Effect of holding time on high strain hysteresis loss of carbon black filled rubber vulcanizates

Hysteresis loss has been measured at constant stress and constant strain, at various holding times under tensile deformation of natural rubber (NR) and styrene-butadiene rubber (SBR) vulcanizates filled with various loadings of carbon black filler. The effects of temperatures (25°C to 150°C), strain rates (3.78 × 10^?5 sec^?1 to 210 × 10^?3 sec^?1) and strain levels (20% to 300%) have been studied. Hysteresis loss and hysteresis loss ratio increase with an increase in strain rate, filler loading, strain level and holding time. It decreases with an increase of temperature. However, higher hysteresis loss and hysteresis loss ratio are observed at constant stress than at constant strain. NR and SBR vulcanizates show similar behavior. Evidence has been produced for the existence of a distinct relaxation process that occurs within first 120 second of holding time at room temperature. This process becomes less important as the strain or the temperature is increased. However, at high temperature another distinct relaxation process has been observed. The activation energy has been found to be 66.3 kJ/mole for the rates at the higher holding time, while it has been found to be 17.3 kJ/mole for the rates at the lower holding time using the data of hysteresis loss at first cycle of 40 phr black filled NR vulcanizates.     

Tensile yield in poly(chlorotrifluoroethylene) and poly(vinylidene fluoride)

Uniaxial tension tests to the yield point were performed on poly(chlorotrifluoroethylene) (PCTFE) and poly(vinylidene fluoride) (PVF2) from room temperature to near the melting point at a strain rate of 2 min^?1. At room temperature and at least two elevated temperatures, measurements were also made at strain rates from 0.02 to 8 min^?1. The properties of these polymers were found to be similar to those of other semicrystalline polymers. In the absence of other transitions, yield energy was found to be a linear function of temperature extrapolating to zero near the melting temperature. The ratio of thermal to mechanical energy to produce yielding is smaller than for glassy polymers. Yield stress is a linear function of log strain rate. The ratio of yield stress to (initial) Young's modulus is about 0.03 at room temperature for both polymers. Yield stress is a linear function of unstrained volume. Yield strain, elastic, and plastic strain all initially increase with temperature, but PCTFE shows a decrease with temperature starting at about 100°C, thus behaving like a glassy amorphous polymer in this region.     

Rheology of polymers containing carbon black

In order to elucidate the flow behavior of electrophotographic toner systems, shear stress was measured as a function of shear rate in a cone and plate rheometer for polymer melts containing carbon blacks of surface area 24 and 625 m²/g at several concentrations and temperatures. Polymers included high and low molecular weight polystyrene and poly(butyl methacrylate). The addition of carbon black to the polymers caused a large increase in viscosity, especially at low shear rates and shear stresses. As the concentration of carbon black was increased, the viscosity at low shear rates became unbounded below a value of the shear stress designated the yield stress. The absolute magnitude of the yield stress depended primarily on the concentration and surface area of the carbon black and was independent of the polymer and temperature. Apparently, carbon black forms an independent network within the polymer at low shear rates which precludes flow. In some cases, the viscosity of polymers filled with carbon black was lower than that of the pure polymer. This effect was favored for polystyrene compared to poly(butyl methacrylate) and was facilitated by increasing the molecular weight of polystyrene, reducing the surface area and concentration of carbon black, and by increasing the temperature and shear rate.     

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.     

Compressive behavior of C/SiC composites over a wide range of strain rates and temperatures

The mechanical behavior of two-dimensional (2D) carbon fiber reinforced silicon carbide (C/SiC) composites is investigated at both quasi-static and dynamic uniaxial compression under temperatures ranging from 293 to 1273 K. Experimental results show that temperature and strain rate dramatically affect the compressive behavior of 2D C/SiC composites. If the temperature is below 873 K, the compressive strength increases with rising temperature. The reason is that the release of thermal residual stress enhances the compressive strength and this enhancement is more significant than the strength degradation due to the high temperature induced oxidation. In contrast, when the temperature rises above 873 K, the compressive strength decreases as temperature rises due to the stronger effect of oxidation induced strength degradation. Moreover, the degradation of compressive strength at strain rate of 10⁻⁴/s and temperatures above 873 K is much more obvious than those at higher strain rates, and the strain rate sensitivity factor of compressive strength increases remarkably at temperature above 873 K. Post-deformation observation shows that failure angles and fracture surfaces are also strongly dependent on testing temperature and strain rate. The change of interfacial strength at high strain rate or high temperature is responsible for the variations.     

Rate-dependence of yielding in ethylene-methacrylic acid copolymers

It is well known that reducing the crystal thickness of polyethylene, by copolymerization with an α-olefin, decreases the yield stress. By contrast, incorporation of methacrylic acid (MAA) - also a noncrystallizable comonomer - results in a marked increase of the yield stress at room temperature at typical strain rates. We show that, in addition to crystal plasticity, one must consider the active mechanical relaxations to understand this phenomenon. For ethylene-methacrylic acid copolymers, the α and β relaxations are important over the range of conditions probed in this study, and the increase in the β relaxation (glass transition) temperature with MAA content is identified as the source of this peculiar behavior. The yield stress of these materials is adequately described by a model combining thermal nucleation of dislocations in the crystals with a Ree-Eyring dependence for yielding in the amorphous phase, all with physically reasonable parameter values. Yield stress master curves may be created from data taken at various temperatures and strain rates, and are presented herein for low-density polyethylene and five ethylene-methacrylic acid copolymers of varying MAA content.     

Experimental investigation and modeling of the tension behavior of polypropylene at different temperature

The mechanical behavior of polypropylene polymer was investigated under the effect of various temperatures. Mechanical properties of polymer were carried out through uniaxial tensile tests for low and high temperatures respectively. The results showed that both yield stress and the elastic modulus of the material decrease with the increase of temperature. Similarly, the post-yielding behavior of the material can be clearly observed at low temperature, and this behavior gradually disappears as the temperature increases. A phenomenological constitutive model is proposed in order to understand the mechanical behavior of polymer by combining the hyperbolic and multi-linear relationships. It is based on the experiments, and the proposed constitutive model is successfully validated by the excellent agreement between model prediction and experimental results.     

Strain rate mediated microstructure evolution for extruded poly(vinylidene fluoride) polymer films under uniaxial tension

The deformation and fracture mechanism during uniaxial tension under controlled strain rates are investigated for extruded poly(vinylidene fluoride) (PVDF) polymer films at room temperature. It was found that both the longitudinal and transversal film‐samples exhibited pronounced strain rate effect, that is, the yield stress increases while the fracture strain decreases with the increasing of strain rates. For the longitudinal film samples, phase transformation from the nonpolar α‐phase to the polar β‐phase occurs during the uniaxial tension, and the extent of the phase transformation enhances when the strain rate decreases. For the transversal film samples, no phase transformation was detected in all tested strain rates. By combining the stress–strain behavior and the X‐ray results, it can be inferred that the conformational change from α to β phase during uniaxial tension contributes to the higher fracture strain of the longitudinal films than that of the transversal films. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 103: 1786–1790, 2007     

Mechanical properties of plastic‐bonded explosive binder materials as a function of strain‐rate and temperature

Compression measurements were conducted on three explosive formulation binders, extruded Estane, plasticized Estane, and plasticized hydroxyl‐terminated polybutadiene, as a function of temperature and strain rate. The mechanical response of the Estane was found to exhibit the strongest dependency on strain rate and temperature and higher flow strength for similar test conditions of the three materials tested. Plasticized Estane was less sensitively dependent on strain rate and temperature, followed by the plasticized HTPB. The visco‐elastic recovery of all three binders is seen to dominate the mechanical behavior at temperatures above the glass transition temperature (T_g). There is a pronounced shift in the apparent T_g to higher temperatures as the strain rate is increased. Two distinct behaviors are observed in the binders below the T_g. At low strain rates, the binders exhibit a yield behavior, followed by a drop in the flow stress, which may or may not recover. At high strain rates, the load drop does not occur and the flow stresses either gradually increase, as in plasticized HTPB, or it levels out as seen in the Estane‐based binders. POLYM. ENG. SCI., 46:812–819, 2006. © 2006 Society of Plastics Engineers     

Estimating time and temperature dependent yield stress of cement paste using oscillatory rheology and genetic algorithms

A controlled shear stress–shear rate rheometer was used to determine the viscoelastic behavior of cement paste incorporating various superplasticizers and subjected to prolonged mixing at high temperature. At a low applied shear stress range, the oscillatory shear strain/stress curve of cement paste was characteristic of a linear elastic solid; while the higher stress range was characteristic of a viscous liquid exhibiting a linear strain increase with increasing applied shear stress. The transition from solid-like to liquid-like behavior occurred over a very narrow stress increment. This transition stress corresponded to the yield stress parameter estimated from conventional flow curves using the Bingham model. The yield stress from oscillatory shear stress tests was estimated using the intersection between the viscous part of the oscillatory shear strain/stress curve and the oscillatory shear stress axis. In this study, equations describing the variation of shear strain versus shear stress beyond the solid–fluid transition for cement pastes incorporating various superplasticizers at different ambient temperatures and mixing times were developed using genetic algorithms (GA). The yield stress of cement pastes was subsequently predicted using the developed equations by calculating the stress corresponding to zero strain. A sensitivity analysis was performed to evaluate the effects of the mixing time, ambient temperature, and superplasticizer dosage on the calculated yield stress. It is shown that the computed yield stress values compare well with corresponding experimental data measured using oscillatory rheology.     

Effects of temperature,strain rate,and cyclic loading on mechanical behavior of silane-modified polyurethane sealant

To evaluate the mechanical properties of modified polyurethane sealants in engineering applications, the influences of temperature, strain rate, and cyclic loading on the mechanical properties of silane-modified polyurethane sealant were experimentally investigated. The monotonic tensile experiments with various strain rates and temperatures were conducted, and strain rate and temperature dependent nonlinear stress–strain curves were obtained. The results showed that the silane-modified polyurethane sealant exhibited temperature dependence at constant strain rate and rate dependence at room temperature. However, it is shown no obvious rate dependence at temperature of 150°C. In addition, the multi-step cyclic loading experiments with mean strain decrease and increase at each step were carried out to analyze the influence of cyclic loading and cyclic loading history at different temperatures. The results demonstrated that the viscous behavior of the materials was evidently observed in the first step and disappeared in other steps for the four-step cyclic loading with mean strain decrease case. Moreover, the cyclic stress relaxation of the materials was not obvious due to the prior cyclic loading with higher mean strain history, while the cyclic stress relaxation of the material continued to occur for the prior cyclic loading with lower mean strain history, and the cyclic strength of the materials decreased with the increase of temperature.     

The deformation behavior of polypropylene film under high strain rates

The relationship between stress and strain for polypropylene film was studied under strain rates from 0.13 to 5.21 s^?1 in order to study the deformation behavior of film under higher strain rates than previous studies. Uniform thickness was obtained in the strain rates from 2.08 to 5.21 s^?1 at 435 K, or from 2.08 to 3.13 s^?1 at 437 K. The temperature rise of film due to the generation of heat from plastic strain influenced the relationship between stress and strain, in particular, at high strain rates and low temperature. Material constants for the constitutive equation of film were determined using the measurements from 2.08 to 5.21 s^?1 at 435 K and from 2.08 to 3.13 s^?1 at 437 K. Film thicknesses during and after transverse direction stretching were successfully predicted by applying the material constants obtained. The authors concluded that the material constants should be determined by applying the stretching conditions, under which there is little or no effect from heat generation and under which film can be stretched uniformly in thickness. POLYM. ENG. SCI., 2013. © 2012 Society of Plastics Engineers     

Stress softening in carbon black-reinforced vulcanizates. Strain rate and temperature effects

Stress softening of carbon black-reinforced butadiene-styrene rubber was studied as a function of the rate and temperature of the original tensile deformation. To a good approximation, stress softening depends on the product of the extension rate and a temperature function which is analytically well represented by the familiar Williams-Landel-Ferry relationship. When the elongation of the original deformation is also varied, a good correlation is obtained between stress softening and the maximum stress attained in the original extension, irrespective of the particular combination of strain, strain rate and temperature used to achieve this stress. Variables which tend to increase the stiffness of the vulcanizate, such as increased degree of crosslinking or carbon black chain structure, also increase stress softening; dilution by plasticizers decreases it. Prestressing at high strain rates and low temperatures affects the stress–strain curve of the softened vulcanizates beyond the elongation of the original extension. Connections are established between stress softening and viscoelastic and failure behavior. The evidence presented favors the contribution of several mechanisms to the general phenomenon of stress softening. These are thixotropy of transient filler structures, network chain rupture, and breakage of “permanent” filler structure. The latter appears to be most important at high strain rates, low temperatures, and with highly reticulated “structure” blacks.     

A formulation of the cooperative model for the yield stress of amorphous polymers for a wide range of strain rates and temperatures

The mechanical response of solid amorphous polymers is strongly dependent on the temperature and strain rate. More specifically, the yield stress increases dramatically for the low temperatures as well as for the high strain rates. To describe this behavior, we propose a new formulation of the cooperative model of Fotheringham and Cherry where the final mathematical form of the model is derived according to the strain rate/temperature superposition principle of the yield stress. According to our development, the yield behavior can be correlated to the secondary relaxation and we propose an extension of the model to temperatures above the glass transition temperature. For a wide range of temperatures and strain rates (including the impact strain rates), the predicted compressive yield stresses obtained for the polycarbonate (PC) and the polymethylmethacrylate (PMMA) are in excellent agreement with the experimental data found in the literature.     

Viscoelastic behavior of flexible slabstock polyurethane foams: Dependence on temperature and relative humidity. I. Tensile and compression stress (load) relaxation

The relaxation behavior of the load in compression and the stress in tension was monitored at constant temperature and/or relatively humidity for a set of four slabstock foams with varying hard-segment content as well as two of the compression molded plaques of these foams. The majority of the compression relaxation tests were done at a 65% strain level in order to be consistent with the common ILD test. The tensile stress relaxation tests were performed at a 25% strain level. Over the 3-h testing period, a linear relationship between the log of compressive load or the log of tensile stress versus log time is observed for most testing conditions. For linear behavior, the values of the slope or the load/stress decay rate are comparable in both the tension and compression modes with the values being slightly higher in magnitude for the compression mode. These rates of decay are in the range of ?2.2 × 10 ^?2 to ?1.7 × 10 ^?2 for a 21 wt % hard-segment foam and ?3.2 × 10^?2 to ?2.4 × 10^?2 for a 34 wt % hard-segment foam. Increasing %RH at a given temperature does bring about a steady decrease in the initial load or initial stress as well as a slight increase in the rate of relaxation. The effect of temperature on the relaxation behavior is most significant at temperatures near 125°C and above. The FTIR thermal analysis of the plaques indicates that this significant increase is due to additional hydrogen bond disruption and possible chain scission taking place in the urea and urethane linkages that are principally present in the hard segment regions. The relaxation behavior in both tension and compression is believed to be mostly independent of the cellular texture of the foam at the strain levels given above. This conclusion is based on the similar relaxation behavior between the plaques and the foams. © 1994 John Wiley & Sons, Inc.     

Mechanical behavior of polytetrafluoroethylene around the room-temperature first-order transition

The effect of the room-temperature first-order transition on the plastic yield behavior of polytetrafluoroethylene (PTFE) has been investigated. Stress-strain curves were measured at different strain rates and temperatures. Tensile creep under constant dead load was also measured as a function of temperature and stress level. The effect of degree of crystallinity was investigated by using both a rapidly quenched and slow-cooled polymer. Observations were extended to large deformations, so that the phenomenon primarily observed was plastic yield rather than linear viscoelastic behavior. The curve of yield stress vs. temperature in the temperature range from –50 to +68°C was found to be almost identical with the curve of elastic modulus vs. temperature; the yield stress shows a marked local decrease at the first-order transition. The yield elongation was almost constant (at about 5%) over this same range, which is in accord with the above result. The more highly crystalline polymer is always more rigid than the less crystalline polymer at small deformations, but above 19°C its stress-strain curve shows a “cross-over” in stress level with the curve of the less crystalline polymer as extension increases. That is, above 19°C the less crystalline polymer shows a more rapid rate of “strain hardening”, even though the strain-hardening effect is pronounced in both polymers. Attempts to apply time-temperature superposition to creep data at different temperatures were partially successful; the lateral shifts required corresponded to an activation energy of approximately 80 kcal. The experimental observations suggest a model of the solid-state structure of PTFE which could be described as an “elastic-plastic network”, in which crystalline domains are connected by elastic amorphous regions, and in which the crystalline domains can flow plastically at sufficiently high stress or temperature.     

Time and temperature effects on the tensile yield properties of polypropylene

Tensile tests were made on polypropylene films as a function of aging temperature from 80 to 130°C at a strain rate of 5 cm min^-1. Polypropylene films aged at 60 and 100°C and at time intervals up to 180 min were also stretched at the same strain rate. The yield stress and initial modulus were found to be linear functions of temperature, extrapolating to a zero value close to the thermodynamic melting point of the polymer (170°C). The work of yield, the plastic and yield strains also decreased with increase in aging temperature but the elastic strain increased. The plastic strain, yield strain, yield stress, and initial modulus for the 60°C aged film had larger values than the corresponding values for the 100°C aged film at equivalent time intervals and all properties decreased with increasing log time of aging. These decreases in properties were explained in terms of decrease in the density (crystallinity) of aged PP films. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 65: 625–633, 1997     

Nonlinear stress properties of poly(styrene-block-butadiene-block-styrene) melt under elongational and shear deformation

Effects of block copolymerized structure on nonlinear stress properties under elongational and shear deformation were investigated. Samples used in this study were poly(styrene-block-butadiene-block-styrene) (SBS, weight rate of S/B = 40/60) and polystyrene (PS) as a reference. Tensile stress–strain and shear stress relaxation properties were measured at the molten state. SBS showed high elasticity after reaching the yield point under elongational deformation at room temperature. PS melt showed substantial tensile stress increase after the yield point as strain rates increased. However, SBS melt did not exhibit noticeable tensile stress rise at higher elongation, and this property was almost independent of strain rates. Stress relaxation experiments revealed that the damping function of SBS melt was more strain-softening than that of PS melt. The results suggested that the block copolymerized structure decreases melt elasticity under elongational and shear deformation. A transmission electron micrograph indicated that the lack of melt elasticity in SBS melt is caused by orientation of the lamellar structure toward the stretched direction during deformation. © 1995 John Wiley & Sons, Inc.     

Tensile mechanical properties and constitutive model for HTPB propellant at low temperature and high strain rate

To investigate the mechanical properties and fracture mechanisms of hydroxyl‐terminated polybutadiene (HTPB) propellant at low temperature and high strain rate, uniaxial tensile tests were conducted over the range of temperatures 233 to 298 K and strain rates 0.4 to 14.14 s^?1 using an INSTRON testing machine, and scanning electron microscope (SEM) was employed to observe the tensile fracture surfaces. The experimental results indicate that the deformation properties of HTPB propellant are remarkably influenced by temperature and strain rate. The characteristics of stress–strain curves at low temperatures are different from that at room temperature, and the effects of temperature and strain rate on the mechanical properties are closely related to the changes of properties and the fracture mechanisms of HTPB propellant. The dominating fracture mechanism depends much on the temperature and changes from the dewetting and matrix tearing at room temperature to the particle brittle fracture at low temperature, and the effect of strain rate only alters the mechanism in a quantitative manner. Finally, a nonlinear viscoelastic constitutive model incorporating the damage evolution and the effects of temperature and strain rate was developed to describe the stress responses of this propellant under the test conditions. During this process, the Schapery‐type constitutive theories were applied and one damage variable was considered to establish the damage evolution function. The overlap between experimental results and predicted results are generally good, which confirms that the developed constitutive model is valid, however, further researches should be done due to some drawbacks in describing the deformation behaviors at very large strain. © 2015 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2015 , 132, 42104.     

Fracture behavior of polypropylene/ ethylene- diene-terpolymer blends : Effect of temperatures,notch radius and rubber content

The mechanical fracture and ductile-brittle transition (DBT) behavior, hysteresis phenomenon and the plastic zone size of polypropylene (PP) / ethylene-propylene-diene terpolymer (PP/EPDM) blends were investigated by varying EPDM content and notch radius under different temperatures. An increase in test temperature or rubber content in the PP/EPDM blend results in lower yield stress and Young's modulus. The ductile-brittle transition temperature (DBTT) of the notched impact strength decreases with the increase of the EPDM content. However, the DBTT is fairly independent of the notch radius. SEM morphologies of the fracture surfaces indicate that two separate modes, localized and mass shear yielding, work simultaneously in these blends. The plane-strain localized shear yielding dominates the brittle failure at lower temperatures, whereas the plane stress mass shear yielding dominates the ductile fracture at higher temperatures. The presence of EPDM rubber decreases the yield stress of the PP/EPDM blend due to the overlapping stress fields of adjacent particles, resulting in higher hysteresis energy. The relationships among the test temperature, hysteresis loss energy and the size of plastic zone are discussed in detail.