Mechanism of fracture in glassy polymers. II. Survey of crazing response during crack propagation in several polymers

Of nine glassy polymers so far investigated, eight yield evidence that fracture propagation involves the formation and breaking of craze material. All eight produce fracture surfaces exhibiting interference colors to one extent or another and even the colorless areas cause low angle x-ray scattering. Ranked in terms of decreasing ease of colored surface formation, these polymers are poly(methyl methacrylate), poly(ethyl methacrylate), polystyrene, acrylonitrile—styrene copolymer, poly-α-methylstyrene, poly(vinyl acetate), a polyhydroxy ether, and polycarbonate. Only rigid poly(vinyl chloride) has failed to show evidence of precrack craze formation.     

Cyclic crack propagation and molecular kinetics of polymers

Cyclic tests in tension were performed on PMMA and PC center-notched plate specimens. Frequencies between 0.1 and 100 Hz at temperatures from ?78 to +55°C were investigated. Correlations between crack growth rates, described in the terms of stress intensity K, and the appropriate values of the loss factor tan δ were studied. It was concluded that, in the investigated conditions, a direct correspondence exists between the crack growth rate and tan δ.     

Bush region in the propagation of electrical degradation in polymers

The model of electrical degradation describes the observed growth of damage in polymers quantitatively. It is shown that the fractal approach can be used to explain the non-monotonic behaviour of voltage versus scale for electrical degradation.     

The influence of temperature and frequency on fatigue crack propagation in polymers

Summary Centrally notched plate specimens of PMMA and PC were cycled in tension between constant stress intensity limits and crack growth was monitored against the number of cycles. A range of frequencies between 0.1 IIz and 100 Hz, and of temperatures between – 70 °C and + 40 °C was investigated. It was found that the cyclic crack growth decreased with decreasing temperature and/or increasing frequency. A linear relationship between crack length and number of cycles was observed. Application of the cyclic crack propagation law proposed byArad-Radon-Culver, namelyd(2a)/dN = ⁿ where is (K _max ² -K _min ²) and K_max andK _min are the respective values of maximum and minimum stress intensity factors, indicates that the indexn is unaffected by temperature or frequency variations in the investigated range (II regime of fatigue crack propagation) and the law would be a valid model if the term is suitably determined.

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Zusammenfassung Ermüdungsversuche im Rahmen der linearelastischen Bruchtheorien wurden ausgeführt auf zentralgekerbten Platten von PMMA und PC, sowie Rißwachstum als Funktion der Belastungszahl gemessen. Frequenzen von 0.1 Hz bis 100 Hz und Temperaturen von – 70 °C bis 40 °C zeigten, daß sich das Rißwachs-tum mit verringerter Temperatur und/oder erhöhter Frequenz verringerte. Eine lineare Abhängigkeit der Rißlänge von Belastungszahl wurde festgestellt. Die Benutzung der Rißausbreitung-Analyse von Arad-Radon-Culverd(2a)/dN =ⁿ, wo ist (K _max ² -K _min ²), zeigt, daß der Indexn nicht beeinflußt ist von Temperatur oder Frequenzwechsel in dem untersuchten Bereich (das sogenannte zweite Regime des Ermüdungswachstums). Wenn man die Konstante festgestellt hat, dann ist die Arad-Radon-Culver-Methode direkt benutzbar.

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With 12 figures     

Electron emission during deformation of polymers

Electron emission was detected during deformation of both carbochain and heterochain polymers in vacuum. It was found that the features of emission are similar to those observed in molecular scissions under drawing of unoriented and oriented polymers. This fact indicates that there is a relationship between the fracture process and electron emission under deformation of polymers. This relationship is also obvious from the experiments with interruption of loading when electron emission during the repeated loading does not begin immediately at the moment of load application, but can be recorded only at the degree of deformation which is higher than that reached during the first loading. The interconnection between deformational electron emission and molecular scissions allowed visualization of the fracture process in the subsurface layers of polymers using an electron-optical convertor which gives a mechanoemission image of a stretched sample. It is supposed that the deformation-induced electron emission of polymers is caused by ionization of stressed macromolecules resulting from tunnel transitions of electrons into deep traps. During deformation, the traps are destroyed and a part of electrons escapes in vacuum.     

Alternating crack propagation during directional drying

The propagation of fractures during the drying of a colloidal silica suspension confined in a vertical microtube is investigated. During the drying process, the particle concentration increases until gel formation. In the gelled region, the tensile stresses increase and lead to the formation of two vertical perpendicular cracks propagating in the drying direction, dividing the tube into four equivalent regions. Throughout the drying process, these two fractures do not propagate at the same velocity. The top crack inhibits the propagation of the crack that is left behind, and the slow propagation of a fracture is followed by the rapid propagation of the other.     

Mechanical selfsimilarity of polymers during chemical gelation

Network polymers near their gel point exhibit selfsimilar mechanical behavior, as expressed by power law relaxations. The range of selfsimilarity is defined by two limiting length scales. The upper limit is the correlation length, defined by the linear size of the typical cluster, and a lower limit, roughly given by the size of one preformed linear chain, i. e., the mean distance between crosslinks. The correlation length increases with the approach to the gel point, and diverges at the critical extent of reaction, i. e., the gel point where the infinite cluster is formed. Above the gel point, it decreases again with further crosslinking. Dynamic mechanical measurements of the complex modulus at the gel point show a power law in the frequency dependence over the entire frequency range, monitoring selfsimilarity. Swelling effects reduce the fractal dimension of the percolation cluster form 2.5 to 2. It is shown how the power law G() ^1/2, found by experiment, is connected to the structure of the polymeric cluster.Presented at the Physikertagung 1987 in Berlin.     

Intramolecular reactions in vinyl polymers as a means of investigation of the propagation step

The Flory-Wall expressions for the fraction of substituents remaining of a vinyl copolymer, when substituents are removed of random from adjacent 1.3 positions, are extended to the case of nonrandam copolymerization. A copolymer composition equation is desired for the case in which the type of monomer preceding the active free radical chain and affects the propagation reaction. The distribution of lengths of sequences in copolymers is discussed.     

Temperature changes visualization during chemical wave propagation

Magnetic resonance imaging was used for two-dimensional temperature visualization of chemical waves propagation in the autocatalytic exothermal reaction of thiosulfate oxidation by chlorite. The technique presented is based on the temperature dependence of the water chemical shift. Temperature maps were acquired by employing the TurboFLASH imaging method. The results obtained allow one to judge about directions of buoyancy flows. Two types of convection critical modes in a vertical tube during the wave propagation were detected.     

Radiation-induced conductivity in polymers during long-term irradiation

Radiation-induced conductivity (RIC) in polystyrene, poly(ethylene terephthalate), polyvinylcarbazole, and low-density polyethylene during long-term (to 3.6 × 10³ s) irradiation with 50-keV electrons (dose rate of 6–830 Gy/s) was experimentally and theoretically studied. It was shown that the nonmonotonic RIC kinetics in the polymers is a direct consequence of the generation and the subsequent transport of charge carriers in them in the presence of traps distributed over a broad energy range almost according to the exponential law. This phenomenon has no relation to degradation and crosslinking processes that occur in irradiated polymers. The nonmonotonic RIC kinetics in polymers is a universal phenomenon, and it is described satisfactorily in terms of the Rose-Fowler-Vaisberg model.     

Clay-catalyzed reactions of coagulant polymers during water chlorination

The influence of suspended clay/solid particles on organic–coagulant reactions during water chlorination was investigated by analyses of total product formation potential (TPFP) and disinfection by-product (DBP) distribution as a function of exchanged clay cation, coagulant organic polymer, and reaction time. Montmorillonite clays appeared to act as a catalytic center where the reaction between adsorbed polymer and disinfectant (chlorine) was mediated closely by the exchanged clay cation. The transition-metal cations in clays catalyzed more effectively than other cations the reactions between a coagulant polymer and chlorine, forming a large number of volatile DBPs. The relative catalytic effects of clays/solids followed the order Ti-Mont > Fe-Mont > Cu-Mont > Mn-Mont > Ca-Mont > Na-Mont > quartz > talc. The effects of coagulant polymers on TPFP follow the order nonionic polymer > anionic polymer > cationic polymer. The catalytic role of the clay cation was further confirmed by the observed inhibition in DBP formation when strong chelating agents (o-phenanthroline and ethylenediamine) were added to the clay suspension. Moreover, in the presence of clays, total DBPs increased appreciably when either the reaction time or the amount of the added clay or coagulant polymer increased. For volatile DBPs, the formation of halogenated methanes was usually time-dependent, with chloroform and dichloromethane showing the greatest dependence.     

Electron spin resonance spectra of polymers during fluorination

ESR spectra characteristic of peroxy radicals appeared rapidly in all of eleven hydrogen-containing polymers examined when treated with dilute fluorine. These radicals presumably result from the reaction of hydrocarbon and fluorocarbon radicals, existing at undetectably low steady-state concentrations, with the oxygen impurity content of commercial fluorine. In poly(vinylidene fluoride) films of thickness 11 and 58 μm the radical contents were nearly proportional to surface area rather than volume, in agreement with earlier reports of a shallow depth of penetration. Some polymers exhibited also or exclusively a broad spectral component, varying in character with the polymer; examples are polystyrene, polyethylene, poly (vinyl chloride), poly(vinylidene chloride), polyoctafluoropentadiene, polyhexafluoropropene, and a fluorinated graphite. The broad spectral component did not react with ordinary radical scavengers such as propylene and oxygen, and is probably not due to a fluorocarbon radical but to unknown transition metal fluorides.     

Disentanglement and reptation during dissolution of rubbery polymers

The dissolution mechanism of rubbery polymers was analyzed by dividing the penetrant concentration field into three regimes that delineate three distinctly different transport processes. The solvent penetration into the rubbery polymer was assumed to be Fickian. The mode of mobility of the polymer chains was shown to undergo a change at a critical penetrant concentration expressed as a change in the diffusion coefficient of the polymer. It was assumed that beyond the critical penetrant concentration, reptation was the dominant mode of diffusion. Molecular arguments were invoked to derive expressions for the radius of gyration, the plateau modulus, and the reptation time, thus leading to an expression for the reptation diffusivity. The disentanglement rate was defined as the ratio between the radius of gyration of the polymer and the reptation time. Transport in the second penetrant concentration regime was modeled to occur in a diffusion boundary layer adjacent to the polymer-solvent interface, where a Smoluchowski type diffusion equation was obtained. The model equations were numerically solved using a fully implicit finite difference technique. The results of the simulation were analyzed to ascertain the effect of the polymer molecular weight and its diffusivity on the dissolution process. The results show that the dissolution can be either disentanglement or diffusion controlled depending on the polymer molecular weight and the thickness of the diffusion boundary layer. © 1996 John Wiley & Sons, Inc.     

Some viscoelastic properties of siloxane polymers during irradiation

The dynamic moduli, E′ dyn, and loss tangents, tan δ, of polydimethylsiloxane and polydimethyldiphenylsiloxane polymers have been investigated by an in situ technique during γ-irradiation. These viscoelastic properties were calculated and plotted as a function of irradiation exposure time by measuring the free end displacements and resonance frequencies of polymeric cantilever reeds. The reeds were swept through a small frequency range from about 20 to 100 cycles/sec. The moles of effectively elastic chains per unit volume (v) of the two unfilled polysiloxahes were calculated from in situ modulus data and compared to values obtained utilizing the swelling technique. The approximate molecular weights between entanglements, M_e, of these unfilled polymers were determined by extrapolation of moduli data to zero radiation exposure. The addition of a large silica filler, SiO₂, into the polymers did not alter the crosslinking rates, and the filler did not enter into polymer—filler bonding.     

Development of knotting during the collapse transition of polymers

A dynamic Monte Carlo simulation of the collapse transition of polymer chains is presented. The chains are represented as self-avoiding walks on the simple cubic lattice with a nearest-neighbor contact potential to model the effect of solvent quality. The knot state of the chains is determined using the knot group procedure presented in the accompanying paper. The equilibrium knot spectrum and the equilibrium rms radius of gyration as functions of the chain length and the contact potential are reported. The collapse transition was studied following quenches from good-to poor-solvent conditions. Our results confirm the prediction that the newly formed globule is not yet at equilibrium, since it has not yet achieved its equilibrium knot spectrum. For our model system, the relaxation of the knot spectrum is about an order of magnitude slower than that of the radius of gyration. The collapse transition is also studied for a model in which both ends of the chain remain in good-solvent conditions. Over the time scale of these simulations, knot formation is frustrated in this inhomogeneous model, verifying that the mechanism of knotting is the tunneling of chain ends in and out of the globule.