The effect of annealing on the nonlinear viscoelastic response of isotactic polypropylene

Three series of tensile relaxation tests are performed on isotactic polypropylene at room temperature in the vicinity of the yield point. In the first series of experiments, injection‐molded samples are used without thermal pre‐treatment. In the second and third series, the specimens are annealed at 130°C for 4 and 24 hours, respectively. Constitutive equations are derived for the time‐dependent response of semicrystalline polymers at isothermal loading with small strains. A polymer is treated as an equivalent temporary network of macromolecules bridged by junctions (physical cross‐links, entanglements and crystalline lamellae). Under loading, junctions slide with respect to their positions in the bulk material (which reflects the viscoplastic behavior), whereas active strands separate from their junctions and dangling strands merge with the network at random times (which reflects the viscoelastic response). The network is thought of as an ensemble of meso‐regions (MRs) with various activation energies for detachment of chains from temporary nodes. Adjustable parameters in the stress‐strain relations are found by fitting the observations. The experimental data demonstrate that the relaxation spectrum (characterized by the distribution of MRs with various potential energies) is independent of mechanical factors, but is altered at annealing. For specimens not subjected to thermal treatment, the growth of longitudinal strain does not affect the volume fraction of active MRs and the attempt rate for detachment of chains from their junctions. For annealed samples, the concentration of active MRs increases and the attempt rate decreases with strain. These changes in the time‐dependent response are attributed to broadening of the distribution of strengths of lamellae at annealing.     

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 effect of annealing on the time-dependent behavior of isotactic polypropylene at finite strains

Four series of tensile relaxation tests are performed on isotactic polypropylene at elongations up to the necking point. In the first series of experiments, injection-molded samples are used without thermal pre-treatment. In the other series, the specimens are annealed for 24 h prior to testing at 110, 120 and 130 °C, respectively. Results of mechanical experiments are compared with DSC measurements.A constitutive model is derived for the time-dependent response of semicrystalline polymers at finite strains. A polymer is treated as an equivalent temporary network of macromolecules bridged by junctions (physical cross-links, entanglements and crystalline lamellae). At random times chains separate from their junctions and merge with new ones (the viscoelastic response), whereas junctions slip with respect to their positions in the bulk material (the viscoplastic behavior). The network is thought of as an ensemble of active meso-regions with various potential energies for detachment of chains from temporary nodes and passive meso-domains, where separation of chains is prevented by surrounding radial and tangential lamellae.Experimental data demonstrate that the content of active meso-domains increases with elongation ratio driven by the release of constrained amorphous phase induced by fragmentation of lamellae. In the sub-critical region of deformation (relatively small strains), the growth of the concentration of active meso-regions is associated with breakage of subsidiary (thin) lamellae developed at annealing. In the post-critical region (large strains), an increase in the fraction of active amorphous domains is attributed to disintegration of primary (thick) lamellae.     

Modeling the uniaxial rate and temperature dependent behavior of amorphous and semicrystalline polymers

Strain rate and temperature dependent constitutive equations are proposed for polymer materials based on existing isotropic formulations of viscoplasticity. The proposed formulations are capable of simulating some of the important features of deformation behavior of amorphous and semicrystalline polymers. The materials model is based on the assumption that the evolution of flow stress is dependent on the rate of deformation, temperature, and an appropriate set of internal variables. The proposed theory is capable of modeling yielding, strain softening, and the orientation hardening exhibited by amorphous polymers. It is also possible to model the initial viscoplastic and subsequent nonlinear hardening behavior shown by semicrystalline polymers at large strains. Uniaxial tensile tests with uniform and hourglass specimens are made at temperatures ranging from 23 to 100°C and under various crosshead speeds. Both amorphous polycarbonate and semicrystalline polypropylene sheet materials are tested to characterize the stress and strain behavior of these materials and to determine their appropriate material constants. Load relaxation experiments are also conducted to obtain the necessary material constants describing the rate and temperature dependent flow stress behavior of polypropylene. Simulation results compare favorably against experimental data for these polymer materials.     

Modeling the viscoelastoplastic behavior of amorphous glassy polymers

Constitutive equations are derived for the viscoelastic and viscoplastic responses of amorphous glassy polymers at isothermal loading with small strains. A polymer is modeled as an ensemble of cooperatively relaxing regions (CRR) that are rearranged at random times as they are thermally agitated. At relatively low stresses, CRRs are bridged by links that ensure that the macro-strain in a specimen coincides with micro-strains in relaxing regions. When the average stress exceeds a threshold strength for the links, some of them break, and relaxing domains begin to slide with respect to one another. Rearrangement of CRRs reflects the viscoelastic behavior, whereas sliding of micro-domains is associated with the viscoplastic response of glassy polymers. Kinetic equations are proposed for the evolution of viscoplastic strains and the strength of an ensemble of links. These equations are verified by comparison with experimental data in tensile relaxation tests and in tensile and compressive tests with constant strain rates. Fair agreement is demonstrated between results of numerical simulation and observations for a polyurethane resin and poly(methyl methacrylate).     

Network model for the viscoelastic behavior of polymer nanocomposites

A theoretical network model reproducing some significant features of the viscoelastic behavior of unentangled polymer melts reinforced with well dispersed non-agglomerated nanoparticles is presented. Nanocomposites with low filler volume fraction (∼10%) and strong polymer-filler interactions are considered. The model is calibrated based on results obtained from discrete simulations of the equilibrium molecular structure of the material. This analysis provides the statistics of the network of chains connecting fillers, of dangling strands having one end adsorbed onto fillers, and that of the population of loops surrounding each nanoparticle. The network kinetics depends on the attachment-detachment dynamics of grafted chains of various types and is modeled by using a set of convection equations for the probability distribution functions. The overall viscoelastic response depends strongly on the lifetime of the polymer-filler junctions. The largest reinforcement is observed at low strain rates and low frequency oscillations. A solid like behavior is predicted for systems in which the polymer molecules interact strongly with the nanoparticles, effect which is associated with the behavior of the network of bridging segments.     

Classification of ethylene–styrene interpolymers based on comonomer content

Copolymerization of ethylene and styrene by the INSITE^TM technology from Dow presents a new polymer family identified as ethylene–styrene interpolymers (ESI). Based on the combined observations from melting behavior, density, dynamic mechanical response, and tensile deformation, a classification scheme with 3 distinct categories is proposed. Polymers with up to 50 wt % styrene are semicrystalline and are classified as type E. The stress–strain behavior of low-crystallinity polymers at ambient temperature exhibits elastomeric characteristics with low initial modulus, a gradual increase in the slope of the stress–strain curve at higher strains, and large instantaneous recovery. The structural origin of the elastomeric behavior is probably a network of flexible chains with fringed micellar crystals serving as multifunctional junctions. Polymers with more than 50 wt % styrene are amorphous. Because the range of glass transition temperatures encompasses ambient temperature (nominally 25°C), it is useful to differentiate ESIs that are above the glass transition as type M and those that are below the glass transition as type S. Type M polymers behave as rubber-like liquids. They have the lowest modulus and lowest stress levels. Some elastic characteristics are attributed to the entanglement network. Type S polymers exhibit large strain rate sensitivity with glassy behavior at short times and rubbery behavior at longer times. The term “glasstomer” is coined to describe these polymers. The division between type M and type S is based on chain dynamics, rather than solid state structure, and thus depends on the temperature of interest. At ambient temperature, ESIs with 50 to 70 wt % styrene are classified as type M; polymers with more than 70 wt % styrene are classified as type S. © 1998 John Wiley & Sons, Inc. J. Appl. Polym. Sci. 70: 109–119, 1998     

Mechanical behavior of a semicrystalline polymer before necking. Part II: Modeling of uniaxial behavior

Based on the experimental mechanical characterization presented in Part I of this paper, a model allowing the prediction of the behavior of the studied semicrystalline polymer in the pre‐necking domain was constructed. The modeling of the viscoelastoplastic behavior of polypropylene (PP) was described by partitioning the total strain into a viscoelastic strain and a viscoplastic strain. After being improved with experimental observations, the rheological model of Zener was used to model the viscoelastic behavior of PP. As for viscoplastic behavior modeling, it was based on the characterization of the mechanical behavior performed in the first part of the study. Attention was focused on the strain reversal in order to predict the unloading path. Experimental data from the performed mechanical tests were employed to determine the parameters of the viscoelastoplastic model.     

Constitutive equations for the viscoplastic response of isotactic polypropylene in cyclic tests: The effect of strain rate

A series of uniaxial tensile loading‐unloading tests are performed on injection‐molded isotactic polypropylene at room temperature. In each test, a specimen is stretched up to the maximal strain ?_max = 0.12 with a constant strain rate, $ \dot \varepsilon $, and retracted down to the zero stress with the same strain rate. The cross‐head speeds vary from 5 to 200 mm/min, which covers practically the entire range of strain rates used in conventional quasi‐static tests. A constitutive model is developed for the viscoplastic response of a semicrystalline polymer at small strains. The stress‐strain relations are determined by five adjustable parameters that are found by matching the observations. Fair agreement is demonstrated between the experimental data and the results of numerical simulation. Polym. Eng. Sci. 44:548–556, 2004. © 2004 Society of Plastics Engineers.     

High‐temperature large strain viscoelastic behavior of polypropylene modeled using an inhomogeneously strained network

The effects of microstructural rearrangements during the stretching of semicrystalline polymers and the resultant inhomogeneous strains are modeled by rigid spheres embedded in a polymer network. This results in strain concentrations in the network, which is then caused to yield at realistic overall strains. To simulate the collapse of the original spherulitic morphology, the radii of the spheres decrease at a rate dependent on the shear stress imposed on them by the surrounding network. This results in time‐dependent behavior. The resultant large strain viscoelastic model is implemented in a commercial finite element code and used to predict shapes of necking polypropylene sheet specimens at 150°C. Rate dependence of stress and stress relaxation are also predicted, and the model is shown to be generally effective in its predictions of shapes and forces up to large deformations. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 72: 563–575, 1999     

Interrelation between long‐term viscoelasticity and viscoplastic responses of semicrystalline polymers

Two types of linear low‐density polyethylenes, prepared by metallocene catalysts were studied experimentally in terms of differential scanning calorimetry, dynamic mechanical analysis (DMA), and tensile testing. The different comonomer content and the small amounts of long branching in one of the materials studied strongly affect the crystalline distribution and morphology and, consequently, the DMA and tensile experimental data. From the experimental DMA data, the function of relaxation modulus, treated as a material property, is used to describe the corresponding tensile experimental results. A constitutive analysis that considers the viscoelastic path at small strains and the viscoplastic one at high strains proved to be capable of describing the tensile behavior of the materials. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 88: 1942–1950, 2003     

Tensile creep behavior of unidirectional glass‐fiber polymer composites

The tensile creep behavior of unidirectional glass‐fiber polymer composites was studied at three different temperatures, namely 298, 333, and 353 K. Testing was performed on the pure epoxy matrix, the 0° specimens as well as off‐axis at 15, 30, and 60 degrees in respect to the axis of tension. The creep strain rate was negligible at room temperature, while it was considerable at the higher temperatures examined. The materials exhibit nonlinear viscoelastic behavior, and the creep response of the composites was treated as a thermally activated rate process. The creep strain was considered to include an elastic, a viscoelastic and a viscoplastic part. The viscoplastic part was calculated through a functional form, developed in a previous work, assuming that viscoplastic response of polymer composites arises mainly from the matrix viscoplasticity. The model predictions in terms of creep compliances were found to be satisfactory, compared with the experimental results. POLYM. COMPOS. 26:287–292, 2005. © 2005 Society of Plastics Engineers.     

Mechanical behavior of a semicrystalline polymer before necking. Part 1: Characterization of uniaxial behavior

The behavior of the semicrystalline polymer polypropylene (PP) was studied in the pre‐necking domain. Mechanical tests were performed to characterize its viselastic and its viscoplastic behavior. The usual approach for studying metals was adopted to investigate the effect of heterogeneities caused by spherulitic morphology. The macroscopic stress was split into an effectie stress and a back stress so that the interactions between crystalline lamellae and amorphous phases could be taken into account. An understanding of the relationship between microstructure and the macroscopic strain mechanisms was developed.     

Thermotropic liquid‐crystalline copolyester (Rodrun LC3000)/thermoplastic elastomer (SEBS) in situ composites: II. Mechanical properties and morphology of monofilaments in comparison with extruded strands

Monofilaments of in situ composites were prepared from an immiscible blend of a thermotropic liquid‐crystalline polymer (TLCP), Rodrun LC3000, and a thermoplastic elastomer, styrene–(ethylene butylene)–styrene (SEBS), by a melt spinning process. Mechanical properties and the morphology of the composite monofilaments were investigated and compared with those of the extruded strands previously reported. The stresses at all tensile strains of the composite monofilaments were much higher than those of the extruded strands. The tensile strengths of both extruded strands and monofilaments were comparable, but the elongation at break of monofilaments dropped considerably. The tension sets of composite monofilaments were slightly higher than those of extruded strands. All composite monofilaments with TLCP content of ≤15 wt % exhibited good elastic recovery under the applied strain up to 200%. The dynamic mechanical storage modulus at 25°C of 10 wt % TLCP composite monofilament increased fourfold compared with that of the composite extruded strand and fivefold compared with that of the neat SEBS monofilament. The dramatic enhancement in the mechanical properties of in situ composite monofilaments is due to the formation of finer and longer TLCP fibrils (length‐to‐width ratio > 100) than those formed in the extruded strands. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 90: 518–524, 2003     

Effect of high‐temperature annealing on the elastoplastic response of isotactic polypropylene in loading–unloading tests

A series of uniaxial tensile loading–unloading tests is performed on isotactic polypropylene at room temperature. Prior to mechanical testing, injection‐molded specimens are annealed for 24 h at temperatures T = 145, 150, 155, 158, 160, 163, and 165°C, which cover the entire region of high‐temperature annealing temperatures. A constitutive model is developed for the elastoplastic behavior of a semicrystalline polymer at small strains. The stress–strain relations are determined by six adjustable parameters that are found by matching observations in cyclic tests. Fair agreement is demonstrated between the experimental data and the results of numerical simulation. It is shown that all material constants are affected by the annealing temperature, which is explained by changes in the crystalline morphology driven by thermal treatment. Some of the adjustable parameters experience finite jumps in the vicinity of the critical temperature T_c = 159°C. These jumps are attributed to the α₂ → α₂′ phase transformation. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 90: 186–196, 2003     

Nonlinear viscoelastic and viscoplastic response of glassy polymers

The main features of inelastic mechanical behavior of glassy state were studied theoretically and experimentally in terms of tensile stress‐strain and tensile creep experiments. A theoretical treatment introduced in earlier work, which takes into account the viscoelastic path at small strains and the viscoplastic one at higher stresses, proved to be capable of describing the main aspects of mechanical response of glassy polymers, i.e. nonlinear viscoelasticity during creep procedure, and yield stress, yield strain, strain softening and rate effect in a constant crosshead speed test.     

Tensile strain‐rate response of polymeric fiber composites

The tensile behavior of unidirectional glass‐fiber polymer composites was studied at three different strain rates. Tests were performed on 0° specimens as well as off‐axis specimens at 15°, 30°, 45°, and 90° with respect to the axis of tension. The nonlinear material behavior was modeled through a viscoplastic model based on a one‐parameter plastic potential function developed elsewhere. An effective stress‐effective plastic strain curve was constructed for each strain rate imposed and fitted with a power law. Thus, the tensile stress–strain curve could be predicted in a very accurate way for every strain rate examined and various types of off‐axis specimens. The strain rate‐dependent behavior is described through a scaling law, assuming that a model parameter is a function of the imposed strain rate. Predictions of the material response at strain rates different from those initially studied were found to be successful. POLYM. COMPOS., 26:572–579, 2005. © 2005 Society of Plastics Engineers     

A Monte Carlo simulation study of the mechanical and conformational properties of networks of helical polymers. Part II. The effect of temperature

In a recent article (Carri GA, Batman R, Varshney V, Dirama TE. Polymer 2005;46:3809 [17]) we presented a model for networks of helical polymers. In this article we generalize our results to include the effect of temperature and focus on the mechanical, conformational and thermo-elastic properties of the network. We find that the non-monotonic stress-strain behavior observed at constant temperature also appears in the stress-temperature behavior at constant strain. The origin of this behavior is traced to the induction and melting of helical beads by the application of large strains or reduction in temperature. Other conformational properties of the polymer strands are also discussed. We also study the network entropy and heat capacity, and find a non-monotonic dependence on temperature and strain. Our study shows that the entropy is controlled by the helical content whenever the latter is significant. Otherwise, the entropy corresponds to the one of a network made of random coils. In addition, the study of the heat capacity shows that strain shifts the helix-coil transition temperature significantly. Other results are also discussed.     

Inverse relaxation in polypropylene

Observations are reported on isotactic polypropylene in uniaxial tensile relaxation tests on specimens subjected to tension up to various maximum strains and retraction down to various stresses. Noticeable evolution of shapes of relaxation curves under retraction is revealed with stress at the beginning of relaxation process: with a decrease in this stress, relaxation diagrams characterized by a monotonic decay of stress with time (simple relaxation) become, first, non-monotonic (mixed relaxation), and, finally, monotonically increasing (inverse relaxation). A thorough investigation is performed on the effect of multi-cycle preloading (maximum strain per cycle, minimum stress per cycle, number of cycles, and strain rate) on transition from simple to mixed and to inverse relaxation. It is found that (1) intensity of mixed relaxation increases with maximum strain when this parameter remains below the yield strain and decreases in the post-yield region of deformations, (2) an increase in number of cycles under preloading leads to reduction of intensity of mixed relaxation and transition from mixed to inverse relaxation, (3) inverse relaxation diagrams of specimens subjected to the same preloading program with various strain rates can be superposed to construct a master-curve. A constitutive model is developed in cyclic viscoelastoplasticity of semicrystalline polymers. A polymer is thought of as two-phase continuum composed of amorphous and crystalline regions. Both phases were treated as viscoelastoplastic media whose response was governed by different kinetic equations for evolution of plastic strains and different kinematic equations for changes in relaxation rates and relaxation spectra driven by plastic flow. Good agreement is demonstrated between the experimental data in relaxation tests under retraction and the results of numerical simulation.     

Study on the drawing behavior of poly(L-lactide) to obtain high-strength fibers

The tensile drawing behavior of poly(L -lactide) has been studied in order to obtain high strength fibers. Elongational viscosity measurements indicated that the hot drawing can take place in two temperature regions with different activation energies. Up to 180°C, the deformation proceeds in the semicrystalline state of the polymer having an activation energy of 15–28 kJ/mol, presumably by shear deformation. In the range of 180–190°C, the deformation proceeds in the liquid state of the polymer having an activation energy of 145–165 kJ/mol, leading to a semicrystalline state by strain hardening after displacement of topological defects. By using high deformation rates during drawing in a temperature gradient (tube drawing), the deformation will principally proceed in the semicrystalline region and inhomogeneous draw will take place leading to inferior fiber properties, unless the deformation rate and drawing temperature are strictly adjusted. Homogeneous drawing can be achieved by applying low deformation rates so that the deformation may take place in the liquid state of the polymer in which individual chains can be easily aligned and topological defects can be removed. Poly(L -lactide) fibers with tensile strengths of 2.3 GPa have been produced in this way.