Time-temperature Shift Factor Research Articles

An alternative approach for characterization of the linear viscoelastic behavior of asphalt binders

This study aimed to develop an alternative approach to characterise the linear viscoelastic behaviour of asphalt binders. A rheogram model was firstly proposed based on the Carreau–Yasuda model; its accuracy was substantiated by high R 2 values. The dynamic shear modulus master curve model was then obtained using the relationship between the magnitude of complex viscosity and dynamic shear modulus and the two definitions of the time-temperature shift factor. Afterwards, the phase angle master curve model was derived according to the approximate Kramers–Kronig relation. The proposed approach was demonstrated to be capable of accurately characterising the linear viscoelastic behaviour of selected asphalt binders. In addition, the predicted zero shear viscosity (ZSV) could be potentially employed to evaluate the asphalt binder rutting resistance. Compared with the widely-used Christensen-Anderson-Marasteanu (CAM) model, the developed master curves models were better at constructing the phase angle master curves of selected asphalt binders.

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.

Self-healing master curves of bituminous binders: a non-linear viscoelastic continuum damage framework

In this paper the viscoelastic continuum damage theory was used to investigate the damage and self-healing potential of bituminous binders, considering the effects of rest temperature, thixotropy, and non-linearity. Experimental testing was carried out by using a procedure in which continuous oscillatory shear loading was imparted to the specimens with the inclusion of a single rest period under multiple temperature conditions. Quantification of self-healing included the determination of material integrity gained and damage parameter recovered after the rest period. Such parameters were calculated by excluding time-dependent and non-linear biasing effects, which were directly evaluated by means of a distinct set of experiments. Results were modelled by using the so-called self-healing master curves, constructed by applying the linear viscoelastic time-temperature shift factors. These self-healing master curves are intended to be used as straightforward tools for the prediction of the self-healing response of neat and polymer modified binders in various time-temperature combinations.

Mapping the role of oral cavity physiological factors into the viscoelastic model of denture adhesives for numerical implementation.

Physiological parameters of the oral cavity have a profound impact on any restorative solutions designed for edentulous patients including denture adhesives. This study aims to mathematically quantify the influence of three such variables, namely: the temperature, pH, and the swelling of such adhesives under the influence of saliva on its mechanical behavior. The mathematical quantification is further aimed to implement a material model for such adhesives which considers the impact of such physiological factors. The denture adhesive is experimentally investigated by means of rheological steady state frequency sweep tests to obtain the relaxation spectrum of the material. The relaxation behavior is measured for a wide range of oral cavity temperatures and pH. Also, the adhesive is hydrated and upon swelling to different levels again tested to understand the impact of swelling on the mechanical behavior. The experimentally measured continuous relaxation spectrum is modeled as a viscoelastic material using a discrete set of points based on the Prony series discretization technique. The relaxation spectrums for various temperatures are compared and the possibility of a time-temperature superposition is explored for the model. Similarly, the measured values of Storage and loss modulus are investigated to understand the role of pH and swelling. The results in this study clearly indicated a horizontal shift in the relaxation behavior with increase in temperature. And hence, the time-temperature shift factor was calculated for the adhesive. The relaxation spectrum also showed a strong correlation with swelling of the adhesive and the pH. The influence of these two parameters were captured into the model based on the relaxation time parameter in the Prony series approach. Based on this study the impact of these parameters could be appreciated on the performance and mechanical behavior of denture adhesives and implemented into a Prony series based viscoelastic material model which can be used with numerical simulations.

Time-temperature superposition principle for the shear fracture behaviour of soft adhesive layers: From bulk to interface

Soft adhesive layers have attracted great attention as a commonly used adhesive technique, particularly because of their shear fracture behaviour at extreme loading rates and temperatures. Therefore, the present study examined the shear fracture properties of a soft adhesive layer through systematic rheological experiments, loading-unloading shear tests and shear fracture tests. Due to a similar viscoelastic characteristic in rheological properties and fracture properties, the time-temperature superposition principle (TTSP) was extended from the bulk to the interface to investigate its shear cohesive failure. A shear fracture toughness master curve was defined using the time-temperature equivalence shift factors derived from the rheological properties. The shear fracture behaviour of the soft adhesive layer could be predicted using data from a narrow range of loading rates/temperatures. The results demonstrated the potential of extending the TTSP approach from the bulk to a soft adhesive layer having viscoelastic character, which might be utilised to predict the shear fracture toughness of soft adhesive materials under extreme conditions.

Toward a realistic asphalt mix ageing protocol

The time-associated changes of the asphalt cement properties significantly impact the performance and durability of pavements. Different techniques have been introduced to simulate pavement ageing, most of which use elevated temperatures and neglect factors such as moisture and solar radiation. This research evaluated the coupling effect of solar radiation, heat, and moisture conditioning on the laboratory compacted plant mixes to achieve representative aged samples for performance testing. Rheological and chemical analysis were then performed on samples at various stages of the conditioning process and recovered asphalt cement. Temperature-Sensitivity of the rheological parameters were evaluated using time-temperature superposition shift factors. Carbonyl and sulfoxide indices and carbonyl to sulfoxide ratios were used to assess the kinetics of the age-related chemical changes. This study showed that coupling moisture and solar radiation could alter the chemistry and rheology of conditioned samples.

A triaxial linear viscoelastic characterization framework for asphalt concrete based on the 2S2P1D model

Asphalt concrete materials are known to exhibit pressure dependence in response to mechanical loading. However, for conventional dense-graded asphalt mixtures, only weak pressure sensitivity was noted in the relaxation spectrum, time-temperature shift factors, and low-temperature moduli. Given these facts, a triaxial linear viscoelastic characterization framework was developed, which consisted of a convenient experimental protocol for the confined dynamic modulus test and a modeling approach based on the 2S2P1D model. In this framework, the same relaxation spectrum and time-temperature equivalence were applied across all different confining conditions, while the pressure dependence was fully assigned to the equilibrium modulus. The resultant prediction errors in dynamic modulus were in general below or comparable to typical test variability. Numerical implementation of the modeling method in the time domain was accomplished via Prony discretization of the continuous relaxation spectrum, and was demonstrated via application to triaxial relaxation and creep data. The model's satisfactory performance suggested that the confining condition had an insignificant impact on the molecular processes occurring in the asphalt phase during relaxation, owing to the low aggregate mobility and thus minimal asphalt flow as restrained by the dense structure. Limitations of the proposed modeling scheme as well as methods available from the literature were revealed lastly upon asphalt concrete materials with unconventional gap and open gradations.

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.

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.

Refinement of a 3D finite strain viscoelastic constitutive model for thermally induced shape memory polymers

Refinement of a previously developed 3D finite strain viscoelastic constitutive model for thermally induced shape memory polymers is proposed. In the previous model, the temperature-dependent material parameters consist of two parts: parameters at high and low temperatures. In addition, six parameters are fitted simultaneously only based on a single curve of initial elastic modulus, incurring difficulty in parameter identification. In this paper, the parameters at high temperature are derived from those at low temperature by using a modified Adam-Gibbs model and Arrhenius-type of time-temperature superposition shift factor. In addition, by introducing a physics based viscosity parameter, only three parameters are needed to be determined by the curve of initial elastic modulus. The number of material parameters is thus reduced from seventeen in the old model to thirteen, and the material parameter identification process is much easier to be implemented. Finally, the refined model is validated by comparing with three experimental sets of free recovery from the literature.

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.

Application of time-temperature superposition principle to pull-off tensile strength of asphalt tack coats

Flexible pavements are multilayered structures that are designed to withstand vehicular traffic and thermal loading. Tack coat provides the bonding between these multilayers, which is a critical mechanism to provide a pavement with the monolithic action of asphalt layers to resist traffic and thermal loading, thereby dictating the pavement’s service life. Asphalt binder bond strength (BBS) is an indicator that can be used to evaluate the interlayer bonding ability of tack coat and changes as a function of temperature and loading rate. The focus of this paper is to prove that the time-temperature superposition principle is applicable to the BBS of various tack coat materials. In order to achieve this goal, BBS and dynamic shear rheometer (DSR) tests were conducted on four different tack coats, CRS-2, CRS-1h, NTCRS-1hM, and Ultrafuse. The Pneumatic Adhesion Tensile Testing Instrument (PATTI) was used to determine the BBS at 13 different temperatures ranging from 5 °C to 53 °C. The BBS data showed that adhesive failures between the binder and pull stub of PATTI caused the drop of BBS below 5 °C to 15 °C for hard (CRS-1h) and Non-tracking (NTCRS-1hM, Ultrafuse) tack coat. In addition to the BBS test, DSR tests were performed on the emulsion residue to measure the time-temperature shift factors at the reference temperature of 20 °C. It was found that the time-temperature shift factors determined from the DSR tests could be successfully used to shift the BBS vs. stress rate curves to construct the mastercurve for all four tack coat materials at a residual application rate of 0.14 L/m2 (0.03 Gal/yd2) as long as the BBS test exhibited cohesive failure between the binder and pull-off stubs. A simple method based on the BBS values at two temperatures is proposed to predict the mastercurve for routine characterization of the BBS mastercurve. No definite trend in the BBS mastercurve emerged among the different tack coat application rates for the different tack coats.

Life Prediction of Carbon Fiber Reinforced Polymers using Time Temperature Shift Factor

The properties of Carbon Fiber–Reinforced Polymers (CFRP) are greatly affected under extreme environmental conditions. This paper reports an experimental study to determine the response of IM7-carbon/977-2 cycom epoxy laminates under different humidity and temprature conditions. Short-term 3-point bending creep tests using Dynamic Mechanical Analysis (DMA) were used to test the dry and saturated samples at various temperature levels. The dry coupons were tested at the room temperature (RT) and at 60-120 °C with 20 °C increment and then at 130 °C, 150-180 °C with 10 °C increment for each next test. The saturated (wet) coupons were tested at RT, 40 - 120 °C with 10 °C increment in temperature for each next test and at 145 °C, 150 °C, and 160 °C. The time-temperature shift factor (TTSF) was applied and it is shown that the viscoelastic behavior of the invetigated IM7-carbon/977-2 epoxy laminates, is accurately predicted through the use of TTSF. It has also been shown that determining the viscoelastic behavior at elevated temperatures helps to predict temperature below the glass transition temperature using TTSF. The long-term life of the material is relatively easily predicted using TTSF by conducting traditional short-term laboratory tests.

IMPROVED APPROACH TO MODELLING PRELOAD RELAXATION IN BOLTED COMPOSITE JOINTS

This paper studies the long-term performance prediction for the preload of bolted composite joints. An analytical model based on the authors' previous work was improved, with transferring expressions of different creep stages into segmented forms and modified the use of time-temperature shift factor. Accelerated tests were designed and performed for characterizing the long-term relaxation behavior. Comparisons between the results of the predicted model and accelerated test results indicated that the improved model provided a better validity than existing models such as Shivakumar-Crews's model and Hook-Norton's model for describing the long-term preload behavior.

Flexural fatigue life prediction of CFRP-Nomex honeycomb sandwich beams

Long-term flexural fatigue life of composite sandwich beams consisting of plain weave carbon 3K-70P/epoxy (CFRP) faceplates and Nomex honeycomb core is studied using time–temperature superposition principle (TTSP) by extending our previous study on laminates [Composites Part B: Engineering (19):539-547, 2016]. Considering negligible effect of temperature on the honeycomb core performance, time-temperature shift factors (TTSF) of the sandwich beams is assumed to be same as that of the CFRP faceplates. Hence, TTSFs are taken from previous laminates study. Constant strain rate (CSR) experiments at various temperatures and strain rates are conducted to construct the CSR master curve, followed by prediction and validation of creep strength master curve. Flexural fatigue tests were then conducted at various temperatures and load levels to construct S-N curves at respective temperatures. Finally, fatigue strength master curve is constructed. Within experimental scatter, predicted fatigue behavior at any given (a) frequency and (b) load ratio is confirmed to be in reasonable agreement with the experimental measurements.

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.

The Aging Degree Analysis of EPR Cable Insulation Based on Hardness Retention Rate Measurement

Based on the accelerated thermal aging analysis of Ethylene-Propylene Rubber (EPR) cables, the theoretical relationship between elongation at break retention rate (EAB%) and hardness retention rate was deduced from the mathematical principles of hardness test. The relation curve was compared with the measurement values, and the result shows that there is high coincidence degree between theoretical curve and measurement values. After researching on the experimental data of EAB% and hardness retention rate, combining the “time-temperature shift factors” with Arrhenius equation, the lifetime termination index on account of hardness retention rate is analyzed when the EAB% reduced to 30%-50%. According to comparing theoretical values with the experimental results, hardness retention rate decreased to 10% was proposed as the lifetime termination index of EPR cable.

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.

Application of a Modified Arrhenius Equation to Describe the Time-Temperature Equivalence in Relaxation Analysis of Metal Seals

For the application of the time-temperature superposition principle a suitable relation is needed to describe the time-temperature shift factor α. Therefore, the Arrhenius equation is widely used due to its simple form and often leads to suitable results. Where, the Arrhenius equation presents a linear relation for the temperature-dependent shift factor in logarithmic scale ln(α) with the absolute inverse temperature (1/ϑ). However, in cases with a large temperature range which eventually include more complex reaction processes, the functional relation between ln(α) and (1/ϑ) is nonlinear in the ‘Arrhenius plot’. In those cases, the monotone change of the nonlinear range in the ‘Arrhenius plot’ can be interpreted as a transient range between two approximately linear or constant regions. An extended application of the modified Arrhenius equation from Nakamura (1989) is presented in this study for this transient range. The introduced method was applied to describe the time-temperature equivalence in the relaxation analysis of restoring seal force of metal seals, which are used in lid-systems of transport and interim storage casks for radioactive materials. But, the method is widely valid and can be used for different objectives which are characterized by thermorheologically simple behavior with nonlinear sensitivity to inverse temperature.

Development of master curve models complying with linear viscoelastic theory for complex moduli of asphalt mixtures with improved accuracy

Approximate Kramers-Kronig relations have shown success in constructing master curves in compliance with the linear viscoelastic theory for the magnitude and phase angle of the complex modulus of an asphalt mixture. However, their applications have been limited to either shifting test data without model construction or constructing master curve models without addressing possible asymmetry of the master curves. Taking advantage of the Kramers-Kronig relations, this paper developed two approaches to establish the master curve models of four viscoelastic parameters of asphalt mixtures, including the magnitude and phase angle of the complex modulus as well as the storage modulus and loss modulus. In each approach, the four viscoelastic parameters shared the same time-temperature shift factor equation with exactly the same fitting parameters. Master curves of the viscoelastic parameters were constructed and were identified to have asymmetric shapes. These master curves were further verified to be compliant with the linear viscoelastic theory using black space diagrams and wicket plots, respectively.It was found that the developed two approaches established master curve models with approximately the same accuracy level with R2 values larger than 0.96. The two approaches also produced about the same time-temperature shift factor at each temperature. Therefore, either approach could be selected to accurately construct master curves of the four viscoelastic parameters in a wide frequency range.