Micromechanics of fatigue crack propagation in glassy thermoplastics

By the aid of the optical interference method the size of the craze zone at the crack tip has been measured during fatigue crack propagation (FCP) in two glassy thermoplastics thus giving a basis to re-examine proposed models. In contrast to previous assumptions it has been found, that in PMMA of high molecular weight crack propagation occurs only during a short interval of the loading cycle when the fibrils are stretched most severely and it is not limited by crack tip blunting; between the dimensions of the craze zone and the crack advance per cycle which is also reflected by markings on the fracture surface no simple correlation has been found. In PVC first the craze grows continuously during many loading cycles up to its final size and then the crack propagates by a jump separating the craze zone only partly. Thus at all stress intensity levels investigated the length of the final craze zone has been found to be distinctly larger than the jump spacing on the fracture surface. By aid of SEM-photography it is shown that in PVC during FCP cracking occurs by separation of fibrils instead of void coalescence.     

Discussion of craze formation and growth in amorphous polymers in terms of the multiplicity of glass transition at low temperatures

A craze, the typical deformation zone in an amorphous polymer, can be divided into a precraze and a proper craze. A better understanding of the two corresponding formation processes is possible in terms of glass transition multiplicity.The precraze is associated with the molecular mobility in the confined flow zone, which is part of the main transition. The proper craze corresponds to the mobility in the flow transition zone (terminal zone for shear). A negative pressure generated by nonuniaxial stress is considered to be important for the maintainance of the molecular mobility in these zones belowT _g . The behavior of the zones at negative pressure and low temperatures Tg is considered using a pressure-temperature diagram. The fibril structure of crazes is discussed by a defect diffusion model for the proper glass transition; it is correlated with the sequential physical aging of the corresponding frozen structural defects. Typical mode lengths of the molecular mobilities in the different zones are compared with typical craze parameters. The structure of the craze material is considered to result from confined flow processes which cannot percolate because in the main transition the flow is confined by entanglements, and in the flow transition zone the flow is stopped by releasing the negative pressure due to crack propagation.     

Craze fibril extension ratio measurements in glassy block copolymers

The extension ratios of crazes in triblock copolymer films of poly(2-vinylpyridine)-polystyrene-poly(2-vinylpyridine) [PVP-PS-PVP] which had lamellar microphase domain structure were measured by transmission electron microscopy. The extension ratio when the lamellae were oriented parallel to the craze fibril direction was always greater than that when the lamellae were oriented perpendicular to this direction, reflecting the stretching of the chains of the block copolymer in a direction normal to the interfaces of the lamellar domains.     

Mechanical properties of methanol crazes in poly(methyl methacrylate)

Methanol crazes are grown from sharp cracks in poly(methyl methacrylate) (PMMA). The craze thickness profile is measured using a replica technique after the craze opening displacement profile of the growing craze has been measured with holographic interferometry. The craze strain profile is then computed from these data. The craze surface stress profile is determined by two methods: (1) from the uniaxial strain profile of regions adjacent to the craze as measured from the fringe spacing on the reconstructed hologram and (2) from the craze opening displacement profile using the Fourier transform method of Sneddon. From the surface stress and craze-strain profiles a true stress-strain curve for the craze fibrils has been constructed. The extrapolated fibril yield stress is in good agreement with the yield stress of bulk PMMA plasticized with methanol indicating that surface tension effects do not contribute importantly to craze fibril mechanical properties at room temperature. The craze strain increases from 0.4 near the craze tip to 1.4 near the craze base implying that methanol crazes in PMMA thicken by further straining of the existing craze fibrils and not by drawing new material into the craze from the craze surfaces. The primordial craze thickness, i.e., the original thickness of polymer which fibrillates to form the craze fibrils, is approximately 1 μm and is constant over most of the craze length. This thickness may be determined by diffusion of methanol normal to the craze surfaces in a process zone just behind the craze tip.     

Fatigue crack propagation mechanisms in poly(methyl methacrylate) by in situ observation with a scanning laser microscope

Crack propagation tests were performed on an amorphous polymer, poly(methyl methacrylate), to investigate fatigue crack propagation mechanisms. A scanning laser microscope with a newly developed tensile testing machine was used to observe in situ crack propagation in compact‐type specimens. A crack usually propagated within the craze located at the crack tip under both static and cyclic loading conditions. When a crack stably propagated into the craze under static loading conditions, bright bands composed of the broken craze were observed at the edges along the crack wakes. However, there were successive ridges and valleys in place of bright bands along the crack wakes under cyclic loading conditions. When stable fatigue cracks were propagated at the loading half‐cycle in each cycle, new craze fragments appeared that were similar to the bright bands under static loading. However, the thickness of these fragments decreased in the following loading cycle, and a new valley was formed. This suggested that the valleys were formed by the contact between the fracture surfaces near the crack tip during unloading. Fatigue crack propagation is thought to be due to fibrils weakened by crack closure between fracture surfaces. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 3103–3113, 2001     

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     

Studies of craze fibril deformation during fatigue in polystyrene

Small-angle scattering of synchrotron x-ray radiation has been used to study the effects of fatigue on craze fibril microstructure. The results obtained during unloading and reloading during a single cycle have been compared with those predicted by a model of sinusoidally bent fibrils. In addition the total displacement of the craze boundaries was found from the change in the invariant on unloading. The mean fibril diameter D was measured at the maximum tensile strain in each cycle. Over 250 cycles, D increased by at least a factor of 2 from an initial value of 6.5 nm, with most of this change happening in the first few cycles. The increase in D must occur by fibril coalescence, a mechanism that requires that the material in craze fibrils have considerable molecular mobility, even at room temperature, 70°C below the glass transition temperature.     

A SAXS study of a single crack and craze in plasticized polystyrene

Small-angle x-ray scattering (SAXS) was used to study the structure along a single craze that had broken down to form a crack along part of its length. This study was made possible by use of radiation from the synchrotron source CHESS which is sufficiently intense to permit examination of just a single craze. The total scattering from the craze was in excellent agreement with that expected from a knowledge of its dimensions and fibril volume fraction and width. This fact adds confidence to the interpretation of the scattering pattern of the craze as part diffraction, part reflection, and demonstrates that SAXS is a technique that may be used to measure craze volume within a sample. The craze was shown to grow in width by surface drawing with a constant structure, and then the fibrils broke to form a crack. The broken fibrils contracted and their diameters increased but they appeared to stay parallel with a constant fibril-axis radial distribution function.     

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.     

An evaluation method for SAXS-patterns of fibrillar two-phase systems containing oriented particles of moderate anisotropy and short range correlation

Starting from the theoretical background of Rulands interface distributions, an evaluation method for small angle x-ray patterns arising from oriented fibrillar two-phase structures is proposed. If the fibril contains highly oriented particles with only moderate anisotropy and if the correlations between those particles within the fibril are of short range only, every axial section of the scattering pattern shows a one dimensional Porod law. A procedure of successive model confinement using the well known tools of nonlinear regression analysis is described. The result of such an analysis for the scattering pattern of an oil diluted SBS block copolymer recorded with synchrotron radiation under first-cycle stretching is reported. At=4 nm four contributions to the scattering pattern could be identified: a) fibrils containing well-defined cylinders standing upright; b) fibrils containing lying cylinders under destruction; c) stretched-out polybutadiene chains, connecting two polystyrene cylinders and causing the observable layer line pattern; and d) stretched-out polybutadiene chains looping through the neighboring PS domain and returning to their starting domain. In addition, a simple method for determining the height-to-diameter ratio of cylinders from the form factor envelope is proposed.     

Interferenzoptische Untersuchungen zur Bruchausbreitung unter Wechsellast in PMMA

Zusammenfassung In einem amorphen, transparenten Thermoplasten wurde an einem unter Ermüdungsbelastung sich ausbreitenden Riß das Verhalten des Craze an der Rißspitze untersucht. Dazu wurde eine spezielle Apparatur gebaut, mit der an Miniatur-CT-Proben Ermüdungsbelastungen bis zu 30 N bei Frequenzen bis zu 250 Hz aufgebracht werden können. Der besondere experimentelle Aufbau erlaubt die gleichzeitige Messung der Bruchgeschwindigkeit, der jeweils an der Probe wirkenden Last und des mikroskopischen Interferenzstreifensystems des Craze für jeden beliebigen Zeitpunkt eines Belastungszyklusses.An hochmolekularem PMMA wurden Bruchzähigkeit und Craze-Länge als Funktionen von Bruchgeschwindigkeit und Rißfortschrittsrate in einem weiten Frequenzbereich gemessen.Mit Hilfe des Dugdale-Modells, das die Craze-Zone an der Rißspitze beschreibt, konnte eine neue, charakteristische Materialeigenschaft abgeleitet werden: die Lebensdauer (Zahl der Belastungszyklen) einer Fibrille im Craze als Funktion der lokal am Craze wirkenden Spannung.

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Summary For a propagating crack under cyclic loading conditions the behaviour of the craze at the crack tip in an amorphous transparent polymer has been investigated. A special apparatus has been built to apply a cyclic load up to 30 N at a frequency up to 250 Hz on the cracked sample. The experimental set-up allows the simultaneous measurement of the crack speed, the instantaneous load on the sample and the microscopic interference pattern of the craze at any moment of the cycle.Fracture toughness and craze length as functions of crack speed and fatigue crack growth rate have been measured on PMMA in a wide frequency range.By means of the Dugdale model describing the craze shape at the crack tip, a particular material property could be derived: the lifetime (number of loading cycles) of a fibril in the craze as a function of the local stress applied on the craze.

     

Hard elastic polypropylene-nature,internal friction,and surface energy

Tensile tests were performed at low temperatures, both in liquid and gaseous nitrogen and also at room temperature, using a series of polypropylene (PP) samples with various technological parameters. Crystalline morphology was also measured for film samples. The results show that liquid nitrogen or solvents can induce materials to create hard elasticity, which strongly supports the bulk-microfibril composite structure proposed by Baer et al., and suggests that the nature of hard elasticity is essentially a craze phenomenon. Three conditions of forming hard elastic structure are discussed. The results from long-time relaxation of hard elastic polypropylene (HEPP) and the improvement of necking of the PP samples in ethanol and water suggest that elastic recovery is reduced by internal friction. The relation between morphology and elasticity is also discussed. The methods of estimating the contribution of surface energy in the recovery process and the increase of surface energy of HEPP during the stretching process are provided. The contribution of surface energy to recovery is about 43% to 66% in the first cycle and after relaxation for 1 h at a maximum of 50% strain. The increased surface energy during stretching is about twice the recovery work done by surface energy.     

An unusual fatigue crack-tip plastic zone: The epsilon plastic zone of polycarbonate

Polycarbonate exhibits an extraordinary crack-tip plastic zone under certain fatigue loading conditions. During discontinuous growth (multiple load cycles per crack jump), the plastic zone consists of a leading craze and a pair of sharply delineated shear bands, which together look like the Greek letter epsilon. The kinetics of the development of the epsilon plastic zone and the nature of the transition from discontinuous growth to a shear fatigue fracture mode are discussed.     

A model of environmental craze growth in polymers

A model of environmental craze growth has been developed based on the customary meniscus (or Rayleigh-Taylor) instability model of craze propagation but allowing for the possibility that environmental plasticization may cause the active layer of material adjacent to the craze to be of significant thickness with respect to the fibril spacing. Initially, as the active layer thickness increases, the fibril growth rate increases at constant fibril spacing, but eventually the fibril spacing comes to be controlled only by the active layer thickness and not by the surface tension and stress. This model of craze growth has been coupled to a model of stress-enhanced case II diffusion that is itself based on the Thomas-Windle model. Two main regimes of craze thickness growth are distinguished. In one the craze growth rate is controlled by the velocity of the diffusion front, the meniscus instability growth rate is assumed to be relatively slow, so that a significant plasticized active layer exists whose thickness assures that the meniscus instability front travels at the same speed as the diffusion front. In the other regime the propagation of the craze front is sufficiently fast that it also forms the diffusion front, so the growth rate is controlled by a combination of the two processes: diffusion and meniscus instability.     

SAXS experiments on gel-spun polyethylene fibers

The properties of gel-spun polyethylene fibers hot-drawn to the maximum draw ratio depend on the spinning conditions. Different spinning conditions result in two types of structure in the paraffin oil containing fibers: an isotropic lamellar structure or a shish-kebab structure. Meridional SAXS experiments can identify the structure present. After extraction, these structures are still present but can be detected only in a more indirect way by SAXS experiments because of an excessive contribution of void scattering. During hot-drawing both structures are transformed into a more fibrillar structure. The shish-kebab structures can be drawn only to relatively low hot-draw ratios with an incomplete transformation of the lamellar overgrowth into the fibrils, as demonstrated by the presence of a meridional SAXS maximum/shoulder. This leads to relatively weak fibers. Lamellar structures can be drawn to high draw ratios by chain unfolding. A nearly complete transformation of the lamellae into fibrils is obtained and the fibers have excellent properties. The information about the morphology obtained by SAXS, DSC, WAXS, and SEM can be used to establish a relation between morphology and properties.     

Preparation of muscovite with ultrahigh specific surface area by chemical cleavage

The specific surface area of a muscovite sample increases drastically after exposure to a LiNO₃ solution, e.g., from 3.4 m²/g, corresponding to platelets of ca. 200 silicate layers, to 295 m²/g (platelets of ca. 2–3 silicate layers) after treatment at 180°C under atmospheric pressure for 46 h. The efficiency of the cleavage process decreases with decreasing temperature (down to 50°C). The LiNO₃/H₂O weight ratio is also very important: at 130°C and a reaction time of 46 h, for instance, a value in the range of 1.7–1.8 leads to the highest specific surfaces. The cleaved products have the form of strong papers that disperse readily in water. During the cleaving procedure, not only the particle thickness, but also the diameter decreases. There is no evidence of damage or partial dissolution of the silicate structure after cleavage, by IR spectroscopy and yield. The use of LiCl also leads to an increase in specific surface area, but the effect is weaker than in the case of LiNO₃. Treatment with some other alkaline and alkaline earth nitrates and chlorides did not increase the specific surface area of muscovite significantly.     

Mechanism of fracture in glassy polymers. III. Direct observation of the craze ahead of the propagating crack in poly(methyl methacrylate) and polystyrene

Observation of optical interference fringes at the tip of a crack in a glassy polymer allows the construction of the configurations of the crack tip and the craze that precedes it. The craze extends 25 μ beyond the crack tip in poly(methyl methacrylate) and 550 μ beyond the tip in the polystyrene studied. The craze at the crack tip in PMMA may be seen to deform elastically as much as 100% under stress before crack propagation recommences. Such deformation is estimated to account for as much as 40% of the nominal Griffith energy of crack propagation.     

Deformation and fracture behavior of polystyrene ionomer and ionomer blends

The deformation and fracture behavior of sulphonated polystyrene ionomers, and of blends of these with polystyrene have been investigated. The microstructure of the ionomer, which varies with ion content, appears to have a significant effect on mechanical properties. Both tensile strength and toughness increase appreciably at ion contents near 5 mol%, where clusters become dominant over ion pairs and multiplets. In blends of the ionomers and polystyrene, phase separation occurs and the ionomer component appears in the form of fine particles dispersed in the polystyrene matrix. These particles possess a greater effective entanglement density than the matrix, as a result of ionic crosslinking, and they provide reinforcement against early craze breakdown and fracture. Tensile strength and fracture energy increase rapidly as the ionomer concentration in the blend is increased and they become essentially independent of blend ratio above about 10 wt% of the ionomer. Tests carried out on thin film specimens of the blends show that the dispersed ionomer particles adhere well to the matrix and contribute to the fracture energy both by inducing matrix crazing and by internal fibrillation within the particles.Dedicated to Professor Hans-Henning Kausch on the occasion of his 60th birthday.     

K+-montmorillonite: its electric double layer extension and point of zero charge by diffusion potential

The dependence of the counterion transference number on the distance from the charged surface, that is, on the water (solution) thickness, is used for an approximation of the extension of the electric double layer (edl) in K⁺-montmorillonite.The extension of edl in K⁺-montmorillonite in 10^–2–10^–3 M KCl solutions is approximately 3.7k ^–1, wherek ^–1 is the Debye length.The dependence of the counterion transference number on the pH of water (solution) is used for estimating the point of zero charge (pzc) of K⁺-montmorillonite; the estimated pzc=1.