Dynamic property and constitutive model of polyvinyl butaral material at high strain rates

The polyvinyl butaral (PVB) interlayer of automotive windshield plays an important role in the protection of both pedestrian and passenger, the mechanical property of PVB material should be in‐depth studied. In this article, the systematical uniaxial tensile experiments of PVB material under high strain rates are conducted, the strain rates range from 125.6 to 3768 s^?1. The results of experiments show that there exists a phenomenon of stress spurt caused by the stress hardening in the final stage of tension, and the strain rate exerts great influence on mechanical property of PVB material. Further, the data fitting basing on Mooney–Rivlin model is carried out, it is found that the fitting results are consistent with the experiment data, which means that the Mooney–Rivlin constitution model can describe the large deformation behavior of PVB material. At last, the rate‐dependent mechanical behavior of the PVB material is further investigated in this article. On the basis of the experiment results and Johnson–Cook model, a rate‐dependent constitutive model is proposed to describe the tensile mechanical property of PVB material under high strain rates. This work will be beneficial to the simulation and analysis of automotive collision safety and pedestrian safety protection, which are related to damage of automotive windshield. Copyright © 2014 John Wiley & Sons, Ltd.     

Microstrain investigation of polyethylene

The small-strain mechanical behavior of crystalline polyethylene has been studied by using a microstrain technique with strain resolution on the order of 10^?6. The strain rate was varied from 10^?6 to 10^?4 sec.^?1, and a temperature range of 17–28°C. was investigated. A strong dependence on strain rate and temperature has been observed for the following parameters which characterize the mechanical response of polyethylene in the microstrain region: the initial modulus of the stress–strain curve, the deviation in strain from ideal linear elastic behavior at a given stress amplitude, and the energy dissipated in a deformation cycle. The Young's moduli that were observed by means of tensile tests in the microstrain region were only about 20% lower than the values reported in other investigations at kilocycle and megacycle frequencies. The experimental method made it possible to isolate a deformation process which was attributed to a crystallographic shear mechanism corresponding to a yield point of 27 psi. This shear mechanism is discussed in terms of the various shear processes, such as slip, twinning, and the orthorhombic–monoclinic phase change.     

Strain‐rate dependence of the microstructure and mechanical properties for hot‐air‐drawn nylon 6 fibers

A hot‐air (HA) drawing method was applied to nylon 6 fibers to improve their mechanical properties and to study the effect of the strain rate in the HA drawing on their mechanical properties and microstructure. The HA drawing was carried out by the HA, controlled at a constant temperature, being blown against an original nylon 6 fiber connected to a weight. As the HA blew against the fiber at a flow rate of 90 liter/min, the fiber elongated instantaneously at strain rates ranging from 9.1 to 17.4 s⁻¹. The strain rate in the HA drawing increased with increasing drawing temperature and applied tension. When the HA drawing was carried out at a drawing temperature of 240 °C under an applied tension of 34.6 MPa, the strain rate was at its highest value, 17.4 s⁻¹. The draw ratio, birefringence, crystallite orientation factor, and mechanical properties increased as the strain rate increased. The fiber drawn at the highest strain rate had a birefringence of 0.063, a degree of crystallinity of 47%, and a dynamic storage modulus of 20 GPa at 25 °C. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1137–1145, 2000     

Mechanical behavior of polyester polymer concrete under low strain rate loading conditions

Polymer concrete (PC) has superior mechanical properties in comparison with cement concrete. In this research, the mechanical behavior of polyester polymer concrete (PPC) and its polyester resin were studied at different loading rates. Special specimens for testing the PPC and the polyester resin under low strain rate loading conditions were fabricated. Experiments were performed under different strain rates, from 0.00033 to 0.15 s⁻¹, and results for the PPC and the polyester resin were compared. Furthermore, the influence of strain rate on the mechanical response of the neat polyester and the PPC was investigated. The results show a maximum 40% increase in tensile strength of the neat polyester, while the elastic modulus does not change significantly. The compressive strength of the PPC increases by 25%. These results show that the mechanical behavior of the polyester resin and its PC is extremely sensitive to the strain rate.     

Interrelationship between ultimate mechanical properties of variously structured polyurethanes and poly(urethane urea)s and stretching rate thereof

The ultimate mechanical properties of polyurethane determine their possible applications under various conditions of mechanical action. The mechanical properties of nine polyurethane and polyurethane urea samples were investigated in a range of stretching rates 0.56÷0.002 s⁻¹. A part of experiments was performed at several temperature values under conditions of stepwise variable stretching rates. The interrelationship between rate dependence of strength–strain properties of polyurethane compositions and the structure thereof was ascertained. The influence of molecular structure’s variations, of physical network density and of segmented polyurethane and polyurethane urea morphology on said interrelationship was examined on samples subjected to large strain values. The structure of some samples was radically distorted by plasticizers oppositely influencing micro-phase segregation of soft and hard segments. Multiple kinds of dependency (direct, inverse, moderate and strong) of elastomers’ strength versus stretching rate were demonstrated. Produced data and ascertained regularities are useful to perceive reasons for diversity of mechanical behavior of polyurethane materials and to control properties thereof.     

The effect of strain rate on craze yielding,shear yielding,and brittle fracture of polymers at 77°K

The tensile strength of poly(methyl methacrylate) (PMMA), polycarbonate (PC), polychlorotrifluoroethylene, and polysulfone was measured in liquid nitrogen over the strain rate range of 2 × 10^?4 to 660 min^?1. These polymers deformed by crazing which was induced by the liquid nitrogen. The stress versus log strain rate curve was sigmoidal in that its slope increased and then decreased with strain rate. Above a critical strain rate of about 200 min^?1, which varied somewhat with the polymer, crazing was not observed with the optical microscope; the behavior became brittle, and the tensile strength became constant. The nonlinear behavior of stress versus log strain rate at low strain rates was associated with a decrease in activation volume with increasing strain rate whereas the nonlinear behavior at high strain rates was associated with an increase in density and decrease in length of the crazes with strain rate. The strain rate effect was the basis for calculating the diffusion coefficient of nitrogen into the polymers at 77°K. The shear deformation mode of PC was measured under compression and under tension. The compressive strength versus log strain rate was linear throughout the entire range giving a compression shear activation volume of 360 ų. The shear tensile strength of PC varied only slightly with strain rate when compared to the compressive strength. The brittle fracture stress of PMMA, in the absence of crazing, in compression and in tension, did not vary with strain rate.     

Comparison of optical and mechanical limits of linear relaxation behavior in glassy polycarbonate

The decay in birefringence of glassy polycarbonate held at constant extension has been studied at 23°C, in the time-scale range 10–10³ sec, up to about 6% strain. The results show that, under these conditions, the birefringence can be validly expressed as a linear hereditary integral of the strain history up to a relatively high strain level which is about 3.4% for an experimental time-scale of 100 sec. Comparison with previously obtained data on the stress relaxation behavior of the same polymer shows that, other factors remaining constant, mechanical relaxation is linear only up to about 1.1% strain. The earlier onset of mechanical nonlinearity is discussed and it is suggested that the mechanical relaxation spectrum is richer than the optical spectrum in relatively long relaxation times, corresponding to relatively slow molecular motions. It is further suggested that these slow molecular motions are accelerated first as the polymer is extended beyond the limit of linear viscoelastic behavior. The observed nonidentity between strain limits for linear mechanical and linear optical behavior is discussed in the light of current practices in photomechanical stress analysis.     

Experimental investigation and modeling of the mechanical behavior of PC/ABS during monotonic and cyclic loading

The purpose of this work is to characterize the mechanical behavior of blends of polycarbonate (PC) and acrylonitrile-butadiene-styrene (ABS) during monotonic and cyclic loading. Compression experiments were performed using a SHIMADZU universal testing machine (10⁻⁴ to 10⁻² s⁻¹) and a split Hopkinson pressure bar (1600–5000 s⁻¹), with, the test temperatures ranging from 293 to 353 K. The influence of the rate and temperature on the deformation of PC/ABS is discussed in detail. Based on the investigation of numerous constitutive models, a phenomenological model called DSGZ was chosen to describe the compression behavior of PC/ABS. This model could not accurately reproduce the deformation of polymers at high strain rates when utilizing the same material coefficients for the low and high strain–rate deformations. In addition, this model was unable to capture the deformation features during unloading and subsequent reloading when adopting the original stress–strain updating algorithm. Hence, some improvements to the model have been implemented to better predict the deformation. Finally, the model predictions are shown to be consistent with the experimental results.     

Rheooptical investigation of the crystallization of poly(ethylene terephthalate) under tensile strain

The crystallization of poly(ethylene terephthalate) under uniaxial tensile strain at different extension rates was investigated with optical polarimetry in a temperature range between the glass-transition temperature and the quiescent crystallization temperature. The evolution of the optical properties of the polymer, including the turbidity, birefringence, and dichroism, were monitored simultaneously with the mechanical parameters. To complete the semicrystalline microstructure characterization of the polymer under strain, an online wide-angle X-ray diffraction (WAXD) technique was used in separate experiments, which were performed under the same thermomechanical conditions. For real-time measurements, a high-energy synchrotron radiation source was used. The optical properties provided information about both the crystalline and amorphous phases, whereas the WAXD patterns essentially gave information about the crystalline phase. The two experimental techniques were then used in a complementary way to characterize the semicrystalline microstructure. Significant deviations from the stress-optical rule were found. This was attributed to both transient effects and the appearance of crystallites, which consisted of highly oriented molecular segments that could contribute to the optical anisotropy but not necessarily to the stress. The behavior of the optical dichroism was found to be qualitatively different from that of the birefringence. The latter monotonically increased with the strain, whereas the former first increased with the strain, passed through a maximum, and then decreased to a steady-state value. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1915–1927, 2004     

Tensile strength of Iβ crystalline cellulose predicted by molecular dynamics simulation

The mechanical properties of Iβ crystalline cellulose are studied using molecular dynamics simulation. A model Iβ crystal is deformed in the three orthogonal directions at three different strain rates. The stress–strain behaviors for each case are analyzed and then used to calculate mechanical properties. The results show that the elastic modulus, Poisson’s ratio, yield stress and strain, and ultimate stress and strain are highly anisotropic. In addition, while the properties that describe the elastic behavior of the material are independent of strain rate, the yield and ultimate properties increase with increasing strain rate. The deformation and failure modes associated with these properties and the relationships between the material’s response to tension and the evolution of the crystal structure are analyzed.     

Microstructure and mechanical properties of hot‐air drawn poly(ethylene terephthalate) fibers

Hot‐air drawing method has been applied to poly(ethylene terephthalate) (PET) fibers in order to investigate the effect of strain rate on their microstructure and mechanical properties and produce high‐performance PET fibers. The hot‐air drawing was carried out by blowing hot air controlled at a constant temperature against an as‐spun PET fiber connected to a weight. As the hot air blew against the fibers weighted variously at a flow rate of about 90 ℓ/min, the fibers elongated instantaneously at a strain rate in the range of 2.3–18.7 s⁻¹. The strain rate in the hot‐air drawing increased with increasing drawing temperature and applied tension. When the hot‐air drawing was carried out at a drawing temperature of 220°C under an applied tension of 27.6 MPa, the strain rate was the highest value of 18.7 s⁻¹. A draw ratio, birefringence, crystallite orientation factor, and mechanical properties increased as the strain rate increased. The fiber drawn at the highest stain rate had a birefringence of 0.231, degree of crystallinity of 44%, tensile modulus of 18 GPa, and dynamic storage modulus of 19 GPa at 25°C. The mechanical properties of fiber obtained had almost the same values as those of the zone‐annealed PET fiber reported previously. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 1703–1713, 1999     

Influence of strain rate on the compressive yield stress of CMDB propellant at low,intermediate and high strain rates

The mechanical properties of composite modified double base (CMDB) propellant significantly depend on the strain rate. In particular, the yield stress increases dramatically at higher strain rates. To study this behaviour, low, intermediate and high strain rate compression testing (1.7 × 10⁻⁴ to 4 × 10³ s⁻¹) of CMDB propellant at room temperature was conducted by using a universal testing machine, a hydraulic testing machine and a split Hopkinson pressure bar (SHPB) system, respectively. The yield stress was observed to increase bilinearly with the logarithm of strain rate, with a sharp increase in slope at a strain rate of 5 × 10¹ s⁻¹, which was supported by dynamic mechanical analysis (DMA) testing. The Ree-Eyring model, involving two rate-activated processes, was employed to predict the yield behaviour of CMDB propellant over a wide range of strain rates. The predictions are in excellent agreement with the experimental data.     

Tensile behavior of Nafion and sulfonated poly(arylene ether sulfone) copolymer membranes and its morphological correlations

The tensile stress–strain behavior of Nafion 117 and sulfonated poly(arylene ether sulfone) copolymer (BPSH35) membranes were explored with respect to the effects of the strain rate, counterion type, molecular weight, and presence of inorganic fillers. The yielding properties of the two films were most affected by the change in the strain rate. The stress–strain curves of Nafion films in acid and salt forms exhibited larger deviations at strains above the yield strain. As the molecular weight of the BPSH35 samples increased, the elongation at break improved significantly. Enhanced mechanical properties were observed for the composite membrane of BPSH35 and zirconium phenylphosphonate (2% w/w) in comparison with its matrix BPSH35 film. The stress‐relaxation behavior of Nafion and BPSH35 membranes was measured at different strain levels and different strain rates. Master curves were constructed in terms of plots of the stress‐relaxation modulus and time on a double‐logarithm scale. A three‐dimensional bundle‐cluster model was proposed to interpret these observations, combining the concepts of elongated polymer aggregates, proton‐conduction channels, and states of water. The rationale focused on the polymer bundle rotation/interphase chain readjustment before yielding and polymer aggregate disentanglements and reorientation after yielding. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1453–1465, 2006     

Strain rate and temperature dependence of a nanoparticle‐filled poly(dimethylsiloxane) undergoing shear deformation

The mechanical properties in shear of unfilled and nanoparticle‐filled polydimethylsiloxane (PDMS) networks are reported. The effect of silicate‐based nanoparticles on the mechanical response was studied as functions of rate and temperature using the time–temperature superposition principle. An apparent yielding phenomenon was observed in the filled polymer in spite of the more typical elastomeric behavior exhibited by the pure PDMS network. The time–temperature superposition principle was applied to capture the shear strain rate (10^?4–10^?1 s^?1) and temperature (?40 to 60°C) dependence of the stress response of the filled PDMS at different strains and at the yield point. A power‐law relationship was found to adequately describe the resulting master curves for yield stress in shear. Using a triangular shear displacement profile at 10^?2 s^?1, the effect of temperature (?20 to 80°C) on the recovery from a particularly pronounced Mullins effect was investigated as a function of rest time. Given adequate rest time (between 10 and 10² min), recovery was observed for the temperature range studied. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012     

Biodegradable shape‐memory polymer—polylactide‐co‐poly(glycolide‐co‐caprolactone) multiblock copolymer

In this study, biodegradable shape‐memory polymers—polylactide‐co‐poly(glycolide‐co‐caprolactone) multiblock (PLAGC) copolymers—were synthesized by the coupling reaction of both macrodiols of polylactide (PLLA‐diol) and poly(glycolide‐co‐caprolactone) (PGC‐diol) in the presence of 1,6‐hexanediisocyanate as coupling agent. The copolymers formed were found to be thermoplastic and easily soluble in common solvents. The compositions of the copolymers were determined by ¹H‐NMR and the influences of segment lengths and contents of both macrodiols on the properties of the PLAGC copolymers were investigated. It was found that the copolymers had adjustable mechanical properties which depended on contents and segment lengths of both macrodiols. The copolymers showed such good shape‐memory properties that the strain fixity rate (R_f) and the strain recovery rate (R_r) exceed 90%. By means of adjusting the compositions of the copolymers, PLAGC copolymers with transition temperatures around 45°C could be obtained. The degradation rate determination showed that the PLAGC copolymers have fast degradation rates, the mechanical strengths of the PLAGC copolymers would be completely lost within 1–2 months depending on molecular weights and contents of the both segments of PLLA and PGC. Copyright © 2005 John Wiley & Sons, Ltd.     

The Thermoviscoelastic Constitutive Equation of PP and PA Blends and Its Rate Temperature Equivalency at High Strain Rates

By using Instron 1342 testing system and an improved SHPB technique, PP/PA blends are tested at a wide range of strain rates from 10⁻⁴ up to 10³ s⁻¹ and at a temperature range of 25–80 °C. Their mechanical responses are shown to be sensitive both to the strain rate and temperature. Based on the experimental data of 113 blends at a wide range of strain rates from 10⁻⁴ up to 10³ s⁻¹ and at a temperature range of 25–80 °C, it is shown that the mechanical behavior of this PP/PA blends can be described with ZWT thermoviscoelastic constitutive equation. The corresponding thermoviscoelastic parameters for 113 blends are obtained. The predicted theoretical results coincide quite well with the experimental data.The experimental results also reveal that the rate/time-temperature equivalence relation is shown for PP/PA blends. Raising the temperature is equivalent to the increasing of time (the decreasing of strain rate). Conversely, decreasing the temperature is equivalent to the decreasing of time (the increasing of strain rate). Through introducing a dimensionless parameter , two characteristic parameters: strain rate and temperature T are put together to this unified parameter Z. From experimental results, A/k is fitted, A/k = 8.595 °C, and a unified curve characterizing the rate/time –temperature equivalence relation is obtained.     

The effect of casting solvent on the material properties of poly(γ-methyl-D-glutamate)

The effect of casting solvent on the material properties of poly(γ-methyl-D -glutamate), PMDG, was investigated. The specific solvents used were chloroform, trifluoroacetic acid, dichloroacetic acid, methylene chloride, hexafluoroisopropanol, and tetrachloroethane. The different nature of these solvents controlled the degree of α, β, or random coil contents of the final film. The effect of the morphology on material properties induced by the respective solvents was investigated by dynamic mechanical measurements of the dry films, stress strain behavior of both wet and dry films as well as by wide-angle x-ray diffraction, small-angle light scattering, and optical microscopy. Infrared spectroscopy was used to help determine α or β content. It was found that the casting solvent has considerable influence on material behavior and morphology. These differences are reflected in both the dynamical mechanical (small strain) and stress–strain (large strain) measurements as well as the x-ray scattering and optical microscopy. It was noted by light scattering that all films gave rise to anisotropic rod scattering with the exception of the β film cast from trifluoroacetic acid. This latter film appeared to be optically isotropic.     

Comparison of the transient stress–strain response of rubber to its linear dynamic behavior

Master curves of the small strain and dynamic shear modulus are compared with the transient mechanical response of rubbers stretched at ambient temperature over a seven‐decade range of strain rates (10^?4 to 10³ s^?1). The experiments were carried out on 1,4‐ and 1,2‐polybutadienes and a styrene–butadiene copolymer. These rubbers have respective glass transition temperatures, T_g, equal to ?93.0, 0.5, and 4.1 °C, so that the room temperature measurements probed the rubbery plateau, the glass transition zone, and the onset of the glassy state. For the 1,4‐polybutadiene, in accord with previous results, strain and strain rate effects were decoupled (additive). For the other two materials, encroachment of the segmental dynamics precluded separation of the effects of strain and rate. These results show that for rubbery polymers near T_g the use of linear dynamic data to predict stresses, strain energies, and other mechanical properties at higher strain rates entails large error. For example, the strain rate associated with an upturn in the modulus due to onset of the glass transition was three orders of magnitude higher for large tensile strains than for linear oscillatory shear strains. © 2011 Wiley Periodicals, Inc.* J Polym Sci Part B: Polym Phys, 2011     

Effect of strain rate on the dynamic tensile behaviour of UHMWPE fibre laminates

Ultra-high molecular weight polyethylene (UHMWPE) fibre has great potential for strengthening structures against impact or blast loads. A quantitative characterization of the mechanical properties of UHMWPE fibres at varying strain rates is necessary to achieve reliable structural design. Quasi-static and high-speed tensile tests were performed to investigate the unidirectional tensile properties of UHMWPE fibre laminates over a wide range of strain rates from 0.0013 to 163.78 s⁻¹. Quasi-static tensile tests of UHMWPE fibre laminates were conducted at thicknesses ranging from 1.76 mm to 5.19 mm. Weibull analysis was conducted to investigate the scatter of the test data. The failure mechanism and modes of the UHMWPE fibre laminates observed during the test are discussed. The test results indicate that the mechanical properties of the UHMWPE fibre laminate are not sensitive to thickness, whereas the strength and the modulus of elasticity increase with strain rate. It is concluded that the distinct failure modes at low and high strain rates partially contribute to the tensile strength of the UHMWPE fibre laminates. A series of empirical formulae for the dynamic increase factor (DIF) of the material strength and modulus of elasticity are also derived for better representation of the effect of strain rate on the mechanical properties of UHMWPE fibre laminates.     

Strain rate effects on the mechanical response of polypropylene-based composites deformed at small strains

The mechanical properties and response of two polypropylene (PP)-based composites have been determined for small strains and for a range of strain rates in the quasi-static domain. These two materials are talc-filled and unfilled high-impact PP. Uniaxial tensile tests were performed at different strain rates in order to characterize the mechanical response and the strain rate effect. The experimental results showed that both unfilled and talc-filled high-impact PP were sensitive to strain rate and exhibited nonlinear behavior even at relatively low strains. SEM analysis was conducted to obtain a better comprehension of deformation mechanisms involved during loading by observations of the microstructure evolution. For each of these two materials, two existing modeling approaches are proposed. The first one is a three-parameter nonlinear constitutive model based on the experimental results. The second is a micromechanically based approach for the elastic-viscoplastic behavior of the composite materials. The stress-strain curves predicted by these models are in fairly good agreement with our experimental results. Published in Russian in Vysokomolekulyarnye Soedineniya, Ser. A, 2008, Vol. 50, No. 6, pp. 1051–1059. This article was submitted by the authors in English.