Mechanical and transport properties of drawn low-density polyethylene

Quenched, quenched and annealed, and slowly cooled branched low-density polyethylene films were drawn at 25, 40, and 60°. The true draw ratio λ^L of the volume element was obtained and used to characterize the dependence on plastic deformation of the density, drawing stress, and work of plastic deformation, and the sorption and diffusion of methylene chloride. The effects observed are similar but less drastic than on linear high-density polyethylene. In particular, the transformation from the original lamellar to the final fibrous structure seems to be fastest for λ^L between 3 and 4. But the changes of vapor transport clearly indicate that the transformation is not yet complete even at the highest draw ratio λ^L = 6, just before the sample breaks. Annealing at 90°C of the drawn samples with free ends restores or even increases the transport properties beyond those of the undrawn sample without causing the fibrous structure to revert to the original lamellar structure.     

Yielding of a notched poly(vinyl chloride) sheet

The development of plastic deformation around the crack tip of poly(vinyl chloride), a ductile glassy polymer, has been studied in relation to the Dugdale–Barenblatt model of ductile yielding. Three-dimensional observations reveal that the plastic deformation ahead of the crack tip consists of crazes, shear bands, and their intersections. The formation of the craze is due to a state of plane strain at the immediate vicinity of the crack tip and restricted to early steps of loading. The size and shape of the fully developed plastic zone can be described by the model. The influence of strain hardening beyond the yield point is discussed on the basis of comparison of the plastic zone lengths of poly(vinyl chloride) with those of polycarbonate which always shows shorter lengths than the model predicts.     

Plastic fracture

It has been previously shown that when rigid poly(vinyl chloride) is extended by fully necking the test-piece, subsequent fracture takes place by a novel mechanism. Surface crazes grow into “diamond” -shaped cavities which slowly expand while retaining their shape. We have now found that this new mechanism is of general applicability to a wide range of plastics which fracture after yielding. Examples are given from polycarbonate, poly(ether sulfone), and poly(methyl methacrylate) broken at elevated temperatures. The form of the diamond cavity is determined by the continuation of plastic deformation in the whole test-piece while the diamond grows bigger. After fracture a characteristic cavity is left behind on the fracture surface which demarcates the zone of slow growth. At a given point, which is generally easily observable on the fracture surface, the crack speeds up. This change is believed to correspond to a situation where enough elastic energy is available to propagate a crack. It is favored, not only by the increase in size of the diamond in the test-piece but also by an increase in the average energy stored per unit volume of material.     

Crazing and shear deformation in crosslinked polystyrene

Thin films of polystyrene (PS) are bonded to copper grids and crosslinked with electron irradiation. When the films are strained in tension regions of local plastic deformation, either crazed or plane stress deformation zones (DZs), nucleate and grow from dust particles. the nature of the local deformation, as well as the local extension ration λ, is determined by transmission electron microscopy. The behavior of the PS glass is consistent with its being a network of molecular strands of total density v = v_E + v_X, where v_E is the entangled strand density inferred from melt elasticity measurements of uncrosslinked PS and v_X is the density of crosslinked strands determined from the ratio of the applied electron dose to the electron dose for gelation. when v is less than 4 × 10²⁵ m^?3 (<1.3v_E), only crazes are observed whose microstructure is similar to those in uncrosslinked PS. As v increases from 4 × 10²⁵ to 8 × 10²⁵ m^?3 (from 1.3v_E to 2.5v_E) shear deformation begins to compete with crazing. As v increases above 8 × 10²⁵ m^?3, only shear DZs are observed, the strain in which becomes progressively more diffuse as v increases. The λ in the crazes and DZs correlate well with λ_max, the maximum extension ratio of a strand in a network of density v computed using the Porod×Kratky model. For crazes ln(λ) ? 0.9 ln(λ_max) and for DZs ln(λ) ? 0.55 ln(λ_max). The strain at which crack nucleation is first observed increases as v increases from <5% in uncrosslinked PS with v = 3.3 × 10²⁵ m^?3 to >20% in PS with v = 33 × 10²⁵ m^?3 (v = 10v_E); crosslinking to still higher crosslink densities, e.g., v = 14v_E, results in cracks which propagate in a catastrophic manner at low applied strains. An optimum v thus exists, one not too high to suppress local shear ductility but high enough to suppress crazes which can act as crack nucleation sites. these results are compared with previous results on a variety of linear homopolymers, copolymers, and polymer blends that are characterized by a wide range of v (v = v_E). The transitions from crazing to crazing plus shear and from crazing plus shear to shear only take place at almost identical values of v. In addition the correlation between λ in the crazes and DZs and λ_max for a single network strand is the same for both classes of polymers. This agreement implies that chain scission is the major mechanism by which strands in the entanglement network are removed in forming fibril surfaces. Craze suppression, by either increasing v in the crosslinked polymer or v_E in the uncrosslinked ones, is due to the extra energy required to break more main-chain bonds to form these surfaces.     

Thermal activation parameters for large strain deformation of polyethylene and polycarbonate

Experiments were performed to determine the effects of strain rate, temperature, and pressure on the flow stress of polyethylene and Lexan polycarbonate deformed in shear. The results were analyzed to determine the activation enthalpy and the shear and dilatation activation volumes of the rate-limiting mechanism of the deformation process. Results show that the activation event involves a volume containing several monomer units and that this volume must dilate by as much as 7% during the activation event. The activation enthalpy was approximately 2.5 × 10^?12 erg for polyethylene and 1.1 × 10^?12 erg for polycarbonate. The rate-limiting mechanism for polyethylene seemed to be unchanged by plastic strains of up to 250%.     

Micro and nano layered polymers

The crazing behavior of coextruded microlayer sheets consisting of alternating layers of polycarbonate (PC) and styreneacrylonitrile copolymer (SAN) was investigated as a function of PC and SAN layer thicknesses. In this study, the total sheet thickness remained essentially constant and the PC and SAN layer thicknesses were changed by varying both the total number of layers from 49 to 1857 and the PC/SAN volume ratio.^[1,2] Photographs of the deformation processes were obtained when microspecimens were deformed under an optical microscope. Three different types of crazing behavior were identified: single crazes randomly distributed in the SAN layers, doublets consisting of two aligned crazes in neighboring SAN layers, and craze arrays with many aligned crazes in neighboring SAN layers. The transition from single crazes to doublets was observed when the PC layer thickness was decreased to 6 microns. Craze array development was prevalent in composites with PC layer thickness less than 1.3 microns. It was concluded that SAN layer thickness was not a factor in formation of arrays and doublets; formation of craze doublets and craze arrays was dependent only upon PC layer thickness.     

The thermoelastic effect in glassy polymers

The thermoelastic effect has been measured in compression on four glassy polymers; namely, polystyrene, poly(methyl methacrylate), polycarbonate, and epoxy resin. Quantitative results have been obtained for the first time on three of these polymers. It has been shown that by paying attention to specimen geometry and instrumentation results can be obtained to a high degree of accuracy (better than ±1.5% on a given set of measurements). The polymers are shown to obey the classical Thompson equation for thermoelasticity in solids over the temperature range studied (ca. 220–350°K). By inference such materials can be expected to behave classically in general. The results have been used, as first suggested by Trainor and Haward, to obtain values for the linear thermal expansion coefficient and the values so obtained are shown to be in excellent agreement, in general, with literature values obtained by more conventional methods. Results are given for a range of stress from 5 MN m^?2 to between 25 and 50 MN m^?2 according to ambient temperature. The method affords a measurement of parameters, in particular, linear thermal expansion coefficient. Values of specific heat for the four plastics have been measured by differential scanning calorimetry and the results compared with published data.     

Delayed yielding of polycarbonate under constant load

The time-dependent yielding of glassy polycarbonate subjected to constant tensile loads has been studied. Application of a constant stress of a magnitude between the yield stress and the stress required for propagation of a neck in constant strain tests results in inhomogeneous yielding after a well-defined time lag. This delay time increases with decreasing stress and temperature. The critical stress for slowly cooled material is greater than that for quenched material in which the delay time is divided in two regions. The delay time is regarded as the time required for the initiation of inhomogeneous yielding at either edge of the specimen and growth over a certain distance across the specimen. Geometrical observations revealed that the inhomogeneous yielding is shear yielding which is initiated due to stress inhomogeneities caused by mechanical imperfections at the edge of the specimen. The Eyring treatment of delayed yielding can describe fairly well the stress and temperature dependence of the delay time.     

The effect of strain rate on craze yielding,shear yielding,and brittle fracture of polymers at 77°K

The tensile strength of poly(methyl methacrylate) (PMMA), polycarbonate (PC), polychlorotrifluoroethylene, and polysulfone was measured in liquid nitrogen over the strain rate range of 2 × 10^?4 to 660 min^?1. These polymers deformed by crazing which was induced by the liquid nitrogen. The stress versus log strain rate curve was sigmoidal in that its slope increased and then decreased with strain rate. Above a critical strain rate of about 200 min^?1, which varied somewhat with the polymer, crazing was not observed with the optical microscope; the behavior became brittle, and the tensile strength became constant. The nonlinear behavior of stress versus log strain rate at low strain rates was associated with a decrease in activation volume with increasing strain rate whereas the nonlinear behavior at high strain rates was associated with an increase in density and decrease in length of the crazes with strain rate. The strain rate effect was the basis for calculating the diffusion coefficient of nitrogen into the polymers at 77°K. The shear deformation mode of PC was measured under compression and under tension. The compressive strength versus log strain rate was linear throughout the entire range giving a compression shear activation volume of 360 ų. The shear tensile strength of PC varied only slightly with strain rate when compared to the compressive strength. The brittle fracture stress of PMMA, in the absence of crazing, in compression and in tension, did not vary with strain rate.     

Development of crazes in polycarbonate,investigated by ultra small angle X-ray scattering of synchrotron radiation

The development of crazes in polycarbonate is investigated with the method of ultra small angle X-ray scattering of synchrotron radiation. Measurements at T = 130°C are discussed. The two-dimensional scattering patterns are analysed by means of a simple fibrillar model of the crazes. The geometrical parameters of the crazes as a function of the macroscopic draw ratio λ_d are determined using a curve-fitting procedure. The craze fibril volume fraction ν_f shows a complex dependence on λ_d.     

Low-angle x-ray scattering from crazes and fracture surfaces in polystyrene

Both crazes and fracture surfaces in glassy polymers produce a low-angle scattering of x-rays. Scattering patterns are anisotropic and often show considerable streaking. In the one case (polystyrene) studied extensively so far, detalied analysis suggests that the craze is approximated as a collection of spheroidal or irregular-shaped voids surrounded by material with anisotropic density distribution arising from its orientation in the stress direction. The void dimension is about 90–115 Å and the specific internal surface area about 170 m²/cm³ of craze. These results and those from electron microscopic studies are reasonably consistent.     

Cutting resistance of polyethylene

A thin polyethylene strip was cut along the centerline, the legs being pulled apart to minimize friction. Fracture energy G_c was obtained from the total work expended in cutting and tearing, yielding values of 4 kJ/m² for HDPE, 2 kJ/m² for HDPE crosslinked with 2.5% dicumyl peroxide, and 1 kJ/m² for LDPE. For an oriented sample of HDPE the value was 1.5 kJ/m². These values are considerably smaller than for simple tearing, about 10 kJ/m², suggesting that plastic yielding has been reduced. However, they are much higher than expected in the absence of yielding, about 50 J/m². Values of G_c were found to be proportional to yield stress and decreased in a similar way with temperature. On comparing results for G_c with work-to-break in tension, the diameter of the plastic zone at the cut tip was inferred to be about 15–20 μm, or one to three spherulite diameters, many times larger than the blade tip radius. © 1996 John Wiley & Sons, Inc.     

Plastic deformation of polytetramethylene oxide. I. Influence of molecular weight distribution,crystallinity, and structure

Polytetramethylene oxide with a planar zig-zag structure similar to polyethylene can be obtained with narrow molecular weight distributions. The plastic deformation of samples differing in molecular weight, molecular weight distribution, crystallinity, and structure has been studied. The degree of crystallinity of the undeformed annealed samples, as studied by NMR and DSC, leads to a value of the enthalpy of melting ΔH_m = 167 J g⁻¹, supporting the lower of two previously reported values. The low natural draw ratios and low Young's modulus of the drawn samples, together with the effect of blending a small amount of high molecular weight material into a low molecular weight sample, highlight the role of the flexibility and of the high molecular weight tail of the distribution in the plastic deformation process. The stress required for the propagation of the neck and the tensile strength are found to be linear functions of, respectively, the natural and maximum draw ratio.     

Crazing and fracture in crystalline,isotactic polypropylene and the effect of morphology,gaseous environments,and temperature

Stress crazing is studied in three forms of crystalline, isotactic polypropylene (PP): (1) smectic/nonspherulitic, (2) monoclinic/nonspherulitic, and (3) monoclinic/spherulitic PP. Optical and scanning electron microscopy as well as stress—strain measurements are used to characterize crazing behavior in these three forms as a function of temperature (?210 to 60°C) and of the gaseous environment (vacuum, He, N₂, Ar, O₂, and CO₂). Forms 1 and 2 are found to craze much like an amorphous, glassy polymer in the temperature range between ?210 and ?20°C, irrespective of environment. The plastic crazing strain is large close to the glass-transition range (ca. ?20°C) of amorphous PP and in the neighborhood of the condensation temperature of the environmental gas. Near condensation, the gas acts as a crazing agent inasmuch as the stress necessary to promote crazing is lower in its presence than in vacuum. A gas is the more efficient as a crazing agent, the greater is its thermodynamic activity. Spherulitic PP (form 3) crazes in an entirely different manner from an amorphous, glassy polymer, showing that the presence of spherulites influences crazing behavior much more profoundly than the mere presence of a smectic or monoclinic crystal lattice. Below room temperature, crazes are generally restricted in length to a single spherulite, emanating from the center and going along radii perpendicular, within about 15°, to the direction of stress. They never go along spherulite boundaries. Gases near their condensation temperature act as crazing agents much as in nonspherulitic PP. Above room temperature the crazes are no longer related to the spherulite structure, being extremely long and perfectly perpendicular to the stress direction. Apparently the crystals are softened enough by thermally activated segmental motion to permit easy propagation of the craze. The morphology of the fracture surfaces and its dependence on temperature and environment is described and discussed. Concerning the action of gases as crazing agents it is argued that the gas is strongly absorbed at the craze tip, where stress concentration increases both the equilibrium gas solubility and the diffusion constant. Hence, a plasticized zone is formed having a decreased yield stress for plastic flow. This is considered to be the main mechanism by which the gas acts as a crazing agent. In addition, reduction of the surface energy of the polymer by the adsorbed gas eases the hole formation involved in crazing.     

Crystal‐structure dependence of electroactive properties in differently prepared poly(vinylidene fluoride/hexafluoropropylene) copolymer films

The electroactive properties of two random copolymers of vinylidene fluoride (VDF) and hexafluoropropylene (HFP) were studied. The compositions were 95/5 and 85/15 mol % P(VDF/HFP). For each composition, three different film‐preparation methods were used—solvent casting, melt‐pressed quenched, and melt‐pressed slow‐cooled. The ferroelectric properties observed were strongly dependent on the preparation methods of the films as well as the HFP molar content of the samples. The highest remanent polarizations (P_r) obtained from electric displacement versus electric field (D‐E) hysteresis data are 80 and 50 mC/m² for the 5 and 15% HFP solvent‐cast samples, respectively. The slow‐cooled samples do not exhibit any ferroelectric behavior for either the 5 or 15% HFP copolymers. It was also observed that both the 5 and 15% HFP slow‐cooled samples have a smaller electrostrictive response relative to the other two types of samples. Wide‐angle X‐ray diffraction and DSC results suggest that the 5% HFP sample has a higher crystallinity relative to the 15% HFP sample for each preparation method. In addition, different crystal phases form in the samples resulting from the different preparation methods. Fourier transform infrared results suggest that the slow‐cooled samples are in the nonpolar α phase, whereas the quenched and solvent‐cast samples are more likely in the polar β phase. The slow‐cooled samples do not show a switching peak in their nonpolar α‐phase crystalline state. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2793–2799, 2001     

Rheooptical Fourier transform infrared spectroscopy of the deformation behavior in quenched and slow‐cooled isotactic polypropylene films

Emerging technological applications for complex polymers require insight into the dynamics of these materials from a molecular and nanostructural viewpoint. To characterize the orientational response at these length scales, we developed a versatile rheooptical Fourier transform infrared (FTIR) spectrometer by combining rheometry, polarimetry, and FTIR spectroscopy. This instrument is capable of measuring linear infrared dichroism spectra during both small‐strain dynamic deformation and large‐strain irreversible deformation over a wide temperature range. The deformation response of quenched and slow‐cooled isotactic polypropylene (iPP) is investigated. In quenched iPP, under dynamic oscillatory strain at an amplitude of ～0.1%, the dichroism from the orientation of the amorphous chains is appreciably less than that from the crystalline region. At large irreversible strains, we measured the dichroic response for 12 different peaks simultaneously and quantitatively. The dichroism from the crystalline peaks is strong as compared to amorphous peaks. In the quenched sample, the dichroism from the crystalline region saturates at 50% strain, followed by a significant increase in the amorphous region dichroism. This is consistent with the notion that the crystalline regions respond strongly before the yield point, whereas the majority of postyielding orientation occurs in the amorphous region. Our results also suggest that the 841 cm^?1 peak may be especially sensitive to the ‘smectic’ region orientation in the quenched sample. The response of the slow‐cooled sample at 70 °C is qualitatively similar but characterized by a stronger crystalline region dichroism and a weaker amorphous region dichroism, consistent with the higher crystallinity of this sample, and faster chain relaxation at 70 °C. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 2539–2551, 2002     

Thermally induced low-temperature relaxation of plastic deformation in glassy organic polymers and silicate glasses

A deep analogy between the processes of low-temperature thermally induced relaxation of plastic deformation in amorphous polymers and inorganic glasses is observed. The results of the calculation of the activation energy and activation volume of this relaxation process in terms of the excited state model satisfactorily agree with the experimental data obtained for both epoxy polymer systems and sheet silicate glasses. This evidence allows us to conclude that the initial stage of macroscopic plastic deformation in glassy systems involves small critical displacements of excited atoms (groups of atoms) that are provided by local rearrangements of neighboring particles (entropy fluctuations). In the vicinity of the yield point, the number of excited atoms per unit volume induced by the action of mechanical stresses appears to be quite sufficient (10²⁶–10²⁷ m^?3) for promotion of a marked plastic deformation of glasses and preservation of appreciable amounts of internal energy.     

Crystallite size in highly drawn polyethylene

The size and distortion of crystallites in samples of linear polyethylene were determined before and after plastic deformation. A slowly cooled sample, a quenched sample, and highly drawn films (draw ratio 16) were investigated by different methods. Wide-angle x-ray patterns were analyzed to study the average size of the crystalline mosaic blocks and their distortion. In addition, the longitudinal crystal thickness (in the chain direction) was evaluated by two other approaches, determination of the long period, and the melting temperature of irradiated samples. The results show clearly that the size of the crystalline mosaic blocks changes substantially with drawing of polyethylene. Not only is the lateral crystal thickness affected, but the longitudinal crystal dimensions also change during the drawing process. By the three independent methods we find that the longitudinal crystal thickness after drawing is independent of the value for the undrawn samples, as was reported earlier by Peterlin. The change in crystallite size after drawing is accompanied by a large decrease in crystal volume to about 10% of the value for the undrawn sample. The degree of distortion in the crystals seems not to be affected by the deformation process. These experimental data can be considered evidence for high chain mobility and for the possibility of rearrangement of chain molecules during the process of plastic deformation.     

Inelastic deformation of glassy polyaryleneetherketone: Energy accumulation and deformation mechanism

The plastic deformation of glassy non-annealed polyaryleneetherketone (PAEK) was investigated via deformation calorimetry and thermally stimulated recovery of residual strain. Polymer samples were deformed at room temperature under uniaxial compression up to ε_def =–(40?50)% at a rate of 0.04 min^?1. It was found that PAEK behaves in the deformation process similarly to many other glassy polymers: It stores internal energy excess at loading and contains two types of different inelastic strain carriers, namely the delayed elastic (ε_de) and plastic (ε_pl) strain carriers. The maximum level of the accumulated energy in PAEK reaches ≈ 8.3 J/g, which is close to those for glassy polystyrene and polycarbonate. Nearly all the deformation energy stored in PAEK is carried by the delayed-elastic strain. The carriers of plastic strain carry no extra energy or a very small amount of it. The inelastic deformation of glassy PAEK proceeds in two stages. The carriers of ε_de are nucleated at the first stage of the deformation process, and the carriers of ε_pl are nucleated at the second stage. It was shown that, during glassy-polymer loading, the molecular level structures carrying ε_pl never appear by themselves, but appear only as a result of spontaneous reorganization of ε_de. In other words, the plastic deformation appears in PAEK owing to the two-step process. This situation is typical for all glassy polymers.     

Solvent-induced embrittlement in a crystallizable polyarylate

The effects of solvent-induced crystallization on the micromechanical properties of thin films of polyarylate (PAr) were studied. Under uniaxial extension amorphous polyarylate was observed to deform exclusively by shear deformation with no evidence of crazing. Upon exposure to methylethyl ketone, vapor, or liquid, PAr crystallizes and is subsequently embrittled. Our transmission electron microscopy results clearly show that this embrittlement results from a transition in plastic deformation mechanism from shear yielding to crazing. A detailed examination of the samples revealed that the crazes formed preferentially within the noncrystalline regions and that the craze tips followed a complex trajectory around the crystallites. In some cases the craze tip advance deviated by as much as ±30 from a direction normal to the tensile axis. Because crazes are inherently more susceptible to forming cracks than shear deformation zones, crystallization reduces the fracture toughness of the polymer. This type of embrittlement, via a transition in plastic deformation mechanism, is believed to be a general behavior for solvent-crystallizable thermoplastics.