Temperature Shift Factors Research Articles

A novel methodology of predicting temperature and rate effects on tensile properties of viscoelastic materials

A novel methodology to predict the tensile properties of viscoelastic materials as a synergistic function of temperature and loading/displacement rate is presented in this paper. The model is based on the amount of energy dissipated during tensile loading, requiring less input data compared to existing models. The deformation activation energy was measured and accordingly an energy-based temperature shift factor was suggested. Additionally, to describe the material’s rate dependency, two new types of energy-based loading/displacement rate shift factors based on the Eyring and Cooperative models were derived. The shift factors were implemented into the theory of viscoelasticity to predict the material tensile behavior at different temperatures and loading/displacement rates. In addition, a new failure criterion was suggested to predict the mechanical strength of the tested materials through the definition of a critical energy level, which determined the maximum energy that a material would be able to dissipate before failure. The model was applied to two different viscoelastic materials; an epoxy adhesive, and an angle-ply glass/epoxy fiber-reinforced polymer (GFRP) composite, two common viscoelastic materials used in the structural and construction industries. To determine the accuracy of the model, the results obtained from the model were compared to the results obtained from experiments. It was observed that the suggested methodology well predicted the stress–strain curves of the tested materials in the linear region and yield stress up to the post-yield region and failure point. In addition, the strength surface of the studied materials, which showed the synchronous effect of temperature and loading/displacement rate on the ultimate tensile strength in a 3-dimensional representation, was introduced.

Practical Methods to Construct Asphalt Binder Master Curves and Calculate Christensen–Anderson Model Parameters

Asphalt binder master curves are applied to describe the rheological behavior of asphalt binders. A standard for constructing asphalt binder master curves and fitting a model to the results does not presently exist. In this study, a pairwise interpolation is established for free shifting of isotherms. The pairwise interpolation method yields time–temperature shift factors that are in good agreement with the Gordon and Shaw method and can be more easily implemented without sophisticated software. Subsequently, practical methods to calculate the Christensen–Anderson (CA) model crossover frequency and R parameters are compared. The relationship between reduced frequency and the tangent of the phase angle in logarithmic space is generally linear over the tangent of phase angle values spanning from 0.2 to 0.5 and can be used to determine the crossover frequency. Two approaches that generally yielded acceptable model accuracy were identified for calculating the CA model R value: (1) least squares optimization to minimize the sum of squared errors for storage and loss moduli; and (2) fitting a line to log (log dynamic shear modulus) versus the tangent of the phase angle over the tangent of the phase angle values spanning between 0.5 and 2. Based on the asphalt binders evaluated in this study, the CA model can accurately reflect asphalt binder rheological behavior when the dynamic shear modulus exceeds 105 Pa and the phase angle is less than 70° for unmodified asphalts or less than 60° for polymer-modified asphalts.

Thermo-Viscoelastic Characterization of 3D Printing Polymers

Polymer materials used in 3D printing exhibit degradation of material mechanical properties when exposed to thermal environments and thermal expansions can induce residual stresses in products or molds, which may result in dimensional instability and subsequent structural failures. In this study, based on linear thermo-viscoelastic principles, material degradation master curves, shift functions, and glass transition temperatures for four different polymers used for 3D printing techniques such as MultiJet Printing and Digital Lighting Process were measured by using a dynamic mechanical analyzer. Based on the single frequency test, the glass transition temperature was measured. In addition, dynamic measurements were carried out over a frequency range at isothermal condition and storage modulus vs. frequency curves were obtained. Then, the storage moduli curves measured at different temperatures were superposed into master curves using the frequency–temperature superposition principle and shift factors were calculated as a function of temperature. Subsequently, the complex moduli curves that were measured in the frequency were curve-fitted onto generalized Maxwell models by using the least squares method and the master curves of relaxation moduli at reference temperature were obtained. The effects of temperature, frequency, and time on dynamic moduli and relaxation behaviors of four polymers used for 3D printing were evaluated. Experimental results showed that Polymers C and D could be suitable to use at the service temperature above 100 °C and Polymer C was highly crosslinked and showed low modulus reduction after about a year. The master relaxation curves obtained through this process can be utilized to predict the long-term performance of polymer molds made by 3D printing at a given environmental condition.

STRESS PROPERTIES OF HIGH DENSITY POLYETHYLENE PIPES UNDER CONSTANT PRESSURE IN THE LONG TERM

Due to its durability, plastics pipes are normally used for water transport. It replaced the metal pipes .the long term hydrostatic pressure test according to ASTMD2837-02 and EN921 -1994 requires very long periods for testing from 1000~ 10000 hours ,which makes the test is expensive and consuming, the objective of this research to find a method to use a short –term test result predict the behavior of the plastic pipe for the long –term .for this purpose the short –term tests are carried at elevated temperatures 50oc ,60oc and 80oc and the curves of stress versus time were plotted . A time –temperature superposition approach is used to predict the creep curves at lower temperatures such as 20oc, 25oc and 30o c and 40o c. the stress curves are essentially parallel. This led to the thought that a shift factor aT , could be applied to move from one curve to another .it may be seen from chart. 1 that the three curves from 50oc ,60oc and 80oc are separated by a uniform distance log aT Williams ,landel and Ferry developed an empirical relationship for this temperature shift factor explain below: Log at = Where c1 ,c2 are constant Tref is a reference temperature.

Evaluation of the Viscoelastic Temperature and Pressure Shift Factor Over the Full Range of Shear Rates**

Abstract A method of determining uniquely the best fitting temperature shift parameters of viscosimetric data over the full range of shear rates, based on the Carreau formula, has been presented in Part I. The method is in accordance with the temperature-time superposition principle of viscoelasticity and works fully numerically, thus providing an objective approximation criterion with optimal compensation of scatter and dispensing with any visual control at all, and includes, if necessary, the Rabinowitsch and Bagley corrections. Evaluations of this kind have been carried out for a multitude of old and new measurements of current types of thermoplastics (PE, PP, PS, PA, PC, PMMA, etc.), for which capillaries as well as rotational systems had been employed. In this way, a comprehensive viscosity data bank is built up containing a 5 or 6-parameter set for each material as a compact information about its flow behaviour and serving as a valuable means for numerical process analyses. At the same time, the usual shift formulas (Arrhenius, WLF, etc.) are compared in respect of their applicability and the typical parameter ranges are marked out. Some attention is given to the physical meaning of the material parameters. Part II deals with the validity of the temperature shift principle in general, the incorporation of correction procedures and the evaluation of the pressure dependence of the viscosity.

Dynamic modulus master curve construction of asphalt mixtures: Error analysis in different models and field scenarios

Asphalt mixture stiffness is a key property in any pavement long-life performance analysis; it is used to predict a material’s strain response for any given applied stress. To accurately describe experimental data, different mathematical models have been reported in literature, which allow for extrapolation to ranges not evaluated in laboratory tests. However, a precision analysis comparing each of them is necessary. This study evaluated 50 data points from five temperatures, ten loading frequencies, and 48 different asphalt mixtures to construct dynamic modulus master curves. Sigmoidal, Christensen-Anderson-Marasteanu (CAM), and Havriliak-Negami (HN) models were calibrated with three different target error functions, in addition to 2 Springs, 2 Parabolic creep elements, and 1 Dashpot (2S2P1D) to analyze their relative and absolute errors. In the first part, the mechanical analogs (2S2P1D and HN) achieved the best results. In the second part, the error added by the Williams-Landel-Ferry (WLF) and polynomial function, which describe the time–temperature shift factors used to construct the dynamic modulus master curves, was calculated; this suggested that the polynomial function better fits the master curves’ shift factors. In the third part, three Enhanced Integrated Climate Models (EICM) with different pavement depths and temperatures throughout the year together with the influence of vehicle speed and a depth equation were used to meet a reduced frequency interval that represents practical field conditions. Therefore, by filtering the errors found in part one using the field-representative reduced frequency interval, the fitting models (based on regression adjustments) can reach lower error levels closer to those of the mechanical analog models although still greater than those of the 2S2P1D model. In summary, it is possible to obtain a reliable pavement stiffness prediction using a less robust model as long as the dynamic modulus tested database is wide enough to express the desired reduced frequency range. Nevertheless, the use of a mechanical approach model such as 2S2P1D better describes the dynamic modulus experimental results, which leads to a more reliable prediction in addition to enabling characterization of the rheological behavior of asphalt materials.

Rheological Characterization and Modeling of Thermally Unstable Poly(3-hydroxybutyrate-co-3-hydroxyvalerate) (PHBV).

Presently, almost every industry uses conventional plastics. Its production from petroleum and extensive plastic pollution cause environmental problems. More sustainable alternatives to plastics include bioplastics such as poly(3-hydroxybutyrate-co-3-hydroxyvalerate) (PHBV), which is produced by bacteria and is biodegradable even in seawater. High temperature sensitivity as well as massive thermal degradation cause difficulties during the processing of PHBV. The aim of this work is to create a detailed rheological characterization and master curves to gain deeper knowledge about the material and its processing parameters. The rheological characterization was performed with frequency sweeps in the range of 0.1 rad/s to 628 rad/s and time sweeps over 300 s. Creating master curves at the reference temperature of 180 °C with the software IRIS delivers Carreau and Arrhenius parameters. These parameters allow for a calculation of the master curves for all other temperatures by means of the temperature shift factor. Moreover, the rheological measurements reveal a minimum rheological measurement temperature of 178 °C and a surprisingly high activation energy of 241.8 kJ/mol.

Characterization of viscoelastic bending stiffness of uncured carbon-epoxy prepreg slit tape

In support of computational modeling of tow placement at elevated temperature, the creep response of IM7/8552 uncured prepreg slit tape material during 3-point bend loading at different temperatures is measured using an RSA III dynamic mechanical analyzer. Short term creep experiments were conducted for a duration of 1000 s at ten different temperatures ranging from −5°C (below Tg of 0 °C) to 40 °C, with the latter being the nominal processing temperature for the tow. Results show that the tow material obeys the time-temperature superposition principle (TTSP) in the temperature range selected for the creep experiments. Using the TTSP, creep compliance master curve spanning more than eight logarithmic decades is obtained for the nominal processing temperature of 40 °C. The time–temperature shift factor is observed to follow closely the William-Landel-Ferry (WLF) model, with the WLF parameters obtained by least square fitting of the experimentally determined shift factors utilizing closed form shifting algorithm (CFS). The WLF model for the material is used to extend the master curve to a range of temperatures above glass transition temperature (Tg) of the material. The creep compliance data is further employed to obtain the retardation spectra of the material using an algorithm based on the work of a co-author and applied recently to a different material system by the authors. Details for extraction of the retardation spectra from the creep compliance results are provided. Results from these studies demonstrate that the creep compliance reconstructed from the retardation spectra accurately represent the experimental results while providing baseline data to quantify the importance of viscoelastic behavior in wrinkle formation during advanced manufacturing of aerospace components.

Behaviour of binder blends: experimental results and modelling from LVE properties of pure binder, RAP binder and rejuvenator

The first objective of this study is to highlight the effect of the rejuvenator on the linear viscoelastic (LVE) properties of various blends of a fresh 50/70 binder and a reclaimed asphalt pavement (RAP) binder, with a rejuvenator (a mixture of vegetal oils). A total of 17 binders (including pure fresh and RAP binders) produced as blends of two base binders and a rejuvenator in various proportions were tested. Dynamic shear rheometer tests were performed, and the experimental results were modelled using the 2S2P1D model. The second main objective was to present and analyse two different approaches for estimation of 2S2P1D parameters and temperature shift factors of binder blends, based on reduced experimental data (only data for the base constituents). Good correlation was found between the direct determination and the estimated results. However, a more accurate estimation was performed with the second approach.

Residual life prediction of marine EPR cable under discontinuous operation

It is known that marine cable is responsible for the transmission of electric energy and electrical signals of the ship. In order to predict the residual life of cable under discontinuous operation, a non-destructive online life prediction model is established based on retention rate of hardness (RRH). This study takes the marine ethylene propylene rubber (EPR) cable as the research object. Using time temperature superposition principle, the optimal time temperature shift factor is calculated using particle swarm optimisation and steepest descent method. After that the main curve was fitted exponentially to acquire the relationship between RRH and ageing time. Compared with the existing model, the results indicate that the proposed model has higher prediction accuracy. On this basis, the residual life prediction model based on RRH of marine EPR under discontinuous operation is presented by adding time parameters. The effectiveness of the method is verified by simulation. Thus, it provides theoretical guidance for solving the problem of marine cable replacement time.

Viscoelastic model with complex rheological behavior (VisCoR): incremental formulation

A thermo-rheologically complex linear viscoelastic material model, accounting for temperature and degree of cure (DoC), is developed starting with series expansion of the Helmholtz free energy and systematically implementing simplifying assumptions regarding the material behavior. In addition to the temperature and DoC dependent shift factor present in rheologically simple models, the derived novel model contains three cure and temperature dependent functions. The first function is identified as the rubbery modulus. The second is a weight factor to the transient integral term in the model and reflects the current temperature and cure state, whereas the third function is under the sign of the convolution integral, thus affecting the “memory” of the material. An incremental form of this model is presented which, due to improved approximation inside the time increment, has better numerical convergence than most of the similar forms. Parametric analysis is performed simulating stress development in a polymer, geometrically constrained in the mold during curing and cool-down. The importance of using proper viscoelastic model is shown, and the role of parameters in the model is revealed and discussed.

Hydrogen isotope replacement changes hydration and large scale structure, but not small scale structure, of agarose hydrogel networks.

Agarose samples of low (Ag1) and high (Ag2) O -methyl content on position 6 of the galactose residue were studied in H2O and D2O. Differential scanning calorimetry, turbidity and rheological measurements showed a [Formula: see text] 2 ° C shift in the coil-to-helix transition temperature, indicating higher helix stability in D2O. The differential scanning calorimetry data could be superimposed using a temperature shift factor, suggesting similar extents of helix aggregation in both solvents. Small angle X-ray scattering of H2O and D2O gels were essentially identical, indicating no change in the small scale ( [Formula: see text] 0.05-20 nm) network structure on isotopic exchange. Larger ([Formula: see text] 1 μm) scale heterogeneities were more pronounced in deuterium gels. The 1HT2 relaxation times were measured at different H/D ratios. These relaxation times were analyzed using a model assuming regular solution mixing of H2O, HDO and D2O between the solvent and gel phases. The fit results suggested that H2O has higher affinity for the agarose network than HDO and D2O. The difference, however, was much larger for the Ag2 sample. This finding implies that the higher hydrophobic effect observed in D2O affects the hydration state much more strongly for the more hydrophobic (and more polarizable) agarose sample Ag2. As a consequence, Ag2 (but not Ag1) gels retained more H2O than D2O. In contrast, the bulk rheology of either hydrogel was not affected by the isotopic exchange.

Application of TTSP to non-linear deformation in composite propellant

A series of constant-rate tensile tests and relaxation tests were conducted to assess the mechanical properties of the hydroxy-terminated polybutadiene (HTPB) propellant. The relaxation modulus master curve was acquired using relaxation tests at the linear viscoelastic segment, and stress-reduced time master curves at different strain levels were established to determine whether the time–temperature superposition principle (TTSP) could be used to assess the non-linear mechanical property of the HTPB propellant. Results showed that the mechanical properties of HTPB propellant strongly depend on temperature; the extent of this dependence is enhanced with decrease in temperature, and the TTSP can be used in non-linear segments. With the application of the TTSP, the ultimate strength and the stress–strain curves of constant-rate tensile tests can be predicted at any temperature and strain rate, and the predicted σ–ε responses matched the test results closely, but led to some errors at high temperatures, this is because of some errors in the time–temperature shift factors.

Modelling the storage modulus, transition temperatures and time–temperature superposition characteristics of epoxies and their composites

Epoxies are widely used as adhesives and matrix material for composites in civil infrastructure. As such structures are likely to be exposed to a wide variety of environmental conditions over long service lives, knowledge of their time–temperature sensitivity is desirable. The present study proposes a model describing the evolution of storage modulus for epoxies and their composites subject to forced dynamic excitations over wide temperature and frequency ranges. The model is tested against results for one rubber toughened epoxy and one carbon–epoxy composite. Results show a good agreement between the model and experiments, both in terms of temperature and frequency effects. Moreover, the model is shown to provide an unambiguous definition of the frequency dependent glass transition temperature, which is found to naturally follow the expected Arrhenius relationship with regards to frequency. Activation energies for the glass transition temperature evaluated by the new approach are in good agreement with results from the literature. It is also shown that when accounting for the effect of frequency on the glass transition, the evolution of the time–temperature shift factor is continuous across the glass transition.

Experimental investigation and modeling of dynamic thermomechanical behavior of 4-harness satin weave carbon/epoxy composites

Theoretical and experimental studies on the compressive mechanical behavior of 4-harness satin weave carbon/epoxy composite laminates under in-plane loading are conducted over the temperature range of 298–473 K and the strain rate range of 0.001–1700/s in this article. The stress–strain curves of 4-harness satin weave composites are obtained at different strain rates and temperatures, and key mechanical properties of the material are determined. The deformation mechanism and failure morphology of the samples are observed and analyzed by scanning electron microscope (SEM) micrographs. The results show that the uniaxial compressive mechanical properties of 4-harness satin weave composites are strongly dependent on the temperature but are weakly sensitive to strain rate. The peak stress and elastic modulus of the material have the trend of decrease with the increasing of temperature, and the decreasing trend can be expressed as the functional relationship of temperature shift factor. In addition, SEM observations show that the quasi-static failure mode of 4-harness satin weave composites is shear failure along the diagonal lines of the specimens, while the dynamic failure modes of the material are multiple delaminations and longitudinal splitting, and with the increasing of temperature, its longitudinal splitting is more serious, but the delamination is relatively reduced. A constitutive model with thermomechanical coupling effects is proposed based on the experimental results and the increment theory of elastic–plastic mechanics. The experimental verification and numerical analysis show that the model is shown to be able to predict the finite deformation behavior of 4-harness satin weave composites over a wide range of temperatures.

Fluxing as a new tool for bitumen rheological characterization and the use of time-concentration shift factor (ac)

The concept of temperature shift factor (aT) as defined by Doolittle, relating the free volume of a viscoelastic material at the current and reference states is briefly examined together with the resultant William-Landel-Ferry equation. This paper highlights the fact that change in free volume arise not only from temperature variations but can also result from the absorption of solvents and thus a generalized Doolittle relation may also be applied to a solvent concentration shift factor (ac). To validate this concept, a small scale laboratory investigation was carried out by blending 40/60 penetration grade bitumen with various proportions of one type of cooking oil and conducting dynamic shear rheometer frequency sweeps at a range of temperatures. By applying time-concentration superposition to each flux content, it was possible to shift horizontally (ac) each set of complex modulus data measured at each test temperature, so that all sets superimpose onto the master curve of the base bitumen at a preselected reference temperature. A direct relationship between conventional time-temperature shift and the proposed time-concentration shift factors was thus demonstrated using a sample of penetration grade bitumen and one type of vegetable oil. Further experimentation with other bitumen-flux combinations is necessary prior to recommending general adoption of the proposed tool.

Experimental and modeling investigation on the dynamic response of granite after high-temperature treatment under different pressures

In this work, the dynamic compressive mechanical properties of Beishan granite are investigated under the condition of uniaxial load and confined pressure, respectively. The purpose of this investigation is to study the effect of hydrostatic pressure and pre-heating temperature on the strength property and failure of such material. The investigation is carried out with the use of a large-diameter split-Hopkinson pressure bar (SHPB), which is equipped with an active confining device. The dynamic stress–strain behaviors of the granite samples under different confined conditions are obtained with a pre-heating temperature ranging from 25 to 800°C. We analyzed the temperature-dependent variation of the peak stress, peak strain and elastic modulus of the material under selected values of confined pressure. It is observed that the uniaxial compressive behavior of Beishan granite under unconfined pressure is strongly dependent on the pre-heating temperature. The values of the peak stress and the elastic modulus both decrease as the pre-heating temperature increases, while the value of the peak strain increases with the rise of pre-heating temperature, indicating a characteristic change from elastic-brittle to elastic–plastic. Under confined pressure, the strength of the material can be greatly improved, and higher pre-heating temperature tends to bring down the value of the strength. With the confined configuration, the strengthening of the peak stress is not significantly associated with the value of the confined pressure; instead the dependence on the strain rate becomes more remarkable. For the temperature effect, the value of the peak stress can be linearly correlated with the temperature level through comparative analysis. Moreover, the elastic modulus of the material can be associated with the temperature by a functional form, known as the temperature shift factor. Finally, an elastoplastic-damage constitutive model is established to predict the dynamic mechanical behavior of the material after high-temperature treatment under different confined pressures.

Application of Time-Temperature Superposition Principle on Fatigue Failure Analysis of Asphalt Binder

The linear amplitude sweep (LAS) test has been proposed for fatigue specifications of asphalt binders. Recently, a newly developed fatigue failure definition and energy-based failure criterion have been proposed for improving the LAS procedure and data interpreting; however, these improvements only affect LAS data conducted at a constant temperature. This paper, therefore, discusses the loading temperature effects on LAS-based binder fatigue, damage evolution, and final fatigue failure occurrence. Experimental results indicate that both damage characteristic curves (DCCs) and the failure criterion derived from the simplified-viscoelastic continuum damage (S-VECD) model are strongly affected by the testing temperature. However, the temperature shift factors determined from the dynamic shear modulus testing within the linear viscoelastic domain have been proven to be effective in eliminating the temperature influence for both fatigue DCCs and the failure criterion. The validation on binder phase demonstrates that the time-temperature superposition principle (TTSP) shift factor is only a function of temperature and is independent of strain level. TTSP application on both undamaged and damaged material behaviors is able to greatly improve the testing efficiency of the LAS-based binder fatigue characterization.

Temperature Effects of Linear Amplitude Sweep Testing and Analysis

Fatigue cracking is a critical distress in asphalt pavements. The linear amplitude sweep (LAS) test has recently been proposed for accelerated fatigue characterization of asphalt binders (AASHTO TP 101). The fatigue resistance of asphalt pavements depends on temperature because of the inherent viscoelastic nature of the asphalt binder contained in the pavement. This study sought to develop recommendations for the selection of LAS test temperature based on climatic performance grades (PGs). Developing recommendations for selecting the test temperature involved two components: investigation of climatic data for a wide range of PGs and investigation of the effect of linear viscoelastic dynamic shear modulus on the observed failure mechanism in the LAS test. Results demonstrate that test temperatures should be selected such that linear dynamic shear moduli fall within the range of 12 to 60 MPa to avoid the confounding effects of flow or adhesion loss. On the basis of the aforementioned moduli range—coupled with the analysis of pavement temperature data corresponding to a range of PGs and geographic regions—it is recommended that the LAS test temperature be selected as the average climatic PG minus 4°C. In addition, temperature effects are incorporated into simplified viscoelastic continuum damage modeling of LAS test results to enable the prediction of fatigue performance under any temperature and loading history of interest using LAS test results at a single temperature coupled with linear viscoelastic time–temperature shift factors.

Prediction of color changes in acetaminophen solution using the time–temperature superposition principle

A prediction method for color changes based on the time–temperature superposition principle (TTSP) was developed for acetaminophen solution. Color changes of acetaminophen solution are caused by the degradation of acetaminophen, such as hydrolysis and oxidation. In principle, the TTSP can be applied to only thermal aging. Therefore, the impact of oxidation on the color changes of acetaminophen solution was verified. The results of our experiment suggested that the oxidation products enhanced the color changes in acetaminophen solution. Next, the color changes of acetaminophen solution samples of the same head space volume after accelerated aging at various temperatures were investigated using the Commission Internationale de l’Eclairage (CIE) LAB color space (a*, b*, L* and ΔE*ab), following which the TTSP was adopted to kinetic analysis of the color changes. The apparent activation energies using the time–temperature shift factor of a*, b*, L* and ΔE*ab were calculated as 72.4, 69.2, 72.3 and 70.9 (kJ/mol), respectively, which are similar to the values for acetaminophen hydrolysis reported in the literature. The predicted values of a*, b*, L* and ΔE*ab at 40 °C were obtained by calculation using Arrhenius plots. A comparison between the experimental and predicted values for each color parameter revealed sufficiently high R2 values (>0.98), suggesting the high reliability of the prediction. The kinetic analysis using TTSP was successfully applied to predicting the color changes under the controlled oxygen amount at any temperature and for any length of time.