Time-temperature Equivalence Principle Research Articles

Performance Degradation Prediction and Reliability Evaluation of Rubber Aging in Natural Environment Under Alternating Cyclic Thermal Load

With a focus on predicting the degradation of rubber performance in the natural environment and evaluating its reliability, the distribution law of accelerated aging life is analyzed through the accelerated aging test of hot oxygen. A Weibull distribution model is then established to verify the consistency of the accelerated aging mechanism. Through the constant stress accelerated aging test data, the aging characteristics of the rubber under alternating thermal stress load in the natural environment are inferred. The concept of thermal stress amplitude coefficient is proposed, and its numerical value is calculated by the combination of numerical simulation and single-peak curve fitting. Under the principle of time-temperature equivalence, the segmentation time equivalent method and the overall temperature equivalent method are employed to calculate the rubber performance degradation curve under natural environment aging conditions. Finally, according to the Weibull distribution, the aging reliability of the rubber over time is simulated. This research can provide a reference for the aging reliability evaluation of products under alternating stress.

Investigation on a novel time-and temperature-dependent cohesive zone model

This paper presents a novel formulation of a cohesive zone model able to effectively approximate the time-and temperature-dependent fracture process along a defined interface. The formulation relies on the assumption that the relaxation behavior of the traction is the origin of the time effects, and time temperature equivalence principle can be introduced in solving the temperature effects. A series basic hypotheses are introduced according to the previous research work and will be complied in the paper. By connecting N Maxwell models in parallel and letting the time-independent traction calculated by PPR cohesive zone model as the input parameter, the time-dependent traction will be output by numerical integration. Reduced time considering the effects of temperature will replace the real time in the numerical integration. With the tool of the user subroutine element, the novel formulation is implemented in FEM code ABAQUS. Typical load cases including constant tensile test and relaxation test are analyzed to illustrate the special properties of the formulation. With three set of input parameters, the proposed model can be utilized in a wide range of applied loading rates and temperatures as validated by the remarkable agreement with the experimental data in the case of the double sandwich cantilever beam made of solid propellant/insulation adherents bonded along the liner interface.

Dielectric loss prediction of silicone rubber after moisture absorption under AC corona

Silicone rubber (SR) is widely used in HVDC/HVAC external insulation equipment because of its excellent electrical insulation performance and good hydrophobicity. In this paper, the variation of dielectric loss of SR after moisture absorption under AC coronas of 8.1 kV cm−1, 10.8 kV cm−1, 13.5 kV cm−1, 16.2 kV cm−1, 18.8 kV cm−1 and 21.6 kV cm−1 was investigated, respectively. Then, an equivalence equation of time and electric field intensity of corona, which was inspired by a time-temperature equivalence principle, was put forward. The test results verified the validity of the equivalence equation of time and electric field intensity of AC corona in describing the trend of dielectric loss of SR after moisture absorption under AC corona. At last, the aging time, reaching different dielectric losses of SR after moisture absorption under AC coronas of 10.0 kV cm−1, 15.0 kV cm−1 and 20.0 kV cm−1, was predicted. This study would help to guide the operation and maintenance of the silicone rubber on external insulation equipment.

Loading rate and temperature dependence of flexural behavior in injection-molded glass fiber reinforced polypropylene composites

This paper is concerned with the influence of loading rate/temperature and frequency/temperature on static flexural behavior and dynamic mechanical properties of injection molded glass fiber reinforced polypropylene (GFPP) composites, respectively. Furthermore, the mechanism of long-term durability of PP and GFPP was investigated by the master curve of storage modulus constructed based on the Time-Temperature-Superposition (TTSP) method. Three-point bending tests at various loading rates/temperatures and dynamic mechanical analysis (DMA) at various frequencies/temperatures are performed. The time-temperature dependence of static flexural properties (modulus, E, and strength, σ) and dynamic properties (storage modulus, E’) in PP and GFPP is discussed. The results show that both static flexural behavior and dynamic mechanical behavior of PP and GFPP have significant time-temperature dependent phenomenon, which conforms to the time-temperature equivalence principle. The long-term durability of GFPP depends on the matrix resin rather than the GF reinforcement and its interface at temperatures above the glass transition temperature (Tg).

Experimental Research on Dynamic Stability of Asphalt Mixture Based on Time-Temperature Equivalence Principle

Asphalt mixture is a kind of a viscoelastic material with viscoelastic characteristic of time-temperature equivalence. This paper, from the engineering practical consideration, and the perspective of time-temperature equivalence principle, based on the Rutting Test of Asphalt Mixture,has obtained equivalence relations of the effect of wheel speed and temperature on asphalt mixture rut index by different wheel speed and different temperatures rutting test, so as to provide the data support for the research of anti-rutting mechanism of asphalt pavement.

Study on the Compressive Mechanical Properties of HTPB Propellant at Low Temperature

To study the low temperature effects of compressive mechanical properties on Hydroxyl-terminated polybutadiene (HTPB) propellant, a quasi-static mechanical experiment was conducted. The results show that compressive mechanical parameters are closely related to strain rate and low temperature. With the decrease of temperature and increase of strain rate, the modulus and compressive strength of HTPB propellant increase obviously. Based on the time-temperature equivalence principle (TTEP), the master curves of compressive strength and initial modulus for HTPB propellant were obtained, which can facilitate the structural integrity analysis of the propellant.

A Phononic Crystal-Based High Frequency Rheometer

Dynamic Mechanical Analysis (DMA) allows for the measurement of the complex shear modulus of an elastomer. Measurements at frequencies above the frequency range of the device can be reached thanks to the Time–Temperature Equivalence principle. Yet, frequencies higher than a few kHz are not attainable. Here, we propose a method exploiting the physics of bubble phononic crystals to measure the complex shear modulus at frequencies of a few tens of kHz. The idea is to fabricate a phononic crystal by creating a period arrangement of bubbles in the elastomer of interest, here PolyDiMethylSiloxane (PDMS), and to measure its transmission against frequency. Fitting the results with an analytic model provides both the loss and storage moduli. Physically, the shear storage modulus drives the position of the dip observed in transmission while the loss modulus controls the damping, and thus the level of transmission. Using this method, we are able to compare the high-frequency rheological properties of two commercial PDMS and to monitor the ageing process.

Tensile Mechanical Properties of HTPB Propellant at Low Temperature

To study the low temperature effects of tensile mechanical properties on Hydroxyl-terminated polybutadiene (HTPB) propellant, a quasi-static mechanical experiment was conducted. The results show that tensile mechanical parameters are closely related to strain rate and low temperature. With the decrease of temperature and increase of strain rate, the modulus and tensile strength of HTPB propellant increase obviously. Based on the time-temperature equivalence principle (TTEP), the master curves of tensile strength and initial modulus for HTPB propellant were obtained, which can facilitate the structural integrity analysis of the propellant. The damage of propellant is matrix tearing and dewetting between the filled particles and matrix.

Multi-scale analysis of the effect of loading conditions on monotonic and fatigue behavior of a glass fiber reinforced polyphenylene sulfide (PPS) composite

Abstract In this paper, two kinds of PPS/GF composite samples (PPS-0°, PPS-90°) were prepared with two different fiber main orientations related to the injection direction. A wide range of their properties were discussed. Using DMTA analysis, it was shown that the PPS/GF composite under study obeyed the time-temperature equivalence principle. Moreover, Perez model was verified and gave a good estimation of the viscoelastic properties of the PPS/GF. Monotonic and fatigue behaviors and fatigue life of PPS/GF were investigated. Fiber's orientation, applied amplitude and loading frequency effects were emphasized. Self-heating effect on fatigue strength was also analyzed. SEM fracture surface observations allowed analyzing, at the local scale, the main deformation mechanisms occurring during mechanical loading. No evident damage development was observed for both monotonic and fatigue loading. PPS matrix plasticity appeared to be the predominant deformation mechanism until a semi-ductile or semi-brittle final failure depending on the loading conditions and local microstructure.

Study on the Change Laws of Dynamic Modulus of Asphalt Mastic with Different Framework Types

In order to study the change laws of dynamic modulus with different framework types under different frequencies and temperatures and obtain the dynamic moduli with wider frequency ranges and temperature ranges, asphalt mastic specimens through removing coarse aggregates in AC-13, SMA-13 and OGFC-13 asphalt mixture were prepared. The dynamic moduli with different frequencies and temperatures were measured by simple performance tests, and the master curves of dynamic modulus of asphalt mastics were acquired by the time-temperature equivalence principle. The results show that the dynamic moduli of asphalt mastic increase with the increase of load frequencies under the same temperature, and the dynamic modulus order is AC- 13>SMA-13>OGFC-13. In addition, the dynamic moduli of asphalt mastic decrease when the temperatures rise. The dynamic moduli with wider frequency and temperature ranges are obtained from the master curves of dynamic modulus of asphalt mastic.

Compressive mechanical properties of HTPB propellant at low temperatures and high strain rates

To study the compressive mechanical properties of the hydroxyl-terminated polybutadiene (HTPB) propellant at high strain rates (700–1900/s) and low temperatures (−50 °C to 25 °C), we conducted a dynamic mechanical experiment using cylindrical specimens on a split Hopkinson pressure bar (SHPB). In addition, scanning electron microscopy was employed to observe the compressive fracture surfaces. The experimental results indicate the effectiveness of the proposed SHPB testing for the HTPB propellant. The effects of the strain rate and low temperature remarkably influenced the variations in stress. The lower temperatures and higher the strain rate generated an obvious increase in the modulus and compressive strength. Even at −50 °C and 1900/s, the propellant still maintained its viscoelastic characteristics. On the basis of the time–temperature equivalence principle, we obtained the master curves of the mechanical parameters. The propellant mainly exhibited transgranular fracture damage, increased porosity, and matrix tearing after impact.

Controlled hydrophilic/hydrophobic property of silica films by manipulating the hydrolysis and condensation of tetraethoxysilane

Controlling surface wettability is an important road to afford the materials with anticipated functional properties, such as anti-fogging, anti-icing and self-cleaning. Manipulating the surface topography and chemical composition is a promising strategy to achieve the expected functional properties. Herein, we concurrently realized the control of surface topography and chemical composition of the film materials via exploiting a simply one step method through the hydrolysis and condensation of tetraethoxysilane (TEOS) to form silica sol-gel films. By adjusting the amount of water, TEOS and basic catalyst, the hydrophilic or hydrophobic chemical groups on the silica particles surface were well controlled. As a result, the sol-gel silica films exhibiting a controllable and wide range contact angles from 7.7±1.5° to 121.6±1.8° were obtained by this simple one-step method. The inorganic nonmetallic, metallic and polymer materials surface could maintain different wettability by the modification of controlled wettability silica films. Furthermore the wettability of silica film could be easily changed from hydrophobicity to superhydrophilicity through a heat-treatment due to the decrease of hydrophobic chemical groups conforming to the time-temperature equivalence principle. Raising temperature and extending holding time were equivalent to chemical bond breaking which result in the wettability change of silica films.

Measurement of Dynamic Modulus and Master Curve Modeling of Hot Mix Asphalt from Senegal (West Africa)

The main purpose of this paper is to model the master curve of dynamic modulus |E*| for Hot Mix Asphalt mix designed with aggregate from Senegal named basalt of Diack and quartzite of Bakel. The prediction model used is the Witczak model, used in the Mechanistic-Empirical Pavement Design Guide. A study has been conducted in the Laboratory of Pavements and Bituminous Materials. Six different HMA (BBSG 0/14 mm) were subjected to complex modulus test by tension-compression according to the European or Canadian procedure using the same range of temperatures and frequencies. For each mixture studied the uniqueness of modulus curves in the Cole-Cole or in Black diagrams have shown that the asphalt mixes are thermorheologically simple materials and the Canadian test process is suitable for determining the HMA complex modulus mix designed with the aggregates from Senegal. This implies their tender with the principle of time-temperature equivalence. The test results were used to model the master curves of HMA studied. A correlation with the results of dynamic modulus measured have shown an accuracy of R2 = 0,99 and p = 0,00 in STATISTICA software, which allows to conclude that the sigmoidal model has good modeling of the dynamic modulus.

Influence of oxidation process on photocatalytic activity of photocatalyst coatings by mechanical coating technique

Titanium (Ti) coatings on alumina (Al2O3) balls fabricated by mechanical coating technique (MCT) were oxidized in air at a series of relatively low temperatures with the oxidation time of 3h and 50h. Crystal structure and microstructure of the coatings were investigated. Photocatalytic activity of the coatings was evaluated and discussed. The results showed that titanium dioxide (TiO2) films on Ti or Ti/TiO2 coatings were fabricated by the MCT and subsequent heat oxidation. The oxidized coatings started to show the mixed-phase of anatase and rutile, at the temperature of 873K for 3h and 773K for 50h. With extending the oxidation time from 3h to 50h, the oxidative effect of relatively lower temperatures of 773K to 973K almost reached to that of higher temperatures, which is similar to the time–temperature equivalence principle. Photocatalytic activity of anatase TiO2 at 673K is higher than that of mixed-phase or rutile TiO2 under UV irradiation.

Shape Recovery of Viscoelastic Beams After Stowage

The deployment of viscoelastic structures that have been held stowed for a given time duration can be formulated as a viscoelastic boundary value problem in which the prescribed condition switches from constant displacement to constant traction. This paper presents closed-form expressions for the load relaxation and shape recovery of a linear viscoelastic beam subject to such time-varying constraints. It is shown that a viscoelastic beam recovers to its original shape asymptotically over time. The analytical solutions are employed to investigate the effect of temperature and stowage time on the time required to achieve recovery with a specified precision. Based on the time-temperature equivalence principle, the relationship between recovery time and holding duration is concisely presented on a single plot. It is found that recovery time increases with holding duration but with a diminishing effect.

Time to failure prediction in rubber components subjected to thermal ageing: A combined approach based upon the intrinsic defect concept and the fracture mechanics

In this contribution, we attempt to derive a tool allowing the prediction of the stretch ratio at failure in rubber components subjected to thermal ageing. To achieve this goal, the main idea is to combine the fracture mechanics approach and the intrinsic defect concept. Using an accelerated ageing procedure for an Ethylene–Propylene–Diene Monomer (EPDM), it is first shown that the average molar mass of the elastically active chains (i.e. between crosslinks) can be used as the main indicator of the macromolecular network degradation. By introducing the time–temperature equivalence principle, a shift factor obeying to an Arrhenius law is derived, and master curves are built as well for the average molar mass as for the ultimate mechanical properties. Fracture mechanics tests are also achieved and the square root dependence of the fracture energy with the average molar mass is pointed out. Moreover, it is shown that the mechanical response could be approximated by the phantom network theory, which allows to relate the strain energy density function to the average molar mass. Assuming that the fracture of a smooth specimen is the consequence of a virtual intrinsic defect whose the size can be easily estimated, the stretch ratio at break can be therefore computed for any thermal ageing condition. The estimated values are found in a very nice agreement with EPDM experimental data, making this approach a useful tool when designing rubber components for moderate to high temperature environments.

Dynamic Mechanical Properties of Phenolic Resin/Chlorinated Butyl Rubber Composites

Chlorinated butyl rubber composites were prepared by a compounding and vulcanizing process using phenolic resin (PF) as the vulcanizing agent and carbon black as filler. Instead of using the conventional vulcameter method to determine the vulcanizing parameters, the vulcanization temperature and time were obtained by differential scanning calorimetry (DSC) and tensile testing, respectively. Dynamic mechanical analysis (DMA) showed that, higher PF content resulted in higher E′ and lower tanδ, and variations of E′ and tanδ with temperature were consistent with the time-temperature equivalence principle. It is proposed that chlorinated butyl rubber using phenolic resin as the vulcanizing agent could be used as potential damping materials in the temperature range 20–100°C and frequencies 0.1–100 Hz.

Lifetime Prediction of Nitrile Butadiene Rubber Used for O-Ring Sealing

This work predicts the service life of nitrile butadiene rubbers used for O-ring sealing. The principle of time-temperature equivalence was adopted to shift the thermal ageing behaviors of rubbers and construct a master curve by superposition. The lifetime of rubbers were estimated from the master curves.

Study on the Viscoelastic Performance of Asphalt Mixture Based on Dynamic Modulus

The fitting models of dynamic modulus of asphalt mixtures were studied in this paper. UTM dynamic modulus tests were adopted to determine the dynamic modulus of two asphalt (A, B) mixtures. Then, the WLF equation and Arrhenius formula, based on the time-temperature equivalence principle, were used to get the shift factors and master curves of asphalt mixtures. Combined with Sigmoidal model and CAM model, it was founded that the Arrhenius formula was more suitable to get the master curves of asphalt mixtures. What is more, the CAM model was more suitable to fit master curves of both asphalt mixtures.

Studying Viscoelastic Properties of Asphalt Mixture Basing on CAM Model in the Full-Temperature-Full-Frequency Range

In order to study viscoelastic properties of asphalt mixture, an advanced Shear Rheometer is used. The continuous dynamic frequency scanning test is carried out, which can get full-temperature-full-frequency master curve of asphalt mixture by the time-temperature equivalence principle. The CAM model acts as the rheological model for studying viscoelastic properties of asphalt mixture, because CAM model’s parameters have clear physical meaning. Then viscoelastic properties of asphalt mixture are studied basing on the four equations of CAM model in the full-temperature-full-frequency range.