Smooth Master Curve Research Articles

Stress relaxation experimental research and prediction of GFRP pipes under ring deflection condition

Abstract Glass fiber-reinforced plastic (GFRP) pipes are widely used as buried pipes in petrochemical and other industries. At present, in-depth studies have been conducted on GFRP pipes in terms of internal hydrostatic pressure, axial compression, and cyclic internal pressure, especially limited research has been carried out on transverse load, especially stress relaxation behavior. In this study, GFRP pipes with three different component contents were subjected to different initial deflections at different temperatures and subjected to stress relaxation tests for 1000 h. The findings demonstrate that the stress relaxation behavior of GFRP pipes is not affected by the initial deflection. Rather, it is primarily influenced by temperature and sand entrapment content, which are identified as the key factors determining the stress relaxation behavior of GFRP pipes. In addition, the time-temperature superposition principle (TTSP) was used to pass the test results to obtain a smooth master curve and verify the applicability of TTSP on GFRP pipes. Subsequently, the relaxation performance of GFRP pipes was predicted after 50 years. This research result contributes to a more comprehensive understanding of the stress relaxation behavior of GFRP through accelerated testing and offers crucial insights into the application of GFRP pipes.

Temperature and Frequency Dependence of the Dynamic Viscoelastic Properties of Silicone Rubber.

Temperature-frequency sweep tests were performed on silicone rubber to investigate the dynamic viscoelastic properties. The test results show that the viscoelasticity of silicone rubber presents significant temperature dependence and frequency dependence. The dynamic viscoelastic test curves at different temperatures can be shifted along the logarithmic frequency coordinate axis to construct smooth master curves at the reference temperature of 20 °C, covering a frequency range of 10 decades, which indicates thermorheological simplicity on a macro level and frequency temperature equivalence of the silicone rubber material in the experimental temperature range. The van Gurp-Palmen plot and Cole-Cole plot for the test data at various temperatures merge into a common curve, which further validates thermorheological simplicity. The temperature dependent shift factors of silicone rubber material were well characterized by the Williams-Landel-Ferry equation. Moreover, the fractional-order differential Kelvin (FDK) model, the fractional-order differential Zener (FDZ) model, and the improved fractional-order differential Zener (iFDZ) model were used to model the asymmetric loss factor master curve. The result shows that the iFDZ model is in good agreement with the test results, indicating that this model is suitable for describing the asymmetry of dynamic viscoelastic properties of silicone rubber.

TTS package: Computational tools for the application of the Time Temperature Superposition principle

The TTS package has been developed in R software to predict the mechanical properties of viscoelastic materials, at short and long observation times/frequencies by applying the Time Temperature Superposition (TTS) principle. TTS is a physical principle used in material science to estimate mechanical properties beyond the experimental range of observed times/frequencies by shifting data curves obtained at other temperatures relative to a reference temperature in the dataset. It is a methodology related to accelerated life-tests and reliability, whereas the TTS library is one of the first open source computational tool to apply the TTS principle. This R package provides free computational tools to obtain master curves that characterize materials from a thermal-mechanical approach. The TTS package also proposes, implements and explains our own method to obtain the shift factors and the master curve in a TTS analysis, based on horizontal shifting of the first derivative function of viscoelastic properties. This procedure provides shift factors estimates and smooth master curve estimates using B-spline fitting, in a fully automatic way, without assuming any parametric expression. Williams-Landel-Ferry (WLF) and Arrhenius TTS parametric models are also implemented in the TTS package. They can be fitted from shifts obtained by the our first derivative based method.

Effects of Physical Hardening on Low-Temperature Properties of Asphalt Binders Containing Reclaimed Asphalt Pavement

Abstract Reclaimed asphalt pavement (RAP) materials are widely used in sustainable construction of the asphalt pavement, which has evident advantages in solving the problem of material costs and waste disposals. However, there are few studies on the influence of RAP materials on the physical hardening of asphalt binders. In this paper, the physical hardening rate from the dynamic mechanical analysis test and grade loss deduced by the extended bending beam rheometer experiment were used to characterize the physical hardening of the RAP-modified asphalt binder at low temperatures. The results show that the loading time–conditioning time superposition principle is suitable to determine the physical hardening rate of RAP-modified asphalt binder through a smooth master curve and verification of the typical 2S2P1D rheological model, and grade loss can be predicted by the physical hardening rate using their good correlation. The RAP binders can accelerate the degree of physical hardening and increase the thermal stresses of the asphalt binder, and these effects are more evident for the RAP binder with longer aging time and higher content. The base asphalt with less wax content will act as a regenerant, which can accommodate more content of the RAP materials to produce a new usable asphalt binder.

Effect of Screw Speed and Oyster Mushroom Addition on Textural Characteristics of Soy Protein Extrudates and Master Curve of Specific Mechanical Energy

The effect of screw speed and oyster mushroom addition on the texture characteristics (hardness, gumminess, and chewiness) and specific mechanical energy (SME) was determined via factorial experiment design. Individually increasing screw speeds had little effect compared to the effects of oyster mushroom addition. However, the combined effects of screw speed and oyster mushroom addition significantly reduced (p ≤ 0.05) all the texture characteristics. The hardness (3521.35 g) and gumminess (2717.85) of the meat analog extruded at the maximum screw speed of 160 rpm and 15% oyster mushroom addition are close to the chicken breast’s characteristics, respectively. The oyster mushroom–soy protein extrudates are chewier than the non-hydrated texturized vegetable protein (TVP) and chicken meats. The SME values of the single-screw extrusion were linearly affected by the increasing screw speed, which also lies in the range < 200 kJ/kg for producing meat analog with acceptable characteristics. Applying the superposition technique successfully shifted the individual curves of the SME into a smooth master curve vertically, allowing an interpolating in the prediction of SME value at a given screw speed value.

Novel concentration master curve and rheological characterization of recycled asphalt binders.

The recycling of asphalt pavements requires a good understanding of the material's characteristics. However, the rheological behavior of recycled binder is still not well understood. In this study, a novel method is introduced to construct the master curve of the recycled binders. The concentration of reclaimed asphalt pavement (RAP) binder is used to find the shift factors of the master curve. This master curve is called the concentration master curve (CMC). To verify the applicability of the concept, the CMC was plotted for three different RAP sources procured from two states and the capital of India. The percentage of RAP binder content in the recycled binders was varied (0, 15, 25, 40, 65, 80, and 100%) by weight of the total binder. In all three cases, smooth master curves were obtained. To calculate the allowable RAP, an alternative approach based on the damping energy area (DEA) of recycled binders was proposed. It was found that the allowable RAP content based on the DEA criteria was 40-50% less compared to the conventional high PG temperature (PGH) criterion. An attempt is made to understand the rheological interaction between the RAP binder and RA using the recycled binder compatibility index (RBCI). It was observed that the RAP source is the determining factor behind the compatibility and interaction level between the RAP binder and RA in a recycled binder.

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

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

Validation of partial time-temperature superposition principle in thermorheologically complex asphalts

This study aims to validate the applicability of the partial time–temperature superposition principle to simulate the behavior of thermorheologically complex modified asphalts. Six different asphalts were used to analyze this complexity using dynamic mechanical tests within the linear viscoelastic regime. The results showed that the complexity of polymer-modified asphalts is attributable to the formation of an entanglement network generated during the modification via physical and chemical processes based on the polymer type. It was also found that this network increased the modulus and decreased the viscous component at high temperatures, thereby improving the performance of modified asphalts. Despite the observed complex behavior, smooth and continuous master curves were obtained for viscoelastic properties different from the phase angle in frequency and time domains. For the phase angle and loss modulus master curves, the overall trend of the disjointed isothermal curves was simulated using a rheological model.

Long-Term Creep Behavior Prediction of Sol-Gel Derived SiO2- and TiO2-Wood Composites Using the Stepped Isostress Method.

In this study, methyltrimethoxysilane (MTMOS), methyltriethoxysilane (MTEOS), tetraethoxysilane (TEOS), and titanium(IV) isopropoxide (TTIP) were used as precursor sols to prepare wood-inorganic composites (WICs) by a sol-gel process, and subsequently, the long-term creep behavior of these composites was estimated by application of the stepped isostress method (SSM). The results revealed that the flexural modulus of wood and WICs were in the range of 9.8–10.5 GPa, and there were no significant differences among them. However, the flexural strength of the WICs (93–103 MPa) was stronger than that of wood (86 MPa). Additionally, based on the SSM processes, smooth master curves were obtained from different SSM testing parameters, and they fit well with the experimental data. These results demonstrated that the SSM was a useful approach to evaluate the long-term creep behavior of wood and WICs. According to the Eyring equation, the activation volume of the WICs prepared from MTMOS (0.825 nm3) and TEOS (0.657 nm3) was less than that of the untreated wood (0.832 nm3). Furthermore, the WICs exhibited better performance on the creep resistance than that of wood, except for the WICMTEOS. The reduction of time-dependent modulus for the WIC prepared from MTMOS was 26% at 50 years, which is the least among all WICs tested. These findings clearly indicate that treatment with suitable metal alkoxides could improve the creep resistance of wood.

Characterization of physical aging by time-resolved rheometry: fundamentals and application to bituminous binders

Physical aging is a ubiquitous phenomenon in glassy materials and it is reflected, for example, in the time evolution of rheological properties under isothermal conditions. In this paper, time-resolved rheometry (TRR) is used to characterize this time-dependent rheological behavior. The fundamentals of TRR are briefly reviewed, and its advantages over the traditional Struik’s physical aging test protocol are discussed. In the experimental section, the TRR technique is applied to study physical aging in bituminous binders. Small-diameter parallel plate (SDPP) rheometry is employed to perform cyclic frequency sweep (CFS) experiments over extended periods of time (from one to 8.6 days). The results verify that the mutation of rheological properties is relatively slow during physical aging (mutation number N′mu << 1), thus allowing rheological measurements on a quasi-stable sample. The effects of temperature, crystallinity, and styrene-butadiene-styrene (SBS) polymer modification on the physical aging of bitumen are evaluated. The time-aging time superposition is found to be valid both for unmodified and for polymer-modified bitumen. Vertical shifts are necessary, in addition to horizontal time-aging time shifts, to generate smooth master curves for highly SBS-modified bitumen.

Strain rate and temperature dependence of the mechanical properties of polymers: A universal time-temperature superposition principle.

Establishing the Time-Temperature and Frequency-Temperature Superposition Principles (TTSP and FTSP) to describe the mechanical behavior of polymeric materials is always of paramount significance. In this work, by adopting the classic coarse-grained model, we investigate the validity of these superposition principles for a series of networks, such as the pure polymer network, interpenetrating polymer networks composed of stiff and flexible networks (IPNs-SF), interpenetrating polymer networks composed of different cross-linking networks (IPNs-DC), polymer nanocomposites (PNCs), and surface grafted modified PNCs. The study focuses on the three critical mechanical properties such as the stress relaxation, the storage modulus versus the frequency obtained from the dynamic periodic shear deformation, and the uniaxial tensile stress-strain. The glass transition temperature (Tg) is about 0.47 for the simulated polymer network (CL400), and a smooth master curve is obtained for the stress relaxation process by setting the reference temperature Tref = 0.6 via the horizontal shifting process, indicating the validity of TTSP. Furthermore, similar smooth master curves are also achieved for both dynamic periodic shear and uniaxial tensile deformation, which exhibit similar trends and share the identical linear viscoelastic regime in the temperature interval above Tg: 0.55<T<1.0. Importantly, the Williams-Landel-Ferry and Vogel-Fulcher-Tammann equations are both adopted to quantitatively analyze non-linear TTSP behavior when the temperature approaches Tg. For the three mechanical properties, we emphasize that the master curve from TTSP or FTSP is independent of the reference temperature if it is higher than Tg, and based on the linear relation of the shift factor versus the inverse of the temperature higher than Tg, we propose a universal framework for the description of the TTSP or FTSP on the various mechanical properties. Then, we verify that the TTSP seems to be valid for the IPNs-DC system, while it does not hold for both PNCs and IPNs-SF systems because of their structural and dynamic heterogeneity. Furthermore, for PNCs filled with NPs grafted with polymer chains, the TTSP recovers back to be valid because of the enhanced compatibility between polymer and NPs attributed to the grafted polymer chains.

Application of time–temperature superposition principle to Chinese fir orthotropic creep

The application of time–temperature superposition principle (TTSP) to orthotropic creep in dry Chinese fir (Cunninghamia lanceolata [Lamb.] Hook.) was investigated through a sequence of short-term tensile creep for longitudinal (L), radial (R), and tangential (T) specimens in the temperature range of 30–150 °C. A visual assessment for the validity of TTSP was carried out by applying the approximated complex plane (ACP). The results showed that TTSP was well matched for R and T specimens using horizontal shift factor to construct master curves. As for L specimen, an additional vertical shift factor was applied to construct a smooth master curve, owing to the temperature-dependent compliance. Based on the application of ACP, the creep model governed by a power law was proposed to successfully depict the master curve for each main anatomy direction. The present study partially provided the firsthand data in verifying the applicability of TTSP of the orthotropic viscoelasticity of Chinese fir wood, and successfully constructed the rheological model to predict the orthotropic creep response. More importantly, the result can function as the base to the structural safety designs for the engineering structures of Chinese fir in practice.

Evidence of mechano-sorptive effect during moisture adsorption process under hygrothermal conditions: Characterized by static and dynamic loadings

The viscoelasticity of Chinese fir (Cunninghamia lanceolata [Lamb.] Hook.) was examined during moisture adsorption at a relative humidity step (RHstep) mode (made up of RHramp and RHisohume periods) from 0 to 90% RH and temperatures ranging from 30 to 80°C. The viscoelastic tests were carried out by static and dynamic loadings. The moisture adsorption resulted in an increase in compliance or damping. The phenomena that more pronounced mechano-sorptive (MS) effect during RHramp periods than RHisohume periods were observed, indicating that the MS effect could be detected by both static and dynamic loading tests. At 70 or 80°C dynamic loading tests, the lignin transition was observed. Before the occurrence of the lignin transition, or when temperature at or below 60°C, a smooth master curve of E″ vs. E′ was formed and indicated that during the adsorption process the temperature not only accelerated the viscoelastic processes, but also increased their intensity.

An extension of the fractional model for construction of asphalt binder master curve

Knowledge and prediction of viscoelastic behaviour of asphalt binder is of great interest in order to design asphalt mixtures for civil construction of road and airports with good performances. The capability of a fractional model – requiring a very limited number of parameters – to describe and predict the linear viscoelastic behaviour of asphalt binder subjected to sinusoidal oscillations is investigated. Experimental data of complex modulus, |G*|, and phase angle, δ, are used to validate the proposed constitutive model. Based on the proposed extension of a fractional model, complex modulus isotherms for a range of frequencies can be created simply starting from isochronals at frequency value of 1 Hz. Furthermore, a mathematical procedure derived from the same model is proposed in order to compute the shift factors and automatically create the master curve, thus avoiding further errors due to manual adjustments. This shifting procedure requires only a few isotherms to create a smooth master curve able to describe asphalt binder behaviour under a wide range of temperature and loading conditions. When the fractional model is adopted and the mathematical shifting procedure is applied, only a temperature sweep test at 1 Hz is needed in order to create complex modulus and phase angle master curves.

The creep master curve construction for the polyamide 6 by the stepped isostress method

The creep test illustrates the tendency of materials to deform under constant loading; however, this test requires a very long testing time. The use of the time-stress superposition principle (TSSP) allows the prediction of the material performance very beyond the testing time by the construction of the creep master curve. Recently, a new accelerated creep testing method, called the stepped isostress method (SSM) was proposed. This technique requires specific handling of the test data in the construction of the master curve. Initially the method was used on technical yarns. This paper focuses on the effectiveness of this method for specimens having a large thickness. The considered material is a polyamide 6. A smooth creep master curve has been obtained. The obtained master curves by the SSM technique and the classical TSSP method are consistent. This result proofs the robustness of the SSM technique in the construction of the master curve.

New method for estimating shift factors in time–temperature superposition models

Prediction of polymer properties at short and long observation times is usually performed through time–temperature superposition (TTS) models, which make use of some calculated shift factors. Although TTS principle has been used for many decades, no firm rules have been developed for obtaining the master curves. In the absence of reliable long-term data, it has been a common practice to try to minimize the discrepancy between the individual shifted curves. It was reported that a TTS method is more reliable as that discrepancy is minimized. In this study, a new method for obtaining the shift factors is presented. The optimal shift factors were estimated by minimizing the distance between the single curve derivatives with respect to the derivative of the curve at the reference temperature. That shift factors were tested with some classical models. The data were analyzed by statistical methods, making use of bootstrap resampling and spline estimation. The shift factors obtained from the proposed method allow for obtaining smooth master curves. The accuracy of the estimations was evaluated.

A Practical Dynamic Modulus Testing Protocol

Abstract The dynamic modulus test is widely accepted by pavement agencies as the critical parameter for the recently proposed mechanistic empirical design procedure and the candidate of the simple performance test to accompany the Superpave volumetric mix design process. However, the specified dynamic modulus test procedure is time-consuming and costly. State pavement agencies are seeking a more practical test protocol. This paper presents a method for identifying a practical dynamic modulus testing procedure. The currently well-adopted method of calculating the dynamic method is discussed and compared to the more fundamental dynamic modulus calculation method by using actual experimental data from two different asphalt mixtures. It was found that the NCHRP report proposed method produces higher modulus values, but the difference is less than 10 %, as indicates that the simple peak to peak method can be used in the calculation without compromising accuracy. A comprehensive dynamic modulus test, which incorporates strain level, test temperature, and frequency, was performed on one asphalt mixture. Experimental data were analyzed with t-test at the 95 % level of confidence. The analysis results show no statistical difference between the dynamic modulus for the two studied strain levels and no permanent damage was found on tested specimens for all three test temperatures. Comparison of the master curves built by different temperature and frequency combinations illustrates redundancy in test temperature and frequency. A more practical dynamic modulus test procedure is proposed based upon the evaluation. This research shows that three test temperatures, 4.4°C, 21.1°C, and 37.8°C, and six frequencies, 25, 10, 5, 1, 0.5 and 0.1 Hz, plus one additional frequency of 0.01 Hz at 37.8°C are adequate to build a smooth master curve to satisfactorily characterize asphalt mixtures.

Rubber friction: Comparison of theory with experiment

We have measured the friction force acting on a rubber block slid on a concrete surface. We used both unfilled and filled (with carbon black) styrene butadiene (SB) rubber and have varied the temperature from -10 °C to 100 °C and the sliding velocity from 1 μm/s to 1000 μm/s. We find that the experimental data at different temperatures can be shifted into a smooth master-curve, using the temperature-frequency shifting factors obtained from measurements of the bulk viscoelastic modulus. The experimental data has been analyzed using a theory which takes into account the contributions to the friction from both the substrate asperity-induced viscoelastic deformations of the rubber, and from shearing the area of real contact. For filled SB rubber the frictional shear stress σ(f) in the area of real contact results mainly from the energy dissipation at the opening crack on the exit side of the rubber-asperity contact regions. For unfilled rubber we instead attribute σ(f) to shearing of a thin rubber smear film, which is deposited on the concrete surface during run in. We observe very different rubber wear processes for filled and unfilled SB rubber, which is consistent with the different frictional processes. Thus, the wear of filled SB rubber results in micrometer-sized rubber particles which accumulate as dry dust, which is easily removed by blowing air on the concrete surface. This wear process seams to occur at a steady rate. For unfilled rubber a smear film forms on the concrete surface, which cannot be removed even using a high-pressure air stream. In this case the wear rate appears to slow down after some run in time period.

Separating stress and time dependent effects in the temperature dependent creep of polyethylene nanocomposites

AbstractThe nonlinear time dependent creep of linear‐low density polyethylene (LLDPE) reinforced with montmorillonite layered silicate was investigated. A previous study related the time/stress dependence of creep compliance of the material at room temperature using the Burger and Kohlrausch‐Williams‐Watts models. Using both the creep and recovery compliance curves, we employ the Schapery formulation to study the relationship between deformation, time, stress, and temperature of LLDPE nanocomposites. Smooth mastercurves are constructed using time–temperature–stress superposition principles. The stress and temperature‐related creep constants and shift factors were determined for the material using the Schapery nonlinear viscoelastic equation. The prediction results confirm the enhanced creep resistance of nanofillers even at extended time scales and low temperatures. POLYM. ENG. SCI., 50:1646–1657, 2010. © 2010 Society of Plastics Engineers

Is there a lowest upper bound for superconductive transition temperatures?

The values of superconductive transition temperatures Tc in conventional crystalline metallic superconductors are widely scattered, depend on the details of the Fermi surface (especially the density of states N(EF)), and are typically below 1 K. By far the highest Tc 's (~100 K) are found in the cuprates, and there Tc is apparently insensitive to the geometry of the Fermi surface, while it depends strongly on dopant density and configuration. For the cuprates there is a smooth master curve Tcmax(<R>) for the highest Tc's as a function of the average number <R> of Pauling resonating bonds/atom in the parent (undoped) insulator. The existence of such an <R>-dependent optimized Tc is suggested by analogies with the microscopic theory of optimized molecular glass networks (such as window glass), but it remains to derive a rigorous quantum theory of the origin of Tcmax(<R>).