Visco‐hyperelastic constitutive model for modeling the quasi‐static behavior of polyurethane foam in large deformation

Flexible polyurethane foam is widely used in numerous applications such as seats and mattresses, due to its low stiffness and its ability to absorb deformation energy. The main objective of this article is to model the quasi‐static mechanical behavior of three types of polyurethane foam in large deformation and to compare these three foams with three proposed models. The uniaxial compression/decompression tests at three different strain rates were performed. The test results show that the three foams present different plateau stresses, maximum stresses, and abilities to absorb energy. Moreover, polyurethane foam also presents a nonlinear hyperelastic behavior and a viscoelastic behavior in large deformation. Three visco‐hyperelastic models which include a hyperelastic component and a memory component are proposed to model these behaviors. Model parameters were identified using the experimental data and a proper identification method. These models were validated on these three types of foam with the aim to present comparison results. The comparison results show that Ogden's viscoelastic model best agrees with the experimental results. POLYM. ENG. SCI., 55:1795–1804, 2015. © 2014 Society of Plastics Engineers     

Nonlinear load–strain modeling of polypropylene geogrids during constant rate‐of‐strain loading

This article describes a rate‐dependent hyperbolic model that was developed to predict the tensile load–strain behavior of a polypropylene geogrid reinforcement material under monotonic and stepped constant rate‐of‐strain testing. A more general three‐component model previously reported in the literature was also used in the current study but with some modifications to compute model parameters. Details of the trial and error procedure to select three‐component model parameters, not previously reported in the literature, are explained. Both models gave similar good agreement between measured and predicted constant rate‐of‐strain tests. The accuracy of the three‐component model to simulate stepped constant rate‐of‐strain tests was judged to be better, but for practical purposes, the simpler hyperbolic model was judged to be satisfactory. An advantage of the hyperbolic model is that the model parameters are easy to determine, only monotonic constant rate‐of‐strain tests are required, and numerical implementation is simple. However, the hyperbolic model is restricted to monotonic or stepped constant rate‐of‐strain load paths. An advantage of the more complicated three‐component model is that it has been demonstrated in previous studies to be more general and thus can be used for other load paths and other polymeric reinforcement material types that do not have characteristic hyperbolic load–strain behavior. POLYM. ENG. SCI., 55:1617–1627, 2015. © 2014 Society of Plastics Engineers     

Investigation of the strain‐rate‐dependent mechanical behavior of a photopolymer matrix composite with fumed nano‐silica filler

With the evolution of additive manufacturing, there is an increasing demand to produce high strength and stiffness polymers. Photopolymers are very commonly used in stereolithography and fused deposition modeling processes, but their application is limited due to their low strength and stiffness values. Nano‐sized fibers or particles are generally embedded in the polymer matrix to enhance their properties. In this study, we have studied the effect of fumed nano‐sized silica filler on the elastic and viscoelastic properties of the photopolymer. The uniaxial testing coupons with different concentrations of silica filler have been fabricated via casting. We observed improvement in mechanical properties by the addition of the nano‐sized filler. As polymers exhibit time‐dependent mechanical response, we have conducted tensile tests at different strain rates as it is one of the most common modes of deformation, and is commonly used to characterize the parameters of the rate‐dependent material. We noticed significant dependence of the mechanical properties on the strain rate. quasi‐linear viscoelastic (QLV) model, which combines hyperelastic and viscoelastic phenomena, has been employed to capture the response of the material at different strain rates. We found out that the QLV model with Yeoh strain energy density function adequately describes the rate‐dependent behavior of the material and has reasonable agreement with the experimental results. POLYM. ENG. SCI., 59:1695–1700 2019. © 2019 Society of Plastics Engineers     

Modeling the large‐strain constitutive behavior of polycarbonate under isothermal and anisothermal conditions

The tensile behavior of polycarbonate was studied at large strains below the glass‐transition temperature. Experiments were carried out at a series of constant temperatures and also under conditions of falling temperatures. The specimens necked with a natural draw ratio of approximately 2, and the study was mainly focused on the necked material. Isothermal experiments revealed an elastic mechanism that initiated beyond the natural draw ratio. A model consisting of an Eyring process and two Gaussian elastic mechanisms was found to be applicable to both the isothermal and anisothermal stress‐relaxation and stress–strain results. The same model also produced reasonable estimates of the stresses generated during the necking process. In addition, a simple relationship between the isothermal and anisothermal stress relaxation was demonstrated. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 96: 2105–2116, 2005     

Temperature‐dependent solubility of wax compounds in ethanol

The ability of ethanol to dissolve wax compounds, as an alternative to traditional lipid solvents, was investigated for the recovery of cuticular lipids from biomass. The solubilities of fatty esters with carbon chain lengths from 40 to 54 were measured in ethanol over a temperature range of 30–80°C. The greatest increase in solubility was observed between 40° and 60°C for the long chain waxes that are characteristic of flax cuticle lipids. The solubility of a 52‐carbon wax increased by a factor of four over this temperature range. The Van't Hoff equation was used to estimate enthalpy of solution values. Ethanol was an effective lipid solvent at these modestly elevated temperatures and offers an economical method to recover lipid co‐products from biomass prior to conversion to bioethanol.     

Strain‐rate‐dependent mechanical properties of polypropylene separator for lithium‐ion batteries

The mechanical integrity of battery separators is critical for battery safety and durability. A comprehensive study of strain‐rate‐dependent tensile and puncture properties of a polypropylene lithium‐ion battery separator is presented here with a new model. Due to anisotropy of the polymeric membrane, tensile testing was conducted for different directions. Results showed that tensile strength and elastic modulus were increased 1000% and 500%, respectively, for different directions. It was also demonstrated that tensile strength changed 10 to 25% with strain rate (1.67 × 10^?4 to 1.67 × 10^?1 s^?1) for different directions. An equation was obtained for the first time for flow stress versus strain rate at varied tensile directions with respect to machine direction. Moreover, puncture testing was performed and it was shown that puncture strength was increased 140% with increasing strain rate from 0.25 to 250 mm min^?1. Two failure modes were also observed in puncture samples. Finally, Eyring's model was used to calculate activation enthalpy of the porous polypropylene separator. © 2020 Society of Chemical Industry     

Finite element modeling of polymer hot embossing using a glass‐rubber finite strain constitutive model

A hyperelastic–viscoplastic constitutive model for amorphous polymers was used in finite element simulations of micro‐hot embossing across the glass transition. The model was selected for its ability to capture finite strain temperature and rate dependence over a wide range of temperatures, including across the glass transition. The simulations focused on the glass transition temperature regime, and particularly probed the effects of time and temperature during cooling and mold release. The results show that strong temperature sensitivity of the material across the glass transition leads to a wide range of required embossing force and springback. The interplay between changes in material properties upon cooling and stress relaxation can lead to significant increases in embossing force during the cooling stage, especially when high cooling rates are employed. The effects of thermal expansion also complicate the problem during rapid cooling. Nonlinear material behavior is shown to affect results in parametric hot embossing studies. Careful tailoring of embossing temperature, cooling rate, and demolding temperature is critical in acceptable feature replication. The best results are found for moderate cooling rates, which allow adequate time for stress relaxation in the material prior to mold release. POLYM. ENG. SCI., 2009. © 2009 Society of Plastics Engineers     

A visco-elastoplastic constitutive model for large deformation response of polycarbonate over a wide range of strain rates and temperatures

The principal purpose in this paper is to present a combined experimental and analytical study to understand the mechanical behavior of polycarbonate (PC) under a wide range of temperatures (−40 °C to 100 °C) and strain rates (0.001 up to 5000 s⁻¹). Firstly, the experiments were conducted to obtain stress-strain response from low to high rates and temperatures. Then a robust physically consistent rate and temperature-dependent constitutive model is proposed to characterize large deformation mechanical behavior of PC. According to viscoelastic theory, a nonlinear-viscoelastic model is employed to understand the elastic response. Yielding behavior is described via cooperative model. As respect to post-yield regime, it is described by the conflict and interaction between softening and hardening behavior based on the integral-form softening and kinematic hardening model. The proposed constitutive model is successfully validated by the excellent agreement between model prediction and experiment results.     

Temperature‐dependence modeling of highly crosslinked polymer networks

The dependence on the temperature of the state of a highly crosslinked polymer network can be modeled as a function of well‐defined molecular‐level network parameters to yield a simple applied model equation. The tightness and strength (modulus of elasticity) of the crosslinked networks formed, as well as any further tightening of the network due to further curing, can easily be compared with the parameters A, M, and α (the coefficient of branching) and the m/E ratio and, therefore, with parameters directly related to molecular‐level characteristics of the system. The crosslinking contribution to the network is represented by A and M, the former representing the frequency of crosslinking and the latter having the dimensions of an energy. The ratio m/E, that is, the ratio of the average number of degrees of freedom of chain segments between crosslinking nodes (m) to the average energy of nonbonded atom interactions between the same segments (E), and α model the noncrosslinked contribution to the characteristics of the network. These are the same parameters that appear in the simple equation modeling the dependence of the characteristics of the network on the temperature within a limited temperature range. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 88: 2416–2426, 2003     

Shear‐rate‐dependent rheology effects on mass transport and surface reactions in biomicrofluidic devices

Consideration is given to shear‐rate‐dependent rheology effects on mass transport in a heterogeneous microreactor of rectangular cross section, utilizing both numerical and analytical approaches. The carrier liquid obeys the power‐law viscosity model and is actuated primarily by an electrokinetic pumping mechanism. It is discovered that, considering the shear‐thinning biofluids to be Newtonian fluids gives rise to an overestimation of the saturation time. The degree of overestimation is higher in the presence of large Damkohler numbers and electric double layer thicknesses. It is also increased by the application of a favorable pressure gradient, whereas the opposite is true when an opposed pressure gradient is applied. In addition, a channel of square cross section corresponds to the maximum fluid rheology effects. Finally, the numerical results indicate the existence of a concentration wave when using long channels. This is confirmed by analytical solutions, providing a closed form solution for wave propagation speed. © 2015 American Institute of Chemical Engineers AIChE J, 61: 1912–1924, 2015     

Temperature‐dependent permeability of polyelectrolyte complex capsule membranes having N‐isopropylacrylamide domains

As a microcapsule with temperature sensitivity, poly(methacrylic acid)–polyethylenimine complex capsules containing N‐isopropylacrylamide units were designed. Two kinds of copolymers of methacrylic acid and N‐isopropylacrylamide were synthesized by free‐radical copolymerization. Partly crosslinked poly(methacrylic acid)–polyethylenimine complex capsules containing the methacrylic acid–N‐isopropylacrylamide copolymers were prepared at 40 or 25°C. The permeation of phenylethylene glycol through the capsule membranes was investigated. Permeability of the capsules prepared at 25°C increased monotonously with increasing temperature from 10 to 50°C. Permeability of the capsules prepared at 40°C also increased with increasing temperature up to 25°C but decreased above 30°C. Also, the degree of swelling of the membranes prepared at 40°C decreased above 30°C. Differential scanning calorimetry measurement showed that N‐isopropylacrylamide units underwent more efficient transition in the capsule membranes prepared at 40°C than in the membranes prepared at 25°C. The capsule membranes prepared at 40°C might have domains in which N‐isopropylacrylamide units are concentrated, whereas these units should distribute uniformly in the capsule membranes made at 25°C. Such a difference in distribution of N‐isopropylacrylamide units might result in the different permeation property of the capsule membranes. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 77: 2703–2710, 2000     

Viscoplastic constitutive modeling of polymers—Flow rules and the plane strain response

Plane strain compression tests, measuring both axial and transverse forces, are performed on ultra‐high molecular weight polyethylene up to true axial strains of ?0.4. As the deformation proceeds, the transverse stress becomes an increasing proportion of the axial stress, with the proportion growing from its initial value of 0.5 up to a value of 0.8. A constitutive model is applied that combines Ogden models and Eyring processes. It is found that when a Levy‐Mises flow rule is used in conjunction with the Eyring model, the predicted ratio of transverse to axial stress remains much smaller than that observed, and is not greatly affected by changes in the Ogden exponent. However, when the flow rule is replaced by one that incorporates strain‐induced anisotropy, realistic predictions are possible. For each Ogden model, we associate a flow rule for which the transverse strains in both the Ogden and Eyring models are individually zero. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2009     

A rate‐type nonlinear viscoelastic–viscoplastic cyclic constitutive model for polymers: Theory and application

A thermodynamically consistent rate‐type viscoelastic–viscoplastic constitutive model is developed in the framework of isothermal and small deformation to describe the nonlinear and time‐dependent deformation behaviors of polymers, e.g., ratchetting, creep, and stress relaxation. The model is proposed on the base of a one‐dimensional rheological model with several springs and dashpot elements. The strain is divided into viscoelastic and viscoplastic parts, and the stress is also decomposed into two components. Each stress component is further divided into elastic and viscoelastic sub‐components. The viscoelasticity is described by introducing pseudo potentials, and the ratchetting is considered by the viscoplastic flow which is derived by the codirectionality hypotheses. The capability of the proposed model to describe the nonlinear and time‐dependent deformation of polymers is then verified by comparing the simulations with the corresponding experimental results of polycarbonate (PC) polymer. It is shown that the nonlinear and time‐dependent stress–strain responses of the PC can be reasonably predicted by the proposed model. POLYM. ENG. SCI., 56:1375–1381, 2016. © 2016 Society of Plastics Engineers     

Viscoelastic behavior and constitutive modeling of PP/HNT composites prepared by water‐assisted extrusion

Poly(propylene) (PP) nanocomposites containing 5, 10, and 15 wt% unmodified halloysite nanotubes (HNTs) were prepared using extrusion with and without water injection. Scanning electron microscopy micrographs show that HNT aggregates prepared by water injection are smaller than those prepared by conventional melt extrusion (without water injection). The nanocomposites prepared by water injection exhibit higher storage modulus (G′) and complex viscosity (η*) values than those by conventional melt extrusion. Stress relaxation results indicate that the interaction between HNTs and PP matrix at low concentration (5 wt%) is stronger than its non‐water injection counterpart. Subsequently, for 5 wt% HNT sample, the transient viscosity is simulated numerically using the Kaye–Bernstein–Kearsley–Zapas (K‐BKZ) integral constitutive equation along with experimentally determined damping functions. It is found that the samples prepared by water injection exhibit a more obvious overshoot behavior than conventional samples and the Papanastasiou‐Scriven‐Macosko (PSM) model can predict the transient viscosity of the samples more accurately than Wagner model. Further, the relationship between the dispersion of HNTs and the damping factors in the constitutive models is discussed. The results of this investigation would improve the theoretical understanding of possible polymer–filler interaction during shear flow. POLYM. ENG. SCI., 59:1585–1592 2019. © 2019 Society of Plastics Engineers     

Rheological behavior of semi‐aromatic transparent polyamide

The rheological behaviors of semi‐aromatic transparent polyamide (SATPA) melt are investigated using a capillary rheometer. The effects of shear rate, shear stress, and temperature on the apparent viscosity η_a of SATPA are discussed. A correlation of non‐Newtonian index with temperature is obtained. The results show the shear thinning of SATPA; meanwhile η_a decreases with increasing temperature and shear rate, and the viscous flow activation energy is further obtained from temperature dependence of the samples. It was concluded that the apparent viscosity η_a is sensitive to temperature at lower shear rate owing to the higher viscous flow activation energy; on the contrary, the influence of temperature effect on the apparent viscosity becomes minor at higher shear rate due to the lower viscous flow activation energy. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 97: 1586–1589, 2005     

Temperature‐ and pH‐sensitive IPNs grafted onto polyurethane by gamma radiation for antimicrobial drug‐eluting insertable devices

Temperature‐ and pH‐sensitive interpenetrating polymer networks (IPNs) and semi‐interpenetrating polymer networks (s‐IPNs) were γ‐ray grafted onto polyurethane (Tecoflex^®; TFX) to obtain vancomycin‐eluting implantable medical devices with minimized risk of infections. N‐isopropylacrylamide (NIPAAm) was grafted onto TFX catheters and films via a preirradiation oxidative method (method P) or via a direct method (method D). The PNIPAAm network facilitated acrylic acid (AAc) inclusion and subsequent polymerization/crosslinking, under specific reaction conditions. IPNs and s‐IPNs systems were characterized regarding the amount of grafted polymers, surface properties (FTIR‐ATR, ESEM, EDX), thermal behavior (DSC), and their temperature‐ and pH‐responsiveness. Loading and release of vancomycin for preventing in vitro growth of Staphylococcus aureus were also evaluated. Antimicrobial activity tests and hemo‐ (hemolysis, protein adsorption, thrombogenicity) and cyto‐compatibility (cell viability and production of cytokines and NO) assays indicated that the modification of TFX by γ‐radiation may improve the performance of polyurethanes for biomedical applications. © 2013 Wiley Periodicals, Inc. J. Appl. Polym. Sci., 2014 , 131, 39992.     

Temperature‐dependent transition of crystal phases in the electrospinning process of poly(vinylidene fluoride‐co‐hexafluoropropylene)

The temperature‐dependent transition of the crystal phases of poly(vinylidene fluoride‐co‐hexafluoropropylene) (PVDF‐HFP) was investigated in the electrospinning process. A solution of PVDF‐HFP in N,N‐dimethyl acetamide (DMAc) produced only the β‐phase‐dominant crystal up to 70 °C, irrespective of the spinneret temperature. In a mixed solvent of DMAc and acetone, however, the crystal phase of the electrospun fibers was dependent on temperature: β‐phase‐dominant at 30 and 50 °C and α‐phase‐dominant at 70 °C. The transition was related to a change of the coagulation rate during electrospinning, because the less perfect α phase is preferable to the β phase at a higher coagulation rate. The temperature‐dependent increase of the coagulation rate was more drastic in the presence of acetone, so the transition took place only in the mixed solvent. At elevated temperature, acetone not only raised the evaporation rate of the solvent but promoted the phase separation of the polymer resulting from the lower critical solution temperature behavior, which was rheologically traced. © 2019 Society of Chemical Industry     

Cooperative viscoplasticity theory based on the overstress approach for modeling large deformation behavior of amorphous polymers

A micromechanically based formulation of the cooperative model is incorporated into the viscoplasticity theory based on overstress (VBO) model. The plastic shear strain rate given by the cooperative model is used as a flow function which is responsible for rate and temperature dependence in the VBO model. In this way, thermomechanical analysis can be performed under different loading rates and temperatures of amorphous polymers. Introducing strain softening, the temperature‐ and strain‐rate‐dependent elasticity moduli are two other modifications of the VBO formulation. The validity of the newly proposed cooperative VBO model is demonstrated by modeling the uniaxial compression behavior of poly(methyl methacrylate) under different temperatures and strain rates. © 2013 Society of Chemical Industry     

Stress-strain behavior of a polyurea and a polyurethane from low to high strain rates

The large deformation stress-strain behavior of thermoplastic-elastomeric polyurethanes and elastomeric-thermoset polyureas is strongly dependent on strain rate. Their mechanical behavior at very high strain rates is of particular interest due to their role as a protective coating on structures to enhance structural survivability during high rate loading events. Here we report on the uniaxial compression stress-strain behavior of a representative polyurea and a representative polyurethane over a wide range in strain rates, from 0.001 s⁻¹ to 10,000 s⁻¹, successively marching through each order of magnitude in strain rate using equipment relevant for testing at each particular rate. These results are further analyzed in association with recently reported compressive data on the same materials by Yi et al. [Polymer 2006;47(1):319-29] and intermediate rate tensile data on the same polyurea by Roland et al. [Polymer 2007;48(2):574-8]. The polyurea tested is seen to undergo transition from a rubbery-regime behavior at low rates to a leathery-regime behavior at the highest rates, consistent with the earlier compression study as well as the recent tension study; the polyurethane tested is observed to undergo transition from a rubbery-regime behavior at the low rates to a glassy behavior at the highest rates. The uniaxial compression data for the polyurea are found to be fully consistent with the recently reported uniaxial tension data over the range of rates studied, demonstrating the consistency and complementary aspects of testing at high rates in both compression and tension.