Time Temperature Stress Superposition Research Articles

Flexural creep behavior of hierarchical bamboo structure using time-temperature-stress superposition principle

The long-term flexural creep properties of graded hierarchical bamboo are important to structural design in civil construction. The present study conducted the short-term flexural creep tests at a series of temperature (30–170 °C) and stress (7–15 MPa) conditions, for the bamboo from both inner and outer parts. The application of time-temperature superposition principle (TTSP) and time-temperature-stress superposition principle (TTSSP) was analyzed for the creep behavior of bamboo with regard to hierarchical structure. The results confirmed the feasibility of TTSP and TTSSP in flexural creep of bamboo by horizontal shifting. A creep model based on Findley power law was successfully employed to predict the flexural creep response of bamboo. Additionally, the sample from inner part of bamboo displayed a more pronounced flexible creep response compared with the sample from outer part, attributing a low fiber volume fraction in inner part due to bamboo growth strategy. The findings in this study broaden the knowledge of bamboo rheology, and is helpful for further work on the bamboo growth strategy effect on mechanical properties.

Characterization of creep deformation behavior of porous polymer membrane under Small-Punch test

This study investigated creep deformation behavior of a porous polymer membrane under biaxial stress by using the small-punch test. We first conducted a mechanical test for creep deformation, using uniaxial tension to examine creep compliance, which revealed that creep compliance was strongly dependent on applied stress in a nonlinear creep-deformation relationship. Using the time–temperature–stress superposition principle (TTSSP), we obtained a master curve that unified the compliance curves for various applied stresses. Next, a small-punch test was conducted to apply biaxial stress to the membrane. This method was also able to apply a stress gradient to the membrane during the test. Creep deformation due to the small-punch test was found to be dependent on the applied load. Additionally, we created a homogenous model based on the finite element method (FEM) and the TTSSP of nonlinear creep theory. The FEM model predicted creep deformation behavior during a small-punch test for various load levels with good accuracy.

Time-temperature-stress equivalence in compressive creep response of Chinese fir at high-temperature range

Predicting long-term viscoelasticity properties of wood is important for designing dimensions for structure-used wood and optimizing thermo-mechanical treatment technique. In this study, compressive creep of Chinese fir wood was tested at a series of temperature (140–220 °C) and stress (0.03–0.15 MPa) conditions. The time-stress superposition principle (TSSP) and time-temperature-stress superposition principle (TTSSP) were applied to predict long-term creep behavior. Changes of chemical components and anatomical features of wood cell wall after creep test were investigated by Raman spectroscopy and scanning electron microscopy. The results showed that quasi-linear change of strain was acquired when temperature at or below 180 °C. TSSP and TTSSP were feasible to predict compressive creep at an up-threshold temperature of 180 °C. When temperature was 200 and 220 °C, obvious non-linear strain was obtained, and TSSP and TTSSP failed to construct master curves. Much significant degradations of carbohydrates was found at 200 °C, which could explain why TSSP failed to construct master curves from a chemical point of view. Crack and rupture on the cell walls and among the cell corners were observed when temperature at or above 200 °C and stress at or above 0.09 MPa. From an anatomical point of view, the destruction of wood cell structures could explain why TSSP failed to construct master curves. The finding in this studies broads the knowledge of the viscoelasticity of wood, and is helpful for further investigations on the thermo-mechanical manufacturing techniques.

Creep deformation behavior of polymer materials with a 3D random pore structure: Experimental investigation and FEM modeling

This study investigates the creep deformation behavior of polyvinylidene difluoride (PVDF) with a 3D random pore structure. The test sample was a hollow fiber polymeric membrane with sub-micron-sized pores and an open cellular structure, which plays a critical role for water purification. Uniaxial tensile test was carried out for the polymeric membrane and it was found that the membranes underwent elasto-plastic deformation and creep deformation. In order to establish a numerical model, the finite element method (FEM) was employed. Using the Surface Evolver software, a 3D random pore structure was created in the representative volume element (RVE). The established computational model can predict both elastic and plastic deformation. Furthermore, the time–temperature–stress superposition principle (TTSSP) is employed for our FEM model to compute creep deformation. The present model enables the prediction of macroscopic and microscopic deformation behavior of porous materials that have a 3D random pore structure.

Nonlinear Creep Deformation of Polycarbonate at High Stress Level: Experimental Investigation and Finite Element Modeling

It is well known that polycarbonate (PC) undergoes time-dependent deformation (i.e., creep deformation), and nonlinear creep deformation is often experienced at high stress level. Using the time–temperature–stress superposition principle (TTSSP), we obtain a new master curve, which covers higher stress level, and successfully establish a new modeling method of creep deformation of PC. First, to investigate the effect of applied stress level on the creep compliance (i.e., stress-dependent nonlinear creep deformation), this study conducted various creep tests with eight different stress levels. We found that the creep compliance curve strongly depended on the applied stress level; in particular, a higher stress level induced a larger difference in creep compliance. According to the TTSSP, the creep compliance curve at each stress level shifts with the creep time (i.e., stress reduced time). When we appropriately selected the stress reduced time, we obtained the master curve of creep compliance, which is unified with respect to various applied stresses. However, we found that the stress-shifted factor is not compliant with the previous TTSSP, especially in the higher stress regime. Therefore, this regime was also considered to obtain a new master curve that can cover a wide range of stress levels. Finally, our established creep model (master curve and stress shift factor) was introduced into FEM, and then this numerical model was verified by comparison with experimental data. Our model may be useful for predicting the creep deformation of PC subjected to a wide range of applied stresses.

Accelerated creep and creep-rupture testing of transverse unidirectional carbon/epoxy lamina based on the stepped isostress method

Accelerated methods for measuring long-term viscoelastic properties of fiber reinforced polymer (FRP) composites are important for reducing the time needed to characterize material behavior. Most of them are based on the time-temperature-stress superposition principle (TTSSP), or some variation. This paper investigates the applicability of the stepped isostress method (SSM) to study tensile creep of unidirectional carbon FRP (CFRP) lamina used in rehabilitating prestressed concrete structures. The SSM employs a load-stepping approach, typically with three to five steps for a single specimen resulting in creep-rupture. Theoretical analysis of the experimental method (previously lacking) is discussed and modifications to the testing and analysis protocol are shown to improve validity of the master curves compared to conventional creep curves and traditional TTSSP creep master curves at room temperature. Finally, three failure criteria are compared for predicting creep-rupture of CFRP laminates based on the accelerated testing method.

Effect of service temperature on the shear creep response of rigid polyurethane foam used in composite sandwich floor panels

This paper presents an experimental and analytical study about the effect of temperature on the shear creep response of a rigid polyurethane (PUR) foam within the scope of sandwich panel application in building floors. Shear creep tests were carried out on a foam (87.4kg/m3) subjected to shear stress levels of 11%, 22% and 44% of its shear strength at temperatures of 20°C, 24°C and 28°C – a range likely to be found in the envisaged application – for more than 1300h. The results obtained show that the foam’s creep response increases with both stress level and temperature. Findley’s power law, extended to include Arrhenius equations describing the temperature dependency of its viscoelastic parameters, was fitted to the experimental creep curves, thus allowing to model the time-temperature-stress dependent shear creep behaviour of the PUR foam. The proposed model provided a good fit to the experimental creep curves within the linear viscoelastic range. Practical design equations were also derived for the time-temperature dependent (i) shear modulus, (ii) creep coefficient, and (iii) shear modulus reduction factor. Finally, the time-temperature-stress superposition principle (TTSSP) and the time-stress superposition principle (TSSP) were used to yield “master curves” that compared well with the proposed model’s predictions.

Effect of service temperature on the flexural creep of vacuum infused GFRP laminates used in sandwich floor panels

This paper presents an experimental and analytical study about the effect of temperature on the flexural creep of GFRP laminates produced by vacuum infusion. Such laminates are considered for use in the faces of sandwich panels for building floor application. Flexural creep tests were carried out in a three point bending configuration for stress levels of 15%, 25% and 35% of the laminate's flexural strength, and temperatures of 20 °C, 24 °C and 28 °C (a range likely to be found in the envisaged application), with durations between 1000 h and 2215 h. The creep response was observed to increase both with temperature and stress level. Findley's power law was used to model the experimental results, and extended to include an Arrhenius equation for temperature dependence of the creep response. The proposed model provided a good fit to the experimental creep curves, and was used to derive a set of practical design equations for the time-temperature dependent (i) flexural modulus, (ii) creep coefficient, and (iii) flexural modulus reduction factor. Finally, the time-temperature-stress superposition principle (TTSSP) and the time-stress superposition principle (TSSP) were used to obtain “master curves” that compared well with the proposed model's predictions.

Application of time-temperature-stress superposition principle on the accelerated physical aging test of polycarbonate

The effect of physical aging on the polymer mechanical properties is very important for long-term safety assessment of engineering application. In this paper, the physical aging tests of polycarbonate (PC) were conducted systemically under different temperature and uniaxial tensile stress level. It was shown that both temperature and stress have obvious accelerated effect on the physical aging of PC. The higher the temperature and stress level are, the faster the aging process is. To predict the long-term behavior after physical aging using the short-term test results of PC, the elongation-at-break was chosen as the index of the severity of physical aging. An Arrhenius-type time–temperature–stress superposition principle (TTSSP) was proposed to evaluate long-term performance using short-term test data. Using the proposed method, time and cost can be dramatically reduced for the assessment of long-term physical aging performance of polymeric material. POLYM. ENG. SCI., 55:2215–2221, 2015. © 2015 Society of Plastics Engineers

Development of characterisation models for incremental permanent deformation model for asphalt concrete in confined compression

Permanent deformation modelling research at North Carolina State University has produced the so-called incremental model that fits the primary and secondary regions in permanent strain growth. Triaxial repeated load permanent deformation tests are conducted on Federal Highway Administration-Accelerated Loading Facility and NY9.5B mixtures to evaluate the effects of temperature, stress, and load time on permanent deformation and, therefore, to determine the form of the incremental model to account for these effects. The test results suggest that the slope in the log(ϵvp)−log(N) plot is constant regardless of these three major factors. This observation provides the basis for two modelling approaches: the functionalised model and the shift model. The functionalised model is formulated by expressing the coefficients of the incremental model in terms of the reduced load time and deviatoric stress. The shift model, based on the time-temperature–stress superposition principle, utilises the strain mastercurve and reduced load time and deviatoric stress shift functions. A composite loading test that is composed of varying load times and deviatoric stresses is proposed as the model calibration test. It is found that the permanent strain growth under the complex loading histories predicted by the calibrated models is in good agreement with the measured permanent strain growth.

Time-Temperature-Stress Superposition Principle: Brief Description and Application to Polymer Creep Behavior

A new accelerated characterization model for creep performances was briefly introduced first, which considers both the effects of temperature and stress level, named time-temperature- stress superposition principle (TTSSP). TTSSP assumes that the influence of stress level on the intrinsic time is similar to that of temperature for the creep behavior, as well as damage and physical aging. The creep curves at different state can be shifted into a master curve at reference state using TTSSP. Then the long-term creep behavior of viscoelastic materials at lower temperature and/or stress level can be predicted from the short-term ones. Finally, TTSSP was used to investigate the nonlinear creep behavior of high-density polyethylene (HDPE). It was shown that the long-term creep behavior of HDPE can be predicted successfully.

Application of time–temperature–stress superposition on creep of wood–plastic composites

Time–temperature–stress superposition principle (TTSSP) was widely applied in studies of viscoelastic properties of materials. It involves shifting curves at various conditions to construct master curves. To extend the application of this principle, a temperature–stress hybrid shift factor and a modified Williams–Landel–Ferry (WLF) equation that incorporated variables of stress and temperature for the shift factor fitting were studied. A wood–plastic composite (WPC) was selected as the test subject to conduct a series of short-term creep tests. The results indicate that the WPC were rheologically simple materials and merely a horizontal shift was needed for the time–temperature superposition, whereas vertical shifting would be needed for time–stress superposition. The shift factor was independent of the stress for horizontal shifts in time–temperature superposition. In addition, the temperature- and stress-shift factors used to construct master curves were well fitted with the WLF equation. Furthermore, the parameters of the modified WLF equation were also successfully calibrated. The application of this method and equation can be extended to curve shifting that involves the effects of both temperature and stress simultaneously.

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

Flexural creep of long fiber-reinforced thermoplastic composites: Effect of processing-dependent fiber variables on creep response

Flexural creep properties were studied as a function of fiber weight fraction and processing-induced fiber alignment in extrusion/compression-molded, long fiber-reinforced thermoplastic (LFT) nylon 6/6, polypropylene, and high-density polyethylene and their 10 wt.% and 40 wt.% E-glass fiber reinforced LFT composites. The residual fiber lengths and probability distribution parameters were near-equal, regardless of the initial fiber length and processing. Creep compliances decreased with increasing fiber weight fraction, and clear influence of fiber alignment was found in model parameters. Processing-induced fiber alignment imaged using X-ray radiography, was correlated with the creep compliances of strategically sectioned specimens, and tested as per ASTM D-2990. Longitudinal fibers aided in lowering the creep compliance, and the range in compliance decreased with lower preferential fiber alignment. Creep compliances from flexural creep tests and dynamic mechanical analysis/static creep tests were combined using time–temperature–stress superposition (TTSSP) to construct long-term master curves that correlated closely with long-term tests.

Effects of temperature and stress on the short- and long-term compressive behavior of expanded polystyrene

ABSTRACT: The short- and the long-term compressive behavior of an expanded polystyrene (EPS) geofoam were both evaluated to assess the effects of temperature and stress. The short-term compressive strength decreased bi-linearly as temperature increased with a transition point at the temperature of 43oC. For the long-term compressive creep behavior, three accelerated creep test methods were used in the evaluation: stepped isothermal method (SIM), time–temperature superposition (TTS), and time–temperature–stress superposition (TTSS). The results from these three tests were compared with that of the conventional creep test at room temperature. Due to the 43°C transition in the short-term compressive strength, the predicted creep strains from SIM and TTS, employing a higher temperatures than 43°C, were found to be much higher than those from the conventional test. Furthermore, the activation energies were significantly different at temperatures above and below 43°C. On the other hand, the creep strains predicted from the TTSS tests were similar to those from the conventional method. The TTSS tests employed test temperatures below 44°C. Instead of using elevated temperatures, higher stress levels were used to accelerate the creep. A modified four-parameter Weibull model was developed to predict the linear and non-linear creep behavior, and a good agreement was found with test data from TTSS and the conventional method.

Flexural creep behavior of discontinuous thermoplastic composites: Non-linear viscoelastic modeling and time–temperature–stress superposition

Flexural creep behavior of nylon 6/6, polypropylene and high-density polyethylene long fiber thermoplastic (LFT) composites was studied according to ASTM D-2990. Neat polymers were tested for baseline data and compared with the 40 wt.% E-glass reinforced LFTs, all processed by compression molding. All materials exhibited non-linear viscoelasticity and showed a succession in creep resistance consistent with static flexural yield strength. A four parameter empirical model used for short fiber thermoplastics (SFT), proposed by Hadid et al., was found to provide an excellent fit to the experimental data. Time-compliance data from flexural creep and dynamic mechanical analysis (DMA) were combined to utilize short-term flexural creep tests to predict lifetime of the composites. A time–temperature–stress superposition (TTSSP) procedure was used, where stress-based vertical shifts were applied in addition to horizontal shifts used in a traditional time–temperature superposition (TTSP). Master curves obtained by this method projected the long-term creep properties, the order of creep resistance being consistent with the flexural creep data.

Nanorheological Investigation of Polymeric Surfaces by Atomic Force Microscopy

A developed nanomechanical analysis of atomic force microscopy (AFM) based on the JKR theory has been applied to butyl rubber; isoprene-co-isobutylene rubber (IIR, butyl rubber). The force–deformation (F–δ) plots converted from force–distance curves of IIR varied with several experimental conditions, i.e., temperature, scan velocity and maximum loading force. We analyzed the plots by the JKR analysis referring to the 'two-points method' proposed by Walker and co-workers. It was found that the apparent Young's modulus and adhesive energy obtained from the method revealed well-defined appearance when plotted against maximum sample deformation. In conclusion, the 'time–temperature–stress superposition principle', which is one of the major characteristics of viscoelastic materials, proved to be valid even at nanometer scale.

Application of Time-Ageing Time and Time-Temperature-Stress Equivalence to Nonlinear Creep of Polymeric Materials

Based on the observations that high temperature accelerates creep rate of polymer while physical ageing plays a reverse role, and that there is an analogy between the influences of stress and temperature on the intrinsic times of polymers, the time-ageing time superposition principle (TASP) and the time-temperature-stress superposition principle (TTSSP) are used to evaluate the long-term creep behavior of poly(methyl methacrylate) (PMMA). PMMA specimens were aged for 2 to 120 hours at identical temperature, their short-term creep strains with 2-hour test duration were measured under various stress levels ranging from 14 to 30 MPa at room temperature, and modeled by means of time-ageing time equivalence and time-stress equivalence. The results show that the creep rate increases with stress, but decreases with ageing time. The ageing time shift factors vary with the stresses at which the shifts are applied. The ageing shift rate is independent on imposed stress in linear viscoelastic region, while it decreases with increasing stress when the material behaves in a nonlinear viscoelastic manner. The master creep compliance curve up to about 1-month at reference ageing time 120 hours and stress 18 MPa, which is nearly 2.5 decades longer than the test duration, is constructed by shifting the creep curves horizontally along the logarithmic time axis. The result illustrates that TTSSP, combined with TASP, provides an effective accelerated test technique for long-term mechanical behaviors of polymers.

Time-Temperature-Stress Equivalence Applied to Accelerated Characterization of Creep Behavior of Viscoelastic Polymer

Temperature induced change, and stress induced change as well, in intrinsic timescale were investigated by nonlinear creep tests on poly(methyl methacrylate). With four different experimental temperatures, from 14 to 26 degrees centigrade, time-dependent axial elongations of the specimen were measured at seven different stress levels, from 14 MPa to 30 MPa, and modeled according to the concept of time-temperature-stress equivalence. The test duration was only 4000 seconds. The corresponding temperature shift factors, stress shift factors and temperature-stress shift factors were obtained according to the time-temperature superposition principle (TTSP), the time-stress superposition principle (TSSP) and the time-temperature-stress superposition principle (TTSSP). The master creep compliance curve up to about two-year at a reference temperature 14 degrees centigrade and a reference stress 14 MPa was constructed by shifting the creep curves horizontally along the logarithmic time axis using shift factors. It is shown that TTSSP provides an effective accelerated test technique in the laboratory, the results obtained from a short-term creep test of PMMA specimen at high temperature and stress level can be used to construct the master creep compliance curve for prediction of the long-term mechanical properties at relatively lower temperature and stress level.

Application of Time-Temperature-Stress Superposition Principle to Nonlinear Creep of Poly(methyl methacrylate)

The uniaxial tensile creep of a commercial grade Poly(methyl methacrylate) was measured for 4000 seconds under various temperatures and stress levels ranging from 14 oC to 26 oC and 6 MPa to 32 MPa. The resultant creep compliance curves depart from each other for stresses beyond a critical value which varies with temperature, indicating nonlinear viscoelastic behavior. The time-temperature-stress superposition principle (TTSSP) was used to construct a smooth master compliance curve with a much longer time-scale interval from the short-term tests at higher stresses and temperatures. It is shown that the master curve covers a period of over 290 days, which is nearly 3.9 decades longer than the test duration. Moreover, it is verified that the time-temperature shift factors are dependent on stresses at which the shifts are applied, and that the time-stress shift factors are dependent on reference temperatures.