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

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

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.     

玻璃纤维增强树脂基复合材料弯曲强度时间温度相关性

研究了玻璃纤维增强树脂基复合材料 (GFRP) 层合板弯曲强度高温加速试验的时间温度相关性。在不同的温度和加载速率下进行了三点弯曲试验。通过弯曲强度控制曲线的时间温度移动因子曲线分析了GFRP层合板的弯曲强度时间温度相关性。探讨了低温短时和高温长时的失效机理。通过玻璃纤维拉伸延迟断裂试验,对GFRP层合板的低温短时弯曲强度的时间温度相关性进行了修正。修正后的弯曲强度控制曲线的时间温度移动因子曲线与基体树脂动态杨氏模量的时间温度移动因子曲线非常吻合,表明GFRP层合板的弯曲强度取决于基体树脂的粘弹性性能。      

Simplified determination of long-term viscoelastic behavior of amorphous resin

The time-temperature superposition principle has been applied to predict accurately the long-term viscoelastic behavior of amorphous resin at a temperature below the glass transition temperature from measuring the short-term viscoelastic behavior at elevated temperatures. A simplified method for the determination of the long-term viscoelastic behavior of amorphous resin using dynamic mechanical analysis is proposed. The automatic horizontal and vertical shifting method is used to construct the smooth storage modulus master curve, and then the accurate time-temperature shift factors can be obtained. The validity of our simplified determination method is confirmed experimentally.     

Accelerated testing for long-term durability of GFRP laminates for marine use

Our proposed accelerated testing methodology for the long term durability of polymer composites is based on the time–temperature superposition principle to be held for the viscoelasticity of polymer matrix. The long term flexural fatigue life of plain woven glass fiber/vinyl-ester (GFRP) laminates for conventional marine use was predicted based on the proposed methodology. As results, the flexural fatigue strengths of GFRP laminates decreases strongly with increasing time and temperature as well as the number of cycles to failure. The long term fatigue strength at any time, temperature and number of cycles to failure can be predicted using the master curves of fatigue strength obtained based on our proposed accelerated testing methodology.     

Effect of initial imbibed moisture content on flexural fatigue behavior of polyamide 66/hectorite nanocomposites at laboratory condition

Imbibed moisture affects the mechanical properties of polymers and influences the performance of products made out of them during service. Flexural fatigue tests were conducted under deflection control mode using a custom built, table-top flexural fatigue test rig at laboratory condition on PA66/hectorite nanocomposites (PA66CN). Dynamic mechanical analysis studies of PA66CN revealed significant plasticization effect of water on moduli and damping factor with increase in imbibed moisture content. A decrease in induced flexural stress amplitude and rise in temperature of specimen with increase in moisture content result in increased fatigue life at a constant cyclic end deflection. The microstructure of failed flexural fatigue specimens manifested a rubbery behavior. The extent of rubberiness is directly related to the difference between specimen temperature at cyclic steady state and glass transition temperature.     

Study of the Effect of Aging Progression on Creep Behavior of PPE Composites

In this study, creep behavior of stainless fiber-PPE composites was analyzed in an oil environment at elevated temperatures, and the effects of physical aging on creep behavior were intensively investigated. The results showed that the creep phenomena of metal fiber-PPE composite with pre-aging treatment correlated with the Arrhenius time-temperature reciprocation law and within the aging range; time-aging time superposition also held good. Thus, prediction of short-term creep behavior for any pre-aging time was possible, based on the grand master curve of the creep compliance master curves and the shift factor for aging progression. It was clarified that a pre-aged composite can withstand higher temperatures and longer times. It was also observed that the energy of activation during creep decreased with an increase in pre-aging treatment time. This revised version was published online in August 2006 with corrections to the Cover Date.     

The Combined Influence of Molecular Weight and Temperature on the Physical Aging and Creep Compliance of a Glassy Thermoplastic Polyimide

The effect of molecular weight on the viscoelastic performance of anadvanced polymer (LaRC-SI) was investigated through the use of creepcompliance tests. Testing consisted of short-term isothermal creep andrecovery with the creep segments performed under constant load. Thetests were conducted at three temperatures below the glass transitiontemperature of five materials of different molecular weight. Through theuse of time-aging-time superposition procedures, the material constants,material master curves and aging-related parameters were evaluated ateach temperature for a given molecular weight. The time-temperaturesuperposition technique helped to describe the effect of temperature onthe timescale of the viscoelastic response of each molecular weight. Itwas shown that the low molecular weight materials have higher creepcompliance and creep rate, and are more sensitive to temperature thanthe high molecular weight materials. Furthermore, a critical molecularweight transition was observed to occur at a weight-average molecularweight of _w 25,000 g/mol below which, the temperature sensitivity of thetime-temperature superposition shift factor increases significantly. Theshort-term creep compliance data were used in association with Struik'seffective time theory to predict the long-term creep compliance behaviorfor the different molecular weights. At long timescales, physical agingserves to significantly decrease the creep compliance and creep rate ofall the materials tested. Long-term test data verified the predictivecreep behavior. Materials with higher temperature and lower molecularweights had greater creep compliance and higher creep rates.     

Applicability of Fatigue Life Prediction Method to Polymer Composites

A prediction method of fatigue strength under an arbitraryfrequency, temperature, and stress ratio is proposed for polymercomposites and its validity is confirmed for the flexural fatiguestrength of satin-woven CFRP laminates. This method is based upon fourhypotheses: (a) same failure process under constant strain-rate (CSR),creep, and fatigue loadings, (b) same time-temperature superpositionprinciple for all failure strengths, (c) linear cumulative damage lawfor nondecreasing stress process, and (d) linear dependence of fatiguestrength upon stress ratio. This method was applied to the flexuralfatigue strength of various unidirectional CFRPs, and the verificationand limitations of this method were discussed.     

Isothermal physical aging characterization of Polyether-ether-ketone (PEEK) and Polyphenylene sulfide (PPS) films by creep and stress relaxation

This paper considers the experimental characterization of isothermal physical aging of PEEK and PPS films using a dynamic mechanical analyzer. Using the short-term test method established by Struik, momentary creep and stress relaxation curves were measured at several temperatures within 15–35°C below the glass transition temperature (T _g ) at various aging times. Stress and strain levels were such that the materials remained in the linear viscoelastic regime. These curves were then shifted together to determine momentary master curves and shift rates using the PHYAGE program. In order to validate the obtained isothermal physical aging behavior, the results of creep and stress relaxation testing were compared and shown to be consistent with one another using appropriate interconversion of the viscoelastic material functions. Time–temperature superposition of the master curves was also performed. The temperature shift factors and aging shift rates for both PEEK and PPS were consistent for both creep and stress relaxation test results.     

Long-term creep-rupture failure envelope of epoxy

An accelerated testing methodology based on the time-temperature superposition principle has been proposed in the literature for the long-term creep strength of polymer matrices and polymer composites. Also, it has been suggested that a standard master curve may be a feasible assumption to describe the creep behavior in both tension and compression modes. In the present research, strength master curves for an aerospace epoxy (8552) were generated for tension and compression, by shifting strength data measured at various temperatures. The shift function is obtained from superposition of creep-compliance curves obtained at different temperatures. A standard master curve was presented to describe the creep-rupture of the polymer under tension and compression. Moreover, long-term creep-rupture failure envelopes of the polymer were presented based on a two-part failure criterion for homogeneous and isotropic materials. Ultimately, the approach presented allows the prediction of creep-rupture failure envelopes for a time-dependent material based on tensile strengths measured at various temperatures, considering that the ratio between tensile and compressive strengths is known.     

A relationship between non-exponential stress relaxation and delayed elasticity in the viscoelastic process in amorphous solids: Illustration on a chalcogenide glass

Inorganic glasses are viscoelastic materials since they exhibit, below as well as above their glass transition temperature, a viscoelastic deformation under stress, which can be decomposed into a sum of an elastic part, an inelastic (or viscous) part and a delayed elastic part. The delayed elastic part is responsible for the non-linear primary creep stage observed during creep tests. During a stress relaxation test, the strain, imposed, is initially fully elastic, but is transformed, as the stress relaxes, into an inelastic and a delayed elastic strains. For linear viscoelastic materials, if the stress relaxation function can be fitted by a stretched exponential function, the evolution of each part of the strain can be predicted using the Boltzmann superposition principle. We develop here the equations of these evolutions, and we illustrate their accuracy by comparing them with experimental evolutions measured on GeSe₉ glass fibers. We illustrate also, by simple equations, the relationship between any kind of relaxation function based on additive contribution of different relaxation processes and the delayed elastic contribution to stress relaxation: the delayed elasticity is directly correlated to the dispersion of relaxations times of the processes involved during relaxation.     

Accelerated testing for long-term fatigue strength of various FRP laminates for marine use

The prediction of long-term fatigue life of various FRP laminates combined with resins, fibers and fabrics for marine use under temperature and water environments were performed by our developed accelerated testing methodology based on the time–temperature superposition principle (TTSP). The five kinds of FRP laminates were prepared under three water absorption conditions of Dry, Wet and Wet + Dry after molding. The three-point bending constant strain rate (CSR) and fatigue tests for these FRP laminates at three conditions of water absorption were carried out at various temperatures and loading rates. As results, the mater curves of fatigue strength as well as CSR strength for these FRP laminates at three water absorption conditions are constructed by using the test data based on TTSP. It is possible to predict the long-term fatigue life for these FRP laminates under an arbitrary temperature and water absorption conditions by using the master curves. The characteristics of time, temperature and water absorption dependencies of flexural CSR and fatigue strengths of these FRP laminates are clarified.     

Lebensdauerermittlung bei mehrachsigen wechselnden Beanspruchungen im niedrigen und hohen Temperaturbereich

Life time assessment on multiaxial cyclic loadings at low and high temperatures For the calculation of fatigue strength of components made out of ductile materials under complex cyclic load different assessments are present. As typical representatives of stress theories the shear stress intensity hypothesis (SIH) as well as the method of critical plane approach (MKS) are considered and compared for rigid and non rigid principle stress directions. Furthermore for synchronous loads the calculation methods are compared with Bach's method. The calculation method becomes more complex, if time dependent material properties at corresponding high temperatures have to be taken into account. In this case the application of viscoplastic material models is necessary, which allows the consideration of combination of creep and fatigue. As an example a modified material model by Chaboche / Nouailhas is used in order to present the calculation of multiaxial creep fatigue tests.     

Residual strength distribution of impacted glass/epoxy laminates with embedded shape memory alloy at low temperature

This paper evaluated the strength reduction and probabilistic behaviors of the residual flexural strength for impacted glass/epoxy laminates with embedded shape memory alloy (SMA) wires at various temperatures. A series of impact tests were performed on base (glass/epoxy laminates without SMA wires) and SMA laminates (glass/epoxy laminates with embedded SMA wires) at temperatures of 293 K, 263 K and 233 K. Three point flexural tests were then carried out so as to investigate the post-impact strength at the aforementioned temperatures. Strength reduction behavior of impacted laminates could be described by Caprino’s residual strength prediction model. A probabilistic model was developed in order to estimate the variation in residual strength of the impacted laminates with temperature. As the temperature decreased, the variation in residual strength increased due to the embrittlement of the constituent materials of the laminates at lower temperatures. When compared to the base laminates, the SMA laminates exhibited a higher variation in residual strength, especially at lower temperatures.     

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.     

Experimental analysis on the time-dependent bonding of FRP laminates under sustained loads

Fiber reinforced composite materials are frequently used in the rehabilitation or upgrading of existing structures. From a design point of view, current international guidelines on FRP strengthening applications do not give rules based on rigorous approaches to evaluate the reliability and durability of strengthening interventions with respect to long-term behavior. In order to give a contribution on this topic, the authors have carried out a creep experimental program on retrofitting systems, either of carbon or glass fibers and subject to different stress values in regime of constant temperature. The tests have been carried out by means of a dedicated test device that provided a pure bending stress state in the strengthened beam, being the external loads held constant over time. In this paper the results of their investigation and critical analysis are presented.     

A systematic methodology for creep master curve construction using the stepped isostress method (SSM): a numerical assessment

Long-term creep of viscoelastic materials is experimentally inferred through accelerating techniques based on the time–temperature superposition principle (TTSP) or on the time–stress superposition principle (TSSP). According to these principles, a given property measured for short times at a higher temperature or higher stress level remains the same as that obtained for longer times at a lower temperature or lower stress level, except that the curves are shifted parallel to the horizontal axis, matching a master curve. These procedures enable the construction of creep master curves with short-term experimental tests.The Stepped Isostress Method (SSM) is an evolution of the classical TSSP method. Higher reduction of the required number of test specimens to obtain the master curve is achieved by the SSM technique, since only one specimen is necessary. The classical approach, using creep tests, demands at least one specimen per each stress level to produce a set of creep curves upon which TSSP is applied to obtain the master curve.This work proposes an analytical method to process the SSM raw data. The method is validated using numerical simulations to reproduce the SSM tests based on two different viscoelastic models. One model represents the viscoelastic behavior of a graphite/epoxy laminate and the other represents an adhesive based on epoxy resin.     

Continuous fibre composites with a nanocomposite matrix: Improvement of flexural and compressive strength at elevated temperatures

Polymer layered silicate nanocomposites can improve the flexural and compressive strength of continuous fibre reinforced composites by means of increasing the matrix modulus. A three-phase thermoplastic composite consisting of a main reinforcing phase of woven glass fibres and a polyamide 6 (PA6) nanocomposite matrix was fabricated. Flexural testing of a conventional PA6 fibre composite has shown a decrease of the flexural strength upon increasing temperature. This behaviour is associated with the decrease of the matrix modulus, especially above T_g. The nanocomposite used in this study has a modulus that is much higher than unfilled PA6, even above T_g and after moisture conditioning. The results showed that the fibre composites with a nanocomposite matrix have a more than 40% increased flexural and compressive strength at elevated temperatures. This also means that the temperature at which the materials can be used is increased by 40–50 °C. Therefore, by using a nanocomposite matrix the high temperature performance of fibre composites can be improved without any change in processing conditions. The combination with other advantages of nanocomposites in areas such as barrier properties, flammability and creep makes this a very attractive approach.     

On the strengthening effect of increasing cycling frequency on fatigue behavior of some polymers and their composites: Experiments and modeling

Effect of cycling frequency on fatigue behavior of neat, talc filled, and short glass fiber reinforced injection molded polymer composites was investigated by conducting load-controlled fatigue tests at several stress ratios (R = −1, 0.1, and 0.3) and at several temperatures (T = 23, 85 and 120 °C). A beneficial or strengthening effect of increasing frequency was observed for some of the studied materials, before self-heating became dominant at higher frequencies. A reduction in loss tangent (viscoelastic damping factor), width of hysteresis loop, and displacement amplitude, measured in load-controlled fatigue tests, was observed by increasing frequency for frequency sensitive materials. Reduction in loss tangent was also observed for frequency sensitive materials in DMA tests. It was concluded that the fatigue behavior is also time-dependent for frequency sensitive materials. A Larson–Miller type parameter was used to correlate experimental fatigue data and relate stress amplitude, frequency, cycles to failure, and temperature together. An analytical fatigue life estimation model was also used to consider the strengthening effect of frequency in addition to mean stress, fiber orientation, and temperature effects on fatigue life.