Time-temperature Superposition Research Articles

Rheological Behavior Features of Feedstocks with a Two-Component Wax–Polyolefin Binder Compared to Analogs Based on Polyoxymethylene

Despite the large number of studies devoted to different compositions of polymer binders for PIM technology, the actual task is still a comparative analysis of the properties of different types of binders to determine their advantages and disadvantages and optimize the compositions used. In this regard, this study aims at the identification and comparative analysis of the rheological properties of the most demanded feedstocks with binders based on polyoxymethylene and a wax–polyolefin mixture under the condition of using identical steel powder filler. The rate of change in the volume fraction of the liquid phase of the binder in the compared feedstocks with temperature change was determined by the calculation–experimental method. As shown, the temperature dependence of the viscosity of feedstocks with a binder based on a polymer blend depends on factors with variable power, i.e., the viscosity change with temperature occurs by different mechanisms with their relaxation spectra. Thus, the principle of temperature–time superposition for feedstocks with multicomponent binders is not applicable, and the study of the viscosity of such materials should involve a wide range of shear rates and temperatures using experimental methods. Capillary rheometry was used to measure the flow curves of feedstocks based on polyoxymethylene and wax–polyolefin binders. The analysis of flow curves of feedstocks showed that feedstocks with a binder of solution–thermal type of debinding have significantly lower viscosity, which is an advantage for molding thin-walled products. However, their difference of 1.5 times sensitivity to the shear rate gradient leads to their lower resistance to “jets” and liquation of components because of shear rate gradients when molding products with elements of different cross-sectional areas.

Scaling of the linear viscoelasticity of entangled poly(ethylene oxide) aqueous solutions

The dynamic modulus of polymer solutions and melts can be expressed as a universal function of reduced frequency when the modulus is scaled by a characteristic value according to the scaling theory of polymer physics. Although the plot of the scaled modulus as a function of the scaled frequency supports the theory, it suffers from considerable scattered distribution of data points around the hypothetical master curve. Compared with the master curve of the time–temperature superposition (TTS) of polymer melts, the master curve of polymer solutions has poor quality. Furthermore, the scale factors of polymer solutions may not show a clear dependency on molecular weight and concentrations. Experimental errors and molecular weight distribution appear to enhance the inaccuracy of the master curve. Therefore, we apply a global optimization for the superposition of the viscoelastic data of polymer solutions with various molecular weights and concentrations. The global optimization resulted in the superposition of data as accurate as that of TTS. Furthermore, the numerically determined shift factors, which were relative scale factors, showed clear dependences on molecular weight and concentrations. We compared our global optimization with previous scaling methodologies.

Unveiling the temperature-dependent mechanisms of viscoelasticity of sand-enhanced epoxy

The viscoelastic behavior of epoxy is critical for its engineering performance and applications. This work focuses on the improvement of its viscoelastic performance by using natural sand particles as fillers. Experiments are carried out to investigate the static and dynamic viscoelastic properties of epoxy with various sand particles content. Static mechanical tests demonstrated an increase in the elastic modulus, albeit at the cost of reduced strength at higher sand content due to stress concentrations. Dynamic tests indicated substantially improved storage modulus and damping of epoxy after being filled with the sand particles. Moreover, the glass transition temperature of the epoxy shows a substantial rise upon the addition of sand particles, signifying an augmentation in its heat resistance. Static viscoelastic characterization revealed an elevation in both room and high-temperature relaxation moduli upon incorporating sand. By applying time-temperature superposition principles, long-term relaxation curves are obtained, which can provide a reference for engineering design. These viscoelastic investigations offer insights into the underpinning mechanisms governing the performance of sand-reinforced epoxy. This enables the rational design of sand particle reinforced epoxy for customized durability, heat resistance, and vibration damping.

Interpreting test temperature and loading rate effects on the fracture toughness of polymer-metal interfaces via time–temperature superposition

Interpreting test temperature and loading rate effects on the fracture toughness of polymer-metal interfaces via time–temperature superposition

The Time-Temperature Superposition of Polymeric Rubber Gels Treated by Means of the Mode-Coupling Theory.

Viscoelastic relaxation measurements on styrene-butadiene rubbers (SBRs) doped with carbon nanotube (CNT) at different concentrations around the sol-gel transition show the time-temperature superposition (TTS). This process is described in terms of the mode coupling theory (MCT) approach to viscoelasticity by considering the frequency behavior of the loss modulus E″(ω) and showing that the corresponding TTS is linked to ω1/2 decay. From the analysis of the obtained data, we observe that the interaction between SBRs and CNT determines different levels of decay according to their concentration. Systems with the lowest CNT concentration are only characterized in the studied T-range by their fragile glass-forming behavior. However, at a specific temperature TL, those with the highest CNT concentration show a crossover towards pure Arrhenius that, according to the MCT, indicates the presence of kinetic glass transition (KGT), where system response functions are characterized by scaling behaviors.

Cross-scale analysis of asphalt binder tensile fracture using molecular dynamics simulation

The tensile failure behavior of asphalt binder is crucial for longevity and durability of asphalt concrete, which is one of most common infrastructure materials. This study provides a cross-scale approach to investigate tensile fracture of asphalt binder using MD simulations. First, two asphalt models for asphaltene-doped and saturate-doped binders were constructed at nanoscale. Tensile simulations were then conducted to observe the evolution of nanovoids and changes in voids surface area. Using tensile strength values at various temperatures and strain rates, the master curve of tensile strength was established based on time-temperature superposition. Results show that cohesive cracking in asphalt binders begins with nanovoids, which rapidly evolve into larger cavities and form thinning filamentation structures, eventually resulting in a complete crack. Locations with lower concentrations of polar components are more likely to initiate nanovoids. After complete fracture, voids surface area of asphaltene-doped binder is larger than that of saturate-doped binder. Increasing the proportion of asphaltene enhances tensile strength of asphalt binders. As expected, tensile strength increases with strain rate but decreases with temperature The time-temperature superposition method is shown to be effective in obtaining macroscale tensile strengths from MD simulations that are comparable to experimental measurements. This study presents an effective simulation method to obtain cross-scale parameters, providing new insights into crack initiation and propagation in asphalt binders.

Long-term life prediction of wearable CFRP lower limb exoskeleton suit by applying a multi-scale FEA and time-temperature superposition

This study explores the application of Carbon Fiber Reinforced Plastics (CFRP) in lightweight design for wearable exoskeleton suits, crucial for success in industrial settings. We aimed to predict the lifespan of the exoskeleton in terms of temperature and time rather than merely confirming its ability to withstand loads. The material’s viscoelastic behavior, establishing a master curve for long-term creep compliance, was characterized using Dynamic Mechanical Analysis (DMA). We also performed mechanical tests under various temperature conditions to measure strength in the load and fiber directions and carried out statistical analysis. From the test results, we constructed the master curves considering the probability of predicting the long-term strength variations. Subsequently, A multi-scale model assessed the exoskeleton frame’s failure, revealing no failures in the current model under given load conditions, with the highest failure index of 0.7 for matrix tensile failure. Combining the predicted long-term strength results, the lifespan prediction for matrix tensile failure under a reference temperature of 50°C was approximately five years. The findings and methodology of this study can serve as a guide for predicting long-term performance and lifespan when applying CFRP to exoskeletons.

Effects of non-linearity and thixotropy in linear amplitude sweep testing for the evaluation of self-healing of bituminous binders

Linear amplitude sweep tests have been demonstrated to have good potential in being used for the evaluation of self-healing properties of neat and polymer-modified bituminous binders. Past research works, however, have neglected the effects of material non-linearity and thixotropy. This implies that the whole material integrity loss is attributed to damage and all restoration to self-healing, thus resulting in the possible overestimate of both damage and self-healing when evaluating the fatigue performance of materials. In the study described in this paper, specific experimental and analytical methods were adopted with the purpose of separating non-linearity and thixotropy in LAS healing tests. Non-linearity was assessed by means of multiple strain sweep tests carried out to determine the material non-linear viscoelastic moduli at specific testing temperatures. Thixotropy was considered by coupling self-healing LAS testing with a purposely defined test in which loading was applied to the undamaged material after a rest period equal to that applied in self-healing tests. Obtained results were processed by means of an analytical approach based on the simplified viscoelastic continuum damage model. Quantification of self-healing included the determination of material integrity and damage parameters recovered after the rest period. Such parameters, calculated by excluding time-dependent and non-linear biasing effects, can be used as straightforward indicators of the self-healing potential of neat and polymer-modified bituminous binders. Moreover, obtained results substantiate the concept that time–temperature superposition is still applicable when non-linearity is incorporated into the simplified viscoelastic continuum damage model.

Enhancing heat modification efficiency of Chinese fir wood through fly ash impregnation: A comprehensive evaluation using time-temperature superposition and cluster analysis

Catalytic degradation via fly ash impregnation (Im) has proven effective in reducing the heat modification (HM) temperature required for wood. To accurately gauge the intensity of HM on wood following Im, the physiomechanical properties of Im-HM treated wood were investigated across various treatment conditions (temperature: 80–140°C, duration: 1–4 h, and fly ash concentration: 2–8%), and compared them to conventional HM (CoHM) wood. Two mathematical methods (time-temperature superposition and cluster analysis) were employed to elucidate the relationships between treatment conditions and resulting properties. Results indicated that Im-HM treated wood exhibited comparable dimensional stability and visual appearance to CoHM wood, while retaining superior mechanical properties. The acid-catalyzed effect of Im-HM demonstrated significant dependence on treatment temperature, duration, and concentration, providing an avenue to regulate catalytic intensity. Employing the time-temperature superposition principle, master curves for weight percentage loss (WPL), modulus of elasticity (MOE) and anti-swelling efficiency (ASE) were constructed under a reference condition (80°C and 2% concentration), covering processing duration up to 20 hours. These master curves facilitated understanding the relationship between temperature, duration and concentration when evaluating catalytic intensity. Cluster analysis, based on the physiomechanical properties of Im-HM and CoHM wood, offered a clear interpretation of HM intensity. Notably, Im-HM treatment at 140°C for 4 hours with an 8% concentration exhibited HM intensity similar to CoHM treatment at 200°C. Through the integration of time-temperature superposition and cluster analysis, this study assesses Im-HM intensity, providing a valuable reference for the industrial application of Im-HM treatment.

Characterization of Potting Epoxy Resins Performance Parameters Based on a Viscoelastic Constitutive Model.

To describe the evolution of residual stresses in epoxy resin during the curing process, a more detailed characterization of its viscoelastic properties is necessary. In this study, we have devised a simplified apparatus for assessing the viscoelastic properties of epoxy resin. This apparatus employs a confining cylinder to restrict the circumferential and radial deformations of the material. Following the application of load by the testing machine, the epoxy resin sample gradually reduces the gap between its surface and the inner wall of the confining cylinder, ultimately achieving full contact and establishing a continuous interface. By recording the circumferential stress-strain on the outer surface of the confining cylinder, we can deduce the variations in material bulk and shear moduli with time. This characterization spans eight temperature points surrounding the glass transition temperature, revealing the bulk and shear relaxation moduli of the epoxy resin. Throughout the experiments, the epoxy resin's viscoelastic response demonstrated a pronounced time-temperature dependency. Below the glass transition temperature, the stress relaxation response progressively accelerated with increasing temperature, while beyond the glass transition temperature, the stress relaxation time underwent a substantial reduction. By applying the time-temperature superposition principle, it is possible to construct the relaxation master curves for the bulk and shear moduli of the epoxy resin. By fitting the data, we can obtain expressions for the constitutive model describing the viscoelastic behavior of the epoxy resin. In order to validate the reliability of the test results, a uniaxial tensile relaxation test was conducted on the epoxy resin casting body. The results show good agreement between the obtained uniaxial relaxation modulus curves and those derived from the bulk and shear relaxation modulus equations, confirming the validity of both the device design and the testing methodology.

The effect of curing temperature on hardening, thermal, and mechanical characteristics of adhesive for retard‐bonded prestressed tendon

AbstractThe effect of curing temperature on hardening, thermal, and mechanical characteristics of adhesive for retard‐bonded prestressed systems is investigated in detail. To evaluate the degree of hardening of the adhesive, the cone penetration and Shore hardness of two samples are tested throughout the curing process under conditions of 25, 35, 45, 55, and 65°C. The thermal performance and curing reaction are characterized using differential scanning calorimetry and Fourier transform infrared spectroscopy, respectively. The mechanical properties with respect to the cure temperatures are characterized by compression strength tests. Experimental results present that after curing under conditions ranging from 25 to 65°C, the hardness of the samples reached its maximum values (85–90 D). As the temperature increased from 25 to 65°C, there was a greater degree of curing cross‐linking, resulting in an increase in compressive strength from 55 to 72 MPa. Based on Shore hardness–time experimental data, a logarithmic model is proposed for predicting the hardness of adhesives at any given time for engineering applications. Additionally, the time–temperature superposition principle is utilized to extrapolate the curing time of the adhesive under low‐temperature conditions. The research findings are of significant importance for the assessment of adhesive hardening.

Systematic methodologies to surveil and evaluate the early imperceptible thermal degradation of EPDM composite

Without knowledge and resultful surveillance of the early degradation of polymers, it is challenging to realize the high reliability of high-end equipment and the screening and grading of waste plastics. Their reliability evaluation and lifetime prediction are also unfulfillable for a lack of sensitive characterization techniques. This work, taking commercial ethylene propylene diene monomer (EPDM) composite as an example, explores a variety of multi-scale evaluation methods to identify its early thermal aging behaviors and molecular mechanisms, including various spectroscopic technology, swelling-equilibrium tests, scanning electron microscope (SEM), thermal analysis, contact angle tests and mechanical properties. Only some methods can give the perceptible indicators of the slight thermal degraded EPDM, namely fluorescent probe technology, infrared spectroscopy for gas mixtures, swelling-equilibrium tests and specific mechanical properties. Other methods are inferior in early aging identification. Both fluorescent probe technology and infrared spectroscopy for gas mixtures can recognize the thermal degradation induced products within 5 h at a temperature lower than 120 °C, while elongation at break can reflect the damage of EPDM within 5 h at 60 °C. Based on the time-temperature superposition principle, the master curve of the thermal aged EPDM is constructed using the data of elongation at break, which predicts that 50% retention of elongation at break occurs after 10.5 years at 30 °C. We further propose a new aging evaluation methodology to reflect the aging degree comprehensively, which is based on the standardized sequence numbers obtained from the above sensitive characterization methods.

Accurate and efficient determination of glass thermo-viscoelastic properties using creep compliance master curve construction approach

An accurate and efficient method for determining the thermo-viscoelastic properties of glass was proposed using a creep compliance master curve construction approach based on the time-temperature superposition principle. This method mainly involved obtaining creep compliance at multiple temperatures, constructing the master curve, and converting into relaxation modulus. By applying this method, the shear relaxation modulus and Williams-Landel-Ferry constants were successfully obtained for K9 glass. A smooth creep compliance master curve at 590 °C was constructed covering a vast timescale up to 2.6×105 seconds, despite a single curve's duration being only 619 seconds. Consequently, the derived relaxation modulus encompassed a broad range of relaxation times spanning six orders of magnitude. The high accuracy of the determined thermo-viscoelastic properties was firmly validated across all tested temperatures. Furthermore, the detrimental impact of friction on the method's accuracy can be effectively minimized by selecting a suitably large height-to-diameter ratio for the cylindrical glass specimen.

Master curves construction for viscoelastic functions of bituminous materials

Abstract The performance of bituminous materials is often evaluated using rheological properties measured within the linear viscoelastic region. If there is a univocal temperature dependence of all the relaxation times, data obtained in different operating conditions can be translated onto a logarithmic scale where they partially overlap and merge into a single master curve. This is the well-known time–temperature superposition principle that has been successfully applied for decades. However, the empirical nature of the method has led to many different procedures being used for the graphical construction of the master curve. In addition, the continuously increasing calculating power has led to new approaches, such as the simultaneous modelling of the represented viscoelastic function. Losing track of the basic statements of the method is the hidden drawback of this wide range of available protocols with the risk of artefacts and incongruences being introduced in the construction of the master curves. This review summarizes these basic statements together with the empirical and phenomenological approaches developed over the years. The aim of this study is to help the reader in choosing the most appropriate method to build the master curves. Although the subject of the review is of general application, the field of bitumen is focused on.

Novel hyper-viscoelastic approach to modelling elastomer mechanic behaviour with relaxation spectrum

Elastomers, such as polyurethane, exhibit hyperelastic behaviour and distinct rate dependence under a wide range of strain rates. Herein, a methodology for developing a hyper-viscoelastic constitutive model for succinctly characterising the mechanical behaviour of polyurethane under large deformations and a wide range of strain rates is proposed. The model is constructed using a long-term hyperelastic formulation combined with a rate-dependent viscoelastic model. This model is based on internal state variables and a finite strain formulation. A polyurethane elastomer was used as a sample to develop this model, by way of testing wide strain-rate mechanical behaviour (0.001–5000s−1) and viscoelastic behaviour. The viscoelastic behaviour was obtained using the equivalent time–temperature superposition relation. A parameter-fitting algorithm was adopted to separate the long-term behaviour from the viscoelastic behaviour. The long-term behaviour was modelled using a Mooney–Rivlin hyperelastic model, and its parameters were identified using the least-squares method. The time-dependent viscous effect calculated using the Prony series-based model was approximately determined based on the continuous relaxation spectrum. The characterisation capacity was confirmed through a thorough comparison with experimental curves. This model can be extended to other elastomers, even under tension, without any specific limitations of the internal components.

Low stress creep response of PTFE sealants applied to PEM fuel cells

AbstractViscoelastic properties of polytetrafluoroethylene (PTFE) play a crucial role in forecasting its long‐term behavior in engineering applications. An attempt is made to explore the viscoelastic properties of PTFE sealants that are utilized in polymer electrolyte membrane fuel cell (PEMFC). It is to be noted that PTFE sealants are vulnerable to creep under constant loading at elevated temperatures. Moreover, the creep of sealants will lead to leakage of reactants from the cell, which affects the performance of PEMFC. PTFE is an excellent choice as a sealant material in low‐temperature polymer electrolyte membrane fuel cell (LT‐PEMFC), which operates in the temperature range of 60–80°C. PTFE can be prominently used as sealants in high‐temperature polymer electrolyte membrane fuel cell (HT‐PEMFC), as it possesses no significant change in its physical properties within the temperature range of −150 to 300°C along with the working conditions of HT‐PEMFC. In LT‐PEMFC, the sealants will typically be subjected to low stresses in the range of 1–5 MPa. In this article, the creep response of PTFE sealant material is extensively studied at various temperatures of 25 (room temperature), 35, 45, 55, and 65°C and at three stress levels of 2, 3, and 4 MPa. The time–temperature superposition principle is utilized to develop master curve at a reference temperature of 25°C, to forecast long‐term creep characteristics of PTFE sealants. Moreover, the master curve for creep compliance is developed for 4.5 h.

Thermomechanical characterisation of a thermoplastic polymer and its short glass fibre reinforced composite: Influence of fibre, fibre orientation, strain rates and temperatures

Polycarbonate composites are widely used in products exposed to high strain rate deformation. This paper investigates the thermomechanical properties of polycarbonate and 20 wt% glass fibre reinforced polycarbonate to provide characterisation data and improved mechanistic understanding of the response to load, supported by Dynamic Mechanical Analysis and time–temperature superposition. Compressive behaviour is characterised from 0.001 to 5000 s−1 at room temperature and from −60 to 120 °C at 0.01 s−1; and a thermal imaging camera used to obtain temperature rise data. Quasi-static tensile experiments were also performed in different orientations relative to the injection flow direction. High-rate compression experiments are performed with X-ray imaging. As well as information about rate dependence of yield stresses and softening in the two materials, these data show how adiabatic shear band formation can cause significant softening in the composite. These data will enhance application of these polymers and facilitate development of advanced thermo-mechanical models.

Elaboration of La (Sr/Na) Mn (Ti) O3 ceramic, structural, and morphological investigations, and contribution of direct and indirect interactions on transport properties

The charge carrier's dynamics of La0.7(Sr5/6Na1/6)0.3Mn0.7Ti0.3O3 (LSNMTO) ceramic is conducted using the temperature and frequency dependences of the electrical conductivity and their scaling formalisms. The structural study indicates that LSNMTO crystallizes in a rhombohedral R3‾c perovskite structure with no detectible secondary phases. A phase transition from the high-temperature metallic behavior to the low-temperature semiconductor nature is observed from the electrical conductivity curve at TS-M = 415 K. Further, it is observed that the cation-anion-cation and the cation-cation interactions are present in the material, and play important role in governing the electrical behaviors of LSNMTO. From 200 K to 415 K, the Non-adiabatic Small Polaron Hopping is the predominant conduction process, although the Mott-Variable Range Hopping mechanism governs the conductivity at low temperatures. In the intermediate temperature range, the dynamic of the charge carriers is explained using the Shklovskii Efros model. The frequency-activated conductivity obeyed the universal laws (double-Jonscher and Jonscher laws). At high frequencies, the dispersion of the conductivity spectra is attributed to the presence of hopping and tunneling conduction processes. The Time-Temperature Superposition Principle (TTSP) is obeyed over a large temperature range from 160 K to 350 K. Below 160 K, the deviation from the TTSP is attributed to the coexistence of hopping and tunneling conduction mechanisms. Deviations from the Summerfield scaling and shifts of the isotherms to higher values on decreasing the temperature are due to the local structural disorder in LSNMTO. Therefore, the structural particularities of LSNMTO can result in diverse conduction pathways giving an increase to the deviations from the Summerfield scaling. The studied ceramic exhibits a very motivating maximum negative temperature coefficient of resistance NTCR = −13.36% which is significantly elevated as compared to previously investigated compounds.

Prediction of creep failure life for unidirectional CFRP with heat-resistant epoxy resin as matrix exposed to high temperature under tension load

The accelerated testing methodology (ATM) developed by the authors is the methodology for predicting statistically long-term life of CFRP structures based on the viscoelasticity including the time-temperature superposition principle for matrix resin. The formulae of ATM are expressed as the product of static strength at room temperature, its dispersion, and the viscoelastic parameter of matrix resin that changes with time and temperature history. This methodology ATM was applied to the prediction of long-term creep failure life for unidirectional CFRP with heat-resistant epoxy resin as matrix under heat degradation in this study. Resin impregnated CFRP strands with heat-resistant epoxy resin were molded using a filament winding system as virgin specimens of unidirectional CFRP. Then, heat-degraded specimens were prepared by exposing the virgin specimens under acceleration conditions determined based on the time-temperature superposition principle for chemical deterioration assuming the condition of practical temperature 110°C and period 10 years. Second, the creep strengths of virgin and heat-degraded CFRP strands were statistically predicted based on ATM and the effect of heat degradation on the long-term life of CFRP strands was evaluated. As results, it was cleared that when the creep strength of CFRP strands undergoes thermal aging at the practical condition, in addition to the strength decrease to time due to the viscoelasticity of the resin, a comparable decrease in static strength and increase in this scatter occur.

The Effect of a Liquified Wood Heavy Fraction on the Rheological Behaviour and Performance of Paving-Grade Bitumen

Biomass is one the most abundant renewable energy sources, and it can be processed through different thermochemical methods to obtain oils that can replace the petroleum bitumen used in road construction. For the construction industry to accept the bitumen replacement with bio-oil, it is necessary to know its properties and determine the applicability of conventional testing methods. This research utilized a liquified wood heavy fraction (bio-oil) obtained from waste wood through an innovative thermochemical liquefaction process. The aim was to investigate a kind of bio-bitumen produced by blending this bio-oil with paving-grade bitumen. The rheological behaviour in a wide temperature range, the performance relative to fatigue cracking and permanent deformation sensitivity, and the evolution with oxidative ageing were evaluated for the bio-bitumen and paving-grade bitumens. The bio-oil significantly affected the rheological behaviour of bitumen through an overall decrease in the phase angle and by failing the time–temperature superposition principle. The strong elastic response of the bio-bitumen improved resistance to fatigue and permanent deformation accumulation; however, resistance to oxidative ageing declined. Linear viscoelastic rheological indicators proposed in the literature to assess the material’s performance showed a similar trend of variation with oxidative ageing for bio-bitumen and paving-grade bitumen, though the indicators’ values could not be directly compared.