The Time-temperature Superposition Principle Research Articles

Long-Term Viscoelastic Response of E-glass/Bismaleimide Composite in Seawater Environment

The effect of seawater absorption on the long-term viscoelastic response of E-glass/BMI composite is presented in this paper. The diffusion of seawater into the composite shows a two-stage behavior, dominated by Fickian diffusion initially and followed by polymeric relaxation. The Glass transition temperature (Tg) of the composite with seawater absorption is considerably lowered due to the plasticization effect. However the effect of water absorption at 50 °C is found to be reversible after drying process. The time-temperature superposition (TTS) was performed based on the results of Dynamic Mechanical Analysis to construct the master curve of storage modulus. The shift factors exhibit Arrhenius behavior when temperature is well below Tg and Vogel-Fulcher-Tammann (VFT) like behavior when temperature gets close to glass transition region. As a result, a semi-empirical formulation is proposed to account for the seawater absorption effect in predicting long-term viscoelastic response of BMI composites based on temperature dependent storage modulus and TTS. The predicted master curves show that the degradation of storage modulus accelerates with both seawater exposure and increasing temperature. The proposed formulation can be applied to predict the long-term durability of any thermorheologically simple composite materials in seawater environment.

Reactive extrusion of PLA, PBAT with a multi-functional epoxide: Physico-chemical and rheological properties

The aim of this work was to highlight the presence of long chain branching, LCB, due to the incorporation of a multifunctional epoxide, named Joncryl ®, as a chain extender, into both poly (lactic acid) (PLA) and poly (butylene-adipate-co-terephtalate) (PBAT) polymers. The modified polymers were prepared using a twin-screw reactive extrusion system. It has been demonstrated through this study that these modified biopolymers are thermo-rheologically complex. This complexity may be attributed to the formation of covalent bonds between both polymer and chain extender and leads to a failure of the time-temperature superposition (TTS). The linear viscoelastic properties were predicated on the use of the so-called Van-Gurp–Palmen plots, from which the topology of the modified PLA and PBAT has been studied and analyzed. Indeed, they exhibited a typical feature of a mixture of linear and randomly branched polymers. Furthermore, the resulting linear and branched chains, due to the reactive highly functionalized epoxide, are discussed using rheological investigations (relaxation spectra, flow activation energy) coupled with solution viscometry (solution viscometry properties, hydrodynamic radius) and physico-chemical properties (size-exclusion chromatography).

Reinforced Flax Mat/Modified Polylactide (PLA) Composites: Impact, Thermal, and Mechanical Properties

Polylactide (PLA)/flax mat and modified PLA/flax mat composites were produced by the hot pressing technique. The dispersion of the flax mat in the composites was studied by the scanning electron microscopy (SEM). The PLA composites were subjected to an instrumented falling-weight impact test. The mechanical and thermal properties of the composites were determined by using tensile tests, a thermogravimetric analysis (TGA), and a dynamic-mechanical thermal analysis (DMTA). It was found that the flat mat increased the impact resistance of PLA, but the tensile strength of the modified PLA/flax mat composite decreased slightly compared with that of PLA. Data on the elongation at break pointed to a higher ductility of the modified PLA and its composites. Moreover, the addition of a thermal modifier enhanced the thermal resistance below the processing temperature of PLA and had a marginal effect on its glass-transition temperature. The master curves of the storage modulus were constructed by employing the time-temperature superposition (TTS) principle. The principle of a linear viscoelastic material was fairly applicable to transition from the modulus to the creep compliance for all the systems studied.

Creep and recovery behavior of kenaf/polypropylene nonwoven composites

ABSTRACTThis article reports an exploratory study on the creep and recovery behavior of kenaf/polypropylene nonwoven composites (KPNCs), serving as a bio‐based substitution for polypropylene (PP) plastics in the automotive industry due to the environmental concern. The creep and recovery behavior of KPNC and solid virgin PP were performed by dynamic mechanical analyzer (DMA) which allowed it to be studied extensively. The linear viscoelastic limit (LVL) was found at 1 MPa. Two popular creep models, the four‐element Burgers (FEB) model and the Findley power law (FPL) model, were used to model the creep behavior in this study. The FEB model was found only appropriate for characterizing short‐term creep behavior. In contrast, the FPL model was satisfactory for predicting the long‐term creep performance. The long‐term creep behavior of KPNC in comparison to virgin PP plastic was predicted using the time‐temperature superposition (TTS) principle. The 1‐year creep strains were estimated to be 0.32% for KPNC and 1.00% for virgin PP at 40°C. A three‐day creep test was conducted to validate the effectiveness of the TTS prediction. KPNC showed a better creep resistance and higher recoverability than the virgin PP, especially in a high‐temperature environment. © 2014 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2014, 131, 40726.

Prediction of color changes using the time-temperature superposition principle in liquid formulations.

This study reports the results of applying the time-temperature superposition principle (TTSP) to the prediction of color changes in liquid formulations. A sample solution consisting of L-tryptophan and glucose was used as the model liquid formulation for the Maillard reaction. After accelerated aging treatment at elevated temperatures, the Commission Internationale de l'Eclairage (CIE) LAB color parameters (a*, b*, L*, and E*ab) of the sample solution were measured using a spectrophotometer. The TTSP was then applied to a kinetic analysis of the color changes. The calculated values of the apparent activation energy of a*, b*, L*, and ΔE*ab were 105.2, 109.8, 91.6, and 103.7 kJ/mol, respectively. The predicted values of the color parameters at 40°C were calculated using Arrhenius plots for each of the color parameters. A comparison of the relationships between the experimental and predicted values of each color parameter revealed the coefficients of determination for a*, b*, L*, and ΔE*ab to be 0.961, 0.979, 0.960, and 0.979, respectively. All the R(2) values were sufficiently high, and these results suggested that the prediction was highly reliable. Kinetic analysis using the TTSP was successfully applied to calculating the apparent activation energy and to predicting the color changes at any temperature or duration.

REDUCCIÓN DEL RUIDO ESTRUCTURAL Y LA VIBRACION EN UN PROTOTIPO DE CABINA DE ASCENSOR MEDIANTE LA UNIÓN ADHESIVA DE PANELES

Abstract This paper presents an experimental study for the structural noise and vibration reduction in a cabin elevator by means of adhesive bonded joints of panels. For that noise and vibration measurements are carried out on two prototypes: one of them built with classical panel joining technologies and the other one with adhesive joints. First of all the mechanical properties (relaxation and complex moduli) of two low modulus materials are compared: a silane and a modified silane adhesives. These properties are obtained for both materials by means of dynamic mechanical thermal analysis technique (DMTA), the master curves under direct strain being built-up through a procedure based on the time-temperature superposition (TTS) principle. Next, the influence that these two materials have on the dynamic response of an adhesively bonded metallic beam is investigated, in order to select the right candidate according to design criteria. Finally, an application for an elevator cabin prototype is presented, in which noise and vibration are measured in order to put into evidence the benefits of joining panels by means of adhesive bonded joints in contrast to the traditional joining technologies. Keywords: Noise and vibration reduction; adhesive bonded joints; cabin elevator

A comparative study of the influence of shift factor equations on master curve construction

This paper evaluates the applicability of different shifting techniques for constructing complex modulus master curves using the time-temperature superposition principle (TTSP). A database of complex modulus results of unmodified bitumens, polymer modified bitumens (PMBs), bitumen-filler mastics, unaged and aged bitumens was used together with a Generalized Logistic Sigmoidal Model to assess the validity of seven different shifting approaches. Except for the Laboratoire Central des Ponts et Chaussees (LCPC) method, the construction of master curves was done using the Generalised Logistic Sigmoidal Model and non-linear least squares regression optimization with the aid of the Microsoft Excel Spreadsheet Solver function. The goodness-of-fit for the various shifting techniques and functions was assessed through graphical and statistical methods. From the study, it was found that a numerical shift approach using non-linear least squares produced the best fit between experimental and predicted data in terms of both graphical and goodness-of-fit statistics. The ranking of the other shifting techniques consisted of the LCPC approach, followed by the William, Landel and Ferry (WLF), Modified Kaelble, Viscosity Temperature Susceptibility (VTS), Arrhenius and Log-Linear methods. However, most of the equations are basically empirical and they are not expected to be strictly obeyed by any materials. Discrepancies were still evident, even for the better functions, for those materials that demonstrated a deviation from the thermorheological simplicity of the rheological behaviour as found for highly structured bitumens following high degrees of polymer modification and/or oxidative ageing.

Accelerated creep testing of polymers using the stepped isothermal method

The increasing use of polymers in engineering applications requires suitable accelerated test methods for predicting their long-term behavior. The stepped isothermal method (SIM), originally developed for product testing of geosynthetics, was successfully applied in the presented work to characterize the long-term creep behavior of polypropylene up to approximately 100 years. Based on the time-temperature superposition principle, this method can be described as a short-term creep experiment during which the temperature is elevated stepwise. It is shown that the temperature steps can be rescaled and shifted to generate a master curve matching the prediction of long-term creep resulting from the conventional approach of the time-temperature superposition principle (TTSP). This compliance with established test methods and its good reproducibility suggests that SIM might be a useful tool for accelerated testing of long-term creep behavior, especially for comparative purposes such as quick screening of material formulations during the early development stages, or the at-line assessment of resins as part of quality assurance.

Dynamic Viscoelastic Properties of SBS Modified Asphalt Based on DSR Testing

Five SBS modified asphalts and one base asphalt were selected to carry out frequency sweeps over a wider frequency range using the dynamic shear rheometer (DSR). Six asphalt binders were subjected to sinusoidal loading at 30°C-90°C within the linear viscoelastic limits, and master curves of complex modulus (G*) and phase angle (δ) could be constructed by means of the time-temperature superposition principle (TTSP). The results show that the G* values of SBS modified asphalts are significantly greater than those of base asphalt at low frequencies, but are slightly smaller at high frequencies. Compared with the base asphalt, SBS modified asphalts have narrower master curves of complex modulus, and their phase angles are much smaller within the whole frequency range. This indicates that various properties of SBS modified asphalts, such as high-temperature property, low-temperature property, temperature susceptibility and elastic recoverability, are superior to those of the base asphalt. The G* values of the rolling thin-film oven (RTFO) aged asphalt are larger than those of the unaged asphalt in the whole range of frequencies, demonstrating that the anti-rutting performance of asphalt binder is improved after short-term aging.

Dynamic response of polyurea subjected to nanosecond rise-time stress waves

Shaped charges and explosively formed projectiles used in modern warfare can attain speeds as high as 30,000 ft/s. Impacts from these threats are expected to load the armor materials in the 10 to 100 ns timeframe. During this time, the material strains are quite limited but the strain rates are extremely high. To develop armors against such threats it is imperative to understand the dynamic constitutive behavior of materials in the tens of nanoseconds timeframe. Material behavior in this parameter space cannot be obtained by even the most sophisticated plate-impact and split-Hopkinson bar setups that exist within the high energy materials field today. This paper introduces an apparatus and a test method that are based on laser-generated stress waves to obtain such material behaviors. Although applicable to any material system, the test procedures are demonstrated on polyurea which shows unusual dynamic properties. Thin polyurea layers were deformed using laser-generated stress waves with 1–2 ns rise times and 16 ns total duration. The total strain in the samples was less than 3%. Because of the transient nature of the stress wave, the strain rate varied throughout the deformation history of the sample. A peak value of 1.1×105 s−1 was calculated. It was found that the stress-strain characteristics, determined from experimentally recorded incident and transmitted wave profiles, matched satisfactorily with those computed from a 2D wave mechanics simulation in which the polyurea was modeled as a linearly viscoelastic solid with constants derived from the quasi-static experiments. Thus, the test data conformed to the Time-Temperature Superposition (TTS) principle even at extremely high strain rates of our test. This then extends the previous observations of Zhao et al. (Mech. Time-Depend. Mater. 11:289–308, 2007) who showed the applicability of the TTS principle for polyurea in the linearly viscoelastic regime up to peak strain rates of 1200 s−1.

Linear Viscoelastic Behavior of an Azobenzene Nematic Block Copolymer

We report on the rheological investigation of a nematic block copolymer of an azobenzene methacrylate (MA4) and methyl methacrylate (MMA). Relaxation processes are discussed in terms of chain architecture and viscoelastic response of the polymer. In contrast to analogous random copolymers of MMA and MA4, the present block copolymer did not show validity of the time-temperature superposition (TTS) principle for all material functions. TTS was found to work only for the storage modulus. Rheological steady-state and oscillatory measurements were thus compared in order to obtain further insight into such a peculiar phenomenon.

Life-time prediction of a chloroprene rubber (CR) O-ring using intermittent compression stress relaxation (CSR) and time-temperature superposition (TTS) Principle

Intermittent compression stress relaxation (CSR) testing was used to examine the degradation of a large scale chloroprene rubber (CR) O-ring, rather than a reduced scale copy, as well as predict its life-time. An intermittent CSR jig was designed by considering the O-ring’s environment during use. The testing allowed the observation of the effects of friction, heat loss and stress relaxation by the Mullins effect. Degradation of O-rings by thermal aging was observed between 40 and 120 °C. In the high temperature range of 80–120 °C, the O-rings exhibited linear degradation behavior and satisfied the Arrhenius relationship. The activation energy was approximately 72.7 kJ/mol. From the Arrhenius plots, the predicted life-times were 22.8 years and 34.5 years for the 50% and 40% failure conditions, respectively. Using the time-temperature superposition (TTS) principle, full predictions of failure at 40 °C could be made, saving considerable testing time. Between 40 and 80 °C, the activation energy decreased to 58.9 kJ/mol. William-Landel-Ferry (WLF) plotting confirmed that the O-rings show non-linear degradation behavior under 80 °C. The life-time of the O-rings predicted by the TTS principle was 11.1 years and 18.1 years for each failure condition. The life-time predicted by the TTS principle was more conservative than that from the Arrhenius relationship. Open image in new window

Prediction of long-term viscoelastic behavior of amorphous resin based on the time-temperature superposition principle

This paper deals with the prediction of long-term viscoelastic behavior of amorphous resin at a temperature below the glass transition temperature T g from measuring the short-term viscoelastic behavior at elevated temperatures based on the time-temperature superposition principle (TTSP) with vertical shift as well as horizontal shift. The long-term creep compliance as well as short-term and medium-term creep compliances were measured at elevated temperatures. The master curves of creep compliance can be constructed from measured data by shifting vertically as well as horizontally. The master curves of creep compliance constructed from measured data by short-term and medium-term creep tests agree well with those measured by long-term creep tests. Furthermore, the horizontal and vertical shift factors obtained from constructing the master curve are independent of the time period of creep tests. Therefore, the long-term viscoelastic behavior at a temperature below T g can be predicted accurately from measuring the short-term viscoelastic behavior at elevated temperatures based on the TTSP with vertical shift as well as horizontal shift.

Predicting Compressive Creep Behavior of Virgin HDPE Using Thermal Acceleration

The subject of this paper is the compressive creep behavior of viscoelastic materials, such as high-density polyethylene (HDPE), commonly used to manufacture a multitude of civil engineering products, including polymeric piling, decking, and fender elements. Accelerated methods to predict the tensile creep of polymers are already available. The time-temperature superposition (TTS) model is the basis of several available methods, and one of its derivatives, the stepped isothermal method (SIM), is the basis for an ASTM standard for tensile creep. In this paper, both TTS and SIM have been adapted to study the time- and temperature-dependent compressive creep of HDPE. Experimental test results on virgin HDPE indicate that both TTS and SIM are applicable for predicting compressive creep with some limitations. Preliminary results indicate that the tested virgin HDPE loaded in compression is expected to creep by approximately 2% in 100 years when loaded to an ultimate stress of 2.8 MPa (400 psi) at room temperat...

Comparison of Accelerated Compressive Creep Behavior of Virgin HDPE Using Thermal and Energy Approaches

This article compares two available approaches for accelerating the creep response of viscoelastic materials, such as High Density Polyethylene (HDPE), which is increasingly gaining attention for use in construction. Thermal acceleration methods to predict the tensile creep of polymers are already available. The Time-Temperature Superposition (TTS) phenomenon is the basis of several available methods, and an ASTM standard for tensile creep of geosynthetics is based on one of its derivatives, the Stepped Isothermal Method (SIM). In this article, both TTS and SIM have been adapted to study the compressive creep of virgin HDPE. An alternate approach, based on the equivalence of strain energy density (SED) between conventional constant-stress creep tests and strain-controlled stress-strain tests, is also adapted for accelerated compressive creep of HDPE. There is remarkably a good agreement among the creep behaviors obtained from conventional tests, TTS, SIM, and SED predictions for virgin HDPE.

Creep compression behaviour of a polyurethane foam from cryogenic temperatures: size effect and long-term prediction

The objective of this work was to predict the long term behavior of Polyurethane foam (PU) at very lowtemperature, by applying the timetemperature superposition principle (TTSP). The experimental background of the TTSP was based on a Dynamical Mechanical Analysis technique. Two issues arise from this experimental approach: the relevance of the temperature range to apply the TTSP, and the possible sizeeffect associated to the small DM A samples. Firstly, on the studied temperature range (�170°C; +180°C) many transitions hbeen observed, particularly from �20°C. Thus to apply the TTSP, it would be necessary to limit the temperature range (between temperature of molecular transitions, i.e. from �20°C up to 80°C). At very low temperatures, DMA spectra did not evidence any viscoelastic domain. However a deformation has been measured during creep tests in the same temperature range. So it would be necessary to determine which micromechanism is responsible for the observed deformation. Secondly, it was important to determine if the volume of DMA sample was representative. Several techniques have shown that a representative volume would be reached between 8 and 12mm 3 .

Thermal aging of a blend of high‐performance fibers

AbstractThe focus of this work is the study of the thermal aging of high‐performance fibers used in the making of fire protective garments. Accelerated thermal aging tests were carried out on fabric samples made up of a blend of Kevlar® (poly p‐phenylene terephthalamide) and PBI (poly benzimidazole) staple fibers, as well as on yarns pulled from this fabric, by means of exposure to elevated temperatures, comprised between 190°C and 320°C. All samples underwent loss of breaking force retention. The material thermal life, defined as the time required for the fibers to attain a 50% reduction of the original breaking force, ranged between a dozen of days at the lowest exposure temperature, to less than an hour at the highest. Breaking force data were fitted using the Arrhenius model following two different approaches, namely the extrapolated thermal life value and the shift factors yielded by the time‐temperature superposition (TTS). The Arrhenius model seemed to describe appropriately the overall aging process, as inferred from the excellent fit obtained when using both approaches, although activation energies provided from both approaches are different. To follow the chemical evolution of the material with thermal aging, Fourier‐transform infrared (FTIR) analyses were conducted. The qualitative analysis of the FTIR spectra showed little evidence of chemical changes between the aged and the nonaged samples, indicating either that the aging process carries on without significant modification of the chemical structure of the fibers, or that FTIR is not an appropriate method to spot such a modification. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2010

Time-temperature superposition principle for bituminous mixtures

ABSTRACT In the small strain domain (amplitudes below about 10−4), when considering 1D approach, the bituminous mixtures behaviour is linear viscoelastic, with a great thermal sensitivity and respects the Time-Temperature Superposition Principle (TTSP). In this paper, the generalisation of the TTSP is proposed for 3D. Measurements of complex Youngs modulus (E*) and complex Poisson's ratio (v*) during cyclic loadings are presented. v* is also shown dependent on frequency and temperature and respects the TTSP. A key result is that a very close shift factor is obtained for E* and v*. In a second step, experiments in the non linear domain (considering strains up to some percents) allow to propose a generalisation in the non linear domain of the TTSP. This work is associated with modeling development using the general thermo-viscoplastic model « DBN » (Di Benedetto & Neifar).

Viscoelastic Behaviors of Ultrahigh Molecular Weight Polyethylene Under Three-Point Bending and Indentation Loading

Dynamic mechanical properties under three-point bending and deformation behavior under indentation loading of an ultrahigh molecular weight polyethylene (UHMWPE) were investigated in this study. Dependence of its viscoelastic properties on temperature, frequency, load level, specimen geometry and heating rates were examined. The results showed that temperature and frequency had significant effects on the response of UHMWPE to the dynamic load. With the increase in temperature, the storage modulus (E') was decreased and the loss angle (tan delta) was increased, indicating an increase in the trend in viscoelastic response of the polymer at high temperature. On the other hand, when frequency was increased, higher E' and lower tan delta were observed, suggesting that the material behaved more elastically. While the two heating rates of 5 degrees C/min and 10 degrees C/min had little effect on E' and tan delta, the load level significantly influenced the dynamic mechanical properties of the polymer. UHMWPE showed quite different responses at 0.5 and 20 Hz than at 1-10 Hz, which is worth further investigation. The results from indentation experiment showed that temperature, specimen geometry and load level had significant effects on the response of UHMWPE to the indentation load. With the increase in temperature, the penetration depth was increased, indicating an increase in the deformation trend in the polymer at high temperature. High load led to high penetration. The time-temperature superposition (TTS) method could be used to predict the long-term penetration behaviors of the polymer. From TTS analysis, the activation energy associated with penetration deformation was obtained. Further analysis showed that it might be possible to increase the resistance of UHMEPE to indentation deformation by increasing the thickness and/or decreasing the diameter of the polymer samples.

Structure-stress relaxation relationship in polystyrene/fluorohectorite micro-and nanocomposites

Sodium fluorohectorite (FH) was incorporated into polystyrene (PS) in amounts of 4.5 and 7 wt.% by melt mixing, with and without latex precompounding. The latex precompounding was used for the latex-mediated predispersion of FH particles. The related masterbatch was produced by mixing PS latex with the water-swellable FH, followed by drying. The dispersion of FH in PS was studied by transmission-, scanning electron-, and atomic force microscopy techniques (TEM, SEM, and AFM, respectively). The stress relaxation in the PS composites was determined in short-term isothermal tests. The latter were performed at various temperatures between 25 and 75°C. The direct melt mixing of FH with PS resulted in microcomposites, whereas the masterbatch technique gave rise to nanocomposites. The master curves (relaxation modulus vs. time), constructed by applying the time-temperature superposition principle (TTSP), showed that the Williams-Landel-Ferry (WLF) equation, the Maxwell model, and the Findley power law were fairly applicable to the experimental results obtained.