The alpha–beta transformation in polypivalolactone. II. A simple mechanical model

A simple mechanical model based on the equilibrium rate theory of Burte and Halsey is presented in order to explain the stress–strain curve of polypivalolactone (PPL) fibers. A semiquantitative application of this model indicates that the PPL alpha–beta transformation implies the cooperative deformation of at least thrity chain units and that the free energy difference between the alpha and beta states is of the order of 2 kcal/mole of monomer.     

Strain hardening of polymer glasses: Effect of entanglement density,temperature, and rate

The strain hardening behavior of model polymer glasses is studied with simulations over a wide range of entanglement densities, temperatures, strain rates, and chain lengths. Entangled polymers deform affinely at scales larger than the entanglement length as assumed in entropic network models of strain hardening. The dependence of strain hardening on strain and entanglement density is also consistent with these models, but the temperature dependence has the opposite trend. The dependence on temperature, rate, and interaction strength can instead be understood as reflecting changes in the flow stress. Microscopic analysis of local rearrangements and the primitive paths between entanglements is used to test models of strain hardening. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3487–3500, 2006     

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     

Effect of tensile load on the actuation performance of pH‐sensitive hydrogels

pH‐responsive hydrogels are capable of converting chemical energy to mechanical work. To optimize their use as actuators, their response when operating against an external load must be fully characterized. Here, the actuation strain of a model pH‐sensitive hydrogel as a function of different constant loads is studied. The experimental actuation strain, produced by switching the pH from 2 to 12, decreases significantly and monotonically with increasing initial tensile load. Two models are developed to predict the actuation strain as a function of applied stress. Simple mechanical models based on the change in hydrogel modulus and cross sectional area due to the change in pH are unsatisfactory as they predict only a small change in actuation strain with increasing external stress. However, the model based on the elastic and mixing free energy functions derived from the Flory–Huggins theory is found to accurately account for the actuation strain as a function of stress. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 218–225     

On the relevance of the 8‐chain model and the full‐network model for the deformation and failure of networks formed through photopolymerization of multifunctional monomers

Crosslinked networks were synthesized by copolymerization of mono‐functional tert‐butyl acrylate (tBA) with diethyleneglycol dimethacrylate (DEGDMA) or polyethylene glycol dimethacrylates (PEGDMA). By varying the chain length and concentration of the difunctional PEGDMA, we obtained tBA‐PEGDMA copolymer networks while by varying the concentration of difunctional DEGDMA, we obtained tBA‐DEGDMA crosslinked networks. The various materials were submitted to large deformations through uniaxial tension tests. For moderate weight percent of crosslinking agent, up to 20%, the networks showed standard S‐shape stress–strain curves, characteristic of rubber‐like elasticity. Two macromolecular models, the 8‐chain model and the full‐network model, were applied to fit the uniaxial tensile response of the materials. Both models provide good representations of the overall uniaxial stress–strain response of each material. After fitting to stress–strain data, the network models were employed to predict the shear modulus and the elongation at break. Neither the 8‐chain nor the full network model were capable of predicting the failure strain or shear modulus, indicating these models are best used to describe stress–strain relations rather than predict mechanical properties for the network polymers considered here. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 1226–1234, 2008     

A molecular theory of stress–strain relationship of spherulitic materials

A primitive molecular theory for stress–strain relationship of spherulitic polymers is presented based on a consideration of changes in conformational free energy in the tie chains and floating chains located between crystalline lamellae within an ideal spherulite which is assumed to undergo an affine deformation. Numerical stress–strain curves are calculated as a function of temperature, crystallinity, and tie chain fraction.     

Grafting on wool. II. Stress–strain behavior of grafted fiber in water

The stress–strain behavior and hysteresis properties of various grafted wool fibers were studied. Three distinct regions on the stress–strain curve and hysteresis properties characteristic of the native wool fiber remain substantially intact, even though a large amount of a rigid polymer occurs. It was suggested that the microfibril and the matrix nature in the native wool fiber exist in the grafted wool structures. The electron microscopic results were also supported. These results can be explained on the basis of Menefee's model that the longitudinal mechanical behavior is more directly controlled by a high modulus matrix.     

Stress-dependent dynamic compliance spectra approach to the nonlinear viscoelastic response of polymers

The present work reports a discrete, stress-dependent dynamic compliance spectra method which may be used to predict the mechanical response of nonlinear viscoelastic polymers during strain-defined processes. The method is based on the observation that the real and complex parts of the discrete dynamic compliance frequency components obtained from creep measurements are smooth, easily fit functions of stress. Comparisons between experimental measurements and model calculations show that the model exhibits excellent quantitative agreement with the basis creep measurements at all experimental stress levels. The model exhibits good quantitative agreement with stress relaxation measurements at moderate levels of applied strain. However, the model underestimates the experimental stress relaxation at an applied strain of 3.26%. The stress relaxation error appears to be a real material effect resulting from the different strain character of creep and stress relaxation tests. The model provides a good quantitative agreement with experimental constant strain rate measurements up to approximately 4% strain, after which the model underestimates the experimental flow stress. This effect is explained by the time dependence of the stress-activated configurational changes necessary for large strains in glassy polymers. © 1998 John Wiley & Sons, Inc. J. Polym. Sci. B Polym. Phys. 36: 2301–2309, 1998     

Understanding the elastomeric properties of polymer networks

It is shown that Monte‐Carlo (MC) simulations of the elastic behaviour of chains in networks using realistic rotational‐isomeric‐state (RIS) chain models are able to reproduce experimentally observed deviations from Gaussian network behaviour in uniaxial extension and also to interpret, quantitatively, stress‐optical properties. In stress‐strain behaviour, an increase in the proportion of fully extended chains with increasing macroscopic strain gives rise to a steady decrease in the rate of change of the Helmholtz energy of a network, causing a reduction in network modulus at moderate macroscopic strains. There is no need to invoke a transition from affine to phantom chain behaviour as deformation increases. To evaluate stress‐optical properties, the average orientation of segments with respect to the deformation axis is calculated, taking into account the interdependence of segment orientation and chain orientation as chains become more extended and aligned under uniaxial stress. The MC method gives, in agreement with experiment, values of stress‐optical coefficient that are dependent upon both deformation ratio and network‐chain length. The method highlights serious shortcomings in the classical Gaussian model of stress‐optical behaviour. Applications of the simulation methods to the quantitative modelling of the stress‐strain behaviour of poly(dimethyl siloxane) networks and the stress‐optical behaviour of polyethylene networks are described.     

Effects of molecular characteristics and processing conditions on melt‐drawing behavior of ultrahigh molecular weight polyethylene

The effects of molecular characteristics and processing conditions on melt‐drawing behavior of ultrahigh molecular weight polyethylene (UHMW‐PE) are discussed, based on a combination of in situ X‐ray measurement and stress–strain behavior. The sample films of metallocene‐ and Ziegler‐catalyzed UHMW‐PEs with a similar viscosity average MW of ～10⁷ were prepared by compression molding at 180 °C. Stress profiles recorded at 160 °C above the melting temperature of 135 °C exhibited a plateau stress region for both films. The relative change in the intensities of the amorphous scattering recorded on the equator and on the meridian indicated the orientation of amorphous chains along the draw axis with increasing strain. However, there was a substantial difference in the subsequent crystallization into the hexagonal phase, reflecting the molecular characteristics, that is, MW distribution of each sample film. Rapid crystallization into the hexagonal phase occurred at the beginning point of the plateau stress region in melt‐drawing for metallocene‐catalyzed UHMW‐PE film. In contrast, gradual crystallization into the hexagonal phase occurred at the middle point of the plateau stress region for the Ziegler‐catalyzed film, suggesting an ease of chain slippage during drawing. These results demonstrate that the difference in the MW distribution due to the polymerization catalyst system dominates the phase development mechanism during melt‐drawing. The effect of the processing conditions, that is, the including strain rate and drawing temperature, on the melt‐drawing behavior is also discussed. The obtained results indicate that the traditional temperature–strain rate relationship is effective for transient crystallization in to the hexagonal phase during melt‐drawing, as well as for typically oriented crystallization during ultradrawing in the solid state. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2455–2467, 2006     

Molecular rheology of concentrated polymer systems. I

The primitive chain model of Doi and Edwards is generalized to include the short-time relaxation process. Stress relaxation after a sudden imposition of strain is studied in detail. It is shown that in the linear region (small strain) stress relaxation occurs in two steps, the relaxation of chain segments between the fixed entanglement points, and the relaxation of the entanglement points, in accordance with the conventional picture, whereas in the nonlinear region (large strain) there appears a new relaxation process between the above two. The characteristic time of this process is the Rouse relaxation time which the entire chain would have if there were no entanglements, and increases with the square of the molecular weight. This result is consistent with experimental observations.     

Evaluation and modeling of the mechanical properties of graphite nanoplatelets based rubber nanocomposites for pressure sensing applications

Acrylonitrile butadiene rubber (NBR) compounds filled with different concentrations of graphite nanoplatelets were experimentally investigated. The stress–strain curves of the nanocomposites were studied, which suggest good filler–matrix adhesion. The large reinforcement effect of the filler followed the Guth model for non‐spherical particles. The effect of graphite nanoplatelets on the cyclic fatigue and hysteresis was also examined. The loading and unloading stress–strain relationships for any cycle were described by applying Ogden's model for rubber nanocomposites. With this model for incompressible materials, expressions may be developed to predict the stress–strain relationship for any given cycle. The dissipated energy increased with graphite nanoplatelets concentrations and decrease with number of cycles. The rate of damage accumulation becomes marginal after first ten cycles. The rate of damage increases as the amount of graphite nanoplatelets increase into the rubber matrix. Copyright © 2011 John Wiley & Sons, Ltd.     

Nonlinear stress relaxation of an entangled linear polystyrene in single step‐strain flow: A quantitative theoretical investigation

The nonlinear stress relaxation of a nearly monodisperse, moderately entangled polystyrene solution (i.e., roughly seven entanglements per chain at equilibrium) in single step‐strain flow is investigated quantitatively by a detailed comparison of an existing set of experimental data with a simulation based on the tube model. The proposed simulation enables the effects of primary nonlinear relaxation mechanisms other than chain retraction to be identified more clearly and investigated individually. Two peculiar nonlinear relaxation behaviors are observed in this experiment. One is concerned with an apparent enhancement in the stress relaxation at short times, and the other is responsible for a seeming slowdown of the stress relaxation at long times. These findings are discussed within the tube model, in view of the effects of convective constraint release, partial strand extension, and nonaffine deformation. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1281–1293, 2003     

Polyurethanes. IV. Effect of poly(propylene glycol) tacticity on the properties of block copolyether-urethanes

Block copolyèther–urethane–ureas containing isotatic polypropylene glycols were synthesized and their dynamic mechanical properties compared to the analogous atactic structures. At poly(propylene glycol) molecular weights below 1000, tacticity appears to have little effect on the stress–strain properties of the block copolymers. At higher molecular weights, the ability of the isotatic polyglycol segments to crystallize under strain can effect cyclic deformation properties.     

Cold,warm, and hot programming of shape memory polymers

In this article, programming is classified as hot, warm, and cold, based on the temperature zone within which the programming is conducted. The strain and stress locking and releasing mechanisms are discussed within the thermodynamics framework. A new formula is developed for quantifying the strain recovery ratio of cold-programmed SMPs. Stress fixity ratio and stress recovery ratio are also defined based on the understanding of stress locking and recovery mechanisms. State-of-the-art literature on warm and cold programming is reviewed. Well-controlled programming as well as free strain recovery test and constrained stress recovery test are conducted, in order to validate the memory mechanisms discussed in this study. It is found that, while programming temperature has an insignificant effect on the final free shape recovery, it has a significant effect on the stress recovery. The recovery stress programmed by cold programming may be lower, equal to, or higher than that by hot programming, due to the different stress locking mechanisms and other factors such as damage during the thermomechanical cycle. Cold, Warm, and Hot Programming of Shape Memory Polymers © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 1319–1339     

The mechanism and a slip model for the initial plastic deformation of amorphous polyethylene under uniaxial tension

The mechanical behaviors of a polyethylene (PE) bulk consisting of amorphous molecular chains under uniaxial tension have been explored using molecular simulations. The stress–strain relationship and the plastic deformations of the PE bulk have been analyzed. Two deformation stages were found in the stress–strain curve, the elastic stage with a straight linear part of the curve and the plastic stage with a flat sawtooth‐like part. The Young's modulus calculated from the elastic part is in good agreement with experimental results. Some key parameters such as the energy variations in different terms reveal that the interchain slip should be chiefly responsible for the initial plastic deformations of amorphous PE under uniaxial tension. In order to address how this slip influences the plastic deformations, the mechanical details of a single chain have been elucidated when it was pulled out from two PE clusters consisting of regular and amorphous chains, respectively. The interchain slip, found as the basic movement style, is responsible for the movement of the stretched chain. Both the critical slip force and the critical slip length have been found in these two cases. For the straight chain pulled out from the cluster with regular chains, the critical slip force is about 1.81 nN and the critical slip length is about 40 polymerization degrees. While for the chain in the amorphous cluster, the critical force is about 0.86 nN and the critical length is almost the same. Based on the simulation results, a meso slip model has been deduced to explain the behaviors of the amorphous PE bulk under uniaxial tension. With reference to the slip model of single crystals and polycrystals a constitutive relation was obtained by considering the Young's modulus, the equivalent slip stress and the average orientation parameters of each chain. The comparison of the results from the constitutive relation and the simulations proves that this model does well in predicting the mechanical behaviors of amorphous PE under uniaxial tension in general. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 986–998     

Manipulation of mechanical properties of short pineapple leaf fiber reinforced natural rubber composites through variations in cross-link density and carbon black loading

The aim of this paper is to demonstrate that the stress–strain behavior of natural rubber reinforced with short pineapple leaf fiber (PALF) can easily be manipulated by changing the cross-link density and the amount of carbon black (CB) primary filler. This gives more manageable control of mechanical properties than is possible with conventional particulate fillers alone. This type of hybrid rubber composite displays a very sharp rise in stress at very low strains, and then the stress levels off at medium strains before turning up again at the highest strains. The composites studied here contain a fixed amount of PALF at 10 part (by weight) per hundred rubber (phr) and varying carbon black contents from 0 to 30 phr. To change the cross-link density, the amount of sulfur was varied from 2 to 4 phr. Swelling ratio results indicate that composites prepared with greater amounts of sulfur and carbon black have greater cross-link densities. Consequently, this affects the stress–strain behavior of the composites. The greater the cross-link density, the less is the strain at which the stress upturn occurs. Variations in the rate of stress increase (although not the stress itself) in the very low strain region, while dependent on fillers, are not dependent on the crosslink density. The effect of changes in crosslinking is most obvious in the high strain region. Here, the rate of stress increase becomes larger with increasing cross-link density. Hence, we demonstrate that the use of PALF filler, along with the usual carbon primary filler, provides a convenient method for the manipulation of the stress–strain relationships of the reinforced rubber. Such composites can be prepared with a controllable, wide range of mechanical behavior for specific high performance engineering applications.     

Deformational,swelling, and potentiometric behavior of ionized poly(methacrylic acid) gels. II. Experimental results

The deformational, swelling, and potentiometric behavior of poly(methacrylic acid) gels was measured as a function of the degree of crosslinking, ionic strength, and degree of ionization. The comparison of the stress–strain behavior with theoretical relations derived in the preceding part has shown that the relations are valid only if an increase is assumed in the number of monomeric units in the statistical chain segment with increasing degree of neutralization of the gel. This dependence is affected by the salt content in the swelling solution and is also dependent on the activity coefficient of counterions. The pK₀ values for an undissociated gel approach pK₀ = 5.0 and increase somewhat with degree of neutralization. The swelling equilibria are in qualitative agreement with theoretical assumptions; their quantitative agreement depends on the activity coefficient of counterions.     

Effect of chain entanglements on plastic deformation behavior of ultra‐high molecular weight polyethylene

Samples of ultra‐high molecular weight polyethylene, in which the chain topology within the amorphous component was altered using two‐stage processing, including crystallization at high pressure in the first step, were produced and their deformation behavior in the plane‐strain compression was studied. Deformation and recovery experiments demonstrated that the state of the molecular network governed by entanglement density is one of the primary parameters controlling the response of the material on the imposed strain, especially at moderate and high strains. Any change in the concentration of entanglements markedly influences the shape of the true stress–true strain curve. The strain hardening modulus decreases while the onset of strain hardening increases with a decrease of the entanglement density within the amorphous component. Density of entanglements also influences the amount of rubber‐like recoverable deformation and permanent plastic flow. In material of the reduced concentration of entanglements permanent flow appears easier and sets in earlier than in the material with a higher entanglement density, becoming a favorable deformation mechanism at moderate strains. As a result, strong strain hardening is postponed to higher strain when compared with the samples of equilibrium entanglement density. In the samples of an increased entanglement density the molecular network becomes stiffer, with a reduced ability of strain induced disentangling of chains. Consequently, there is a less permanent flow and strain hardening begins earlier than in the reference material of an unaltered chain topology. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 276–285, 2010     

Tensile properties of ultradrawn polyethylene

High-density polyethylene filaments prepared by a solid-state deformation in an Instron capillary rheometer show unusually high crystal orientation, chain extension, axial modulus, and ultimate tensile strength. The Young's modulus and ultimate tensile strength have been determined from stress–strain curves. Gripping of this high modulus polyethylene has been a problem heretofore, but the measurement of ultimate tensile strength has now been made feasible by a special gripping procedure. Tensile moduli show an increase with sample preparation temperature and pressure. Values as high as 6.7 × 10¹¹ dyne/cm² are obtained from samples extruded at 134°C and 2400 atm and tested at a strain rate of 3.3 × 10^?4 sec^?1. The effect of strain rate and frequency on modulus has also been evaluated by a combination of stress–strain data and dynamic tension plus sonic measurements over nine decades of time.