The Time-temperature Superposition Principle Research Articles

Proposing a novel double sigmoidal model to fit the master curve for various polymer-modified asphalt

ABSTRACT Master curve technique is frequently used to characterize the linear viscoelasticity of polymer modified asphalt (PMA), however, there is no widely accepted master curve for PMA. This study aims to propose a novel double sigmoidal model that can be used universally for all asphalts, especially highly modified PMAs. To do so, one plain asphalt and six representative PMAs are examined. Extended temperature sweep tests (−40°C to 140°C) are conducted to grasp the whole picture of the master curve. Three representative mathematical models (CAM, sigmoidal, double sigmoidal) are selected and compared in terms of fitting in both modulus and phase angle. The results suggest that double sigmoidal model suits all types of asphalts for all testing temperature ranges, and it features the ability to model the rubbery state and rubbery-viscous transition of highly modified PMA (RMSE < 0.02). A phase angle expression of the double sigmoidal model is also developed, which shows great potential in characterizing the strength of polymer network within the PMA. Also, it avoids the impact from the partial break of the time-temperature superposition principle (TTSP) and reveals the true shape of the phase angle master curve. Finally, master curve models are recommended based on different testing temperature ranges.

(Invited) Graphene Oxide-Based Membranes: Viscoelastic Properties and Application to Broadband Microspeakers

Graphene and graphene derivatives have attracted attention as materials for acoustic transduction [1-3]. Graphene oxide (GO) membranes and borate cross-linked graphene oxide (X-GO) membranes combine high stiffness, low mass density, and high loss coefficient. We show [4] that these mechanical properties are ideal for efficient, broadband, electro-acoustic transduction, where the acoustic diaphragm should be light, stiff, and internally damped. We present a quantitative comparison of the figure of merit, (E/ρ 3)1/2, where E is Young's modulus and ρ is the mass density, and the material performance index, tan δ (E/ρ 3)1/2, where tan δ is the loss coefficient. GO and X-GO exhibit high figures of merit, comparable to that of wood and exceeding that of aluminum and thermoplastics. The material performance indices of GO and X-GO exceed that of wood, thermoplastics, and aluminum. The latter are common diaphragm materials in acoustic transducers.For acoustic applications, it is important to understand the frequency dependent viscoelastic response. The complex modulus G = G' + iG'' of GO and X-GO membranes was measured by dynamic mechanical analysis and analyzed by the application of the time-temperature superposition (TTS) principle of polymer rheology. We find that X-GO shows a more than 30% increase in storage modulus G’ over the frequency range of 1 to 10 kHz, exceeding 55 GPa at 10 kHz. There is a reduction in loss coefficient tan δ = G''/G' for X-GO of ≈30% over the same frequency range, reaching tan δ = 0.04 at 10 kHz, which is approximately one order of magnitude larger than that of aluminum.A quantitative comparison of microspeaker performance was conducted at a fixed diaphragm mass m = 15-20 g and 14 mm x 8 mm size, including GO, X-GO, oak wood, polyethylene terephthalate (PET), aluminum, and titanium. Scanning laser measurements confirm pistonic operation of X-GO membranes. Microspeaker sound pressure level response was measured in both time and frequency domains. X-GO diaphragms exhibit 45% higher damping than aluminum membranes in microspeaker assemblies. Consequently, X-GO membranes enable the upshift of loudspeaker breakup frequency by 1/6 to 1/2 octave above speakers assembled with oak wood, PET, aluminum and titanium membranes. GO based materials are thus found to be an exceptional material for electro-acoustic transduction.

Phase separation of chemically crosslinked poly(n-butyl methacrylate-co-methacrylic acid) in mixtures of N,N-dimethyl formamide and water

When a copolymer network of chemically crosslinked poly( n -butyl methacrylate- co -methacrylic acid) was immersed into a bath of N,N -dimethylformamide (DMF) and water, the swollen network underwent phase separation depending on the fraction x w of water in the bath. Swelling ratio, light transmittance, thermomechanics, dynamical mechanical spectra, and tensile property of the gels in baths of different x w 's were investigated. A ternary phase diagram of this system was calculated from theory for comparison of the experimental data. A glass line was also provided in the ternary phase diagram from the estimation by the diluent effect on glass temperature. The results indicated that the polymer-rich phase after phase separation became glassy as the bath composition x w was above 0.75. This resulted in a fundamental change in the thermomechanical behavior of the gel from one of a typical rubber to one a typical glassy polymer. Meanwhile a dynamical gel-to-glass transition was observed in the time-temperature superposition (TTS) master curves. The transition temperature T 0 decrease with increasing x w . A weak-to-tough transition was observed at T − T 0 ≈ 0 K, while a tough-to-brittle transition occurs at T − T 0 ≈ −50 K. A conceptual scheme was proposed to clarify the interplay of phase separation, glass transition in the present work. This scheme could also explain some of the previous work. An example of application in shape memory materials was provided. Highlights • Phase separation inside a gel in equilibrium with solvent/nonsolvent is calculated. • Glass transition line and the Berghmans point is added to the phase diagram. • Thermoelasticity of gel swollen in solvent/nonsolvent is eccentric. • The calculated phase diagram explains the window of mechanical toughening.

Experimental Investigation on Fracture Properties of HTPB Propellant with Circumferentially Notched Cylinder Sample

AbstractTo comprehensively understand the fracture properties of solid propellants, the mode I tensile fracture toughness tests at different temperatures (253.15–343.15 K) and loading rates (2–500 mm/min) were conducted on the newly designed circumferentially notched cylinder sample with different initial crack sizes (4.5 and 6.5 mm) for hydroxyl‐terminated polybutadiene (HTPB) propellant. Test results reveal that the shape of the tensile fracture stress‐strain curves was not significantly influenced by temperature, loading rate and the initial crack size. Higher loading rate and lower temperature can lead to a rise in the tensile fracture toughness of HTPB propellant described by the stress intensity factor, however, continuously increasing loading rate cannot dramatically improve this fracture toughness beyond the rate of 250 mm/min. In addition, the fracture toughness is more sensitive to temperature. Furthermore, the variation of the initial crack size causes obvious changes in the fracture toughness with the coupled effects of low temperature and higher loading rates. At these test conditions, a higher tensile fracture toughness can be obtained with the shorter initial crack. For all the test conditions, there is a linear rise in the strain corresponding to the fracture toughness as temperature increases. Meanwhile, this strain increases with the shorter initial crack. Whereas, the effect of loading rate on this strain is complex. Based on the time‐temperature superposition principle (TTSP), the master curves with a log‐curvilinear form were constructed to predict the mode I tensile fracture toughness of the propellant at different initial crack sizes in a wide range of loading conditions.

Predicting Solute Diffusivity in Polymers Using Time-Temperature Superposition.

We demonstrate a novel application of the time-temperature superposition (TTS) principle to predict solute diffusivity D in glassy polymers using atomistic molecular dynamics simulations. Our TTS approach incorporates the Debye-Waller factor ⟨u2⟩, a measure of solute caging, along with concepts from thermodynamic scaling methods, allowing us to balance contributions to the dynamics from temperature and ⟨u2⟩ using adjustable parameters. Our approach rescales the solute mean-squared displacement curves at several temperatures into a master curve that approximates the diffusive dynamics at a reference temperature, effectively extending the simulation time scale from nanoseconds to seconds and beyond. With a set of "universal" parameters, this TTS approach predicts D with reasonable accuracy in a broad range of polymer/solute systems. Using TTS greatly reduces the computational cost compared to standard MD simulations. Thus, our method offers a means to rapidly and routinely provide order-of-magnitude estimates of D using simulations.

Effect of reclaimed bio-oil and waste crumb rubber on bitumen viscoelasticity

ABSTRACT The application of reclaimed bio-oil has demonstrated many merits in modifying asphalt rubber (AR). However, the traditional rheological methods tend to be ineffective in scoring asphalt rubber modified by bio-oil (BoAR). This study aimed to assess how asphalt viscoelasticity is affected by the complicated interactions of three components in BoAR. Two different liquid additives were incorporated into AR utilizing three mixing sequences. Then the temperature and time dependence of these BoARs were investigated through the total dissipated energy function and process-accelerated fatigue testing, respectively. Furtherly, the master curves were constructed to detect their overall viscoelastic response. Finally, two evaluating methods, i.e. measured transition temperature and functional analysis region, were proposed by applying the time-temperature superposition principle (TTSP) and statistical methods. As a sequence, adding CRM tends to weaken the bitumen viscoelasticity, whereas the bio-oil presents the opposite result. Also, adjusting manufacturing processes utilizing liquid biological oil was proven a practical approach to optimizing the time-temperature sensibility of BoARs. In addition, the proposed rutting analysis region showed superior representativeness and practicability in evaluating the high-temperature properties of viscoelastic materials.

Determination of shift factor for long-term life prediction of carbon/fiber epoxy composites using the time-temperature superposition principle

This study presents the way to determine the shift factor for predicting the long-term behavior of a carbon fiber/epoxy composite using the time-temperature superposition (TTS) principle. We conducted the multi-frequency, creep TTS, and stress relaxation TTS tests and obtained the dynamic mechanical analysis responses such as the storage modulus, creep compliance, and relaxation modulus. A shift factor determining the data movement is essential in creating the master curves. The shift factor was estimated using several methods such as the Arrhenius equation, William–Landel–Ferry equation, and manual shift method. The change in viscoelastic properties over a wide range of time was investigated by comparing the master curves to determine the most rational approach for estimating the shift factor. The master curves were obtained from the three methods based on the storage modulus. For the Arrhenius equation, the smooth master curves could not be obtained when applying a constant activation energy value. Still, using two activation energy values for the carbon fiber reinforced composite, the smooth master curves could be obtained. However, the manual shift method could get the master curves that overlap smoothly in the creep TTS and stress relaxation TTS, even without calculating activation energy values. Since the proposed procedure can estimate the long-term viscoelastic properties reasonably, the life span of the structure can be predicted at the design stage by using the master curves considering the viscoelastic properties.

Temperature Dependence of Conformational Relaxation of Poly(ethylene oxide) Melts.

The time-temperature superposition (TTS) principle, employed extensively for the analysis of polymer dynamics, is based on the assumption that the different normal modes of polymer chains would experience identical temperature dependence. We aim to test the critical assumption for TTS principle by investigating poly(ethylene oxide) (PEO) melts, which have been considered excellent solid polyelectrolytes. In this work, we perform all-atom molecular dynamics simulations up to 300 ns at a range of temperatures for PEO melts. We find from our simulations that the conformations of strands of PEO chains in melts show ideal chain statistics when the strand consists of at least 10 monomers. At the temperature range of 400 to 300 K, the mean-square displacements () of the centers of mass of chains enter the Fickian regime, i.e., . On the other hand, of the monomers of the chains scales as at intermediate time scales as expected for the Rouse model. We investigate various relaxation modes of the polymer chains and their relaxation times (), by calculating for each strand of n monomers. Interestingly, different normal modes of the PEO chains experience identical temperature dependence, thus indicating that the TTS principle would hold for the given temperature range.

Time-temperature superposition of flexural creep response of carbon fiber PEKK composites manufactured using different prepreg stacking sequence

In this work, the long-term creep response of high-performance carbon fiber PEKK (CF/PEKK) composites was evaluated by performing extrapolated short-term flexural creep tests at various temperatures. The time-temperature superposition principle (TTSP) with vertical as well as horizontal shifting was used to generate master curves at reference temperatures of 120°C. Satin weave-based CF/PEKK prepregs were used to manufacture eight-layer composites via compression molding, with three different stacking sequences: (a) zero-direction [0]8 (b) cross-ply [0, 90]4 and (c) quasi-isotropic [90, −45, 45, 0]2 s. The flexural properties under three-point bending arrangement in a universal testing machine were also evaluated. A dynamic mechanical thermal analyzer (DMTA) in three-point bending mode was used to evaluate the temperature-dependent viscoelastic properties of the three types of composites. The creep and creep-recovery behavior was evaluated at 40°C, 80°C, 120°C, 160°C and 200°C. To construct a master curve, extrapolated short-term isothermal creep tests were performed from 120°C to 180°C at the intervals of 10°C. The predicted master curve represents the creep behavior of composites over more than 10 years. It was shown that the quasi-isotropic CF/PEKK composites exhibited 27% and 12% higher creep resistance at 120°C as compared to zero-direction and cross-ply laminates, respectively. Higher flexural modulus (23%) and flexural strengths (33%) were also exhibited by the quasi-isotropic CF/PEKK composites. The final thickness of quasi-isotropic laminates was 8% lower than the 0o laminates. After analyzing the cross-sections of the composites, it was proposed that the superior mechanical properties of the quasi-isotropic laminates could be due to enhanced nesting between neighboring prepreg layers during the compression molding process, which resulted in closer packing of the fibers. It has been shown that the prepreg stacking sequence could affect the creep behavior and flexural properties of the compression-molded CF/PEKK composites.

Comparison of the time-moisture and time-temperature equivalences in the creep properties of Chinese fir

ABSTRACT The present study investigated how the applications of the time-moisture superposition principle (TMSP) under a moisture content (MC) range of 0–14.2% and the time-temperature superposition principle (TTSP) under a temperature range of 30–150 °C would affect to Chinese fir (Cunninghamia lanceolata [Lamb.] Hook.) creep behaviors across grain orientations via a dynamic mechanical analysis instrument. The results showed that both TMSP and TTSP could describe the evolution of creep in the radial and tangential directions. Master curves constructed by TMSP and TTSP overlapped at a reference condition (30 °C, 0% MC), regardless of the grain orientation. In addition, an equivalent relation between the effects of moisture and temperature on the creep behavior was assumed based on TMSP and TTSP. Under the tested temperature, the effect of the per unit MC was equivalent to that at ca. 33 and 44 °C for the radial and tangential specimens, respectively. These findings elucidate the effects of moisture and temperature on the rheological properties of wood cell walls and are helpful for better utilizing wood in civil engineering applications.

Orthotropic Thermo-Viscoelastic Model for Polymeric Battery Separators with Electrolyte Effect

The separator plays a critical role in the safety of lithium-ion batteries. To predict the structural integrity of polymeric separators in abuse scenarios, understanding the thermo-mechanical behaviors of the separators is very important. This paper presents an orthotropic linear viscoelastic material model for a polymeric separator that accounts for temperature and electrolyte effects. In this model, the temperature effect was introduced through the time-temperature superposition principle (TTSP). A time-temperature-solvent superposition method (TTSSM) was developed to model the behavior of the separator in electrolyte solutions based on the viscoelastic framework established in air. The developed model has been implemented in LS-DYNA® finite element (FE) package as a user-defined subroutine, which enables simulations with the thermal expansion/shrinkage behavior. The model parameters have been established for a polypropylene (PP) separator. The model predictions of the material anisotropy, temperature dependence, and solvent effect agree reasonably well with the experimental data. The results also demonstrated that the non-isothermal simulations without considering the thermal expansion/shrinkage behavior of the separator resulted in large errors.

Dynamic mechanical response of ZrCu-based bulk metallic glasses

The thermal stability and the dynamic mechanical relaxation behavior of (Zr50Cu40Al10)100-xDyx (at.%) (x = 0 or 2) metallic glasses were investigated by differential scanning calorimetry (DSC) and dynamic mechanical analysis (DMA). In the case of the (Zr50Cu40Al10)100-xDyx (x = 0 or 2) metallic glasses, atomic mobility increases by introduction of the Dy element. The activation energy of the the main a relaxation process and fragility index were discussed according to the DMA measurements. With the help of the time-temperature superposition (TTS) principle, the master curves of the model alloys were established, the Kohlrausch-Williams-Watts (KWW) function and quasi-point defects (QPD) theory were used to descirbe the master curves of the metallic glasses. The characteristic parameters related to microstructural heterogeneity in the KWW equation and the QPD model, Kohlrausch exponent βKWW and the correlation factor χ were evaluated. In parallel, the elastic, viscoelastic and viscoplastic responses of the model alloys have been analyzed based on the DMA results. Our investigations demonstrated that introduction of the Dy increases the structure heterogeneity of the (Zr50Cu40Al10)100-xDyx (x = 0 or 2) glassy system, which plays an important role in tailoring the dynamic relaxation behavior and mechanical properties of the metallic glasses.

Time-temperature superposition in viscoelasticity and viscoplasticity for thermoplastics

The use of thermoplastics in the automotive industry is continuously increasing. Design of parts require the characterization and numerical modelling of thermo-mechanical behaviour of those materials under wide strain rate (0–300 s−1) and temperature ranges (−30 °C to +85 °C). Large and costly experimental campaigns are therefore necessary to identify all behaviour's sensitivities. Yet, the time-temperature-superposition (TTS) principle may be a powerful tool to strongly reduce the number of required tests.This paper demonstrates the possibility to extend this principle to the viscoplastic domain while keeping the same shift factors identified for viscoelasticity. So, a limited number of tests (DMA and tensile tests at room temperature only) now enable the characterization of whole thermoplastic behaviour. This new approach is implemented in a viscoelastic, viscoplastic behaviour model. A good correlation between numerical simulations and experiments validate the approach.

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.

Experimental mechanics and numerical prediction on stress relaxation and unrecoverable damage characteristics of rubber materials

Stress relaxation and unrecoverable damage deformation are common phenomenon in rubber materials, which greatly induces instability of geometrical dimension and deteriorates the mechanical performances. The present work proposes experimental mechanics and numerical prediction for studying stress relaxation and unrecoverable damage characteristics. A time-dependent strain energy principle is established to describe the relaxation decay over time, and a quasi-plastic function is combined by considering the plastic flow criteria in order to depict the unrecoverable deformation after stress relaxation. Experimental study is conducted on multi-modes hyper-elastic mechanics and stress relaxation performances, and key parameters of the proposed constitutive model are identified by multi-island genetic algorithm (MIGA). The established constitutive equation is integrated in finite element simulation, and the numerical prediction is conducted. Combined experimental results clearly present nonlinear elastic properties, time-decay relaxation, and unrecoverable damage deformation of rubber materials. The numerical results are in good agreement with experiment ones, and the mechanism of relaxation and damage characteristics are explored. Additionally, based on the time-temperature superposition principle (TTSP) method, long-term stress relaxation behavior at low temperature is estimated by the short-term high-temperature test. This work provides efficient methods of experimental mechanics and numerical prediction for predicting the stress relaxation and damage characteristics of rubber materials, which could be also beneficial for characterizing rubber-base devices in engineering applications.

A novel method for determining the time-temperature superposition relationship of SBS modified bitumen: Effects of bitumen source, modifier type and aging

The time-temperature superposition principle (TTSP) is frequently applied in rheological characterization of styrene-butadiene−styrene triblock copolymer (SBS) modified bitumen (SBSMB). The time-temperature superposition relationship is traditionally determined through optimizing the horizontal displacement of isothermal curves to minimize the errors between measured and predicted rheological data. Different from traditional method, the newly proposed method can determine the time-temperature superposition relationship of SBSMB according to its special points of phase angle plateau regions in isochronal curves. Nevertheless, the validity of this new method is only demonstrated for limited sources of SBSMB in previous study. In present paper, the effects of bitumen source, modifier type and aging on validity of the newly proposed method for determining the time-temperature superposition relationship of SBSMB were investigated. The results indicated that the shape of phase angle plateau region can be totally sorted into “convex” and “S” two types for all kinds of SBSMB samples. Although the rheological properties of SBSMB are affected by different bitumen sources and modifier types, the proposed method is demonstrated to be applicable to SBSMB samples prepared by different bitumen sources and modifier types. The proposed method cannot be applied to short-term or long-term aged SBSMB samples due to disappearance of phase angle plateau region. And the shift factors of original SBSMB obtained from the newly proposed method are no longer suitable for its aged SBSMB samples.

Microstructure homogenization of concrete used in nuclear power plants

Nearly all nuclear power plants in the United States are operating past their intended lifetimes or are requesting lifetime extensions. Therefore, understanding changes to the concrete containment structure over time is crucial to evaluate the structure’s continued viability. Concrete materials are heterogeneous particulate composites that exhibit viscoelastic material properties, which can lead to slow deformation over time, causing stress redistribution and the potential for creep cracking. A code to generate random, three dimensional (3D) concrete microstructures has been developed and paired with finite element analysis to predict the long-term viscoelastic properties of concrete. Data from these simulations are used to develop constitutive equations for the viscoelastic behavior of the homogenized concrete. The codes in this work are used to virtualize laboratory experiments, to obtain long-term creep data in a faster, cheaper manner. To validate this work, the simulated creep behavior of concrete is compared to 800 d of experimental data that has been extended to 27 y of data using the Time-Temperature superposition (TTS) principal. Excellent agreement between the simulation results and experimental data is seen.

The Master‐Curve Band considering Measurement and Modeling Uncertainty for Bituminous Materials

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 (Gg) 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 (Gg) model is proved to be the best to analyze the aging effects.

Experimental Study on Dynamic Properties of a Recycled Composite Sleeper and Its Theoretical Model

As a symmetrical structure in track system, the dynamic properties of recycled composite sleepers are important factors affecting the vibration characteristics of track structure. To study the viscoelastic dynamic properties of the composite sleeper, dynamic mechanical analysis (DMA) tests of a composite sleeper at −5 to 30 °C and 1–60 Hz were first carried out, and then the time-temperature superposition (TTS) and the Williams–Landel–Ferry (WLF) formula were used to predict the dynamic properties of a composite sleeper at a wider frequency range. Finally, the generalized Maxwell model was adopted to characterize the dynamic properties of the composite sleeper, which provides parameters and theoretical models for dynamic analysis. The research results show that the composite sleeper has obvious viscoelasticity. Its modulus is large at low temperature or high frequency. On the contrary, the modulus is small at high temperature or low frequency. Under the test conditions, its complex modulus ranges from 1500 to 2700 MPa. The loss factor is in the range of 0.08–0.13. Using the generalized Maxwell model (n = 4), which can better reflect the dynamic properties of the composite sleeper.

Stress relaxation, creep, and recovery of carbon fiber non-crimp fabric composites

Considering that structural composites are typically composed of off-axis plies, i.e. quasi-isotropic stacking sequence, their strength and stiffness are time-dependent due to the viscoelastic character of polymer matrices. This work consists of determining creep, recovery, and stress relaxation of carbon fiber-reinforced polymer (CFRP) composites. Long-term experimental analyses are conducted via dynamic mechanical analysis under several temperatures and stress levels. From the experimental observations, the changes in the relaxation mechanisms are predicted using Fancey's latch model. The rate of relaxation at different temperatures is also covered. Since at certain strain levels the viscoelastic behavior cannot be properly determined, the stress-relaxation is determined using the time-temperature superposition (TTS) principle, considering nine temperatures at three strain levels in order to cover the three main regions of the composite system (glassy, glass transition and rubbery regions). The models and experiments herein presented can be extended to any polymeric system.