Mechanical anisotropy in oriented linear polyethylene of various crystallinities

We have studied the mechanical moduli of oriented linear polyethylene with crystallinities X varying from 0.44 to 0.63 and draw ratios λ = 1–9 by using a dynamic tensile method at 10 Hz and an ultrasonic technique at 10 MHz. Wide-angle X-ray diffraction and birefringence measurements reveal that the chains in the crystalline regions are fully aligned at λ > 4, but the degree of amorphous orientation increases steadily up to the highest draw ratio. From −180°C to the β relaxation region (near 0°C at 10 Hz) the mechanical behavior at all crystallinities is controlled by three factors: molecular orientation, weak c-shear deformation and stiffening effect of taut tie molecules. At low temperature the chain alignment in an oriented sample gives rise to an axial Young's modulus E₀ which is much larger than the transverse Young's modulus E₉₀, with the modulus for the undrawn material lying in-between. However, the results that E₄₅ < E₉₀ and C₄₄ (axial shear modulus) < C₆₆ (transverse shear modulus) imply that a weak c-shear process occurs even at low temperature. At the β relaxation where the amorphous regions are rubbery, the stiffening effect of taut tie molecules becomes prominent and leads to increases in all moduli upon drawing. For the polyethylene with the lowest cyrstallinity a strong c-shear process is activated at the α relaxation (about 50°C at 10 Hz), which gives rise to very low values of C₄₄ and E₄₅. This effect becomes weaker with increasing crystallinity and is hardly observable at X > 0.6.     

Elastic moduli of a liquid crystalline polymer and its in-situ composites

The elastic moduli of a liquid crystalline polyesteramide (LCP) and polycarbonate/LCP in-situ composites with 10 to 80 wt% of LCP have been measured as functions of draw ratio λ from 1 to 15 by an ultrasonic method. For the LCP, the sharp rise of the axial Young's modulus E₃ and the slight decreases of the transverse Young's modulus E₁ and the axial (C₄₄) and transverse (C₆₆) shear modulus with increasing λ result from the alignment of chains along the draw direction. E₁, C₄₄, and C₆₆ follow the lower bounds calculated using the series coupling scheme of the aggregate model. Although E₃ lies close to the lower bound at low λ, it follows the upper bound calculated according to the parallel coupling scheme at λ > 3. The elastic moduli of the composites have similar draw ratio dependences as those of the LCP. The strong increase in E₃ with increasing λ arises from the higher aspect ratio of the LCP domains in the composites and the improved molecular orientation within the domains. The reinforcement effect on the other moduli is much weaker, with E₁ and C₄₄ of the composites only 5 to 30% higher than those of polycarbonate at λ = 15. Since C₆₆ of the LCP decreases to a value below that of polycarbonate at λ > 2, there is a positive reinforcement effect at low λ but a negative effect at high λ.     

Mechanical relaxations and moduli of oriented semicrystalline polymers

A systematic investigation was carried out on the mechanical relaxations and moduli of four drawn semicrystalline polymers: polyoxymethylene, polypropylene, polyvinylidene fluoride and polychlorotrifluoroethylene. Low-frequency tensile and torsional measuremnts were made between-140 and 140°C, and ultrasonic measurements of all five moduli were made by the water-tank method between 0 and 60°C. The patterns of relaxations remain essentially unchanged upon orientation, but there is a marked reduction of the height of relaxation peaks associated with the amorphous phase and, correspondingly, a smaller drop of moduli in the relaxation region. This reflects a lowering of molecular mobility in the amorphous phase due to the constraining effect of taut tie-molecules. The modulus C₃₃ increases sharply with draw ratio λ while the other moduli show little variation, which result from the alignment of molecular chain axes and the production of taut tie-molecules. The λ-dependence of the moduli is consistent with the aggregate model only when the polymer is glassy, that is, when its amorphous phase is comparable in stiffness to the crystalline phase and the polymer can reasonably be regarded as a one-phase material for which the aggregate model is valid.     

Mechanical anisotropy in oriented polychlorotrifluoroethylene

The dynamic tensile modulus (E) and loss (tan δ) of various oriented samples of polychlorotrifluoroethylene have been measured at 0°, 45° and 90° to the draw direction over the range of ? 100 to 160°C. For the cold-drawn samples the mechanical anisotropy at the lowest temperature is determined by the overall chain orientation resulting in E₀ >E₄₅ >E₉₀. Above the γ relaxation (20°C) a shear process is activated leading to a change in the anisotropy pattern to E₀ >E₉₀ >E₄₅. Cold-drawing followed by annealing gives rise to further changes so that E₉₀ >E₀ >E₄₅ above the β relaxation (120°C). The effect of annealing has been attributed to the relaxation of the amorphous regions and the development of lamellar texture, and the anisotropy in tan $\text{δ}\text{E}$ at the β relaxation is found to be consistent with the interlamellar shear model.     

Elastic constants and thermal expansivity of gel-spun polyethylene fiber and its composites

The five independent stiffness constants, C₁₁, C₃₃, C₄₄, C₆₆, and C₁₃, and the axial and transverse thermal expansivity of unidirectional gel-spun polyethylene fiber reinforced composites have been measured as functions of fiber volume fraction V_f. The axial extensional modulus C₃₃ and axial Poisson's ratio v₁₃ follow the rule of mixtures, while the axial shear modulus C₄₄, transverse shear modulus C₆₆, and transverse plane-strain bulk modulus C_t ( = C₁₁ − C₆₆) obey the Halpin-Tsai equation. Extrapolation to V_f = 1 gives the five stiffness constants of gel-spun polyethylene fiber. The tensile property of the fiber is highly anisotropic, with the axial Young's modulus about 40 times higher than the transverse Young's modulus. In contrast, the axial shear modulus exceeds the transverse shear modulus by only 5%. A similar treatment of the thermal expansivity data in terms of the Schapery equations gives an axial thermal expansivity of −1.25 × 10⁻⁵ K⁻¹ and a transverse thermal expansivity of 11.7 × 10⁻⁵ K⁻¹ for the fiber.     

Elastic moduli of liquid crystalline copolymers

Dynamic tensile and shear moduli measurements have been carried out on highly oriented thermotropic liquid crystalline copolymers formed by random copolymerization of 2-hydroxy-6-naphthoic acid, terephthalic acid and p-aminophenol. This liquid crystalline copolymer is known as HNATA. Application of the aggregate model of units of structure gives rise to an estimation of the orientation angle θ = 5° and a chain modulus E_c = 230 GPa. The fall in tensile modulus with increasing temperature is related to two factors: a decrease in the intrinsic chain modulus and a reduction in the shear modulus.     

Dynamic mechanical analysis of fibers. I. Effect of experimental variables and material type

Depending upon the fiber material, some of the experimental variables can have a profound effect on the dynamic tensile modulus vs. temperature data. With the use of an experimental fiber (25°C < T_g < 75°C; T_m > 220°C; hot stretched), the effect of several variables, e.g., moisture/volatiles, annealing/relaxation, frequency (strain rate), pretension, and % strain on the modulus retention term [(E_100°C/E_25°C) × 100] have been studied. Of these variables, pretension and especially % strain dramatically increase the modulus retention and this effect is attributed to the elastic orientation under force (EOF), i.e., it exists only in the presence of tensile forces and is reversible. Such an effect was insignificant for Kevlar (T_g ? 375°C) and absent for steel wire. Dynamic modulus measurements at 25°C using sonic techniques also support the EOF phenomenon in polyethylene yarns (T_g ～ ?30°C) but not in Kevlar polymide yarns (T_g ～ 375°C).     

Molecular Orientation and Mechanical Properties of Poly(Vinyl Alcohol) Fibers

Abstract

A number of poly(vinyl alcohol) fibers with different draw ratios was characterized by measuring the birefringence, crystalline orientational order, crystallinity, tensile strength, and modulus. The birefringence, tensile strength and modulus increased with increasing draw ratio whereas the crystallinity and crystalline order parameters remained constant within narrow limits. The increase in birefringence has to be attributed solely to an increase in chain orientation in the amorphous phase of the semicrystalline fiber. The tensile strength and modulus are therefore directly related to the chain orientation in the amorphous phase. With the aid of a simple two-phase model it was found that the modulus of the amorphous phase in its disordered conformation was 4.8 GPa. The intrinsic birefringence of the amorphous phase was found to be 79 × 10^?3, i.e. much higher than the value obtained for the crystalline phase (52 × 10^?3). When this value was used in calculations, it was found that the order parameter of the amorphous phase increased from around 0.1 for a draw ratio of 1 to approximately 0.6 for a draw ratio of 5, whereas the order parameter of the crystalline phase was close to 1 for all draw ratios.     

Roller drawing of polyoxymethylene

The roller drawing of polyoxymethylene (POM) sheets was carried out in the temperature range of 140–157°C. The mechanical properties, the molecular orientation, and the microstructure of the roller-drawn POM sheets were investigated by means of tensile test, dynamic viscoelasticity, wide-angle X-ray diffraction, small-angle X-ray scattering, visible dichroic spectrum, electron microscopy, and so on. The Young's modulus and the tensile strength increased with increasing draw ratio up to draw ratio, λ of 14–15. The improvement of the mechanical properties is concerned with structural changes, such as the increase in orientation function in the crystalline and amorphous regions and the formation of taut tie molecules and crystalline bridges in the intercrystallite and interfibrillar regions. In the higher draw ratio range (λ > 15), the increase in Young's modulus and tensile strength was restricted by the formation of interfibrillar microvoids.     

Relationships between mechanical properties and relaxation processes in polymers. Nylon 6

The dynamic-mechanical properties as a function of temperature and frequency were measured for five samples of polycaprolactam (nylon 6) containing different amounts of hydrosoluble products. Low- and high-speed tensile properties and Izod impact strength were determined between ?190° and 100°C for the same samples by using autographic methods. The influence of the mechanical relaxation processes on moduli, yield strength σ_y, yield strain ε_y, tough-brittle transition temperature, elongation at break ε_R, and tensile and Izod fracture energies was investigated. It has been found that some mechanical properties, such as modulus and yield properties, can be directly related to specific relaxation phenomena, whereas as far as other properties, such as the ultimate properties, are concerned, the existing correlation can be concealed by the interference of purely mechanical phenomena which depend on the testing technique used, the testing conditions, and the previous history of the material.     

Equilibrium disperse dye sorption by drawn polypropylene films

Isotactic polypropylene (PP) films drawn at various temperatures ranging from 100 to 155°C have been dyed at 80°C with p-aminoazobenzene (PAAB) or C.I. Disperse Yellow 7 (Y-7). The equilibrium dye sorption (M₀) of PAAB obtained for these films decreased with an increase in draw ratio (λ) of the films. The M₀ values of Y-7, however, increased with increasing in λ similarly the crystallinities of these films increased slightly with draw ratios. By use of fine structural data of these films, the change in M₀ of Y-7 for drawn PP films were analyzed in terms of a mosaic-block structural model. The increase in M₀ with increasing in λ was thus ascribed to enhanced sorption by the amorphous side region between crystalline cores located parallelly in the direction to the molecular axis. The side regions of the drawn systems become rich in interfibrillar tie chains in a higher range of λ. The side region seem to have a strong affinity particularly to a long rodlike dye molecule such as Y-7; this feature is probably associated with the amount of the amorphous chains having extended chain conformation, the fraction of which increases during drawing.     

Mechanical properties of crosslinked polyurethanes

Stress–strain and stress–relaxation behavior of polyurethane elastomers based on poly(ethylene adipate), poly(ethylene maleate), polyethylene glycol, and 4,4′-diphenylmethane diisocyanate (MDI) have been studied. The elastomers were crosslinked by an excess of MDI and by dicumyl peroxide (DiCup); the latter was supposed to form additional crosslinks on the unsaturated bonds. The determined values of Young's modulus, Mooney-Rivlin elastic parameters C₁ and C₂, relaxation moduli E(10 sec) and E(100 sec), as well as relaxation speed were used to estimate the effect of MDI- and DiCup-formed crosslinks on the mechanical behavior of polyurethanes. It was found that while the elastomers crosslinked by MDI only apparently displayed viscoelastic properties, the polyurethanes additionally crosslinked by DiCup exhibited more elastic behavior. The results obtained were explained on the basis of changes in the amount of secondary bonding due to the additional network junctions formed by DiCup at nonpolar groups.     

Influence of thermal and mechanical histories on the viscoelastic behavior of drawn polyethylene

Storage and loss elasticity complex moduli E′ and E″ and temperatures at which the α relaxation takes place are studied with respect to thermal history, deformation speed, and molecular weight distribution of drawn linear polyethylene. Maximum values of E′ and E″ increase with draw ratio of the hot-drawn samples, and the α relaxation temperatures increase by around 10°C when the polyethylene filaments are annealed at 110°C. The activation energy of the process, considered as a single one because the symmetrical shape of the maxima, increases with draw ratio, and this increase is less pronounced when the filaments are annealed. Annealing of the filaments produces a decrease in their E′ values, but this decrease is almost negligible for filaments obtained from polyethylene with a broad molecular weight distribution. The final crystallinity of the filaments drawn at room temperature and subsequently annealed is higher for the filaments obtained at lower drawing speed.     

Auxetic polypropylene films

Auxetic materials are those exhibiting negative Poisson's ratio (ν) behavior. Polymeric auxetic extruded products in the form of cylinders and fibers have previously been reported. This article reports the successful production of auxetic polypropylene films (～0.15‐mm thick) using a melt extrusion process. Video extensometry and tensile testing techniques have been used to measure the in‐plane Poisson's ratios and Young's moduli of the auxetic film, both on an Instron tensile testing machine and a Deben microtensile testing machine. The film is elastically anisotropic with the Poisson's ratio and Young's modulus along the extrusion (x) direction being ν_xy = ?1.12 ± 0.06 and E_x = 0.34 ± 0.01GPa, respectively, while the Poisson's ratio and Young's modulus in the transverse (y) direction to the extrusion direction are ν_yx = ?0.77 ± 0.01 and E_y = 0.20 ± 0.01GPa, respectively. POLYM. ENG. SCI., 45:517–528, 2005. © 2005 Society of Plastics Engineers     

Dynamic mechanical properties of polypropylene composites filled with ultrafine particles

The dynamic moduli of isotactic polypropylene (PP) filled with ultrafine SiO₂ and micron sized glass particles are measured in the temperature range 30–130°C at frequency 10 Hz. The storage moduli of PP composites, E′_c, increase with filler content and decreasing filler size in the whole range of temperature. The loss moduli of PP composites, E″_c, increase with filler content and decreasing filler size above 40°C. The intensity of the broad despersion which appears at ca. 60°C increases with filler content and decreasing filler size. By assuming that the energy is not dissipated in the effective volume, namely, filler volume plus that of immobilized interfacial region, the effective volume fraction is evaluated from the relative loss modulus, E″_cE″₀ at 60°C. The effective volume fraction increases with filler content and decreasing filler size. The effect of addition of ultrafine particles on the broad dispersion at ca. 60°C resembles the effect of increasing crystallinity of pure PP. It is concluded that the broad dispersion which appeared at ca. 60°C seemed to be assigned to the grain boundary of PP composities or crystalline boundary of pure PP.     

Analysis of the tensile stress-strain behavior of elastomers at constant strain rates. I. Criteria for separability of the time and strain effects

Considering the case where the relaxation time spectrum is preserved at finite deformations, a theoretical analysis of the tensile stress-strain relation of elastomers at constant strain rates has been carried out. The finite strain effect is taken into account by replacing the Cauchy strain by a general strain function, ?(?), in the Boltzmann superposition integral. The analysis shows that there are two cases where the time and strain effects are separable when: (1) the segment of the stress relaxation modulus which coincides with the experimental time of stretching can be represented by a single power law; and (2) the general strain function, ?(?), is linearly proportional to the Cauchy strain. Separability of the time and strain effects, therefore, can be achieved by adjusting the stretching time (or strain) and temperature, if the relaxation time spectrum remains unchanged by the deformation. The tensile stress-strain relations derived from the theoretical analysis were applied to analyze data on a crosslinked styrene butadiene rubber obtained in the temperature range ?40 to 60°C. Γ(?), which describes the strain dependence of tensile stress, B_?, the ratio of isochronal stresses at different strains, and a_i, slope of a segment of the relaxation modulus E_i(t) on log t plot, were obtained directly from the experiment. Values of Γ(?), B_? and a_i obtained at ?40°C are quite different from those obtained at ?30°C or higher. Results obtained from our analysis are generally in agreement with those obtained by an empirical method for analyzing the experimental data.     

Effect of annealing and orientation on microstructures and mechanical properties of polylactic acid

Two types of polylactic acid (PLA) films (one amorphous and one semi‐crystalline) were produced by sheet extrusion. Talc was used as a nucleation agent for the semi‐crystalline PLA. The films were annealed above their T_g or were uniaxially orientated in two ways: (1) via a drawing system in front of the extruder and die or (2) via a three‐roller stretching system. The slower crystallization rate and lower melting stress of the PLA resulted in amorphous film using the drawing system. Annealing above T_g increased crystallinity and polymer chain relaxation, which resulted in increases in both strength and toughness. Stretching above T_g also produced simultaneous crystallization and chain relaxation, which resulted in increases in both modulus and toughness. Both modulus and tensile strength in the stretching direction were higher than in the crosswise direction. Talc acted not only as a rigid filler to reinforce the PLA, but also as a nucleation agent for the PLA, especially during annealing. POLYM. ENG. SCI., 2008. © 2008 Society of Plastics Engineers     

The effect of aspect ratio of inclusions on the elastic properties of unidirectionally aligned composites

This paper examines the influence of aspect ratio α, from zero to infinity, on the effective elastic moduli of a transversely isotropic composite. The reinforcing inclusions, which could be flakes or short fibers, are assumed to be spheroidal and unidirectionally aligned. Of the five independent elastic constants, the longitudinal Young's modulus E₁₁ and in-plane shear modulus μ₁₂ appear to increase with increasing aspect ratio, while the transverse Young's modulus E₂₂, out-plane shear modulus μ₂₃, and plane-strain bulk modulus K₂₃, generally decrease. It is further noted that E₁₁ is more sensitive to α when α > 1 but the others are more so when α < 1. The present analysis was carried out by the combination of Eshelby's and Mori-Tanaka's theories of inclusions.     

Dynamic mechanical properties of methacrylic-acid-grafted polyethylene films

A dynamical mechanical relaxation study has been made of low density polyethylene films to which methacrylic acid has been grafted by γ irradiation. The grafted films retain the original degree of crystallinity and show only slight changes in melting points and melt viscosities. This indicates that the grafted methacrylic acid side chains are long, few in number, and completely phase separated from the polyethylene matrix. Three dispersion regions are observed in plots of the loss modulus, E″ vs. temperature at constant frequency and these are labeled γ, β, α′, in order of increasing temperature. The α′ peak, above 215°C was assigned to microbrownian segmental motions accompanying the T_g of polymethacrylic acid. The β peak, at ?20°C, was assigned to motions accompanying the T_g of branched polyethylene, and the γ peak, at ?120°C, was assigned to local motions of a few CH₂ sequences in polyethylene.