scholarly journals The Master-Curve Band considering Measurement and Modeling Uncertainty for Bituminous Materials

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Quan Liu ◽  
Jiantao Wu ◽  
Pengfei Zhou ◽  
Markus Oeser
Keyword(s):  
Measurement Errors ◽  
Master Curve ◽  
Superposition Principle ◽  
Original Data ◽  
Model Parameters ◽  
Aging Effects ◽  
Rheological Models ◽  
Modeling Uncertainty ◽  
Sigmoidal Model ◽  
Time Temperature Superposition Principle

This paper proposes using the master-curve band (MCB) to incorporate the unavoidable measurement errors and modeling uncertainty into the bitumen master-curve construction. In general, the rheological property of bitumen within the linear viscoelastic region is characterized by the master curve of modulus and/or phase angle, provided that the bitumen complies with the time-temperature superposition principle (TTSP). However, the master-curve construction is essentially a mathematical fitting process regardless of whether or not the original data is perfect enough to fit. For this reason, the MCB was introduced to consider the uncertainty information instead of a single master curve. Rheological data of four kinds of bitumen including unaged and aged bitumen were used to construct the MCBs. The results indicated that the generalized sigmoidal model showed the widest master-curve band, followed by Christensen-Anderson-Marasteanu (CAM) and CAM ( G g ) models. The width of MCB was a useful tool to identify the sensitivity of bitumen to rheological models. The sensitivity of bitumen to rheological models is associated with the number of active parameters in rheological models and model parameters’ confidence intervals. The construction of an MCB was beneficial to select the rheological models. Accordingly, the CAM ( G g ) model is proved to be the best to analyze the aging effects.

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>.

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.

scholarly journals Master Curve Establishment and Complex Modulus Evaluation of SBS-Modified Asphalt Mixture Reinforced with Basalt Fiber Based on Generalized Sigmoidal Model

Polymers ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1586 ◽  
Author(s):  
Guojin Tan ◽  
Wensheng Wang ◽  
Yongchun Cheng ◽  
Yong Wang ◽  
Zhiqing Zhu
Keyword(s):  
Master Curve ◽  
Mechanical Response ◽  
Complex Modulus ◽  
Superposition Principle ◽  
Asphalt Mixture ◽  
Basalt Fiber ◽  
Loading Frequency ◽  
Modified Asphalt ◽  
Dynamic Mechanical ◽  
Sigmoidal Model

Basalt fiber has been proved to be a good modified material for asphalt mixture. The performance of basalt fiber modified asphalt mixture has been widely investigated by extensive researches. However, most studies focused on ordinary static load tests, and less attention was paid to the dynamic mechanical response of asphalt mixture incorporating with basalt fiber. This paper aims to establish the master curve of complex modulus of asphalt mixture incorporating of styrene-butadiene-styrene (SBS) polymer and basalt fiber using the generalized Sigmoidal model. Both loading frequency and temperature were investigated for dynamic mechanical response of asphalt mixture with basalt fiber. In addition, based on the time-temperature superposition principle, the master curves of complex modulus were constructed to reflect the dynamic mechanical response at an extended reduced frequency range at an arbitrary temperature. Results indicated that the generalized Sigmoidal model in this paper could better reflect the dynamic mechanical response accurately with correlation coefficients above 0.97, which is utilized to predict the dynamic mechanical performances accurately. Simultaneously, the modulus values exhibit an increasing trend with loading frequency and decrease versus temperature. However, the phase angle values showed different trends with frequency and temperature.

scholarly journals Experimental Study on Statistic Failure Properties of Composite Considering Temperature Effect

2021 ◽  
Vol 2101 (1) ◽  
pp. 012062
Author(s):  
Zhun Liu ◽  
Xiaoning Zhao ◽  
Xuanxiu Liu ◽  
Lei Song ◽  
Qing Nie
Keyword(s):  
Mechanical Performance ◽  
Superposition Principle ◽  
Strength Properties ◽  
Shear Loading ◽  
Model Parameters ◽  
Loading Conditions ◽  
Plane Shear ◽  
Performance Requirements ◽  
Time Temperature Superposition Principle ◽  
Equivalent Strength

Abstract Advanced composite has been widely used in many fields with high mechanical performance requirements. Aim to characterize the reliability of composite, a statistic failure model was established based on Weibull distribution. Strength tests at various temperatures were conducted under tensile, compressive and in-plane shear loading conditions. As the temperature rises from 25 °C to 180°C, the strengths at different loading conditions reduces by nearly 60% except that the longitudinal tensile one reduces by only 16%. Equivalent strength at reference temperature was obtained based on time-temperature superposition principle. Then, the model parameters were determined with transferred test data using the median rank method, and statistic characterizations of different strength properties were further studied. Results show that the failure probability of composite is independent of temperature. Among all the strengths, the longitudinal compressive strength possesses the smallest shape parameter and correlation coefficient R of the fitting result, which means the strongest randomness of failure.

scholarly journals 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>.

scholarly journals Glass Transition Behavior of Wet Polymers

Materials ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 730
Author(s):  
Hai Li ◽  
Rui Xiao
Keyword(s):  
Glass Transition ◽  
Master Curve ◽  
Relaxation Spectrum ◽  
Superposition Principle ◽  
Small Strain ◽  
Amorphous Polymers ◽  
Mechanical Tests ◽  
Transition Behavior ◽  
Time Temperature Superposition Principle ◽  
Fractional Zener Model

We have performed a systematical investigation on the glass transition behavior of amorphous polymers with different solvent concentrations. Acrylate-based amorphous polymers are synthesized and treated by isopropyl alcohol to obtain specimens with a homogenous solvent distribution. The small strain dynamic mechanical tests are then performed to obtain the glass transition behaviors. The results show that the wet polymers even with a solvent concentration of more than 60 wt.% still exhibit a glass transition behavior, with the glass transition region shifting to lower temperatures with increasing solvent concentrations. A master curve of modulus as a function of frequency can be constructed for all the polymer–solvent systems via the time–temperature superposition principle. The relaxation time and the breadth of the relaxation spectrum are then obtained through fitting the master curve using a fractional Zener model. The results indicate that the breadth of the relaxation spectrum has been greatly expanded in the presence of solvents, which has been rarely reported in the literature. Thus, this work can potentially advance the fundamental understanding of the effects of solvent on the glass transition behaviors of amorphous polymers.

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.

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.

scholarly journals Formulating the history matching problem with consistent error statistics

2021 ◽  
Author(s):  
Geir Evensen
Keyword(s):  
Simulation Model ◽  
Measurement Errors ◽  
History Matching ◽  
Critical Role ◽  
Bayes Theorem ◽  
Conditional Probability Density ◽  
Model Parameters ◽  
Rate Data ◽  
Matching Problem ◽  
Reservoir Prediction

AbstractIt is common to formulate the history-matching problem using Bayes’ theorem. From Bayes’, the conditional probability density function (pdf) of the uncertain model parameters is proportional to the prior pdf of the model parameters, multiplied by the likelihood of the measurements. The static model parameters are random variables characterizing the reservoir model while the observations include, e.g., historical rates of oil, gas, and water produced from the wells. The reservoir prediction model is assumed perfect, and there are no errors besides those in the static parameters. However, this formulation is flawed. The historical rate data only approximately represent the real production of the reservoir and contain errors. History-matching methods usually take these errors into account in the conditioning but neglect them when forcing the simulation model by the observed rates during the historical integration. Thus, the model prediction depends on some of the same data used in the conditioning. The paper presents a formulation of Bayes’ theorem that considers the data dependency of the simulation model. In the new formulation, one must update both the poorly known model parameters and the rate-data errors. The result is an improved posterior ensemble of prediction models that better cover the observations with more substantial and realistic uncertainty. The implementation accounts correctly for correlated measurement errors and demonstrates the critical role of these correlations in reducing the update’s magnitude. The paper also shows the consistency of the subspace inversion scheme by Evensen (Ocean Dyn. 54, 539–560 2004) in the case with correlated measurement errors and demonstrates its accuracy when using a “larger” ensemble of perturbations to represent the measurement error covariance matrix.

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