On the Relation between Stress Relaxation and Constant Strain Rate Tensile Behavior for Linear Viscoelastic Materials; An Engineering Approach

2012 ◽  
Vol 729 ◽  
pp. 314-319 ◽  
Author(s):  
Gábor Bódai ◽  
Tibor Goda
Keyword(s):  
Stress Relaxation ◽  
Master Curve ◽  
Superposition Principle ◽  
Constant Strain Rate ◽  
Relaxation Modulus ◽  
Tensile Tests ◽  
Time Frequency ◽  
Construction Methods ◽  
Linear Viscoelastic ◽  
Time Temperature Superposition Principle

The present paper, as a first step summarizes briefly the master curve construction methods applying the stress relaxation and DMTA based approach. Then, authors make recommendation to increase the covered time (frequency) domain of relaxation modulus master curve coming from standard tensile tests-performed at wide temperature range-by utilizing the time-temperature superposition principle. The proposed approach is used for natural rubber, whose tensile tests, for the sake of simplicity, are replaced by calculated engineering stress-strain curves. All in all, the proposed method gives fast and reliable way for engineers to identify the parameters of spring-dashpot models.

The Stress-Relaxation Behavior of Rice as a Function of Time, Moisture and Temperature

2017 ◽  
Vol 13 (2) ◽  
Author(s):  
Pan Wang ◽  
Li-jun Wang ◽  
Dong Li ◽  
Zhi-gang Huang ◽  
Benu Adhikari ◽  
...  
Keyword(s):  
Stress Relaxation ◽  
Moisture Content ◽  
Master Curve ◽  
Superposition Principle ◽  
Relaxation Modulus ◽  
Maxwell Model ◽  
Relaxation Behavior ◽  
Stress Relaxation Behavior ◽  
Linear Viscoelastic ◽  
Single Rice

Abstract: Stress-relaxation behavior of single rice kernel was studied using a dynamic mechanical analyzer (DMA) in compression mode. The relaxation modulus was measured in a moisture content range of 12–30 % on dry basis (d.b.) and a temperature range of 25–80°C. A constant stain value of 1 % (within the linear viscoelastic range) was selected during the stress-relaxation tests. The relaxation modulus was found to decrease as the temperature and moisture increased. A master curve of relaxation modulus as a function of temperature and moisture content was generated using the time–moisture–temperature superposition principle. Results showed that the generalized Maxwell model satisfactorily fitted the experimental data of the stress-relaxation behavior and the master curve of relaxation modulus (R2> 0.997). By shifting the temperature curves horizontally, the activation energy of the stress relaxation was obtained which significantly decreased with increase in the moisture content.

Application of TTSP to wood-development of a vertical shift factor

Holzforschung ◽  
2017 ◽  
Vol 71 (1) ◽  
pp. 51-55 ◽  
Author(s):  
Fuli Wang ◽  
Tianlai Huang ◽  
Zhuoping Shao
Keyword(s):  
Stress Relaxation ◽  
Master Curve ◽  
Goodness Of Fit ◽  
Superposition Principle ◽  
Relaxation Curve ◽  
Shift Factor ◽  
Vertical Shift ◽  
Wood Development ◽  
Time Temperature Superposition Principle

Abstract The applicability of the time-temperature superposition principle (TTSP) to wood has been investigated aiming at the prediction of long-term mechanical properties of wood by both horizontally and vertically shifting of short-term stress relaxation data obtained by experiments. The expression of TTSP considering the vertical shift factor (bT) for wood is proposed the first time. The results showed that: (1) TTSP applied to poplar and the master curve that was obtained from 1 h of tests at 283.2, 303.2, 320.2, 343.2, and 363.2 K in a relative humidity (RH) of 60% could predict the stress relaxation behavior for approximately 42 years at 283.2 K and 60% RH. (2) There was a linear correlation between lgaT and T-1, lg aT=6590.40 T-1-23.64 (R2=0.994), which followed the Arrhenius equation well, while the apparent activation energy was 34.6 kcal mole-1. (3) The bT had a linear relationship with temperature, and the relation was lgbT=0.0013T-0.37 (R2=0.999). (4) The long-term relaxation curve of the long-term verification test had high goodness of fit with the master curve. The results can be interpreted that the TTSP expression considering the bT proposed in this paper is rational.

Estimation of Master Curves of Relaxation Modulus and Tensile Properties for Solid Propellant

2013 ◽  
Vol 871 ◽  
pp. 247-252 ◽  
Author(s):  
Boh Wi Seo ◽  
Jae Hoon Kim
Keyword(s):  
Stress Relaxation ◽  
Tensile Properties ◽  
Solid Propellant ◽  
Master Curve ◽  
Classical Method ◽  
Viscoelastic Behavior ◽  
Temperature Shift ◽  
Relaxation Modulus ◽  
Tensile Tests ◽  
Shift Factor

The stress relaxation modulus E(t) is one of the most important properties of viscoelastic materials such as solid propellant, and it is used to define the viscoelastic behavior based on the influence of time and temperature. In this paper, stress relaxation tests are conducted under constant strain 2% for 600 seconds in the range of temperature 60°C to-60°C and tensile tests are performed for solid propellants under constant cross head rate 5 mm/min in the same temperatures as stress relaxation tests. Based on the results, time-temperature shift factors are obtainedby shifting the relaxation modulus curves horizontally and the master curve of relaxation modulus is generated. The master curve of relaxation modulus according to classical method and Williams-Landel-Ferry (WLF) method are discussed. Also, the master curve of tensile properties are drawn using predetermined shift factor and the results are discussed.

Integration of Atomistic Simulation with Experiment Using Time−Temperature Superposition for a Cross-Linked Epoxy Network

2019 ◽  
Author(s):  
Ketan Khare ◽  
Frederick R. Phelan Jr.
Keyword(s):  
Master Curve ◽  
Glassy State ◽  
Superposition Principle ◽  
Quantitative Comparison ◽  
Time Shift ◽  
Data Sets ◽  
Epoxy Network ◽  
Temperature Superposition ◽  
Time Temperature Superposition ◽  
Time Temperature Superposition Principle

<a></a><a>Quantitative comparison of atomistic simulations with experiment for glass-forming materials is made difficult by the vast mismatch between computationally and experimentally accessible timescales. Recently, we presented results for an epoxy network showing that the computation of specific volume vs. temperature as a function of cooling rate in conjunction with the time–temperature superposition principle (TTSP) enables direct quantitative comparison of simulation with experiment. Here, we follow-up and present results for the translational dynamics of the same material over a temperature range from the rubbery to the glassy state. Using TTSP, we obtain results for translational dynamics out to 10<sup>9</sup> s in TTSP reduced time – a macroscopic timescale. Further, we show that the mean squared displacement (MSD) trends of the network atoms can be collapsed onto a master curve at a reference temperature. The computational master curve is compared with the experimental master curve of the creep compliance for the same network using literature data. We find that the temporal features of the two data sets can be quantitatively compared providing an integrated view relating molecular level dynamics to the macroscopic thermophysical measurement. The time-shift factors needed for the superposition also show excellent agreement with experiment further establishing the veracity of the approach</a>.

STRESS RELAXATION OF MAGNETORHEOLOGICAL FLUIDS

2002 ◽  
Vol 16 (17n18) ◽  
pp. 2655-2661
Author(s):  
W. H. LI ◽  
G. CHEN ◽  
S. H. YEO ◽  
H. DU
Keyword(s):  
Stress Relaxation ◽  
Viscoelastic Model ◽  
Relaxation Modulus ◽  
Damping Function ◽  
Mr Fluids ◽  
Large Step ◽  
Linear Viscoelastic ◽  
Predicted Values ◽  
Two Parameters ◽  
Step Strain

In this paper, the experimental and modeling study and analysis of the stress relaxation characteristics of magnetorheological (MR) fluids under step shear are presented. The experiments are carried out using a rheometer with parallel-plate geometry. The applied strain varies from 0.01% to 100%, covering both the pre-yield and post-yield regimes. The effects of step strain, field strength, and temperature on the stress modulus are addressed. For small step strain ranges, the stress relaxation modulus G(t,γ) is independent of step strain, where MR fluids behave as linear viscoelastic solids. For large step strain ranges, the stress relaxation modulus decreases gradually with increasing step strain. Morever, the stress relaxation modulus G(t,γ) was found to obey time-strain factorability. That is, G(t,γ) can be represented as the product of a linear stress relaxation G(t) and a strain-dependent damping function h(γ). The linear stress relaxation modulus is represented as a three-parameter solid viscoelastic model, and the damping function h(γ) has a sigmoidal form with two parameters. The comparison between the experimental results and the model-predicted values indicates that this model can accurately describe the relaxation behavior of MR fluids under step strains.

Effect of Fiber Orientation and Strain Rate on the Nonlinear Uniaxial Tensile Material Properties of Tendon

2003 ◽  
Vol 125 (5) ◽  
pp. 726-731 ◽  
Author(s):  
Heather Anne Lynch ◽  
Wade Johannessen ◽  
Jeffrey P. Wu ◽  
Andrew Jawa ◽  
Dawn M. Elliott
Keyword(s):  
Stress Relaxation ◽  
Strain Rate ◽  
Material Properties ◽  
Poisson’S Ratio ◽  
Constant Strain Rate ◽  
Tensile Tests ◽  
Poisson's Ratio ◽  
Fiber Direction ◽  
Linear Region ◽  
Rate Dependent

Tendons are exposed to complex loading scenarios that can only be quantified by mathematical models, requiring a full knowledge of tendon mechanical properties. This study measured the anisotropic, nonlinear, elastic material properties of tendon. Previous studies have primarily used constant strain-rate tensile tests to determine elastic modulus in the fiber direction. Data for Poisson’s ratio aligned with the fiber direction and all material properties transverse to the fiber direction are sparse. Additionally, it is not known whether quasi-static constant strain-rate tests represent equilibrium elastic tissue behavior. Incremental stress-relaxation and constant strain-rate tensile tests were performed on sheep flexor tendon samples aligned with the tendon fiber direction or transverse to the fiber direction to determine the anisotropic properties of toe-region modulus E0, linear-region modulus (E), and Poisson’s ratio (ν). Among the modulus values calculated, only fiber-aligned linear-region modulus E1 was found to be strain-rate dependent. The E1 calculated from the constant strain-rate tests were significantly greater than the value calculated from incremental stress-relaxation testing. Fiber-aligned toe-region modulus E10=10.5±4.7 MPa and linear-region modulus E1=34.0±15.5 MPa were consistently 2 orders of magnitude greater than transverse moduli (E20=0.055±0.044 MPa,E2=0.157±0.154 MPa). Poisson’s ratio values were not found to be rate-dependent in either the fiber-aligned (ν12=2.98±2.59, n=24) or transverse (ν21=0.488±0.653, n=22) directions, and average Poisson’s ratio values in the fiber-aligned direction were six times greater than in the transverse direction. The lack of strain-rate dependence of transverse properties demonstrates that slow constant strain-rate tests represent elastic properties in the transverse direction. However, the strain-rate dependence demonstrated by the fiber-aligned linear-region modulus suggests that incremental stress-relaxation tests are necessary to determine the equilibrium elastic properties of tendon, and may be more appropriate for determining the properties to be used in elastic mathematical models.

Prediction of fiber-directional flexural strength of carbon fiber-reinforced polypropylene based on time–temperature superposition principle

2017 ◽  
Vol 52 (6) ◽  
pp. 793-805 ◽  
Author(s):  
Tsuyoshi Matsuo ◽  
Masayuki Nakada ◽  
Kazuro Kageyama
Keyword(s):  
Carbon Fiber ◽  
Flexural Strength ◽  
Master Curve ◽  
Superposition Principle ◽  
Bending Test ◽  
Thermoplastic Composites ◽  
Fiber Reinforced ◽  
Temperature Superposition ◽  
Time Temperature Superposition ◽  
Time Temperature Superposition Principle

This study verified that the time–temperature superposition principle for fiber-directional flexural strength can be applied to thermoplastic composites undergoing instantaneous fast phenomena such as impact failure and long-term phenomena such as creep failure, by constructing the time- and temperature-dependent master curve of relaxation modulus of thermoplastic resin. The master curve could be transformed to another master curve that predicts fiber-directional flexural strength of carbon fiber-reinforced thermoplastic composites based on the micro-buckling failure theory expressed mainly by the resin’s elastic modulus. The experimental results obtained from high-speed bending test, static bending test at various temperatures, and creep bending test demonstrated that kink band failure occurred on the compressive surface of the specimen at every test condition. This validation and verification related to thermoplastic composites made it possible to predict static and dynamic flexural strengths at arbitrary temperature and creep flexural strength.

Viscoelastic Characterization of an Epoxy-Based Molding Compound

1995 ◽  
Vol 390 ◽  
Author(s):  
V. H. Kenner ◽  
M. R. Julian ◽  
C. H. Popelar ◽  
M. K. Chengalva
Keyword(s):  
Stress Relaxation ◽  
Strain Rate ◽  
Constant Strain Rate ◽  
Viscoelastic Behavior ◽  
Tensile Tests ◽  
Prony Series ◽  
Master Curves ◽  
Molding Compound ◽  
Relaxation Curves

ABSTRACTThis paper describes the viscoelastic characterization of a highly filled epoxy molding compound commonly used in electronic packaging applications. Both stress relaxation tests and constant strain rate tensile tests were conducted. The material was found to be nonlinear in its viscoelastic behavior and to be amenable to horizontal shifting to form master curves. A representation of the master stress relaxation curves in terms of a Prony series is given, and the use of this representation illustrated in the context of both linear and nonlinear representations of the viscoelastic behavior to predict the results of the constant strain rate experiments.

scholarly journals Seven-Parameter Linear Viscoelastic Model Applied to Acoustical Damping Materials

2015 ◽  
Vol 137 (6) ◽  
Author(s):  
E. Gourdon ◽  
C. Sauzéat ◽  
H. Di Benedetto ◽  
K. Bilodeau
Keyword(s):  
Superposition Principle ◽  
Viscoelastic Model ◽  
Wide Frequency Range ◽  
Linear Viscoelastic ◽  
Mechanical Element ◽  
Element Approach ◽  
Time Temperature Superposition Principle ◽  
Damping Materials ◽  
Physical Features ◽  
Linear Viscoelastic Model

In this paper, linear viscoelastic rheological properties of acoustical damping materials are predicted. A rheological model, based on a mechanical element approach, is presented. It consists of a combination of two springs, two parabolic elements, and one dashpot (2S2P1D). This model is applied to different acoustical damping materials. Its specificity comes from the fact that elements might be linked to structural and physical features. Parameters might be experimentally determined by tests. Application of the 2S2P1D linear viscoelastic model can adequately predict the behavior of acoustical damping materials with good accuracy. If the material verifies the time–temperature superposition principle (TTSP), the proposed model can predict the behavior on a wide frequency range, even with a small number of available data.

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