The effect of time and temperature on the mechanical behavior of epoxy composites

A crosslinked epoxy resin consisting of a 60/40 weight ratio of Epon 815 and Versamid 140 and composites of this material with glass beads, unidirectional glass fibers and air (foams) were tested in tension, compression and flexure to determine the effect of time and temperature on the elastic properties, yield properties and modes of failure. Unidirectional continuous fiber-filled samples were tested at different fiber orientation angles with respect to the stress axis. Strain rates ranged from 10^?4 to 10 in./in.-min and the temperature from ?1 to 107°C. Isotherms of tangent modulus versus strain rate were shifted to form master modulus curves. The moduli of the filled composites and the foams were predictable over the entire strain rate range. It was concluded that the time-temperature shift factors for tangent moduli and the time-temperature shift factors for stress relaxation were identical and were independent of the type and concentration of filler as well as the mode of loading. The material was found to change from a brittle-to-ductile-to-rubbery failure mode with the transition temperatures being a function of strain rate, filler content, filler type and fiber orientation angle, indicating that the transition is perhaps dependent on the state of stress. In the ductile region, an approximately linear relationship between yield stress and log strain is evident in all cases. The isotherms of yield stress versus log strain rate were shifted to form a practically linear master plot that can be used to predict the yield stress of the composites at any temperature and strain rate in the ductile region. The time-temperature shift factors for yielding were found to be independent of the type, concentration and orientation of filler and the mode of loading. Thus, the composite shift factors seem to be a property of the matrix and not dependent on the state of stress. The compressive-to-tensile yield stress ratio was practically invariant with strain rate for the unfilled matrix, while fillers and voids raised this ratio and caused it to increase with a decrease in strain rate. The yield strain of the composites is less than the unfilled matrix and is a function of fiber orientation and strain rate.     

Uniaxial extension of polyvinyl chloride in the high-elastic state

The dependence of true stress on the extension ratio of PVC threads has been determined for a wide range of extension rates. Since the polymer subjected to deformation was in the high-elastic state (at temperatures from 90 to 160°), the deformations were predominantly high-elastic. The dependence of true stress on the amount of high-elastic deformation is described by the Mooney-Rivlin equation. Relaxation moduli have been found on the basis of measurements of stress relaxation at constant deformation after various extension ratios were attained at different rates. Within the limits of deformation regimes at which the true stress is an increasing function of extension ratio the relaxation moduli do not depend on extension ratio and rate of extension. This enables one to arrive at a master curve of the relaxation modulus versus relaxation time with the reservation indicated above concerning the increasing character of the dependence of true stress on extension ratio. The relaxation spectrum represented by the high-elasticity plateau has been determined from the relaxation moduli according to the first approximation. The experimental data for a very wide range of deformation regimes and temperatures are presented in the form of an invariant dependence of the ratio of true stress to the rate of deformation on the product of deformation time by extension ratio. The ultimate strength of the specimens frozen rapidly after the attainment of definite extension ratios is determined by the accumulated high-elastic deformation.     

Prediction of long-term ABS relaxation behavior

The applicability of time–temperature superposition to tensile stress relaxation of ABS plastics has been verified at strains from 0.5 to 5% for temperatures in the range of 10–50°C. Master curves have been compiled to predict the long-term stress relaxation at 23°C. and a stress–strain–reduced time surface has been constructed. A comparison of relaxation times and activation energies has confirmed that a strain increase facilitates stress relaxation up to yield. The decay of relaxation modulus at linear viscoelastic strains was shown to be equivalent to that of tensile creep modulus. By normalizing the master curves to originate at yield stress and then converting them into multiaxial from the strain which gives the best data fit with long-term hydrostatic pipe-burst strength was shown to be at yield or beyond. The ABS yield-strain master curves at 23°C. were shown to match satisfactorily the long-term pipe-rupture data. Activation energies for ABS relaxation have been compared below and above the rigid matrix T_g, to assess the degree of stiffening of the polymer in the solid state.     

Linear Hygrothermal Viscoelastic Characterization of Nafion NRE 211 Proton Exchange Membrane

The tensile relaxation modulus of a commercially available proton exchange membrane, Nafion® NRE 211, was obtained over a range of humidity levels and temperatures using a commercial dynamic mechanical analyzer (DMA). Hygral stress relaxation master curves were first constructed, followed by a hygrothermal master curve using the time temperature moisture superposition principle. The hygrothermal master curve was fitted using a 10‐term Prony series and validated using longer term stress relaxation tests. To validate the results from the stress relaxation experiments, short and long‐term creep compliance was converted into stress relaxation modulus using a well‐known viscoelastic conversion formula, and compared with the relaxation modulus obtained under identical conditions. Good agreement was found between the two datasets. It was evident that relaxation data at 2% RH at the test temperatures was not superposable with the master curves obtained at higher relative humidity (10% < RH < 90%) at the temperature range 70 °C < T < 90 °C. It was observed that the longer term relaxation modulus under humid conditions matched well with the hygrothermal master curve; however, the longer term relaxation modulus under dry conditions was significantly higher than the relaxation master curve obtained under dry conditions, raising the possibility of a physical aging process in the ionomer and/or irreversible morphological changes in the membrane under dry conditions.     

Stress relaxation behavior of polyacetal–thermoplastic polyurethane elastomer blends

The yield stress of polyacetal (POM) decreases monotonically with the incorporation of thermoplastic polyurethane (TPU) elastomer in POM/TPU blends as would be anticipated. However, the impact strength of the resultant POM/TPU blends increases initially up to 30% TPU and thereafter decreases with the addition of TPU. Stress relaxation measurements in simple extension were carried out for POM and its blends with 10, 20, and 30% TPU at a constant temperature (30°C). Rate of loss of the relaxation modulus was found to be a nonlinear function of time. It has been demonstrated that the stress relaxation modulus values measured at different strains can be superimposed by a shift along the logarithmic time axis to yield master curves of modulus over an extended time period. It has also been found that while it is possible to determine, at any strain, relaxation curves covering an appreciable time range, the demarcation of linear and nonlinear behavior ranges of stress could not be done for these materials as all the strain values chosen in our experiments were in the region of linear behavior. © 1993 John Wiley & Sons, Inc.     

Time-dependent properties of versamid cured epoxies

Versamid cured-epoxy specimens were loaded in tension, compression, and flexure at different strain rates and temperatures to determine the yield stress and strain, and tangent, secant, and relaxation moduli. A torsion pendulum was used to measure the dynamic properties as a function of temperature and frequency. The time-temperature superposition principle was used to reduce this data to master curves. It was concluded that the time-temperature shift factors for secant moduli up to the yield point, for stress relaxation and for dynamic moduli were identical and were independent of the mode of loading. It was also shown that the presence of fillers or reinforcing agents likewise had no effect on the shift factors.     

The effect of time and temperature on the mechanical behavior of a “plasticized” epoxy resin under different loading modes

Epoxy–Versamid specimens were loaded in tension, compression, and flexure at different strain rates and temperatures to determine mode of failure, yield stress and strain, and tangent and relaxation moduli. Stress-strain curves were used to define brittle, ductile, ductile-rubbery, and rubbery modes of behavior which prevailed in different temperature-strain rate regions. The time-temperature superposition principle was applied to yield stress, initial tangent moduli, and relaxation moduli data for all three types of loading. The transition regions, tangent and relaxation moduli, and shift factors were the same in tension, compression, and flexure. Thus the most convenient mode of loading can be used to determine the general time-temperature dependence. The ratio of compressive-to-tensile yield stress was almost constant over the entire ductile region. Flexural yielding data were used to predict yield stress in tension and compression, and stress relaxation master curves were shown to be related to elastic modulus vs. strain rate curves. The yielding phenomenon was interpreted using Eyring's theory of non-Newtonian viscoplastic flow. The apparent activation energy and activation volume were larger for tension than compression. A theory is offered to explain why yielding can occur in a cross-linked system.     

Effect of fillers on thermoplastic 1,2-polybutadiene rubber: Mechanical and viscoelastic properties

The effects of silica, carbon black, and china clay on the mechanical properties of 1,2-polybutadiene have been investigated. They include stress–strain behavior, tensile strength, elongation, tear strength, tension set, impact strength, and hysteresis. The effect of silane coupling agent on these properties has also been studied. The stress–relaxation behavior of the filled and unfilled systems has also been compared. The rate of relaxation increases with temperature. The dynamic mechanical properties have been determined using a Rheovibron viscoelastometer at 35 Hz at different temperatures. The storage and loss moduli are enhanced by addition of fillers. Silane coupling agent increases storage modulus as well as tan δ_max of the clay-filled polymer. The suitability of Voigt and Reuss models in predicting the composite moduli is examined.     

The nonlinear stress relaxation behavior after a step shear of star-shaped styrene-butadiene rubber filled with precipitated silica: Experiment and simulation

The nonlinear stress relaxation behavior after a step shear strain of star-shaped SSBR/silica compounds containing 21 vol% filler of various surface areas was measured and simulated using constitutive equations. A styrene-butadiene rubber (SBR) gum and SBR filled with silica having BET surface areas of 55, 135, 160, and 195 m²/g were used. Relaxation modulus behavior of the filled compounds was found to be dependent on surface area. Specifically, stress relaxation tests indicated that an increase in surface area led to increase in values of relaxation moduli in both the linear and nonlinear regimes. The time-dependent relaxation modulus exhibited a plateau at long times of relaxation in compounds containing silica of high surface area. Additionally, good time-strain superpositions were achieved for all samples at intermediate times of relaxation, and the strain-dependent damping function decreased with filler surface area. The constitutive equations proposed by Leonov and Simhambhatla and Leonov, modified to include multimodal relaxation of the particle network, were used to predict the time evolution of the relaxation modulus in the nonlinear regime for all samples. The simulations provided good results for the SBR gum for all tested strain levels. Also, in the compounds filled with silica, both models satisfactorily described the experimental observation in the nonlinear regime at low strain levels. However, at higher strain levels, due to a possible slip effect, the simulations overpredicted measured values of the relaxation moduli, thus leading to only qualitative predictions of the observed behavior. It is also possible that neither model accurately captured the floc rupture kinetics of these complex rubber compounds.     

Viscoelastic material characterization and modeling for polyethylene

An extensive set of stress relaxation and constant strain rate tests for characterizing the mechanical responses of a medium density polyethylene and a high density polyethylene that are commonly used in natural gas distribution piping is described and analyzed. The development of coherent master curves for the relaxation modulus, maximum stress, and the time-to-failure for pressurized pipes through a combination of both horizontal and vertical shifting is presented. The relaxation data are used to develop a nonlinear Viscoelastic material model. The model is assessed by making comparisons of the predicted stress-strain response with the measured response in the constant strain rate tests.     

Viscoelastic behavior of galss-reinforced epoxy resin

The viscoelastic behavior of epoxy composites containing various percentage of glass microspheres and random short glass fibers was investigated over a wide range of temperatures. The effect of the second phase is to increase the relaxation moduli of the system and to shift the time dependency to higher times. All the data were shifted to a single master curve at a reference temperature by using independent shift factors that were a function of either temperature or filler content.     

Viscoelastic behavior of Cytec FM73 adhesive during cure

In this work, the viscoelastic properties of Cytec FM73 structural film adhesive were characterized. Several resin plates were cured using various process cycles to achieve a range of final cure states. Specimens cut from these plates were tested using a dynamic mechanical analyzer (DMA) and the glass‐transition temperature at each degree of cure was determined. Stress relaxation tests at different temperatures were then performed using DMA in stress relaxation mode and time‐temperature superposition was used to generate master stress relaxation curves and associated shift functions for each degree of cure. Several different constitutive models were examined for their ability to describe relaxation modulus development during cure. A simple three‐parameter model consisting of a stretched exponential with cure‐dependent terms was found to provide the best results. The results indicate that of the parameters used in the model, relaxation time strongly depends on cure state. The empirical DiBenedetto equation was used to obtain an expression for glass‐transition temperature as a function of degree of cure. This expression was in turn used to derive a new relation to describe stress relaxation time as a function of degree of cure. The shift function was modeled using a simplified form of the Vogel equation with cure‐dependent coefficients. Good correlation between measured relaxation modulus and model predictions was observed. © 2003 Wiley Periodicals, J Appl Polym Sci 91: 2548–2557, 2004     

Build-up of structure and viscoelastic properties in epoxy and acrylate resins cured below their ultimate glass transition temperature

The build-up of structure and viscoelastic properties with conversion during cure below the ultimate glass transition temperature of epoxy and acrylate resins has been investigated. Using a torsional dynamic mechanical analyser, dynamic shear modulus and change in sample thickness was monitored simultaneously, thus giving information on both the physical properties (stiffness) and the progress of the reaction (shrinbdkage) in one experiment. Two step-wise curing epoxy systems and two chain-wise curing acrylate systems with different crosslink densities were studied and compared. The results showed that in the epoxies vitrification was a distinct event, occurring separately from gelation and ending with the end of the cure reaction. In the acrylates vitrification began immediately after gelation, the two events being indistinguishable, and lasted until the end of the reaction, leaving the sample in its transition zone. Scaling of modulus—cure time data obtained at different frequencies showed that the data for each system followed one single curve, independent of frequency over five decades. This made it possible to estimate the modulus development at low frequencies early in the reaction, which is difficult to measure directly. From the shrinkage and storage moduli approximate values of the relaxation modulus as a function of chemical conversion were calculated. The relaxation modulus curves at different conversions were then shifted along the time axis to provide a relaxation master curve. The data and understanding gained in this work provide the basis for analysing the time-dependent mechanical behaviour during cure, e.g. build-up and relaxation of residual stresses.     

Large deformation response of polycarbonate: Time-temperature,time-aging time,and time-strain superposition

Data are presented from tests of the stress relaxation response of a polycarbonate under torsional deformations. Tests were performed on samples over a range of strains from 0.0025 to 0.08, temperatures from 30 to 135°C and aging times from 1800 to 64,800 s. Individual data sets at each strain, temperature and aging time could be described using a stretched exponential form relaxation function, and time-aging time superposition was found to be applicable to the data under all test conditions. The double logarithmic aging time shift rate, μ was found to vary significantly with both temperature and strain. Over the range of temperatures studied the data could be superimposed using conventional time-temperature superposition. However, the master curve was found not to be described by a stretched exponential function. For strains up to 0.07, the data at each temperature could also be superimposed to form a master curve following the principle of time-strain superposition. Interestingly, the master curves found from time-strain and time-temperature superposition did not have the same form. In both the time-aging time and time-temperature superposition analyses it was found that the application of vertical shifts was required for superposition of data.     

Some Aspects of Time-Temperature Superposition Principle Applied for Predicting Mechanical Properties of Solid Rocket Propellants

Optimal test conditions for determining the mechanical properties of rocket propellants (temperatures and strain rates ranges) for delivering master curves were investigated. From master curves it is possible to predict the modulus, maximum stress and maximum strain in vide intervals of temperatures and strain rates, and especially the existing conditions during the ignition of rocket motor. Using the control experiments, at high strain rates, the good agreement between the results obtained from master curves was shown. The obtained results for composite rocket propellants (with carboxy-terminated polybutadiene, CTPB, as a binder), point out the drastic decreasing of maximum strain at high strain rates and low temperatures.     

Application of time‐temperature superposition to energy limit of linear viscoelastic behavior

The energy approach for evaluation of the limits of linear viscoelastic (LVE) behavior is considered. The approach of Foux and Bruller based on the Reiner‐Weissenberg dynamic theory of strength is developed for the temperature effect. Value of the stored energy at the limit of LVE is considered as the material characteristic independent on loading conditions and temperature. Time–temperature superposition principle is extended for the energy calculations. Curves of the stored energy calculated for different temperatures are shifted to each other in the logarithmic time axes similarly as creep compliance and relaxation modulus curves in creep and tension tests, respectively. Temperature is considered as a factor that accelerates transition form linear to non‐LVE at the same stored energy threshold. This is proved by example of polyvinylchloride by comparing temperature dependences of the stress limits of LVE determined in two independent test series: tensile creep and constant strain rate tests. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2009     

Experimental Investigation on High Strain Rate Tensile Behaviors of HTPB Propellant at Low Temperatures

To study the high strain rate tensile behaviors of hydroxyl‐terminated polybutadiene (HTPB) propellant at low temperatures, uniaxial tensile tests were conducted at different strain rates (0.4–42.86 s⁻¹) and temperatures (233–298 K) using an INSTRON testing machine. Scanning electron microscopy (SEM) was employed to observe the tensile fracture surfaces. Experimental results indicate that strain rate, temperature and test environment remarkably influence the tensile behaviors of HTPB propellant. The stress‐strain curves exhibit three different shapes. The elastic modulus and maximum tensile stress increase with decreasing temperature and increasing strain rate. However, the strain at maximum tensile stress decreases with increasing strain rate at low temperatures and there is a maximal value at 298 K and 14.29 s⁻¹. The effects of strain rate, temperature and test environment on the tensile behaviors are closely related to the changes of properties and fracture mechanisms of HTPB propellant. The dominating fracture mechanism depends on not only temperature but also strain rate, and it changes from the dewetting and matrix tearing at room temperature and lower strain rate to the particle brittle fracture at low temperatures. Based on the time‐temperature superposition principle (TTSP), the master curves of mechanical parameters for HTPB propellant were obtained.     

Quantitative relation between the relaxation time and the strain rate for polymeric solids under quasi‐static conditions

Relaxation time is an essential physical quantity reflecting the hysteresis of the microstructure of materials. To associate the relaxation time with the strain rate, the stress–strain curves of six types of polymers at low strain rate were normalized, and a nondimensional generalized Maxwell model incorporating strain‐rate‐dependent relaxation times was obtained by the internal variable theory of irreversible thermodynamics. The results indicate that the constitutive equation may capture well the normalized stress–strain behaviors that are not related to the strain rate. The ratio of the initial modulus to the secant modulus at the maximum stress was also found to not rely on the strain rate anymore. Furthermore, strain‐rate independence occurred only when the relaxation time was proportional to the time interval for stress from zero to the maximum stress. The relaxation time varied in a power law with the strain rate. The explicit relation is helpful for providing a concise and promising solution for predicting the quasi‐static mechanical response of viscoelastic solids. © 2016 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016 , 133, 44114.     

Nonlinear stress relaxation in palladium(II) complexes with triblock copolymers of styrene and butadiene

Above 200% strain, the mechanical response of triblock copolymers which contain styrene and butadiene is modified significantly by complexation with dichlorobis(acetonitrile)palladium(II). This pseudosquare‐planar transition metal salt forms π‐complexes with, and catalyzes the dimerization of, alkene groups in the main chain and the side group of Kraton's butadiene midblock. Between 10 and 100% strain, the plastic flow regime is similar for undiluted Kraton? and its Pd²⁺ complexes, but the level of engineering stress is approximately twofold larger for the complex that contains 4 mol % palladium(II) [Pd(II)]. Nonlinear stress relaxation measurements in the plastic flow regime (i.e., beyond the yield point but before the large upturn in stress) are analyzed at several different levels of strain. Transient relaxation moduli were modeled by a three‐parameter biexponential decay with two viscoelastic time constants. The longer relaxation time for Kraton? increases at higher strain, and in the presence of 4 mol % palladium chloride. A phenomenological model is proposed to describe the effect of strain on relaxation times. This model is consistent with the fact that greater length scales are required for cooperative segmental reorganization at larger strain. The resistance Ω to conformational reorganization during stress relaxation is estimated via integration of the normalized relaxation modulus versus time data. This resistance increases at higher initial jump strain because conformational rearrangements are influenced strongly by knots and entanglements at larger strain. The effect of strain on Ω is analyzed in terms of time‐strain separability of the relaxation modulus. Linear behavior is observed for Ω versus inverse strain (i.e., 1/ε), and the magnitude of the slope [i.e., ?dΩ/d(1/ε)] is threefold larger in the absence of PdCl₂(CH₃CN)₂. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 93: 1329–1336, 2004     

Stress relaxation behavior of biaxially oriented poly(ethylene terephthalate)

The stress relaxation behavior of biaxially oriented semicrystalline poly(ethylene terephthalate) was studied by thermomechanical analysis. Experimental techniques were developed for thin films. Relaxation moduli were measured as a function of stress, time, and temperature. The relaxation modulus was shown to be independent of stress over the range tested. Rate of loss of the relaxation modulus was found to be a nonlinear function of time and temperature up to about 100°C, encompassing the T_g for the polymer. Over the temperature range of 100–120°C it was primarily temperature-dependent. An empirical time—temperature superposition showed that significant losses in modulus can occur at very short times. At temperatures above the T_g these losses can result in significantly reduced film physical properties.