The application of a Gauss-Eyring model to predict the behavior of thermoplastics in tensile experiments

The Gaussian expression for the isothermal tensile deformation of thermoplastics including the proposed strain hardening constant G_p, has been combined with the Eyring flow equation to provide a new relation describing the rate of strain of a thermoplastic in terms of the true stress and the extension ratio under isothermal conditions. In conventional mechanical tests this model can be used to quantify the tendency to strain localization, to predict the natural draw ratio and the inversion point where the true engineering stress passes through a minimum. The latter is expected to correlate with the value of the extension ratio where crazes do not propagate under tension. The equation is most easily demonstrated in constant load experiments where they agree well with published work. However, for a more precise evaluation of the theory the constant G_p should be measured separately and the calculated results compared with other tests on the same material. Where necking occurs it is possible to use a simplified plug flow model to calculate neck profiles. These show that no special assumptions are required to account for necking which results directly from the interaction of geometric thinning and strain hardening, even where true strain softening is absent. The procedure makes it possible to illustrate the way in which the form of the neck can be affected by the rate of extension or in a constant load experiment by the applied load. ©1995 John Wiley & Sons, Inc.     

Micromechanical modeling of the tensile behavior of oriented polyethylene

The stacked lamellar morphology commonly found in extruded semicrystalline materials has a strong influence on the flow direction, with respect to the loading direction, and on the stability and localization phenomena in tensile experiments. A multiscale numerical model was used to simulate the effect on the macroscopic behavior of a stacked lamellar microstructure. The model established a link between the microscopic, the mesoscopic, and the macroscopic levels. The constitutive properties of the material were identified for the crystallographic and amorphous domains. The average fields of an aggregate of individual phases, having preferential orientations, formed the constitutive behavior of the extruded material. The microscopic morphology of the extruded high‐density polyethylene is based on wide‐angle X‐ray diffraction experiments. The macrostructure was described by a finite element model. The microstructure‐induced deformation hardening in the extrusion direction was found to stabilize the macrostructure when it was loaded in the flow direction. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2983–2994, 2004     

The effect of drawing on the transport of gases through polyethylene

A study has been made of the gas transport properties of polyethylene films of two different grades, Hizex 7000F and Rigidex 002-55, one-way drawn at 115°C to draw ratios in the range 1–20. Measurements of the permeability and diffusion coefficients of helium, oxygen, carbon dioxide and nitrogen have been made with a dynamic flow rate technique, utilizing a mass spectrometer detection system, and of oxygen using a commercial OXTRAN system. The samples were characterized by the measurement of density, birefringence and modulus and by wide-angle x-ray diffraction and differential scanning calorimetry. There is a large decrease in both the permeability and diffusion coefficients for all gases with increasing polymer draw ratio, with up to an 80-fold decrease in permeability for the larger permeants compared with the 10-fold decrease observed for helium. The solubilities of all the gases decrease only by a factor of ～ 2. The diffusion results are discussed in terms of geometric impedance and chain immobilization factors. The solubilities, on the other hand, appear to relate primarily to the amorphous volume fraction of the polymer. © 1993 John Wiley & Sons, Inc.     

Rheo-optical Raman study of microscopic deformation in high-density polyethylene under hot drawing

In situ observation of the microscopic structural changes in high-density polyethylene during hot drawing was performed by incorporating a temperature-controlled tensile machine into a Raman spectroscopy apparatus. It was found that the load sharing and molecular orientation during elongation drastically changed at 50°C. The microscopic stress of the crystalline chains decreased with increasing temperature and diminished around 50°C. Moreover, the orientation of the crystalline chains was greatly promoted above 50°C. These microscopic structural changes were caused by the thermal activation of the molecular motion within lamellar crystalline chains owing to the onset of relaxation of the crystalline phase.     

Stepwise fatigue crack propagation in polyethylene resins of different molecular structure

Stepwise fatigue crack propagation in a range of polyethylene resins, some of which are candidates for use in pipes for natural gas distribution, was studied. Examination of the effect of molding conditions on fatigue crack propagation in a pipe resin indicated that fast cooling under pressure produced specimens with the same crack resistance as specimens taken from a pipe extruded from this resin. The mechanism of stepwise crack propagation in fatigue was the same as reported previously for creep loading. Observations of the region ahead of the arrested crack revealed a complex damage zone that consisted of a thick membrane at the crack tip followed by a main craze with subsidiary shear crazes that emerged from the crack tip at an angle to the main craze. The effects of molecular parameters, such as molecular weight, comonomer content, and branch distribution, on the kinetics of fatigue crack propagation were examined. Correlation of creep and fatigue crack resistance made it possible to relate fatigue fracture toughness to molecular parameters by invoking concepts of craze fibril stability developed for creep. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 2355–2369, 1998     

Large tensile deformation behavior of oriented high‐density polyethylene: A correlation between cavitation and lamellar fragmentation

Oriented high‐density polyethylene (HDPE), prepared by melt extrusion drawing, has been employed to address the correlation between cavitation and lamellar fragmentation at large strain. This has been done by investigating the volume strain, elastic recovery properties, and microscopic morphology. The results indicate that the reversible volume strain becomes saturation at a true strain of about 0.3, which is essentially consistent with the critical one related to lamellar fragmentation (point C). Morphological observations on the deformed samples provide structural insights into above deformation behaviors. Enlarged voids are hard to recover due to dominant plastic deformation of crystals once lamellar fragmentation sets in and thus a transition of reversible volume strain with strain is presented. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 1202–1206, 2008     

Mechanical properties of the polypropylene copolymer measured by the impression method

An impression test using a flat indenter with three different diameters 0.5, 1, and 2 mm is proposed to study the plastic flow of a polypropylene copolymer. By comparing the flow characteristics of the impression test with the uniaxial tension and compression tests, it is found that a yield drop occurs in the compression, and geometrical necking appears in tension, but no load drop and only strain hardening is found in the impression tests. Furthermore, the plastic behaviors of the impression before the yield are also similar to those of the compression test because there is a correlation of the stress-strain curve between impression and compression by only adjusting the scaling factors. The plastic zone size underneath the indenter is only slightly larger than the indenter diameter and, as the load is applied, the mean pressure across the face of the indenter is smaller than that of the metals due to the large intermolecular distance in the polypropylene copolymer. The impression test is also used to measure the strength, elastic modules, strain-hardening exponent, and strain-rate sensitivity in a manner of shallow penetration and miniature deformation, which indicates that the impression test can be employed to study the mechanical properties of the thin-film polypropylene copolymer. © 1996 John Wiley & Sons, Inc.     

On the viscoelastic and plastic behavior of semiaromatic polyamides

Different semiaromatic polyamides (SAPA) have been synthesized by step‐growth polymerization of an aliphatic diamine, M (the 2‐methyl 1,5‐pentanediamine), and isophthalic acid, I, or terephthalic acid, T, or mixtures of these two diacids. The influence of the relative amount of randomly distributed MT units on the viscoelastic properties of the materials was investigated. It was shown that the glass transition T_g, as deduced from DSC thermograms, and the relevant mechanical relaxation T_α raise when the content of MT units increases. In contrast, the broad low‐temperature secondary relaxation, called γ, does not markedly depend on the MT content. Samples systematically studied in the absence of any moisture did not exhibit the intermediate‐temperature secondary relaxation, called β, which is characteristic of the wet polyamides. The study of the plastic behavior was focused on the samples MI and I5, which are strictly amorphous, and contain 0% and 50 mol % of MT units, respectively. Mechanical experiments were carried out in both the compression and traction modes, at temperatures ranging from −80°C to T_g. Analysis of the compression data was based on the inspection of the temperature dependence of elastic modulus, E(T), yield stress, ς_y, plastic flow stress, ς_pf, and strain softening ς_y − ς_pf. Whereas the plots of ς_y as a function of temperature, T, reveal some differences between MI and I5 behavior, a unique master curve was obtained by plotting ς_y/E(T) vs. T − T_g, which means that the plastic behavior of these materials is controlled by their chain packing in the glassy state. The strain softening profile of MI and I5 is similar to that already reported in the case of brittle vinyl polymers. This observation is consistent with the traction data, which give evidence for the occurrence of the tensile yielding of MI and I5 at temperatures rather close to T_g. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 1131–1139, 1999     

Temperature and strain rate dependence of yield strain and deformation behavior in polyethylene

The deformation behavior of a range of polyethylene materials which differ with respect to both their short-chain branch content and molecular weight has been studied. Mechanical measurements carried out over a wide range of temperatures have shown that there is a sudden transition in the measured tensile yield strain at a temperature which is dependent on both the grade of material and the applied strain rate. Above the transition temperature all of the materials behave in a nonlinear viscoelastic manner and the wide-angle X-ray scattering patterns obtained have shown that at low applied strains reorientation of the lamellae is observed before necking. Below the transition temperature the materials all behave in an elastic-plastic manner and there is no evidence of lamellar reorientation before necking. This transition in yield mechanism is not apparent when considering the yield stress data alone. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys, 35: 545–552, 1997     

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     

On the phenomena of deformation and neck formation in LLDPE films subjected to uniaxial and biaxial loading conditions

Heterogeneous deformation in the form of dilatational bands is observed under certain biaxial stress states that closely resembles uniaxial necking in LLDPE blown films. The formation and orientation of dilatational bands is a function of film morphology and stress state. The dilatational bands form, with their lengths aligned with the machine direction (MD) of the film, under equibiaxial stress states and nonequibiaxial stress states when the higher principle stress is coincident with the transverse direction (TD). However, homogeneous deformation is observed if the higher principle stress is coincident with the MD. Similarly, uniaxial specimens show necking when the stress is applied in the TD and affine deformation when the stress is applied in the MD. Neck boundary propagation under uniaxial loading is due primarily to the consumption of undrawn material, while dilatational band boundary propagation under an equibiaxial loading also includes simultaneous continued deformation of the drawn material. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2651–2663, 1999     

Role of molten fraction on the structural evolution in stretching and cooling of crosslinked low‐density polyethylene: Real‐time mechano‐optical measurements

We investigated the uniaxial deformation behavior of crosslinked low‐density polyethylene in partially and substantially molten states using a real‐time true stress–strain birefringence system. The stress–birefringence behavior exhibits a multiregime behavior during stretching and holding process. The details of this regime behavior are primarily governed by the degree of unmelted crystallinity as it has a dominant role in the long‐range structural connectivity. When the long‐range physical connectivity is present, a three‐regime nonlinear stress–optical behavior was observed. When the long‐range connectivity is substantially eliminated at higher temperatures, the regime I behavior disappears. Structural studies including cooling process reveal that the lower the proportion of molten material during stretching, the higher the concentration of fibrillar structure and the shorter are the lengths of the kebabs that exhibit twisted lamellae after solidification. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 1825–1841, 2005     

Maximum tensile properties of oriented polyethylene,achieved by uniaxial drawing of solution‐grown crystal mats: Effects of molecular weight and molecular weight distribution

The effects of molecular weight (MW) and MW distribution on the maximum tensile properties of polyethylene (PE), achieved by the uniaxial drawing of solution‐grown crystal (SGC) mats, were studied. The linear‐PE samples used had wide ranges of weight‐average (M_w = 1.5–65 × 10⁵) and number‐average MWs (M_n = 2.0–100 × 10⁴), and MW distribution (M_w/M_n = 2.3–14). The SGC mats of these samples were drawn by a two‐stage draw technique, which consists of a first‐stage solid‐state coextrusion followed by a second‐stage tensile drawing, under controlled conditions. The optimum temperature for the second‐stage draw and the resulting maximum‐achieved total draw ratio (DR_t) increased with the MW. For a given PE, both the tensile modulus and strength increased steadily with the DR_t and reached constant values that are characteristic for the sample MW. The tensile modulus at a given DR_t was not significantly affected by the MW in the lower DR_t range (DR_t < 50). However, both the maximum achieved tensile modulus (80–225 GPa) and strength (1.0–5.6 GPa), as well as those at higher DR_ts > 50, were significantly higher for a higher MW. Although the maximum modulus reached 225 ± 5 for M_n ≥ 4 × 10⁵, the maximum strength continued to increase with M_n even for M_n > 4 × 10⁵, showing that strength is more strongly dependent on the M_n, even at higher M_n. Furthermore, it was found that each of the maximum tensile modulus and strength achieved could be expressed by a unique function of the M_n, independently of the wide variations of the sample MW and MW distribution. These results provide an experimental evidence that the M_n has a crucial effect on the tensile properties of extremely drawn and chain‐extended PE fibers, because the structural continuity along the fiber axis increases with the chain length, and hence with the M_n. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 153–161, 2006     

Melt drawing of ultra‐high molecular weight polyethylene: Comparison of Ziegler‐ and metallocene‐catalyzed reactor powders

The drawing behavior of the ultra‐high molecular weight polyethylene (UHMW‐PE) melts has been studied by comparing the stress/strain curves for two types of samples as polymerized using conventional Ziegler and newer metallocene catalyst systems. Two UHMW‐PE samples, having the same viscosity average molecular weight of 3.3 × 10⁶, but different molecular weight distribution, have been drawn from melt at special conditions. The sample films for drawing were prepared by compression molding of reactor powders at 180°C in the melt. Differences in the structural changes during drawing and resultant properties, ascribable to their broad or narrow molecular weight distribution, were estimated from tensile tests, SEM observations, X‐ray measurements and thermal analyses. The metallocene‐catalyzed sample having narrower molecular weight distribution, could be effectively drawn from the melt up to a maximum draw ratio (DR) of 20, significantly lower than that obtained for the Ziegler‐catalyzed sample, ∼ 50. The stress/strain curves on drawing were remarkably influenced by draw conditions, including draw temperature and rate. However, the most effective draw for both was achieved at 150°C and a strain rate of 5 min⁻¹, independent of sample molecular weight distribution. The efficiency of drawing, as evaluated by the resultant tensile properties as a function of DR, was higher for the metallocene‐catalyzed sample having narrower molecular weight distribution. Nevertheless, the maximum achieved tensile modulus and strength for the Ziegler sample, 50–55 and 0.90 GPa, respectively, were significantly higher than those for the metallocene sample, 20 and 0.65 GPa, respectively, reflecting the markedly higher drawability for the former than the latter. The stress/strain behavior indicated that the origin of differences during drawing from the melt could be attributed to the ease of chain relaxation for the lower molecular weight chains in the melt. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 1921–1930, 1999     

Wide‐angle X‐ray scattering study of the lamellar/fibrillar transition for a semi‐crystalline polymer deformed in tension in relation with the evolution of volume strain

This work is devoted to the study of the deformation mechanisms of a high‐density polyethylene deformed in tension. Specific treatments were applied to synchrotron wide‐angle X‐ray scattering patterns obtained in situ with the aim of quantifying: (i) the evolution of the apparent crystal sizes during the deformation process, (ii) the reorientation dynamics of the fragmented crystals while aligning their chains along the drawing axis during the establishment of the fibrillar morphology, and (iii) the reorientation dynamics of the amorphous chains. In addition, the volume strain evolution was measured using 3D digital image correlation. The cavitation phenomenon was found to mainly occur during the lamellae fragmentation phase. At the end of the deformation process, when the lamellar structure is destroyed, the fragmented crystals have new degrees of freedom and become free to rotate to align their chains along the drawing axis. Crystal fragmentation is then no longer needed to allow material deformation, and there is no further volume strain increase. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 1470–1480     

Stretching temperature and direction dependency of uniaxial deformation mechanism in overstretched polyethylene

In order to elucidate microscopic deformation behavior at different locations in isotropic semicrystalline polymers, the structural evolution of a preoriented high‐density polyethylene sample during tensile deformation at different temperatures and along different directions with respect to the preorientation was investigated by means of combined in situ synchrotron small‐angle X‐ray scattering (SAXS) and wide‐angle X‐ray diffraction (WAXD) techniques. For samples stretched along preorientation, two situations were found: (1) at 30 °C, the sample broke after a moderate deformation, which is accomplished by the slippage of the microfibrils; (2) at 80 and 100 °C, fragmentation of original lamellae followed by recrystallization process was observed resulting in new lamellar crystals of different thickness depending on stretching temperature. For samples stretched perpendicular or 45° with respect to the preorientation, the samples always end up with a new oriented lamellar structure with the normal along the stretching direction via a stress‐induced fragmentation and recrystallization route. The thickness of the final achieved lamellae depends only on stretching temperature in this case. Compared to samples stretched along the preorientation direction, samples stretched perpendicular and 45° with respect to the preorientation direction showed at least several times of maxima achievable stress before macroscopic failure possibly due to the favorable occurrence and development of microdefects in those lamellar stacks with their normal parallel to the stretching direction. This result might have significant consequence in designing optimal procedure to produce high performance polyethylene products from solid state. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 , 52, 716–726     

The influence of short chain branch on formation of shish‐kebab crystals in bimodal polyethylene under shear at high temperatures

Formation of shish‐kebab crystals due to the coil–stretch transition under shear in the molten state using a bimodal polyethylene system with high molecular weight (HMW) fraction having different branch content was investigated. In specific, in situ small‐angle X‐ray scattering (SAXS) and wide‐angle X‐ray diffraction (WAXD) techniques were used to study the structure evolution of shish‐kebab crystals at high temperatures under simple shear. The SAXS results revealed that with the increase of branch content, shish‐kebab crystals became more stable at high temperatures (e.g., 139 °C). However, the shish length of the bimodal PE containing 0.11% branch was shorter than that with no branch. The WAXD results showed that the degree of crystallization for bimodal PE with HMW fraction having 0.11% branch increased with time but reached a plateau value of 1%, while that with no branch increased continuously till 11%. Furthermore, the crystal orientation of bimodal PE with HMW fraction having 0.11% branch was above 0.9 and maintained at a constant value, while that with no branch decreased from 0.9 to 0.1 upon relaxation. This study indicates that even though the crystallizability of the HMW fraction with branch content decreased, they could effectively stabilize the shear‐induced crystalline structure with shorter shish‐kebab crystals. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018 , 56, 786–794     

The temperature window of minimum flow resistance in melt flow of polyethylene. Further studies on the effect of strain rate and branching

The existence of a narrow temperature window (150–153°C) of smooth extrudability coupled with a minimum in flow resistance (extrusion pressure) in high-molecular weight polyethylene (>4 × 10⁵ g mol^?1) was the subject of a previous article where it was associated with strain-induced formation of the mobile hexagonal mesophase. The new findings of this note show that this minimum in flow resistance only sets in above a critical strain rate; this is interpreted in terms of the requirement of a critical strain rate in order to stretch molecules to their fully extended configuration. Furthermore, this critical strain rate is shown to be higher for lower molecular weight materials, in agreement with a priori considerations. Additionally, the temperature at which the pressure minimum occurs in a polyethylene containing methyl branches shifts to a significantly lower value than that for the linear material. This is interpreted in terms of the ? CH₃ groups raising the crystal free energy, thereby lowering the temperature at which the transition to the hexagonal phase occurs.     

Quasiharmonic treatment of infrared and raman vibrational frequency shifts induced by tensile deformation of polymer chains. II. Application to the polyoxymethylene and isotactic polypropylene single chains and the three-dimensional orthorhombic polyethylene crystal

Quasiharmonic equations are derived for stress-induced vibrational frequency shifts in the infrared and Raman spectra of polymer chains subjected to a tensile stress. The expressions are applied to the helical chains of polyoxymethylene and isotactic polypropylene. Observed frequency shifts can be reproduced well by using reasonable anharmonic force constants. A semiquantitative interpretation is given for the close relationship between stress-induced vibrational frequency shifts and the deformation mechanism of the polymer chains. Stress-induced frequency shifts are also calculated for an orthorhombic polyethylene crystal subjected to uniaxial tension along the chain axis or to hydrostatic pressure. The results consistently and reasonably reproduce observed data, not only for the intramolecular vibrational modes but also for the external lattice modes. © 1992 John Wiley & Sons, Inc.