Processing temperature dependent mechanical response of a thermoplastic elastomer with low hard segment

The mechanical responses including monotonic and cyclic tensile responses have been investigated on a microphase-separated poly (styrene-isoprene-styrene) triblock copolymer (SIS). The specimens were injection-molded by using different melt temperatures to acquire different microphase structures. As a result of temperature-dependent segregation driving force, the specimens with reduced microphase separation can be obtained by increasing processing melt temperature from 180 °C to 240 °C. On the basis of stress-strain behavior, Young's modulus was found to increase with increasing PS domain continuity in the order of disorder state to disordered spheres to body-cubic-centered (BCC) spheres to oriented cylinders morphology. Meanwhile, cyclic hysteresis decreases with reduced microphase separation and with decreasing the applied predetermined maximum tensile strain. In addition, the Mooney–Rivlin phenomenological approach was used to evaluate and explore the relationship between the polymer topological networks and the rubber elasticity of thermoplastic elastomers.     

Semi- and fully interpenetrating polymer networks based on polyurethane–polyacrylate systems. I. The polyurethane networks

The polyurethane networks based on commerical prepolymer, Adiprene L-100, and trimethylol propane (system 1) and on toluene diisocyanate, polypropylene gylcol, and trimethylol propane (system 2) were prepared and characterized in a number of ways. The materials constitute the first formed networks in a series of interpenetrating polymer networks and semi-interpenetrating polymer networks to be reported in subsequent papers in this series. System 1 networks were characterized by swelling tests which showed the M _c values to be sensitive to the amount of polyurethane present in the polymerization solvent. Stress–strain, stress–relaxation, and dynamic mechanical analyses wer also conducted. For system 2, M _c was measured, by both the swelling and the Mooney–Rivlin techniques, for materials in which the diol-to-triol ratios had been altered. the latter showed C₁ increasing as M _c decreased while C₂ was small and changed onlyy slightly indicating approximately ideal behavior. These M _c values were about 13 % larger than predicted by swelling.     

Mechanical behavior and microhardness of swollen natural rubber loaded with carbon black

The mechanical behavior and microhardness characteristics of a natural rubber vulcanizate loaded with 40 phr high abrasion furnace carbon black swollen in kerosene were studied. The measured parameters (i.e., the Young's modulus, tensile strength, and elongation at break) varied with the swelling time in kerosene. The hardness degree decreased as the swelling time in kerosene increased. Different models were applied to describe this mechanical behavior. The Mooney–Rivilin relation agreed with the experimental data at low extension ratios, whereas the Blatz relation agreed at high extension ratios only. The strain rate sensitivity was taken into account to describe this mechanical behavior. The strain energy density as a function of the swelling time in kerosene was calculated with three different equations. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

On Mooney and Mooney stress relaxation. II. A nonlinear viscoelastic description: Experimental and numerical results

It has been investigated whether the stress build‐up and the stress relaxation involved in a Mooney test, with subsequent Mooney stress relaxation, can be described by nonlinear viscoelastic theory, more particularly the Wagner constitutive model. For this purpose, the viscoelastic behavior of three nonvulcanized EPDM materials, with similar Mooney viscosity but varying elasticity, has been studied. Relaxation time spectra were obtained from dynamic mechanical experiments, from which the step‐strain stress‐relaxation modulus was calculated. Stress build‐up experiments were performed with a cone and plate system in order to obtain the so‐called damping function (a measure for the deformation sensitivity) of the materials. Using these material functions, the Mooney test was successfully described with the Wagner constitutive model. Experimental and theoretical Mooney stress‐relaxation rates are in close agreement. The predicted Mooney viscosity is up to 25% lower than the measured value. This may be due to nonideal conditions during the Mooney test, such as inhomogeneous heating and secondary flows, and to inaccuracy of the damping function. The model calculations confirm the strong experimental dependence of Mooney measurements on small variations in instrumental conditions such as geometry, rotation speed, and so forth. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 74: 1220–1233, 1999     

Mechanical properties of crosslinked polyurethanes

Stress–strain and stress–relaxation behavior of polyurethane elastomers based on poly(ethylene adipate), poly(ethylene maleate), polyethylene glycol, and 4,4′-diphenylmethane diisocyanate (MDI) have been studied. The elastomers were crosslinked by an excess of MDI and by dicumyl peroxide (DiCup); the latter was supposed to form additional crosslinks on the unsaturated bonds. The determined values of Young's modulus, Mooney-Rivlin elastic parameters C₁ and C₂, relaxation moduli E(10 sec) and E(100 sec), as well as relaxation speed were used to estimate the effect of MDI- and DiCup-formed crosslinks on the mechanical behavior of polyurethanes. It was found that while the elastomers crosslinked by MDI only apparently displayed viscoelastic properties, the polyurethanes additionally crosslinked by DiCup exhibited more elastic behavior. The results obtained were explained on the basis of changes in the amount of secondary bonding due to the additional network junctions formed by DiCup at nonpolar groups.     

Mechanical characterization of agarose micro-particles with a narrow size distribution

A micromanipulation technique was used for the mechanical characterisation of two types of agarose microspheres with different material properties. Narrow-size distributions having a mean diameter in the range of 15–22 µm were prepared using (a) conventional emulsification followed by filtration and (b) membrane emulsification. Single microspheres were compressed to a range of deformations at different speeds up to a maximum of ~ 70 µm/s, and then held at constant deformation to permit relaxation to occur. It was found that the loading data could be satisfactorily described by the Hertz equation up to 30% deformation. The Young's moduli calculated on this basis were found to correlate with the gel strength of the agarose which was used to prepare the microspheres. However, the values of the moduli increased with the compression speed and significant stress relaxation occurred. Consequently, a modified Hertz analysis was employed that accounts for the viscoelastic behaviour. Two relaxation times were sufficient to describe the stress relaxation function. The Young's moduli from the Hertz analysis corresponded to the long-time values of the stress relaxation function, which is reasonable given the relatively slow compression speeds used. The predominant process occurring at short times was ascribed to water transport from the interior of the microspheres and the process occurring at longer times was interpreted as that arising from the residual viscoelasticity of the polymer network. As a result of the stress relaxation during loading, the Tatara model could not be used to describe loading data at large deformations.     

Dynamic mechanical properties of particulate-filled composites

The relative shear moduli of composites containing glass spheres in a rubbery matrix obey the Mooney equation, analogous to the relative viscosity of similar suspensions in Newtonian liquids. However, when the matrix is a rigid epoxy, the relative shear moduli are less than what the Mooney equation predicts but greater than what the Kerner equation predicts. Relative moduli are less for rigid matrices than for rubbery matrices because (1) the modulus of the filler is not extremely greater compared to that of the rigid matrix; (2) Poisson's ratio is less than 0.5 for a rigid matrix; (3) thermal stresses in the matrix surrounding the particles reduce the apparent modulus of the polymer matrix because of the nonlinear stress—strain behavior of the matrix. This latter effect gives rise to a temperature dependence of the relative modulus below the glass transition temperature of the polymer matrix. Formation of strong aggregates increases the shear modulus the same as viscosity is increased by aggregation. Torsion or flexure tests on specimens made by casting or by molding give incorrect low values of moduli because of a surface layer containing an excess of matrix material; this gives rise to a fictitious increase in apparent modulus as particle size decreases. The mechanical damping can be markedly changed by surface treatment of the filler particles without noticeable changes in the modulus. The Kerner equation, which is a lower bound to the shear modulus, is modified and brought into closer aggrement with the experimental data by taking into account the maximum packing fraction of the filler particles.     

Assessing robustness of hyperelastic models for describing nonlinearity of the mechanical response for pristine and swollen carbon black filled elastomers

We consider the hyperelastic response of semi-crystalline ethylene–co-butyl acrylate (EBA) samples filled with carbon black (CB) particles. Such material is structurally complex with its microstructure being characterized by many structural parameters including crosslink density, filler/matrix interfaces, crystallinity, filler network, and chain entanglement which have different degrees of influence on the effective mechanical properties. We evaluate the ability of a number of analytical models to correctly reproduce the non-linear elastic mechanical response of these samples. We do this by considering either dry samples, or samples which are swollen by a non-polar solvent (toluene) at equilibrium, and subjected to uniaxial tension at room temperature. As test cases, we focus on six physical models for the purpose of analyzing the stress–strain curves of samples with different cross-linking densities. Among these frameworks, we show that the Mooney–Rivlin (MR), Ogden, and eight-chain models accurately describe the stress–strain curves of both dry and swollen CB-EBA samples. These findings highlight the possibility of attaining a diverse set of mechanical properties of filled polymer samples by tailoring their structural parameters.     

Study on the Viscoelastic Poisson‘s Ratio of Solid Propellants Using Digital Image Correlation Method

Digital image correlation methods were used for further studies of the viscoelastic Poisson's ratio of solid propellants. The Poisson's ratio and the Young's relaxation modulus of solid propellants were separately determined in a single stress relaxation test. In addition, the effects of temperature, longitudinal strain, preload and storage time on the Poisson's ratio of solid propellants were discussed. The Poisson's ratio master curve and the Young's relaxation modulus master curve were constructed based on the time‐temperature equivalence principle. The obtained results showed that the Poisson's ratio of solid propellants is a monotone non‐decreasing function of time, the instantaneous Poisson's ratio increased from 0.3899 to 0.4858 and the time of the equilibrium Poisson's ratio occurred late when the temperature was varied from −30 °C to 70 °C. The Poisson's ratio increased with temperature and longitudinal strain, decreased with preload and storage time, while the amplitude Poisson's ratio increased with preload, decreases with longitudinal strain and storage time. The time of the equilibrium Poisson's ratio occurred in advance with the increase of longitudinal strain, preload and storage time.     

Amplitude-dependent dynamical behavior of PVC

Results of the amplitude-dependent dynamical behavior of commercial poly(vinyl chloride) are presented. Both the loss factor (internal friction) and the storage Young's modulus are strain amplitude dependent when measured between room temperature and approximately 400 K at a frequency of 50 kHz. The data are interpreted in terms of a hyperbolic sine stress dependence of the strain rate, including an effective stress. The activation volume was found to depend on temperature, with values much larger than those given by the usual mechanical tests (tensile, creep, or stress relaxation). It is suggested that these nonlinear effects are related to the α relaxation. © 1996 John Wiley & Sons, Inc.     

Elastic and swelling behavior of 2-hydroxyethyl methacrylate,diethylene glycol methacrylate,and methacrylic acid copolymers

The elastic and swelling behavior of copolymers of 2-hydroxyethyl methacrylate, diethylene glycol methacrylate, and methacrylic acid crosslinked with ethylene glycol dimethacrylate has been studied. In the range of copolymer composition studied, Young's modulus of the swollen networks increases with the content of methacrylic acid, and its dependence on the content of diethylene glycol methacrylate passes through a maximum. The concentrations of the elastic network chains and determined from Young's moduli of swollen networks are much higher than those calculated from stoichiometry. This effect is attributed to the presence of additional physical crosslinks due to water-induced ordering of the hydrophobic backbone chains. Both the elastic and swelling behavior of the polymers mentioned above are decisive for their application in the preparation of soft contact lenses. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 64: 2141–2148, 1997     

Enhanced mechanical properties of graphene/natural rubber nanocomposites at low content

Graphene/natural rubber (GE/NR) nanocomposites were prepared by a modified latex mixing method combined with in situ chemical reduction. It was found that the GE nanosheets are well dispersed and have strong interfacial interaction with NR. Thus, adding a low content of GE can remarkably increase the tensile strength and the initial tensile modulus of NR. With incorporation of as low as 0.5 phr of GE, a 48% increase in the tensile strength and an 80% increase in the initial tensile modulus are achieved without sacrificing the ultimate strain. But further increasing the GE loading degrades the tensile strength and the ultimate strain. Dynamic mechanical measurement indicates that the storage modulus of the nanocomposites is greatly enhanced with addition of GE, while the loss tangent peak is depressed due to the reduced mobility of the rubber molecules. The reinforcement effect of GE on NR is interpreted as a change in the strain induced crystallization and network structure of the nanocomposites, based on the analysis of Mooney ? Rivlin plots and the tube model.© 2013 Society of Chemical Industry     

Characterization of a glycidyl azide polymer composite propellant: Strain rate effects and relaxation response

Uniaxial tension tests were completed on a developmental GAP/PSAN solid rocket propellant at constant strain rates ranging over three decades and at five different temperatures. An analysis of the maximum stress (strength) and the strain at maximum stress showed that there is a relatively narrow range of temperatures and strain rates that give rise to strains at maximum stress that exceed 18%. The long-term equilibrium strain capability (strain endurance) appears to be between 10% and 12%. The trend of the strength and initial deformation moduli were log-linear with the reciprocal of the strain rate across three decades. However, the shifted master curves were log-curvilinear in form. The relationship between the strength and the initial modulus can be approximated by a power law. A series of stress relaxation tests was completed at a level of 4% strain and at five different temperatures. The initial portion of the shifted master relaxation curve is concave-up with correspondingly high stresses and moduli. It decays with time approaching a log-constant slope. Tensile moduli derived from constant strain rate tests were found to be consistently higher in value than the moduli as a function of time determined from relaxation tests, for an equivalent shifted time. Preliminary evidence suggests that the tensile modulus as a function of the reciprocal of shifted strain rate can be equated to the relaxation modulus as a function of shifted time through an adjustment factor. This relationship extends the relaxation modulus results back a further three and one-half decades of shifted time. © 1995 John Wiley & Sons, Inc.     

Measurement of the nonlinear mechanical properties of a poly(vinyl alcohol) sponge under longitudinal and circumferential loading

Poly(vinyl alcohol) sponges (P‐sponges) have been used as a potential implant material for the replacement and repair of soft tissues, including cartilage, liver, and kidney. However, the application of P‐sponges as tissue replacement materials is almost entirely bounded because of a lack of sufficient mechanical properties. In this study, we characterized the mechanical properties of a fabricated poly(vinyl alcohol) sponge (P‐sponge) under a series of longitudinal and circumferential uniaxial loadings. The nonlinear mechanical behavior of the P‐sponge was also computationally investigated with hyperelastic strain energy density functions, that is, the Ogden, Yeoh, Mooney–Rivlin, and Neo‐Hookean models. A hyperelastic constitutive model was selected to best fit the axial behavior of the sponge. The results reveal that the Young's modulus and maximum stress of the P‐sponge in the longitudinal direction were 16 and 17% greater than that in the circumferential direction, respectively. The Yeoh model, in addition, was selected to represent the nonlinear behavior of the poly(vinyl alcohol) material and could be used in future biomechanical simulations of the soft tissues. These results can be used to understand the mechanical properties of spongy materials in different loading directions. In addition, they have implications for ophthalmic and plastic surgeries and wound healing and tissue engineering purposes. © 2013 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2014 , 131, 40257.     

Step‐strain stress relaxation of carbon black‐loaded natural rubber vulcanizates

Step‐strain stress relaxation experiments were performed on natural rubber vulcanizates of various carbon black (HAF) concentrations by subjecting the samples to a very rapid strain and fixing its length at the deformed state. Time–temperature superposition in the viscoelastic region was evaluated to investigate the effect of temperature on the relaxation times of the rubbery composites. Remarkably, it was observed that, at higher HAF concentrations, increasing the temperature had a lesser effect on decreasing the overall stress values. That was attributed to the lower number of elastomeric chains per unit volume due to the agglomeration of the carbon black particles. The energy barrier resulting from the adsorption of the rubbery chains on the filler particles was insufficient to drastically reduce the diffusion and rearrangement of the polymer chains. The activation energy of the rubber‐like deformation calculated from the time–temperature superposition was shown to be independent of temperature. Interestingly, the viscosity coefficients showed a large increase with a modest addition of the carbon black. This is due to the long‐range nature of the temporary bonds formed between the polymer molecules and the surface‐active carbon black. The stress–strain of the rubbery composites was shown to behave in a Gaussian manner in accordance with the Mooney–Rivlin relationship. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 92: 3387–3393, 2004     

Relaxation of the axial strain induced stresses in double–coated optical fibers

The axial strain induced stresses in double‐coated optical fibers are analyzed by the viscoelastic theory. A closed form solution of the axial strain induced viscoelastic stresses is obtained. The viscoelastic stresses are a function of the radii, Young's moduli, relaxation times and Poisson's ratios of the polymeric coatings. If the applied axial strain linearly increases, the induced stresses increase with the time. On the other hand, if the axial strain is fixed, besides the axial stress in the glass fiber, the stresses exponentially decrease with the time. The relaxation of stresses is strongly dependent on the relaxation times of the polymeric coatings. If the relaxation time of the polymeric coating is very long, the viscous behavior of the polymeric coatings will not appear, and the axial strain induced stresses solved by the viscoelastic theory are the same as those solved by the elastic theory. On the other hand, if the relaxation time of the polymeric coating is very short, the relaxation of stresses is very apparent. A compressive radial stress at the interface of the glass fiber and primary coating will result in an increase of the transmission losses, and a tensile interfacial radial stress will possibly produce debonding at the interface of the glass fiber and primary coating. To minimize this interfacial radial stress, the radius, Young's modulus and Poisson's ratio of the polymeric coatings should be appropriately selected, and the relaxation time of the primary coating should be shortened. Finally, the stresses in single‐coated and double‐coated optical fibers are discussed.     

A methodology to analyse and simulate mechanical characteristics of poly(2‐hydroxyethyl methacrylate) hydrogel

In the present work, the mechanical properties of poly(2‐hydroxyethyl methacrylate) (PHEMA) such as ultimate strength, ultimate strain and shear modulus under compression were measured. Mathematical models for hyperelastic materials, which are often used to study rubbers or tyres and include the Mooney–Rivlin and neo‐Hookean models, were also used to theoretically analyse mechanical nonlinear behaviour of the hydrogel. The simulations based on these models were then implemented and validated by analysis with experimental data for comparison. The accuracy of simulations using the two models was subsequently assessed and discussed in order to determine which model is a feasible representation and reflection of the true behaviour of the hydrogel. This study on the mechanical behaviour of PHEMA under compression stress will ultimately serve for optimization of the design and manufacture of multilayer microfluidic devices in terms of the distribution of pressure induced in the packaging process, since the implementation of thin PHEMA hydrogel free‐standing films is required to be incorporated with harder polymeric material components, such as thermoplastics or thermoset microfabricated platforms. © 2012 Society of Chemical Industry     

Elastic moduli of glassy polymers at low strains

The short time moduli of polystyrene, poly(methyl methyacrylate), and polycarbonate have been measured in the glassy state. The main methods used were as follows: (1) The Young's modulus of a strip was derived by extrapolating to infinite length. (2) A bidirectional strain gauge was used for Young's modulus and Poisson's ratio. (3) A unidirectional bulk modulus was measured by the method of Warfield. The results obtained made it possible to determine all the isotropic moduli including the bulk modulus, and these are compared with those reported in the literature. Poisson's ratio (v) was found to increase with temperature in all cases. For poly(methyl methacrylate), where results reported in the literature vary widely, our values agreed with the lower reported figures (v < 0.36). The Young's modulus of poly(methyl methacrylate) is found to be more dependent on temperature and frequency than with the other two polymers.     

Modeling of the tensile moduli of mechanical,thermomechanical, and chemi‐thermomechanical pulps from orange tree pruning

Stiffness is one of the most relevant properties of composite materials. Although fiberglass has been traditionally used as reinforcement, natural fibers are seen as possible replacements due to concerns for environmental protection. In this work fibers from orange tree prunings were prepared and converted into mechanical, thermomechanical and chemi‐thermomechanical pulps, to be used as reinforcement for polypropylene. Polypropylene composite materials with 20–50% of reinforcing fibers were prepared and mechanically characterized. The intrinsic Young's modulus of the fibers was back calculated by means of the Hirsch model. The moduli were also obtained by Halpin‐Tsai equations with Tsai‐Pagano methods and then compared to establish the influence of the aspect ratio. Finally, a fiber tensile modulus factor was defined in order to characterize the contribution of the fibers to the Young's moduli of the composites. POLYM. COMPOS., 34:1840–1846, 2013. © 2013 Society of Plastics Engineers     

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.