Strain hardening in glassy polymers: Influence of network density on elastic and viscous contributions

In this study, the rate‐ and temperature‐dependent strain hardening and the Bauschinger effect is studied for three glassy polymers. It appeared that for all materials, an equal distribution of elastic and viscous hardening was necessary to accurately predict the Bauschinger effect, as well as the rate‐ and temperature‐dependent strain hardening response. As for the elastic contribution, the viscous contribution appears to increase with an increase in entanglement network density. Investigating the effect of temperature on the Bauschinger effect revealed that at elevated temperatures the model predictions are not accurately enough. It is shown that this is caused by the magnitude of the elastic hardening contribution; to improve the predictions, a temperature‐dependent elastic contribution is necessary. © 2019 The Authors. Journal of Polymer Science Part B: Polymer Physics published by Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019, 57, 1001–1013     

Strain-hardening modulus of cross-linked glassy poly(methyl methacrylate)

The strain hardening modulus, defined as the slope of the increasing stress with strain during large strain uniaxial plastic deformation, was extracted from a recently proposed constitutive model for the finite nonlinear viscoelastic deformation of polymer glasses, and compared to previously published experimental compressive true stress versus true strain data of glassy crosslinked poly(methyl methacrylate) (PMMA). The model, which treats strain hardening predominantly as a viscous process, with only a minor elastic contribution, agrees well with the experimentally observed dependence of the strain hardening modulus on strain rate and crosslink density in PMMA, and, in addition, predicts the well-known decrease of the strain hardening modulus in polymer glasses with temperature. General scaling aspects of continuum modeling of strain hardening behavior in polymer materials are also presented. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 1464–1472, 2010     

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     

Strain hardening and its relation to Bauschinger effects in oriented polymers

The nature of strain hardening in glassy polymers is investigated by studying the mechanical response of oriented polycarbonate in uniaxial extension and compression. The yield stress in extension is observed to increase strongly with predeformation, whereas it slightly decreases in compression (the so-called Bauschinger effect). Moreover, oriented specimens tend to display increased strain hardening in extension, whereas this nearly vanishes in compression. It is shown that these observations can be captured by the introduction of a viscous contribution to strain hardening in terms of a deformation dependence of the flow stress. This can originate either from a deformation-induced change in activation volume, as observed for isotactic polypropylene, or from a deformation-induced change of the rate constant, as observed for polycarbonate, which causes the room temperature yield kinetics of this material to shift from the α into the (α+β) regime. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 1483–1491, 2010     

Does the strain hardening modulus of glassy polymers scale with the flow stress?

Using a generic coarse‐grained bead‐spring model, Hoy and Robbins reproduced important experimental observations on strain hardening, specifically the generally observed Gaussian strain hardening response and its dependence on network density and temperature. Moreover, their simulation results showed that the strain hardening response at different strain rates collapses to a single curve when scaled to the value of the flow stress, a phenomenon that has not yet been verified experimentally. In the present study, the proposed scaling law is experimentally investigated on a variety of polymer glasses: poly(methyl methacrylate), poly(phenylene ether), polycarbonate, polystyrene, and poly(ethylene terephthalate)‐glycol. For these polymers, true stress–strain curves in uniaxial compression were collected over a range of strain rates and temperatures and scaled to the flow stress. It was found that, generally, the curves do not collapse on a mastercurve. In all cases, the strain hardening modulus is observed to increase linearly, but not proportionally to the flow stress. The experimental data, therefore, unambiguously demonstrate that the proposed scaling law does not apply within the range of temperature and strain rate covered in this study. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 2475–2481, 2008     

Why is understanding glassy polymer mechanics so difficult?

In this Perspective, I describe recent work on systems in which the traditional distinctions between (i) unentangled versus well‐entangled systems and (ii) melts versus glasses seem least useful, and argue for the broader use in glassy polymer mechanics of two more dichotomies: systems which possess (iii) unary versus binary and (iv) cooperative versus noncooperative relaxation dynamics. I discuss the applicability of (iii–iv) to understanding the functional form of strain hardening. Results from molecular dynamics simulations show that the “dramatic” hardening observed in densely entangled systems is associated with a crossover from unary, noncooperative to binary, cooperative relaxation as strain increases; chains stretch between entanglement points, altering the character of local plasticity. Promising approaches for future research along these lines are discussed. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Strain hardening of polycarbonate in the glassy state: Influence of temperature and molecular weight

This study is concerned with the temperature and molecular weight dependence of the strain-hardening behavior of polycarbonate. It is shown that the strain-hardening modulus reduces with increasing temperature and decreasing molecular weight. This result is interpreted in terms of temperature accelerated relaxation of the entanglement network. Moreover, it is shown that frozen-in orientations, induced by homogeneous deformations above the glass transition temperature, lead to anisotropic yield behavior that can be fully rationalized (and modelled) in terms of a superimposed stress contribution of the prestrained network. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2041–2049, 2004     

Relationship of deformation behavior to thermal transitions of ethylene/styrene and ethylene/octene copolymers

The stress‐strain response of low‐crystallinity ethylene‐octene (EO) and ethylene‐styrene (ES) copolymers with 7–20 mol % comonomer was compared over a temperature range that spanned the glass‐transition and crystal melting regions. Above the onset temperature of the glass transition, the copolymers exhibited elastomeric behavior with low initial modulus, uniform deformation to high strains, and high recovery after the stress was released. In the glass‐transition range, an initial low‐stress elastomeric response was followed by a distinct “bump” in the stress‐strain curve. On the basis of the temperature and rate dependence of the stress‐strain curve, local strain‐rate measurements, local temperature changes, and recovery characteristics, the “bump” was identified as high strain yielding. Hence, the stress‐strain curve sequentially exhibited the features of elastomeric and plastic deformation. Following high strain yielding, strain hardening dramatically increased the fracture strength. This behavior was defined as elastomeric‐plastic. Elastomeric‐plastic behavior in the broad glass‐transition range constituted a gradual transition from elastomeric behavior at higher temperatures to low‐temperature plastic behavior with high modulus and macroscopic necking. Because of the lower glass‐transition temperature of EO, ?40 °C as compared with ?10 °C for ES, the onset of elastomeric‐plastic behavior occurred at a significantly lower temperature. The concept of a network of flexible chains with fringed micellar crystals serving as the multifunctional junctions that provides the structural basis for elastomeric behavior of low‐crystallinity ethylene copolymers was extended to elastomeric‐plastic behavior by considering a network with a fraction of rigid, glassy chains. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 40: 142–152, 2002     

Mechanical properties of Nafion and titania/Nafion composite membranes for polymer electrolyte membrane fuel cells

Measurements of the mechanical and electrical properties of Nafion and Nafion/titania composite membranes in constrained environments are reported. The elastic and plastic deformation of Nafion‐based materials decreases with both the temperature and water content. Nafion/titania composites have slightly higher elastic moduli. Thecomposite membranes exhibit less strain hardening than Nafion. Composite membranes also show a reduction in the long‐time creep of ～40% in comparison with Nafion. Water uptake is faster in Nafion membranes recast from solution in comparison with extruded Nafion. The addition of 3–20 wt % titania particles has minimal effect on the rate of water uptake. Water sorption by Nafion membranes generates a swelling pressure of ～0.55 MPa in 125‐μm membranes. The resistivity of Nafion increases when the membrane is placed under a load. At 23 °C and 100% relative humidity, the resistivity of Nafion increases by ～15% under an applied stress of 7.5 MPa. There is a substantial hysteresis in the membrane resistivity as a function of the applied stress depending on whether the pressure is increasing or decreasing. The results demonstrate how the dynamics of water uptake and loss from membranes are dependent on physical constraints, and these constraints can impact fuel cell performance. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2327–2345, 2006     

Large deformations in oriented polymer glasses: Experimental study and a new glass-melt constitutive model

An experimental study was made of the effects of prior molecular orientation on large tensile deformations of polystyrene in the glassy state. A new hybrid glass-melt constitutive model is proposed for describing and understanding the results, achieved by parallel coupling of the ROLIEPOLY molecularly-based melt model with a model previously proposed for polymer glasses. Monodisperse and polydisperse grades of polystyrene are considered. Comparisons between experimental results and simulations illustrate that the model captures characteristic features of both the melt and glassy states. Polystyrene was stretched in the melt state and quenched to below T_g, and then tensile tested parallel to the orientation direction near the glass transition. The degree of strain-hardening was observed to increase with increasing prior stretch of molecules within their entanglement tubes, as predicted by the constitutive model. This was explored for varying temperature of stretching, degree of stretching, and dwell time before quenching. The model in its current form, however, lacks awareness of processes of subentanglement chain orientation. Therefore, it under-predicts the orientation-direction strain hardening and yield stress increase, when stretching occurs at the lowest temperatures and shortest times, where it is dominated by subentanglement orientation. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 1449–1463, 2010     

Mechanical behavior of films of miscible polyamide 6/polyamide 6I‐6T blends

The deformation behavior of miscible PA6/aPA blends films under uniaxial and biaxial tensile drawing has been investigated in relation to blend composition. Whatever be the composition, the initial crystalline structure is ill‐ordered and no evidence of spherulitic morphology was shown. At temperatures beyond the activation of the viscoelastic α relaxation, a ductility improvement upon addition of aPA has been revealed in both uniaxial and biaxial stretching. The decrease in the yield stress with increasing aPA content mainly originates from the reduction in crystal fraction. Regarding the observed evolution in ultimate drawability and strain hardening upon addition of aPA, the latter component of the blend is considered to act as a diluent of the macromolecular network, and the experimental data are fairly well accounted for according to Graessley's theory. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1690–1701, 2006     

The influence of molten fraction on the uniaxial deformation behavior of polypropylene: Real time mechano‐optical and atomic force microscopy observations

In this study, we have coupled the real time mechano‐optical measurements with the off‐line structural characterization techniques including AFM, WAXS, and DSC to establish the quantitative relationships between the “true mechano‐optical behavior and developed morphology” as influenced by the fraction of molten phase present in the polypropylene films. Stretching PP in the solid state invariably leads to formation of fibrillar texture. The evolution of surface morphology in partially molten state was found to depend on the fraction of the molten phase present at the start of the deformation. If the samples are strained past the yielding in partially molten state, the birefringence begins a rapid rise. Concurrent with this, the equatorial zones of the spherulites begin to crack while meridional regions remaining intact. This leads to temporary reduction of crystallinity because of destruction of some of the crystals. If held in this strained state, the crystallite thickening was observed while the birefringence increases while the lost crystallinity is recovered. If the films are strained past the strain hardening point, the microfibrillar structure was found to dominate the surface morphology. When the films are stretched in the melting temperature range, they exhibit substantial nodular surface topology. These nodules that were absent in the solid state deformed samples are hard lamellae buried inside amorphous “soft matter”. The tangential lamellae increasingly become dominant as the processing temperature approaches substantially molten state leading to the observation of a* oriented crystallites in the X‐ray analysis. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 925–941, 2006     

Rheological properties of linear and crosslinked polymer blends: Relation between crosslink density and enhancement of elongational viscosity

Strain‐hardening behavior in the elongational viscosity of binary blends composed of a linear polymer and a crosslinked polymer, in which the molecular chains of the linear polymer were incorporated into the network chains of the crosslinked polymer, was studied. Blending the crosslinked polymer characterized as the gel just beyond the sol–gel transition point greatly enhanced the strain‐hardening behavior in the elongational viscosity, even though the amount of the crosslinked polymer was only 0.3 wt %. However, the crosslinked polymer, which was far beyond or below the sol–gel transition point, had little influence on the elongational viscosity as well as the shear viscosity. The stretching of the chain sections between the crosslink points was responsible for the strain‐hardening behavior. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 228–235, 2001     

Monte Carlo simulation of diffusion effects on chain‐extension reactions

The diffusion effects on chain‐extension reactions using carboxyl‐terminated polyamide‐12 as a model reactant with bisoxazolines were investigated by the stochastic Monte Carlo method. Thus, complicated direct modeling and numerical calculations were avoided. The chain‐length dependence and detailed diffusive behavior were discussed in depth. The diffusion effects retarded the progress of chain‐extension reactions and led to lower coupling efficiency. The simulated results indicated that the diffusion effects could make the final molecular weight distributions wider. In the presence of diffusion and with the progress of the coupling efficiency, peaks in the evolution curves of the weight‐average molecular weight and valleys in the evolution curves of the polydispersity index were observed, respectively, when the coupling efficiency was low enough. These phenomena were different from those without diffusion effects and were analyzed in detail. The critical entanglement chain length had strong effects on the simulated results of the diffusion effects, especially when its value was near the average chain length. The results also showed that the effects of the reactant degradation made the molecular weight distribution of the reaction system wider and weakened the diffusion effects on the coupling reaction. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2902–2911, 2006     

Rheological properties and foam processability for blends of linear and crosslinked polyethylenes

The effect of blending crosslinked linear low‐density polyethylene (cLLDPE) on the rheological properties and foam processability of linear low‐density polyethylene was studied. A small addition of cLLDPE, which had a low density of crosslink points, enhanced strain‐hardening behavior in the elongational viscosity to a great degree, although it had little effect on the steady‐state shear viscosity. The enhanced strain hardening reduced heterogeneous deformation during foaming. As a result, a foam with a uniform cell size distribution was obtained. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2159–2167, 2001     

Effect of homopolymer solubilization on triblock gel structure and mechanical response

The linear modulus, swelling behavior, and high strain response of a set of well-characterized model triblock gels were investigated to understand the effect of homopolymer solubilized within the micelle core on gel structure and mechanical properties. Structural parameters were obtained from small-angle X-ray scattering (SAXS) as well as from self-consistent field theory (SCFT) calculations. Experimental results are compared with Neo-Hookean and exponentially strain hardening models for gel behavior and rigid filler effects are discussed. The main conclusion is that the addition of homopolymer to the micelle core increases the chain stretching in both the core and coronal blocks. The total extension of a chain for a given external load is fixed by its length; however, the initial prestretch imparted to the chain due to micellization changes with the size of the micelle core and can greatly reduce the amount of extension observed for a given external force. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 1395–1408, 2010     

Synthesis and characterization of polylactides with different branched architectures

Star‐shaped and comb‐like poly(L‐Lactide)s (PLA) are produced by employing multifunctional initiators, and hyperbranched structure is prepared using a cyclic co‐monomer with hydroxyl group. FTIR, size exclusion chromatography, and H‐NMR techniques are employed to characterize the synthesized polymers, validating the formation of desired structures with chain lengths above the critical length for entanglement. After characterization of the synthesized polymers, the effect of branching on PLA properties is investigated by comparing the crystallization and rheological behavior of branched PLAs to those of a linear commercial grade. Differential scanning calorimetry and optical microscopy observations reveal a remarkable improvement in PLA crystallization due to the nucleation role of branching points. Moreover, synthesized polylactides exhibit strain hardening behavior during elongational viscosity measurements by a sentmanat extension rheometer platform. Significant improvements in crystallization and elongational rheology behavior of the synthesized polymers support the achievement of branched polymer structures. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 522–531     

Poly(dimethylsiloxane)‐based polymer organogelators with L‐lysine derivatives as a organogelation‐causing segment

New poly(dimethylsiloxane)‐based polymer organogelators with L ‐lysine derivatives were synthesized on the basis of synthetically simple procedure, and their organogelation abilities were investigated. These polymer organogelators have a good organogelation ability and form organogels in many organic solvents. In the organogels, polymer gelators constructed a mesoporous structure with a pore size of about 1 μm formed by entanglement of the self‐assembled nanofibers. The L ‐lysine derivatives in the polymer gelators functioned as a gelation‐causing segment and the organogelation was induced by self‐assembly of the L ‐lysine segments through a hydrogen bonding interaction. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 3817–3824, 2006     

Deformable strain sensors based on patterned MWCNTs/polydimethylsiloxane composites

Patterned MWCNT/polydimethylsiloxane (PDMS) nanocomposite strain sensors were achieved by a microelectromechanical system assisted electrophoretic deposition (EPD) technique. With the combined effect of superior intrinsic piezoresistivity of the individual MWCNT and the tunneling effect of the MWCNT network, the stretchable composite demonstrates high sensitivity to the tensile strain. The gauge factor shows a strong dependence on both the initial resistance of the CNT/PDMS composite and the applied strain level. The mechanism is elucidated by analyzing the structure‐property‐function of patterned CNT networks. When the entanglement of a MWCNT network allows effective load transfer, the sensitivity is primarily dominated by the intrinsic piezoresistivity of individual MWCNTs. Conversely, when the MWCNTs interpenetrate loosely, the tunneling effect prevails. The sensitivity of the device can be tailored by the proposed technique since MWCNT film thickness/density can be readily controlled by means of the patterning parameters of the EPD process. The work provides useful guidance for design and development of strain/stress sensors with targeted sensitivity for flexible electronics applications. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2013 , 51, 1505–1512