The entanglement network and craze micromechanics in glassy polymers

Crazes have been grown from crack tips in thin films of the following five polymers: polytertbutylstyrene (PTBS), polystyrene (PS), poly(styrene-acrylonitrile) (PSAN), poly(phenylene oxide) (PPO), and poly(styrene-methyl methacrylate) (PSMMA). These polymers represent a wide range of l_e values, where l_e is the chain contour length between entanglements. Quantitative transmission electron microscopy has been used to analyze the extension ratio λ_craze and displacement profiles for these crazes. From these measurements the craze surface stresses have been computed by using the method of distributed dislocations. This analysis also permits an accurate measure of the level of the applied stress σ_∞. These measurements show that the stress necessary for crazing increases as l_e decreases and that the higher surface stresses present at crack tips generate crazes that have higher λs than isolated crazes in the same polymers. Surface drawing is shown to be the dominant mechanism for craze thickening in all five polymers.     

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.     

Effect of molecular entanglements on craze microstructure in glassy polymers

Thin films of ten glassy polymers are bonded to copper grids and strained in tension to produce crazes, which are then examined in the transmission electron microscope. The average craze fibril extension ratio λ for each polymer is determined from microdensitometer measurements of the mass thickness contrast of the crazes. The extension ratio λ is found to increase approximately linearly with the chain contour length l_e between entanglements, as determined from melt elasticity measurements of the entanglement molecular weight of these polymers. These results are analyzed by comparing them with λ_max, the maximum extension ratio of an entanglement network in which polymer chains neither break nor reptate (i.e., permanent entanglement crosslinks are assumed). The values of λ_max are given by l_e/d where d, the entanglement mesh spacing in the unoriented glass, is computed from d = k(M_e)^1/2 with k determined either from small-angle neutron scattering results on isolated chains in the glass or from coil size measurements in dilute solutions of a θ solvent. The craze extension ratios fall somewhat below λ_max at low λ but increase to well above λ_max for polymers with high l_e. This comparison suggests a significant contribution due to chain breakage (or reptation) in the higher-λ crazes of large-l_e polymers, which may arise from the higher true stresses in the craze fibrils (which for a given applied stress increase proportionally to λ). The results also imply that a useful way to increase the “brittle” fracture stress and decrease the ductile-to-brittle transition temperature of a glassy polymer is to decrease its entanglement contour length l_e.     

The effect of plasticization on craze microstructure

The structure of crazes in plasticized polystyrene has been studied by means of small-angle x-ray scattering and optical interference microscopy. Addition of plasticizer causes a rapid increase in the mean fibril diameter D and a slow decrease in the craze fibril volume fraction v_f. The crazing stress σ_c was also measured and it was found that the product D σ_c is independent of plasticizer concentration. These results are shown to be consistent with the entanglement model for controlling v_f and the meniscus instability model of craze thickness growth.     

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.     

Ar atom emission as a probe of craze formation and craze growth in polystyrene

A report of measurements of Ar emission during the loading of polystyrene and high impact polystyrene in vacuum is presented. Argon was introduced into the material prior to the experiment by storing the samples in an Ar atmosphere. The development of crazes during loading was monitored by videotaped visual observations and scattered light measurements. Increased Ar emission is observed at the onset of crazing, provided that the crazes intersect the surface. The strength of the Ar signal depends upon the extent of crazing; especially intense signals are observed from samples which display significant crazing prior to fracture. High-impact polystyrene shows intense emissions at yield which soon decay due to the depletion of Ar from the near surface material. The emission intensity rises again prior to fracture, when surface crazes become connected to crazes in the bulk. Thus the emission of volatile species during deformation reflects the growth of crazes intersecting the surface, as well as changes in the “connectivity” of the craze network. © 1993 John Wiley & Sons, Inc.     

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.     

DYNAMIC MECHANICAL RESPONSE OF CRAZES IN POLYSTYRENE

Dynamic mechanical analysis was used to study the mechanical properties and microstructureof crazes in polystyrene produced in air or in methanol at different temperatures. A new loss peakwas found at about 82℃,which is assigned to glass transition peak of craze fibrils. The decreaseof glass transition temperature of polymer in craze fibrils is due to the high values of surface tovolume ratio. The glass transition temperature ratio of craze fibrils to bulk material (T_g~l /Tg) hasbeen expressed as a function of the fibrils diameter (d). From T_g~l of craze fibrils,the value of fibrildiameter can be calculated. Annealing the crazed specimen at room temperature makes the fibrilsplastically deform and cause the fibrils to thin slightly,whereas annealing the crazed specimen atthe temperature near T_g of the craze fibrils makes the fibrils bundle together.     

Low-angle electron diffraction from high temperature polystyrene crazes

Low-angle electron diffraction (LAED) was used to study the microstructure of crazes produced at different temperatures T and strain rates in thin films of monodisperse polystyrene (PS). At a slow strain rate of 4.1 × 10^?6 s^?1 both the fibril diameter D and the fibril spacing D₀ of crazes in 1800k molecular weight PS remained constant with temperature up to T ≈ 70°C and then sharply increased as T approaches T_g. At a higher strain rate of ～ 10^?2 s^?1, both D and D₀ increase only slightly with T. The values of D and D₀ over a range of temperature are in very good agreement with those values obtained in bulk samples using small-angle x-ray scattering. The crazing stress was measured as a function of temperature in the thin films of the 1800k molecular weight PS strained at the same slow strain rate used for the LAED measurements. These measurements were analyzed using a simple model of craze growth to reveal the temperature and strain rate dependence of the craze surface energy Γ. At room temperature Γ ≈ 0.076 J/m² (versus Γ ≈ 0.087 J/m² predicted) and was observed to remain constant up to T ≈ 70°C and then decrease by approximately a factor of two at T = 90°C. This decrease in Γ is believed to result from chain disentanglement to form fibril surfaces at sufficiently high temperatures and occurs in the same temperature range in which the craze fibril extension ratio λ was observed to increase.     

Quantitative approaches to particle cavitation,shear yielding,and crazing in rubber-toughened polymers

Models for rubber particle cavitation, shear yielding, and crazing are reviewed, and their ability to predict the large-strain deformation behavior of toughened polymers is discussed. An existing model for void initiation and expansion in rubber particles correctly predicts the observed trends: cavitation resistance increases when either the shear modulus or the surface energy of the rubber is increased, or the particle size is reduced. However, further work is needed to improve quantitative modeling of the thermally- and stress-activated void nucleation step. Shear yielding, which is also a rate process, is much better understood; here, the main problems in modeling relate to the formation and evolution of porous shear bands. Craze growth and failure are also reasonably well understood, but previous attempts at modeling have been hampered by uncertainties about craze initiation. To overcome these difficulties, a new theory of crazing is proposed, which treats initiation as a fracture process, and defines a new materials property, G_nasc, the energy required to form unit area of nascent craze. Because nascent crazes are ∼20 nm thick, G_nasc is low: calculations give values <0.5 J m⁻² for polystyrene. A new criterion incorporating a plasticity factor fits the data of Sternstein and coworkers on crazing under biaxial loading. In combination with theories of particle cavitation and shear yielding, the fracture mechanics model explains why the balance between crazing and shear yielding is governed by particle size, for example in ABS. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1399–1409, 2007     

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.     

The effect of preliminary orientation of polymers via tensile drawing at elevated temperature on solvent crazing

We studied how the preliminary orientation of an amorphous glassy PET via its uniaxial tensile drawing above the glass transition temperature affects the deformation behavior during subsequent tensile drawing in the presence of adsorptionally active environments. The tensile drawing of the preoriented PET samples with a low degree of preliminary orientation (below 100%) in the presence of liquid environments proceeds via the mechanism of solvent crazing; however, when a certain critical tensile strain is achieved (150% for PET), the ability of oriented samples to experience crazing appears to be totally suppressed. When the tensile drawing of preoriented samples is performed at a constant strain rate, the craze density in the sample increases with increasing degree of preliminary orientation; however when the test samples are stretched under creep conditions, the craze density markedly decreases. This behavior can be explained by a partial healing and smoothening of surface defects during preliminary orientation and by the effect of entanglement network. The preliminary orientation of polymers provides an efficient means for control over the craze density and the volume fraction of fibrillar polymer material in crazes.     

Craze initiation of glassy polymers under the action of crazing agent

This paper deals with the formation of crazes that may be caused by an external load on glassy polymers wetted with kerosene. First, the orientation of crazes has been determined when applying a uniaxial tension to a specimen of cold-rolled polyvinyl chloride sheet at various angles to the rolling direction. The critical stress for craze initiation in poly(methyl methacrylate) and polyvinyl chloride rods has been investigated under combined tension–torsion loading. It is shown that: (1) in an anisotropic, as well as an isotropic polymer, the direction of crazes is perpendicular to that of the maximum strain calculated by taking into account the internal stress due to rolling; and (2) under the action of a crazing agent, crazing may occur even under the pure torsional load, i.e., in the absence of dilatational stress.     

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.     

Effect of orientation on the mechanism of plastic yielding of poly(ethylene terephthalate) in adsorption-active media

The effect of the preliminary orientation on the formation of crazes in poly(ethylene terephthalate) during straining in adsorption-active liquids is studied. Poly(ethylene terephthalate) is oriented by drawing at a temperature of 80°C, which is somewhat higher than its glass-transition temperature (～75°C). After orientation, samples are tested in tension in organic liquids at room temperature. At low degrees of preliminary drawing, the shear yield stress during straining in air does not increase significantly. However, the stress of craze widening rises in proportion to the degree of preliminary drawing. Thus, the orientation suppresses crazing and leads to the transition to shear flow. A model is proposed to explain the effect of orientation on crazing. According to this model, craze widening and pulling of a nonoriented polymer into the craze volume result from the formation of pores in the bases of fibrils. The formation of fibrils is caused by straining of the polymer between pores.     

Craze initiation in poly(methyl methacrylate) under biaxial stress

Criteria for craze initiation in poly(methyl methacrylate) have been investigated under various combined loadings including biaxial tension and torsion-compression at 65°C in air and at room temperature in a crazing agent, kerosene. Environmental crazes are observed even under torsion-compression loading when air crazing does not occur, and the stress locus for environmental crazing is very different from that for air crazing. A theoretical model analogous to the Cottrell model in crystal plasticity is proposed. Theoretical crazing loci derived from the model are compared with the experimental results.     

Cloning of two genes (LAT1,2) encoding specific L: -arabinose transporters of the L: -arabinose fermenting yeast Ambrosiozyma monospora

We identified and characterized two genes, LAT1 and LAT2, which encode specific l-arabinose transporters. The genes were identified in the l-arabinose fermenting yeast Ambrosiozyma monospora. The yeast Saccharomyces cerevisiae had only very low l-arabinose transport activity; however, when LAT1 or LAT2 was expressed, l-arabinose transport was facilitated. When the LAT1 or LAT2 were expressed in an S. cerevisiae mutant where the main hexose transporters were deleted, the l-arabinose transporters could not restore growth on d-glucose, d-fructose, d-mannose or d-galactose. This indicates that these sugars are not transported and suggests that the transporters are specific for l-arabinose.     

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.     

Specific features of the formation of poly(vinylchloride)-dye composites based on solvent-crazed nanostructured polymer matrices

Healing and migration of dye molecules in porous nanostructured amorphous-polymer-dye systems prepared by solvent crazing are studied by the method of spectroscopy in the visible spectral region. The conversion of the above processes is controlled by the temperature in the temperature interval above T _g of the bulk polymer. Both processes proceed simultaneously and are independent. After the removal of AALE from the composite and shrinkage of the polymer sample at room temperature, crazes preserve their fibrillar structure, which can be identified by light scattering at 400–600 nm. The main contribution to healing from the fibrillar material of crazes is provided by the reptational mobility of macromolecules, a conclusion that is confirmed by the power dependence of light scattering of the sample on the duration of its thermal treatment with an exponent of 1/4 as well as by the activation energy of this process, which is ∼400 kJ/mol. The kinetic dependences of the intensity of absorption bands of monomer forms of a dye on annealing time have an exponent of 1/2 and show two linear regions. This behavior can be explained by the migration of dye molecules in their monomer form from their absorbed state on the surface of the fibrillar crazed material first into the volume of fibrils and then into the volume of bulk-polymer regions. All the above phenomena are provided by the unique structure of the solvent-crazed polymer material (alternation of the closely spaced regions containing fibrillar material and bulk-polymer regions).     

Craze growth and healing in polystyrene

The kinetics of craze growth and craze healing were studied by dark-field optical microscopy in monodisperse molecular weight polystyrene (PS) that varied in molecular weight from 88,000 to 1,334,000. The following observations were made. (1) G₁ the virgin growth rate, decreased rapidly with increasing molecular weight until M_n ～ 200,000 and then remained constant. (2) G₁ decreased with increasing craze density. (3) The growth rates of approaching craze tips decreased when the craze tips overlapped, and the effect was less for crazes whose parallel growth paths were greater than 40 μm apart. (4) Complete craze healing was observed by comparison of the nucleation times, τ₂, and growth rates, G₂, of healed individual crazes with the craze kinetics of the virgin sample. (5) The extent of healing was characterized using four cases in which τ and G were measured as a function of healing time, temperature, constant stress, and molecular weight. (6) Craze healing times were found to increase with molecular weight and were analyzed in terms of the modified molecular weight of the craze zone. (7) Significant bond rupture was determined to occur during crazing by comparison of healing times with stress relaxation and diffusion data. (8) Craze healing studies provide insight into both crack healing and fracture of glassy polymers.