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     

液压油浸泡对丁腈橡胶动态性能和循环变形的影响

研究液压油浸泡对丁腈橡胶(NBR)动态性能和循环变形的影响。结果表明,液压油浸泡前后NBR的分子结构无明显变化,随着浸泡时间延长,NBR的玻璃化温度升高,动态模量和棘轮应变增大且初期变化明显,粘性变化不大。因此,在设计和使用过程中需考虑NBR构件在液压油浸泡环境下的性能变化。     

The effect of strain rate on the viscoplastic behavior of isotactic polypropylene at finite strains

Two series of uniaxial tensile tests are performed on isotactic polypropylene with the strain rates ranging from 5 to 200 mm/min. In the first series, injection-molded specimens are used without thermal pre-treatment. In the other series of experiments, the samples are annealed for 51 h at 160 °C prior to testing.A constitutive model is developed for the viscoplastic behavior of isotactic polypropylene at finite strains. A semicrystalline polymer is treated as equivalent heterogeneous network of chains bridged by permanent junctions (physical cross-links and entanglements). The network is thought of as an ensemble of meso-regions connected with each other by links (lamellar blocks). In the sub-yield region of deformations, junctions between chains in meso-domains slide with respect to their reference positions (which reflects sliding of nodes in the amorphous phase and fine slip of lamellar blocks). Above the yield point, the sliding process is accompanied by displacements of meso-domains in the ensemble with respect to each other (which reflects coarse slip and fragmentation of lamellar blocks). To account for alignment of disintegrated lamellar blocks along the direction of maximal stresses (which is observed as strain-hardening of specimens in the post-yield regions of deformations) elastic moduli are assumed to depend on the principal invariants of the right Cauchy-Green tensor for the viscoplastic flow.Stress-strain relations for a semicrystalline polymer are derived by using the laws of thermodynamics. The constitutive equations are determined by five adjustable parameters that are found by matching observations. Fair agreement is demonstrated between the experimental data and the results of numerical simulation. A noticeable difference is revealed between the mechanical responses of non-annealed and annealed specimens: (i) necking of samples not subjected to thermal treatment precedes coarse slip and fragmentation of lamellar blocks, whereas cold-drawing of annealed specimens up to a longitudinal strain of 80% does not induce spatial heterogeneity of their deformation; (ii) the elastic modulus increases with the strain rate for non-annealed specimens and decreases for annealed samples.     

The effects of temperatures and volumetric expansion on the diffusion of fluids through solid polymers

This study examines moisture sorption behaviors of two glassy polymers, epoxy and vinylester, immersed in different fluids at two temperatures below the glass transition temperatures of the polymers. The main purpose of this study is to understand the effect of volume‐dependent temperatures and deformations on the diffusion process of solid polymers. Diffusivity coefficients are first determined by assuming the diffusion to follow the classical Fickian diffusion. In some cases, moisture sorption led to quite significant changes of volume, and the diffusion process cannot be well described by the Fickian diffusion. In such situation, the coupled deformation–diffusion model for linear elastic isotropic materials presented by Gurtin 1 is adopted, as a first approximation. This coupled deformation‐diffusion model reduces to a Fickian diffusion model when the coupling parameters are absent and the volume changes in the solid polymers during diffusion are negligible. A finite difference method is used in order to solve for the coupled deformation‐diffusion model. The model is used to predict the one‐dimensional moisture diffusion in thin plates and the multiaxial three‐dimensional moisture diffusion in dogbone specimens. The multiaxial diffusion in the dogbone specimens is used to validate the calibrated material parameters from the standard thin plate diffusion characterization. © 2017 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2017 , 134, 45151.     

Damage in large scale solid state deformation of thermoplastic polymers at elevated temperatures and varying strain rates

Abstract

A key factor which limits the production speed of the polymer die drawing process is the premature fracture of the material on exit from the die. In this paper, the growth of damage in the material during the die drawing process has been studied using a combination of thermoplastic finite element analysis and structural characterisation by means of scanning electron microscopy and small angle X-ray scattering for the specific case of die drawing of polyoxymethylene. It is demonstrated that special profiled dies offer a more beneficial strain rate distribution than the conventional conical dies and allow higher production speeds to be obtained. Voids grow in the material as a result of the tensile stresses pertaining near the die exit and then, crazes appear from within the material at a critical stress level leading ultimately to final fracture. The results suggest that although the crazes initiate at a critical stress, the extent of crazing at the maximum draw ratio obtained (～13) is independent of the type of die and hence the stress level. Fracture of the drawn product occurs at different stresses for different die profiles but always at the maximum draw ratio of 13, suggesting that this relates to the limiting extensibility of a molecular network.     

Energy storage during inelastic deformation of glassy polymers

In this paper, aspects of the microstructural state of glassy polymers that evolve during physical ageing and inelastic deformation were studied. Differential scanning calorimetric (d.s.c.) measurements were performed on specimens of three glassy polymers: polystyrene (PS), polycarbonate (PC) and poly(methyl methacrylate) (PMMA). Materials were subjected to both a quenched and a well annealed heat treatment and subsequently deformed in compression to various levels of strain. Stress-strain curves and companion d.s.c. scans were compared.

The well known enthalpy overshoot at T_g was observed for the annealed samples, showing that ageing is accompanied by enthalpy relaxation. The annealed material was also found to require a higher stress to yield, and the additional work required to strain-soften the annealed polymer to the flow stress level of its quenched companion was found to correlate well with the area of the enthalpy overshoot of the annealed specimen.

Inelastic deformation was found to increase the specific enthalpy of both annealed and quenched specimens. In the annealed material, the enthalpy overshoot at T_g was found to decrease with inelastic strain and was completely erased by about −20% strain. Simultaneously, a pre-T_g exotherm was observed to develop with inelastic strain over a wide range of temperature. The pre-T_g exotherm was found to evolve until essentially reaching a steady-state profile at approximately −25% strain. This evolution coincided with the strain-softening phenomenon observed in the corresponding stress-strain results. A pre-T_g exotherm was also found to evolve with straining of the quenched material. Furthermore, the steady-state exotherms of the quenched and annealed materials were found to be nearly identical, as were their corresponding flow stress values after strain softening.

Finally, a second, post-T_g exotherm was found to develop with further straining beyond strains of −25%. This exotherm was found to increase with inelastic strain and coincided with the occurrence of strain hardening (due to chain orientation) in the materials.

The presence of two distinct and separately evolving exotherms in the inelastically deformed polymers indicates the existence of two separate deformation resistances in glassy polymers, one related to the initial yield and strain-softening behaviour, and the other to the orientation-induced strain hardening of the material. The observation that the pre-T_g exotherm is spread over a wide temperature range reflects the distributed nature of the structural state and may be quantified using a distribution in activation energy for the local rearrangements. The results therefore provide valuable information about the processes that must be accounted for in the development of accurate constitutive models of mechanical behaviour.     

Cavitation during deformation of semicrystalline polymers

Cavitation phenomenon is observed during deformation in many semicrystalline polymers above their glass transition temperature. Numerous voids (cavities) both nanometer and micrometer size are formed inside amorphous phase between lamellae during deformation of a polymer. The cavitation is observed only in tension, never during compression or shearing. Most often used methods of voids detection are: microscopies (SEM, TEM, AFM and light microscopy), small angle X-ray scattering and measurements of density. Usually the voids are detected close to yielding or at yielding, strongly suggesting that yielding is often caused by cavitation. However, there is a competition between two processes: breaking of amorphous phase leading to cavitation and plastic deformation of lamellar crystals. Which process occurs first depends on the relation between compliances of those two phases. If the crystals are weak and defected their deformation occurs (mostly by chain slips mechanism) without cavitation. If the crystals in a polymer are thick and more perfect then the barrier for their deformation, represented by shear yielding stress, is increased and the cavitation sets in first and yielding is determined by the stress needed for cavitation. Further deformation involves deformation of crystals due to rapid local change of stress around voids. The influence of different morphological factors: crystal thickness, crystallinity degree, arrangement of crystalline elements (e.g. in spherulites), morphology of amorphous phase (free volume, entanglements, tie molecules) were analyzed. Experimental factors, such as temperature of deformation and rate of deformation influence remarkably the formation of cavities. Cavitation is generated at points where a high local triaxial state of stress is developed. Triaxiality of stress can be amplified by a notch, even very mild notch with large radius of curvature stimulates generation of cavities. Evolution of nano-cavities into micro-cavities and change of their shapes with increasing deformation were evidenced by SAXS. Initially voids are oriented perpendicularly to deformation direction, however, with increasing elongation they become oriented along deformation direction. Stress whitening is visual sign of cavitation and is caused be light scattering either by microvoids or by assemblies of nanovoids.     

Application of an interpenetrating network model to the solid deformation of a quenched isotactic polypropylene film

The molecular orientation and deformation mechanisms of a quenched isotactic polypropylene (iPP) film deformed at temperatures between 303 K and the melting point are studied. At draw temperature T_E less than 400 K where the degree of crystallinity does not change markedly, a linear relationship between molecular orientations of the crystalline and the amorphous phases is revealed and the slope is estimated about 1.82. The interpenetrating network (IPN) model, that takes into account the plastic response of the crystalline (C) network formed by a small portion of crystallites adhered through intercrystalline links and the pseudo-affine deformation of the crystallite enhanced amorphous matrix (CEAM) network, is able to account for inhomogeneous deformation behavior on the mesoscale accompanied with the localized necking in this T_E range. Meanwhile, the initial Young's modulus and the true yield stress exerted by the deformation of the rigid C network exhibit the Arrhenius type of dependence on T_E. The apparent shear modulus of the CEAM network as a function of T_E is discussed in relation to variations in numbers and average molecular weights of the crystalline and the amorphous sequences being manifested by small consecutive endothermic and exothermic peaks in the DSC curve. The IPN model becomes invalid for deformations above T_E=400 K where morphological changes are induced due to melting of crystallites as proved from the DSC measurement.     

Dilatometric studies of polymers undergoing high and low rate tensile deformation

Specific volume change and stress-strain data were obtained simultaneously during tensile deformation on several plastics known to be resistant to impact loading. Tensile deformation rates of 20 percent/minute and 10⁶ percent/minute and temperatures of ?190° to 55°C were employed. A common sequence of deformation modes was observed in all materials studied (rubber modified acrylics and styrene, ABS materials, polycarbonate, impact grade polypropylenes, and high density polyethylene). In all cases the major mode of deformation to failure at low rates and/or higher temperatures is volume conserving and primarily a shear flow process. At higher rates of deformation or lower temperatures, a transition occurs and the specific volume of the material increases in direct proportionality to the tensile strain above the apparent yield point. Volume increases of 17 to 50% were observed and these were equal to 85 percent or more of the observed tensile strain at failure. These observations indicate that microcavitation may be the major process available for the absorption of mechanical energy at impact rates in plastic materials.     

Investigation of nonelastic response of semicrystalline polymers at high strain levels

The nonelastic behavior at high strains of three semicrystalline polymers [i.e., nylon‐6, poly(ethylene terephthalate), and poly(ethylene 2,6‐naphthalenedicarboxylate] was investigated. For all materials, room temperature tensile strain recovery tests revealed the existence of two components of nonelastic deformation: a fast‐relaxing component (called anelastic) and a slow‐relaxing component (usually called plastic). A strain recovery master curve could be constructed for each material from the strain recovery data obtained at various temperatures. The shift factors versus temperature relationship for the strain recovery master curves allowed us to evaluate an activation energy for the nonelastic strain recovery process. These data were then compared with the activation energy for the glass‐transition process evaluated by dynamic mechanical measurements at low strain. The aim of this comparison was to investigate the influence of viscoelasticity on the nonelastic deformation recovery. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 78: 1664–1670, 2000     

Cyclic voltammetry studies of n-type polymers with non-alternant fluoranthene units

Poly(p-fluoranthenevinylenes) and their dithiocarbamate precursors have been deposited on indium-tin oxide electrodes and electrochemical properties of the obtained films have been investigated by means of cyclic voltammetry studies in acetonitrile solutions containing 0.1 M (n-C₄H₉)₄NBF₄ as supporting electrolyte. It has been found that all investigated polymers display well pronounced n-doping processes. Electrochemical reduction of the dithiocarbamate precursors seems to be associated with C-S bond cleavage with elimination of -SC(S)N(C₂H₅)₂ group. In view of UV-vis spectroscopic data the obtained products, tentatively identified as polymers containing fluoranthene units connected by -CH₂-CH₂- bridges, are somewhat less conjugated than the corresponding poly(p-fluoranthenevinylenes). Reversible electrochemical reduction of poly(p-fluoranthenethanes) occurs at potentials only somewhat (ca. 0.1 V) more negative as found for their poly(p-fluoranthenevinylenes) analogues suggesting relatively weak coupling between fluoranthene kernels in both kinds of investigated polymers.     

Plastic deformation and damage of polyoxymethylene in the large strain range at elevated temperatures

The deformation behaviour of polyoxymethylene has been studied in plane strain compression at temperatures from 120 °C up to 165 °C and in uniaxial tension and simple shear at 160 °C for strain rates from 10⁻⁴ to 1 s⁻¹. In uniaxial tension the stress-strain behaviour was determined by a novel video-controlled testing system. The measurements showed that there was a very significant evolution of volumetric strain, indicating that damage mechanisms play a key role in the plastic deformation behaviour.All tests showed similar deformation stages with a short region of visco-elastic behaviour followed by a rounded yield point. The von Mises equivalent yield stress for these tests showed a linear relationship with logarithmic strain rate, suggestive of an Eyring type thermally activated process. After yielding, all stress-strain curves showed a long plastic deformation regime, which in shear occurred at constant stress. In plane strain compression there was also only a very small increase in stress, in contrast to uniaxial tension where very significant strain hardening was observed at high strains, which is attributed to the onset of structural changes.     

Analytical melting model for extrusion: Melting rate of fully compacted solid polymers

The melting mechanism inside screw extruders is presently analyzed using numerical, iterative methods that are too complex to be used widely by practicing engineers. Our theoretical and experimental investigations of the melting mechanism have produced simple, analytical equations for predicting the melting rate of fully compacted solid polymers without iterative calculations. The accuracy of these equations was found to be satisfactory. Consideration of the temperature and shear dependencies of the melt viscosity was found to be essential for the accurate prediction of the melting rate.     

Characterization of volume strain at large deformation under uniaxial tension in high-density polyethylene

The intensity and origin of volume changes under uniaxial tension is investigated at room temperature in high-density polyethylene samples with a large initial degree of crystallinity. At the macroscopic scale, volume strain is defined as the trace of the finite strain tensor whose components are recorded in situ by means of a 2D video extensometer within a representative volume element situated at the center of the neck. At the microscopic scale, volume strain is ascribed to the competition of cohesive mechanisms and non-cohesive mechanisms. The former are associated both to the packing of oriented chains in the amorphous phase (compaction) and to the decrease of crystallinity (dilatation), as characterized by wide-angle X-ray diffraction analysis. The latter are due to the development of crazes and voids (dilatation) while the spherulitic morphology is progressively transformed into a highly fibrillated structure, as revealed by scanning electron microscopy. Detailed evaluation of the relative importance of these two classes of mechanisms shows that they compensate nearly exactly at moderate strains, so that volume strain is very small in the first stage of the tensile tests. By contrast, the effect of cavitation becomes prominent at large deformation, so that the overall dilatation reaches more than 30% before rupture. It is demonstrated that volume strain measurements obtained from mechanical testing and from microstructural investigation agree fairly satisfactorily.     

The effects of thermomechanical history and strain rate on antiplasticization of PVC

Antiplasticization is mechanically characterized by an increase in the polymer stiffness and/or yield strength upon the incorporation of a small amount of a low-molecular weight diluent. It is attributed to hindrance of the local β-relaxation motions of the polymer. Here, we have studied the effects of thermal treatment, plastic deformation, and strain rate on the antiplasticization of the yield stress of a 95 wt% poly(vinyl chloride)/5 wt% dioctyl phthalate (PVC/5 wt% DOP) compound. Two thermal treatments were applied to the materials - cooling to room temperature from above T_g by a quench or by a slow oven-cool anneal. When compressed at low to moderate strain rates, antiplasticization was observed in the annealed (physically aged) PVC/5 wt% DOP but not in the quenched (unaged) PVC/5 wt% DOP. Load-unload-reload compression cycles revealed that antiplasticization can be erased by plastic strain; the anomalously high yield stress of PVC/5 wt% DOP observed in the first load cycle softens to a value lower than that of the neat PVC in subsequent cycles. The results indicate that disordered, high free volume microstructural states, obtained either from thermal quenching or from plastic straining, liberate the beta motions of the PVC molecule which, in turn, erase antiplasticization of the yield stress. Earlier work on the rate-dependence of yield has demonstrated that beta motions must be stress-activated in order to yield neat PVC when deformed at high strain rates (>100/s). Hence, we have characterized the rate-dependence of the antiplasticization of the yield stress by testing the annealed materials in uniaxial compression over a wide range of strain rates (10⁻⁴/s-3000/s). Antiplasticization was observed in PVC/5 wt% DOP in the low strain rate regime where beta motions are free in neat PVC but hindered in PVC/5 wt% DOP; however, the antiplasticization (elevation of yield stress) gradually diminished with increasing strain rate.     

Prediction of the relationship between the rate of deformation and the rate of stress relaxation in glassy polymers

Kim, et al. (Polymer, 54(15), 3949, 2013) recently reported on the unexpected relaxation behavior of an amorphous polymer in the T_g-region, where the rate of stress relaxation increased with deformation at a strain rate of 1.5 × 10⁻⁴ s⁻¹ but decreased at a strain rate of 1.2 × 10⁻⁵ s⁻¹. This inversion in the ordering with strain rate challenges the underlying structure of the existing nonlinear viscoelastic and viscoplastic constitutive models, where the key nonlinearity is a deformation dependent material clock. The nonlinear stress relaxation predictions of a recently developed stochastic constitutive model, SCM, (Medvedev, et al., J. Rheology, 57(3), 949, 2013) that acknowledge dynamic heterogeneity of the glass have been investigated. The SCM predicts the inversion in the ordering of the mobility with the loading strain rate as reported by the stress relaxation response. The change in perspective on the nonlinear viscoelastic behavior of glassy polymers engendered by the SCM is discussed.     

In-situ SAXS study of the mesoscale deformation of polyethylene in the pre-yield strain domain: Influence of microstructure and temperature

The deformation of polyethylene spherulites at the scale of the lamellar stackings is investigated by in-situ SAXS as a function of draw temperature in comparison with the macroscopic strain. Local elongation strain in equatorial region and local compressive transverse strain in polar region both increase in absolute value and follow linear relations versus macroscopic strain in the visco-elastic range. However, local strains turn out heterogeneous over the whole spherulite volume. This is attributed to the different type of mechanical coupling between the crystalline lamellae and the amorphous layers in the polar and equatorial regions. Increasing the temperature in the range 50–100 °C gradually promotes homogeneous distribution of strain at the local scale. The origin of this phenomenon is discussed in terms of activation of the chain mobility in the crystalline phase that modifies the mechanical coupling between the two phases. This ratio between local and macroscopic deformation increases with temperature up to the macroscopic value.     

Strength and deformation of rigid polymers: structure and topology in amorphous polymers

Glassy polymer is formed because the irregular chain architecture prevents crystallisation. Computer simulations allow Voronoi tessellation of atomic groups (for example monomers) to be carried out and measured along the molecular chain, which reveals significant density fluctuations. A Voronoi polyhedron is constructed for each particle according to a unique mathematical procedure [J Reiner Angew Math 134 (1908) 198]. When measured in terms of Voronoi polyhedra, amorphous structures show wide variations in packing density on the atomic/monomer scale, with a characteristic skewed distribution. The Voronoi method can be applied to all polymers; however, in this paper only uncrosslinked amorphous polymers are considered. Constriction points around a chain segment are defined as a locally specific configuration and arrangement of adjacent chains such that the local density within a sphere of radius approximately equal to two monomer diameters comes close to or below the hypothetical crystalline density. The topological theory of molecular structure developed by Bader defines the concepts of atoms and bonds in terms of the topological properties of the observable charge distribution [Rep Prog Phys 44 (1981) 893]. In polymers the high density regions become an even stronger topological feature, and are referred to as the constriction points.     

Effect of temperature and strain rate on the tensile deformation of polyamide 6

The effects of the draw temperature and the strain rate on the tensile deformation of polyamide 6 (PA6) were investigated using three PA6 samples with different initial shapes and physical dimensions. It is observed that the special double yielding phenomenon is indeed present in PA6, provided that certain temperature and strain rate are given, as well as the appropriate initial structure. The results also show that the dependence of the first yield stress on temperature is nearly linear while on strain-rate is logarithmic. The temperature and strain-rate sensitivity change at the draw temperature in the vicinity of the glass transition temperature of PA6. The double yielding of PA6 is not only the combination of two thermally activated rate processes depending on temperature and strain rate, but also associated with the initial structure of samples. The yielding manner for PA6 seems to be determined by the synergetic effect of both the deformation of amorphous and crystalline phases. Thus some special structure involving the crystalline and amorphous phases should come into being in PA6 exhibiting double yielding. Especially the important role of inter- and intra-link should be taken into account. The theory of partial melting-recrystallization cannot account fully for the double yielding of PA6.     

Cyclic voltammograms obtained from the optical signals: Study of the successive electro-oxidations of rutin

This paper describes a novel method of obtaining cyclic voltammograms (CVs) from optical signals. The obtained CVs correspond to the various specific species involved in the electrode process, which give more detailed information on the system under investigation than the common CV. For this purpose cyclic voltabsorptometry was used to investigate the successive oxidation processes of rutin on a graphite-wax electrode by using a long optical-path thin-layer electrochemical cell. The dynamic UV spectra of rutin showed the information on the structures of the oxidation products at different potentials. Cyclic voltabsorptiograms (CVAs) were measured in three potential ranges at the characteristic absorption wavelengths of rutin, 346, 254 and 296 nm, respectively. The CVs of three species in solution (rutin and its two products) were obtained from the derivative cyclic voltabsorptiograms (DCVAs). Based on this the redox mechanisms of rutin in different CV peaks were discussed.