Frequency-temperature Superposition Research Articles

Temperature influence on the natural and forced vibrations of laminate plates with fractional Zener viscoelastic layers

The paper is devoted to the analysis of the influence of ambient temperature on the linear free and non-linear harmonic vibrations of laminate plates with viscoelastic layers. The Zener fractional material model is adopted. The plate kinematics is described using the refined zig-zag theory. The formulation of vibrations of the plate is based on the physical law with the separation of deviatoric and volumetric deformation. The temperature influence is included using the frequency-temperature superposition principle. The shift factor applied to modify the damping properties of the viscoelastic material is computed using the Willams-Landel-Ferry formula.The paper contains the results of several analyses of laminate plates with various viscoelastic materials for which the material data were available in the literature. In particular, the analyses focus on determination of the properties characteristic for the plates with Zener fractional model under the influence of the ambient temperature.

Dynamic Viscoelastic Behavior of Maize Kernel: Application of Frequency-Temperature Superposition.

Maize kernels were treated using two varieties of drying methodologies, namely combined hot air- and vacuum-drying (HAVD) and natural drying (ND). We performed frequency sweep tests, modified Cole-Cole (MCC) analysis, and frequency-temperature superposition (FTS) on these kernels. The kernels' elastic and viscous properties for ND were higher than those for HAVD. The heterogeneous nature of maize kernel may account for the curvature in MCC plot for the kernel treated by HAVD 75 °C and the failure of FTS. MCC analysis was more sensitive than FTS. The kernel treated by HAVD 75 °C demonstrated thermorheologically simple behavior across the entire temperature range (30-45 °C) in both MCC analysis and FTS. The frequency scale for the kernel treated using HAVD 75 °C was broadened by up to 70,000 Hz. The relaxation processes in the kernel treated by HAVD 75 °C were determined to be mainly associated with subunits of molecules or molecular strands. The data herein could be utilized for maize storage and processing.

Glass spectrum, excess wing phenomenon, and master curves in molecular glass formers: A multi-method approach.

The relaxation spectra of glass formers solely displaying an α-peak and excess wing contribution collected by various methods are reanalyzed to pin down their different spectral evolution. We show that master curve construction encompassing both α-peak and emerging excess wing works for depolarized light scattering (DLS) and nuclear magnetic resonance (NMR) relaxometry. It reveals the self-part of the slow dynamics' spectrum. Master curves are to be understood as a result of a more extensive scaling covering all temperatures instead of strict frequency-temperature superposition. DLS and NMR display identical relaxation spectra; yet, comparing different systems, we do not find a generic structural relaxation at variance with recent claims. Dielectric spectroscopy (DS) spectra show particularities, which render master curve construction obsolete. The DS α-peak is enhanced or suppressed with respect to that of DLS or NMR, yet, not correlated to the polarity of the liquid. Attempting to single out the excess wing from the overall spectrum discloses a stronger exponential temperature dependence of its amplitude compared to that below Tg and a link between its exponent and that of the fast dynamics' spectrum. Yet, such a decomposition of α-peak and excess wing appears to be unphysical. Among many different glasses, the amplitude of the excess wing power-law spectrum is found to be identical at Tg, interpreted as a relaxation analog to the Lindemann criterion.

Comparison of different methods for dynamic characterization of porous-elastic materials

Acoustical simulation of porous-elastic materials requires several properties to be characterized, one of them is the dynamic mechanical behavior of the structure. For this goal, quasi-static mechanical analysis (QMA) is the generally used method executed in the ca. 20-60 Hz frequency range, resulting constant (averaged) mechanical properties. Polymer-based materials, however, are well-known from their time- and frequency-dependent behavior. This implies the need for having frequency-dependent data in a wider frequency range, but the error induced by the fluid motion inside the pores increases with frequency. For that reason, dynamic mechanical analysis (DMA) together with frequency-temperature superposition method was chosen to analyze the possibility of extending the evaluable frequency range. Different measurement setups and strategies were tested and evaluated to minimize the errors coming from machine resonances and other influencing factors, and results were compared to those obtained from the classical QMA measurements. It was finally proven, that with thoroughly chosen technique, DMA can give high quality results for porous-elastic materials as well, in a remarkably wide frequency range.

Validation of a Mathematical-Based Model for the Rheological Characterization of Asphalt Mixtures

Asphalt mixtures are viscoelastic materials whose behavior is highly dependent on temperature and loading frequency. The influence of these factors is described through master curves constructed at a given reference temperature based on the principle of frequency-temperature superposition. These curves are used as inputs in asphalt pavement design procedures based on mechanistic principles and related to their in-service pavement performance. This paper proposes the application of the Kramers-Kronig (K-K) relations to characterize the rheological properties of asphalt materials using a mathematical approach. Due to the complexity of the integration of the K-K relations, an approximate solution of the K–K relations was used to develop a Mathematical-Based Model to predict the master curves for the Dynamic Modulus |E*| and the Phase Angle f. This model was validated using the experimental results of two different asphalt mixtures with different characteristics. The results indicate that the model is accurate, and could be an effective approach to mathematically predict the master curves of the asphalt mixture viscoelastic properties in a wide range of temperatures and frequencies.

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.

Nuclear Spin Relaxation in Viscous Liquids: Relaxation Stretching of Single-Particle Probes.

Spin-lattice relaxation rates R1(ω,T), probed via high-field and field-cycling nuclear magnetic resonance (NMR), are used to test the validity of frequency-temperature superposition (FTS) for the reorientation dynamics in viscous liquids. For several liquids, FTS is found to apply so that master curves can be generated. The susceptibility spectra are highly similar to those obtained from depolarized light scattering (DLS) and reveal an excess wing. Where FTS works, two approaches are suggested to access the susceptibility: (i) a plot of deuteron R1(T) vs the spin-spin relaxation rate R2(T) and (ii) a plot of R1(T) vs an independently measured reference time τref(T). Using single-frequency scans, (i) allows one to extract the relaxation stretching as well as the NMR coupling constant. Surveying 26 data sets, we find Kohlrausch functions with exponents 0.39 < βK ≤ 0.67. Plots of the spin-spin relaxation rate R2─rescaled by the NMR coupling constant─as a function of temperature allow one to test how well site-specific NMR relaxations couple to a given reference process. Upon cooling of flexible molecule liquids, the site-specific dynamics is found to merge, suggesting that near Tg the molecules reorient essentially as a rigid entity. This presents a possible resolution for the much lower stretching parameters reported here at high temperatures that contrast with the ones that were reported to be universal in a recent DLS study close to Tg. Our analysis underlines that deuteron relaxation is a uniquely powerful tool to probe single-particle reorientation.

The relaxation behavior of supercooled and glassy imidacloprid.

Employing dielectric spectroscopy, oscillatory shear rheology, and calorimetry, the present work explores the molecular dynamics of the widely used insecticide imidacloprid above and below its glass transition temperature. In its supercooled liquid regime, the applied techniques yield good agreement regarding the characteristic structural (alpha) relaxation times of this material. In addition, the generalized Gemant-DiMarzio-Bishop model provides a good conversion between the frequency-dependent dielectric and shear mechanical responses in its viscous state, allowing for an assessment of imidacloprid's molecular hydrodynamic radius. In order to characterize the molecular dynamics in its glassy regime, we employ several approaches. These include the application of frequency-temperature superposition (FTS) to its isostructural dielectric and rheological responses as well as use of dielectric and calorimetric physical aging and the Adam-Gibbs-Vogel model. While the latter approach and dielectric FTS provide relaxation times that are close to each other, the other methods predict notably longer times that are closer to those reflecting a complete recovery of ergodicity. This seemingly conflicting dissimilarity demonstrates that the molecular dynamics of glassy imidacloprid strongly depends on its thermal history, with high relevance for the use of this insecticide as an active ingredient in technological applications.

Investigation of frequency dependent mechanical properties of porous materials using dynamic mechanical analyzer and frequency-temperature superposition theory

In acoustic design of engineering applications - such as in the acoustic analysis of passenger vehicles - poroelastic materials are of great importance. One of the most influencing properties in determining their noise-reduction potential is the storage modulus. The purpose of this study is to examine the frequency dependence of storage modulus of selected porous acoustic materials at least up to 1000 Hz. This is executed by using the combined use of dynamic mechanical analyzer and frequency-temperature superposition theory. All other methods for measuring the storage modulus fall short in determining frequency-dependence above 100 Hz: quasi-static mechanical analyzer is mostly used for determining an averaged constant value deduced from low-frequency measurements, while the usage of an electromagnetic shaker capable for high-frequency excitation may include effects of fluid motion inside the pores, thus significantly modifying the results. Frequency-temperature superposition enables to determine the storage modulus values in a wide frequency range, based on low-frequency measurements, where fluid-structure interaction is negligible. It was found that the modulus varied significantly up to and beyond 1000 Hz, and thus, acoustical characterization of these materials can be significantly improved using the proposed method. The work concludes with recommendations to improve the accuracy of the results.

Dynamics in the plastic crystalline phase of cyanocyclohexane and isocyanocyclohexane probed by 1H field cycling NMR relaxometry.

Proton Field-Cycling (FC) nuclear magnetic resonance (NMR) relaxometry is applied over a wide frequency and temperature range to get insight into the dynamic processes occurring in the plastically crystalline phase of the two isomers cyanocyclohexane (CNCH) and isocyanocyclohexane. The spin-lattice relaxation rate, R1(ω), is measured in the 0.01-30MHz frequency range and transformed into the susceptibility representation χNMR ″ω=ωR1ω. Three relaxation processes are identified, namely, a main (α-) relaxation, a fast secondary (β-) relaxation, and a slow relaxation; they are very similar for the two isomers. Exploiting frequency-temperature superposition, master curves of χNMR ″ωτ are constructed and analyzed for different processes. The α-relaxation displays a pronounced non-Lorentzian susceptibility with a temperature independent width parameter, and the correlation times display a non-Arrhenius temperature dependence-features indicating cooperative dynamics of the overall reorientation of the molecules. The β-relaxation shows high similarity with secondary relaxations in structural glasses. The extracted correlation times well agree with those reported by other techniques. A direct comparison of FC NMR and dielectric master curves for CNCH yields pronounced difference regarding the non-Lorentzian spectral shape as well as the relative relaxation strength of α- and β-relaxation. The correlation times of the slow relaxation follow an Arrhenius temperature dependence with a comparatively high activation energy. As the α-process involves liquid-like isotropic molecular reorientation, the slow process has to be attributed to vacancy diffusion, which modulates intermolecular dipole-dipole interactions, possibly accompanied by chair-chair interconversion of the cyclohexane ring. However, the low frequency relaxation features characteristic of vacancy diffusion cannot be detected due to experimental limitations.

Glassy and Polymer Dynamics of Elastomers by 1H-Field-Cycling NMR Relaxometry: Effects of Fillers.

1H spin–lattice relaxation rate (R1) dispersions were acquired by field-cycling (FC) NMR relaxometry between 0.01 and 35 MHz over a wide temperature range on polyisoprene rubber (IR), either unfilled or filled with different amounts of carbon black, silica, or a combination of both, and sulfur cured. By exploiting the frequency–temperature superposition principle and constructing master curves for the total FC NMR susceptibility, χ″(ω) = ωR1(ω), the correlation times for glassy dynamics, τs, were determined. Moreover, the contribution of polymer dynamics, χpol″(ω), to χ″(ω) was singled out by subtracting the contribution of glassy dynamics, χglass″(ω), well represented by the Cole–Davidson spectral density. Glassy dynamics resulted moderately modified by the presence of fillers, τs values determined for the filled rubbers being slightly different from those of the unfilled one. Polymer dynamics was affected by the presence of fillers in the Rouse regime. A change in the frequency dependence of χpol″(ω) at low frequencies was observed for all filled rubbers, more pronounced for those reinforced with silica, which suggests that the presence of the filler particles can affect chain conformations, resulting in a different Rouse mode distribution, and/or interchain interactions modulated by translational motions.

Translational and rotational diffusion of three glass forming alcohols by 1H field cycling NMR relaxometry

1H field-cycling NMR relaxometry was applied to investigate the dynamics of the three glass forming alcohols 2-phenylbutan-1-ol (BEP), 2-(trifluoromethyl)phenetyl alcohol (2TFMP), and 4-(trifluoromethyl)phenetyl alcohol (4TFMP), all having a phenyl ring as substituent. 1H longitudinal relaxation rates, R1, were measured at Larmor frequencies (ν) from 0.01 to 35 MHz in the liquid phase of the three alcohols between 213 and 313 K. Data analysis was performed using master curves built on the basis of the frequency temperature superposition principle exploiting the NMR susceptibility representation. Longitudinal relaxation was considered to arise from two dynamic processes, i.e. translational diffusion and molecular rotations. For the first process a force-free hard-sphere model was used, whereas the phenomenological Davidson-Cole function was employed to model the second motional process. The analysis allowed translational and rotational correlation times to be determined over a wide time scale (10−11 - 10−3 s). The ratio between the two correlation times indicated the formation of hydrogen bonded networks for all alcohols, while their trends with temperature suggested that BEP forms stronger hydrogen bonds. The resulting self-diffusion coefficients were in agreement with the values independently determined from the slope of R1vs ν1/2 at low frequencies.

Self-diffusion micromechanism in Nafion studied by 2H NMR relaxation dispersion.

Field Cycling (FC) 2H nuclear magnetic resonance (NMR) relaxometry was applied to study dynamics in Nafion NR 212 in the temperature range from 300 K to 190 K and water content of λ = 8.2. The sensitive time window of FC was extended up to eight decades using the temperature-frequency superposition principle and master curve. The rotational correlation times obtained from 2H FC NMR coincide with translational correlation times gained from static field 2H NMR diffusometry in the temperature range applied. This fact means that a long-range mass transport in Nafion is coupled to molecular rotations. It is assumed that confined water in Nafion has more ordered oxygen sublattices as compared with bulk water, on a short range is similar to ice. We discuss the possible role of D and L defects, typical for the ordered ice structure and using this concept to describe the processes of self-diffusion of confined water in Nafion, as well as the similarity of temperature and humidity dependence of self-diffusion and proton conductivity.

Method for determining frequency dependent thermomechanical behavior of polymer films at cryogenic temperatures

The purpose of this study was to investigate a parameterized mathematical approach for estimating the complex modulus of a polyimide film at extreme cryogenic temperatures (e.g. 4 K). Such films are used in extreme cryogenic applications such as superconducting magnets and electronic devices. A polymer core of the electronic laminate, Pyralux AP8525R (polyimide), was tested on a TA Instruments Q800 dynamic mechanical analyzer from 140 K to 293 K to obtain complex tensile moduli, and these data were then extrapolated using multiple types of fits. For one predictive method, activation energy of flows, Ea, were calculated using an Arrhenius model and frequency-temperature superposition. All fits were projected to 4 K. A second type of fit was a T3 model. A validation study using Vespel, a material where dynamic modulus had been previously reported at 4 K, was also performed. The validation study indicated that for similar materials (e.g. amorphous aromatic polyimides) a cubic parametrized fit might be the most useful predictive tool. Other polymers reported as tested to 4 K in the literature exhibited a plateau in modulus at low temperatures (sigmoidal fit). From the literature, an amorphous aromatic polyimide and polystyrene showed an increase in modulus at low temperature which is inconsistent with a plateau or sigmoidal fit. The T3, or cubic model, was chosen as the best predictive method for the modulus of the Pyralux core polymer. The theoretical rationale for a cubic fit is discussed, though why (of the three proposed methods) only two polymers to date are reported to exhibit this behavior near 4 K remains unclear.

Glassy and Polymer Dynamics of Elastomers by 1H Field-Cycling NMR Relaxometry: Effects of Cross-Linking.

1H spin lattice relaxation rate (R1) dispersions were acquired by field-cycling (FC) NMR relaxometry between 0.01 and 35 MHz over a wide temperature range on polyisoprene (IR), polybutadiene (BR), and poly(styrene-co-butadiene) (SBR) rubbers, obtained by vulcanization under different conditions, and on the corresponding uncured elastomers. By exploiting the frequency–temperature superposition principle, χ″(ωτs) master curves were constructed by shifting the total FC NMR susceptibility, χ″(ω) = ωR1(ω), curves along the frequency axis by the correlation times for glassy dynamics, τs. Longer τs values and, correspondingly, higher glass transition temperatures were determined for the sulfur-cured elastomers with respect to the uncured ones, which increased by increasing the cross-link density, whereas no significant changes were found for fragility. The contribution of polymer dynamics, χpol″(ω), to χ″(ω) was singled out by subtracting the contribution of glassy dynamics, χglass″(ω), well represented using a Cole–Davidson spectral density. For all elastomers, χpol″(ω) was found to represent a small fraction, on the order of 0.05–0.14, of the total χ″(ω), which did not show a significant dependence on cross-link density. In the investigated temperature and frequency ranges, polymer dynamics was found to encompass regimes I (Rouse dynamics) and II (constrained Rouse dynamics) of the tube reptation model for the uncured elastomers and only regime I for the vulcanized ones. This is clear evidence that chemical cross-links impose constraints on chain dynamics on a larger space and time scale than free Rouse modes.

Systematic differences in the relaxation stretching of polar molecular liquids probed by dielectric vs magnetic resonance and photon correlation spectroscopy.

Relaxation spectra of molecular glass formers devoid of secondary relaxation maxima, as measured by dielectric spectroscopy (DS), nuclear magnetic resonance (NMR) relaxometry, photon correlation spectroscopy (PCS), and Fabry-Perot interferometry, are quantitatively compared in terms of the Kohlrausch stretching parameter βK. For a reliable estimate of βK, the excess wing contribution has to be included in the spectral analysis. The relaxation stretching probed by PCS and NMR varies only weakly among the liquids (βK = 0.58 ± 0.06). It is similar to that found in DS, provided that the liquid is sufficiently nonpolar (relaxation strength Δε≲6). For larger strengths, larger βK DS (narrowed relaxation spectra) are found when compared to those reported from NMR and PCS. Frequency-temperature superposition (FTS) holds for PCS and NMR. This is demonstrated by data scaling and, for the few glass formers for which results are available, by the equivalence of the susceptibilities χPCS ″ωτ∝χNMR ″τ∝χNMR ″ω, i.e., measuring at a constant frequency is equivalent to measuring at a constant temperature or constant correlation time. In this context, a plot of the spin-lattice relaxation rate R1(T) as a function of the spin-spin relaxation rate R2(T) is suggested to reveal the stretching parameter without the need to perform frequency-dependent investigations. Dielectrically, we identify a trend of increasing deviations from FTS with increasing Δε. Depending on the technique and glass former, the relative relaxation strength of the excess wing varies, whereas its exponent appears to be method independent for a given substance. For polar liquids, we discuss possible reasons for the discrepancy between the results from PCS and NMR as compared to those from DS.

Modeling thermal-visco-elastohydrodynamic lubrication (TVEHL) interfaces of polymer-based materials

This paper reports a novel thermal-visco-elasohydrodynamic lubrication (TVEHL) model for analyzing the lubrication behavior of the interface formed by an elastic sphere and a polymer half-space. The temperature-dependent viscoelastic displacement of the polymer surface is calculated through the elastic-viscoelastic correspondence theory and frequency-temperature superposition. The discrete convolution and fast Fourier transform (DC-FFT) algorithm is used for efficient solution computation. The model is verified by comparing results from its degenerated forms with those from thermal-viscoelastic (TVE) contact and thermal-elastohydrodynamic lubrication (TEHL) theories. The results from the current model with and without considering temperature effect are also compared. The new TVEHL model is explored to study the viscoelastic material property, entraining speed, sliding-to-rolling ratio, and the coupled thermal-viscoelasticity effects.

Mechanical characterization of asphalt mixes inter-layer bonding based on reptation theory

A bituminous pavement is composed of several layers. The bonding of the interfaces between these layers is essential to ensure the durability of the pavement structure. Un-bonded interfaces can cause early deterioration of the surface courses due to the poor distribution of mechanical loads induce by the traffic onto the base-layers. The bonding between asphalt layers depends on several parameters such as the laying temperature, the use or not of bitumen emulsions to bond the interfaces. Bonding is usually characterized by shear, tensile or torsion tests. This paper focuses on the effects of loading rate, test temperature, specimens’ size and emulsion content on the shear strength evaluated through the shear and tensile tests. In part 1, the shear bond test (SBT) and tensile adhesive test (TAT) were firstly performed on two-layered specimens bonded or not with emulsion. Their diameters were 100 or 150 mm. The tests were carried out at 50 mm.min-1 and 20 °C to evaluate the laying conditions (laying temperature, use or not of emulsion). These results were then compared to those of one-layer specimens without interface. The results of part 1 investigations showed that: i) the shear strengths of small samples are 1.3 times higher than that of big specimens, ii) the shear strength resulting from different laying conditions can be classified, from the highest to the lowest, as follows: hot on hot (H/H) bonding, hot on cold (H/C) bonding with emulsion C69B2 and hot on cold (H/C) bonding without emulsion, iii) the failure strengths of TAT are 2.2 times lower than those of SBT. In part 2, the SBT was performed on two-layered specimens of 100 mm in diameter at three loading rates (0.5, 5, 50 mm.min-1) and test temperatures (−10 °C, 5 °C, 20 °C). In this second test series, 250 and 500 g.m-2 of bitumen emulsion C69B2 and styrene-butadiene rubber (SBR) polymer emulsion were used to bond the interfaces. Based on these results the master curves of shear strength were built based on the frequency-temperature superposition principle (FTSP). Furthermore, an explanation of the interfaces bonding mechanism based on the bitumens’ macromolecules chains mobility across the interface is proposed. This interpretation required the introduction of some interface bonding parameters: the degree of intimate Dic contact, the degree of healing Dh and the degree of bonding Db. Finally, the master curves of the degree of healing and degree of bonding were also built based on the frequency-temperature superposition principle (FTSP).

NMR Relaxometry: The Canonical Case Glycerol.

We present a quantitative description of the proton spin-lattice relaxation rate R1(T,ω) of glycerol including temperatures from 191 to 360 K and a frequency range 10 kHz < ω/2π < 20 MHz covered by the field-cycling technique. The analysis encompasses the data compiled by Noack and co-workers in 1971, so far, the most complete data set (10 kHz > ω/2π < 117 MHz). Applying frequency-temperature superposition, master curves are constructed extending over 15 decades in frequency/time. They are described by contributions reflecting translational and rotational dynamics mediated by inter- and intramolecular relaxation pathways. The rotational part of the spectral density/susceptibility shows high similarity with those reported by dielectric spectroscopy or photon correlation spectroscopy (PCS). In addition to a Cole-Davidson-like peak, a high-frequency "excess wing" has to be accounted for. Quantitative agreement with the PCS susceptibility is found which probes the same order of the rotational correlation function. The translational contribution is reproduced by applying the force-free hard sphere model, describing diffusion of dipolarly coupled spin systems. Rotational and translational time constants are compared to those from other techniques. Our approach is paradigmatic for the analysis of spin relaxation in glass-forming liquids. It also solves long-standing deficiencies regarding the analyses of deuteron relaxation. Moreover, the case of glycerol is special as its large separation of translation and rotation dynamics, probably because of its hydrogen bond network, is not found in nonassociated liquids.

The Application of Frequency-Temperature Superposition Principle for Back-Calculation of Falling Weight Deflectometer

The falling weight deflectometer (FWD) is a widely used nondestructive test (NDT) device in pavement infrastructure. A FWD test measures the surface deflections subjected to an applied impact loading and the modulus of pavement layers can be determined by back-calculating the measured deflections. However, the modulus of asphalt layers is significantly influenced by temperature; hence, the temperature correction must be considered in back-calculation to evaluate the moduli of asphalt layers at a reference temperature. In addition, the in situ temperature at various pavement depths is difficult to measure. A model for evaluating the temperature at various depths must be established to estimate the in situ temperature of asphalt layers. This study collected the temperature data from a FWD test site to establish a temperature-evaluation model for various depths. The cored specimens from the test site were obtained to conduct dynamic modulus tests for asphalt layers. The FWD tests were applied at the FWD test site and the back-calculation was performed with temperature correction using the frequency-temperature superposition principle. The back-calculated moduli of asphalt layers were compared with the master curve of dynamic modulus to verify the application of the frequency-temperature superposition principle for FWD back-calculation. The results show that the proposed temperature-evaluation model can effectively evaluate the temperature at various depths of pavement. Moreover, the frequency-temperature superposition principle can be effectively employed to conduct temperature correction for FWD back-calculation.