Nucleation and growth of crazes in amorphous polychlorotrifluoroethylene in liquid nitrogen

The density of mature crazes initially increases linearly with stress and then more rapidly at higher stresses. Once the crazes become observable then density was independent of time. The lowest stress at which an appreciable density of crazes was produced corresponds to the proportional limit. The average velocity of mature crazes was constant for a given stress and varied exponentially with the stress. The velocity depended on stress in the same way that the post-yield point stress depended on strain rate, whereas the yield point varied differently being a nonlinear function of the logarithm of the strain rate. The density of crazes was quantitatively related to the concentration of surface defects at which the crazes nucleate. The craze velocity was directly related to the diffusion coefficient of N₂ into the polymer. The analysis indicates that bulk diffusion of the N₂ governs the craze velocity and that plasticization of the tip of the craze is most important for the nucleation and growth of a craze in PCTFE.     

Analyzing polymer crazing as quasifracture

This paper deals with a viscoelastic boundary element method for analyzing a polymer quasifracture usually called a craze in polymers. A time-dependent boundary stiffness is considered on the quasifracture envelope surface. The viscoelastic property of the glassy polymer is represented by a generalized Kelvin model with multiple retardation times. According to the linear viscoelastic correspondence principle, the associated elasticity solution can be solved by applying the general integral boundary element method. Then the viscoelastic solution in the time domain can be obtained by applying a collocation Laplace inversion transformation. Using these methods, the quasifracture problem composed of an isolated craze opening with time-dependent stiffness traction in a stressed rectangular plate is analyzed. The displacement profile and the stress distribution around the craze envelope surface are computed.     

Dependence on strain rate of the nucleation of cracks in polystyrene at 293°K

The processes associated with the deformation and fracture of polystyrene tested in uniaxial tension have been studied over a range of strain rates from 1.4 × 10^?2 to 4.3 × 10^?7 sec^?1 and at constant stresses between 4.1 and 2.9 kg/mm². The effect of strain rate on the surface craze distribution prior to fracture, the fracture stress, the mechanism of nucleation of cracks, and the nature of fracture surfaces associated with slow and fast crack propagation have been determined. The changes in fracture surface appearance have been studied using optical and stereoscan microscopy. The observations are consistent with the model presented in a previous paper. Fracture is preceded by craze formation, cavitation in the craze, coalescence of cavities to form large planar cavities which propagate slowly until a critical stage is reached at which fast crack propagation occurs. The effect of changes of strain rate and material variables on these processes is discussed.     

Crack-craze opening profiles near a crack tip in a polytetrafluoroethylene

The crack opening and craze profiles near a crack tip in a polytetrafluoroethylene have been experimentally investigated. A double-edge-crack plate specimen under uniaxial tensile load was used in the experiment and the experimental procedure was performed using the Digital Image Correlation method, which is a well-established optical-numerical method for estimating full-field displacement. A theoretical model of the stress intensity factor based on linear elastic fracture mechanics combined with a classical saturated expression was proposed. The proposed model is in good agreement with experimental data and predictions of the model may be used to verify the non-linear behavior from crack and craze (cohesive) zones.     

Molecular weight–mechanical property interrelationships. V. Poly(vinyl chloride) fracture surfaces: The effect of molecular weight and vapor environment

The fracture and craze surfaces of four PVC fractions (M?_w = 51000 to 228000) and two bimodal blends were examined with a scanning electron microscope. The fraction with the lowest molecular weight gave brittle fractures when fatigued in nitrogen and ethanol vapor. Walls of crazed ductile matter formed at the surface of higher molecular weight samples. Thickness of this ductile material increased with molecular weight. There appeared to be a balance between craze propagation into the sample and brittle fracture due to dilitational and tensile stresses in the interior regions of the test films.     

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.     

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.     

Aspects of fatigue failure mechanisms in polymer fuel cell membranes

The swelling‐driven fatigue behavior of polymer fuel cell membranes during relative humidity (RH) cycling is investigated. In particular, swelling‐induced membrane stresses are obtained from a numerical model simulating fuel cell RH cycle tests, and compared to the lifetimes obtained experimentally from tests conducted in the absence of electrochemical effects. A strong correlation between the lifetimes of the membranes in the actual tests and model results is obtained. In general, higher RH (or swelling) amplitude results in larger stress amplitudes and shorter lifetime, that is, fewer cycles to failure. Tensile stresses are needed for forming local cavities in the membrane, which may eventually lead to craze formation. Cavitation is less likely to occur in compressed membrane at high humidities. The stress–lifetime plots for polymer fuel cell membranes exhibit similar features to those observed for other polymers. The crazing criterion for polymers suggests that craze initiation during RH cycling is more likely to occur in the low compression regions, such as under the channels, which is in agreement with experimental observations. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 49: 1506–1517, 2011     

Cyclic stress–strain behavior of the dry polycarbonate craze

Equipment and methods have been developed which allow photomicrographic determination of the stress–strain properties of the individual craze. Serial cyclic tensile tests on polycarbonate crazes are described. Under stress the typical dry polycarbonate craze thickens solely by straining; no adjacent polymer of normal density is converted to craze material. The craze exhibits a yield stress followed by a recoverable flow to roughly 40–50% strain at 6000–8000 psi. On return to zero stress the craze exhibits creep recovery at a decelerating rate. The yield stress and loss factor of each cycle decrease with increasing initial strain and cycles initiating at 50% strain or more show completely Hookean behavior. Creep recovery results in recovery of yield stress and loss factor also. Craze tensile behavior is suggested to be essentially an extension of the craze formation process. Decrease in elastic modulus and yield stress with increasing strain are rationalized in terms of strain-produced decrease in density and resultant increase in stress concentration factor on the microscopic polymer elements of the craze. Polymer surface tension and the large internal specific surface area of the craze are suggested to be important factors in the large creep recovery rates of the craze.     

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.     

Kinetics of craze initiation in polystyrene in N-alcohols

The kinetics of craze initiation has been investigated for unmodified and rubber-modified polystyrenes in n-alcohols. The dependence on time and temperature of the critical strain at which crazes could be detected visually was determined with a Bergen elliptical strain device. Sorption studies were also conducted at room temperature on films exposed to the saturated vapor of n-alcohol. The analysis of crazing data in terms of the Eyring model gave activation energies from 9.4 to 17.4 kcal/mole, increasing with increasing chain length of n-alcohol and increasing rubber content. The activation volume multiplied by a stress concentration factor decreased with increasing rubber content and was nearly independent of the chain length of the n-alcohol. The larger the diffusion coefficient, which we measured by sorption experiments, the smaller was the activation energy for craze initiation. The values of diffusion coefficients, estimated from the experimental data on craze initiation, were found to be comparable with those from the sorption experiments. It was concluded that the rate of craze initiation on exposure to liquids is controlled by the diffusion of the molecules of liquid into polymer.     

Mechanisms and micromechanics of fatigue crack propagation in glassy thermoplastics

An iterative approach is used to estimate, from interference optics measurements, the variation of refractive index and, hence, extension ratio along the length of a craze at the tip of a fatigue crack. The finite element method is used to compute craze surface stress distributions which are found to be similar to those obtained for static loading. High extension ratios, in the range 6 to 8 for retarded fatigue crack growth in poly(vinylchloride), are attained in the craze fibrils at the crack tip before crack jump occurs. The craze thickens primarily by surface drawing during the early stages of its growth but in the later stages the fibril creep mechanism predominates. The critical fibril extension ratio is not reached in a single cycle, as in normal fatigue crack propagation, and crack jump does not occur until, typically, after several hundreds of cycles during which the fibrils accumulate considerable damage.Presented in part at the 7th Int. Conference Deformation, Yield and Fracture of Polymers, Cambridge, UK, 11–14 April 1988.     

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.     

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.     

用透射电镜研究PS薄膜银纹的微观结构、变形特性和破坏过程

本文介绍了用透射电镜观察PS薄膜银纹的微观结构、变形特性和破坏过程。实验观察到PS银纹质完整的网络结构和取向银纹质断裂以后的松弛特性。实验发现PS银纹质断裂转变成微裂纹的过程类似有机玻璃慢裂纹区的“撕布”模式,裂端银纹的外形符合Dugdale模型。     

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.     

Cake consolidation in a compression-permeability cell: effect of side-wall friction

A simulation study was made to investigate the transient state stresses, strains, and void ratio distributions in the formation of a filter cake in a compression-permeability cell (C-P cell). A finite-element software package, ABAQUS, was used for the simulation and emphasis was placed on the effect of the cake/cell-surface friction. The validity of the simulation was assessed by comparing simulation results with available experimental data.     

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.     

Properties of fracture surfaces of glassy polymers: Chain scission versus chain pullout

Fresh fracture surfaces formed by tensile failure of craze in molded polystyrene (PS) bars have been compared with the molded surfaces of the same bars, using an atomic force microscope with a thermal probe and operated in local thermal analysis. The results indicate that molecular weight is much higher in the interior of the sample than at the surface. No evidence was found for degradation of the PS chains via chain scission during crazing. Alternative explanations for the low‐molecular weights at the molded surface are discussed. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2010