment ◽  
Curve Fit ◽  
Target Strain ◽  
Linear Viscoelastic ◽  
Relaxation Experiments

Background: Tendon’s mechanical behaviors have frequently been quantified using the quasi-linear viscoelastic (QLV) model. The QLV parameters are typically estimated by fitting the model to a single-step stress relaxation experiment. Unfortunately, overshoot of the target strain occurs to some degree in most experiments. This has never been formally investigated even though failing to measure, minimize, or compensate for overshoot may cause large errors in the estimation of parameters. Therefore, the objective of this study was to investigate the effect of overshoot on the estimation of QLV parameters. Method of approach: A simulated experiment was first performed to quantify the effect of different amounts of overshoot on the estimated QLV parameters. Experimental data from tendon was then used to determine if the errors associated with overshoot could be reduced when a direct fit is used (i.e., the actual strain history was used in the curve fit). Results: We found that both the elastic and viscous QLV parameters were incorrectly estimated if overshoot was not properly accounted for in the fit. Furthermore, the errors associated with overshoot were partially reduced when overshoot was accounted for using a direct fit. Conclusions: A slow ramp rate is recommended to limit the amount of overshoot and a direct fit is recommended to limit the errors associated with overshoot, although other approaches such as adjusting the control system to limit overshoot could also be utilized.

Contribution to the Mathematical Description of Stress-Strain Behavior of Elastomers

1980 ◽  
Vol 53 (4) ◽  
pp. 836-841 ◽  
Author(s):  
K. Tobisch
Keyword(s):  
Energy Density ◽  
Density Function ◽  
Mathematical Description ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Pure Shear ◽  
Simple Extension ◽  
Stress Strain ◽  
Strain Behavior ◽  
Strain Energy Density Function

Abstract Based on the hypothesis of Valanis and Landel that the strain energy density function W(λx,λy,λz)could be represented as the sum of three identical functions ω(λi) of the principal extension ratios λi(i=x,y,z), an expression for ω(λi) is suggested which is distinguished by its relative simplicity. The stress-strain relations developed from this expression are tested successfully by applying them to experimental results of other authors. The types of strain which were examined were simple extension, biaxial extension and pure shear; the elongations were to about 700%.

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