Craze growth and void coalescence in PMMA round notched bars

A study of the kinetics, failure mechanism, and fracture surfaces of PMMA/methanol crazes has been made on notched circular bar specimens subjected to constant tensile loads. Failures were by void growth and coalescence inside the craze away from the notch tip and near to the specimen center. Two distinct features of void coalescence were observed; the first a cluster of very small voids (each of the order of 3.4 × 10³ Å) and the second, separate larger voids which usually caused final failure. An analysis of craze growth, based on fracture mechanics concepts in conjunction with simple flow analysis, suggests that the growth is controlled mainly by the ability of the environment to flow through the voided structure of the craze. Good agreement has been obtained between predicted behavior and experimental data.     

Effect of strain history on craze microstructure

Crazes formed under a constant tensile strain in polystyrene (PS) have a dense network of fibrils with an extension ratio $\text{λ ? 4}$, but a midrib of higher λ forms by drawing fibrils from the craze-matrix interface in the high stress region just behind the craze tip. Stepwise increases in tensile strain during craze growth should thus produce layers of fibrils of different λ, which can be revealed by transmission electron microscopy (TEM) of crazes in stepwise strained PS films. When the time interval between strain increments of 0.5–1% is one minute, TEM images show ‘ridges’ of lower λ fibrils, corresponding to the position of the craze-matrix interface at the time of the strain increments. The ridges appear to be the analogue of the bulge remaining on a macroscopic fibre which has been allowed to stress age by stress relaxation before resuming drawing and imply that rapid stress ageing must occur near rthe craze-matrix interface so that more material is drawn into the craze in preference to increasing the λ of the existing fibrils.     

Influence of rubber content on static and dynamic properties of polystyrene

Mechanical properties, deformation modes under both uniaxial tension and compression, low temperature mechanical relaxation behavior, and resistance to fracture under dynamic loading have been investigated for a medium impact grade of polystyrene, Shear yielding is the dominant mode of plastic deformation in compression while matrix crazing, together with some tearing and cavitation of the rubber phase, occurs in tension. The craze microstructure, as determined by transmission electron microscopy (TEM), is typical of that noted in polystyrene, with sharp craze-bulk interfaces and a characteristic midrib section. The presence of a third phase, possibly a processing aid, is evident in the TEM scans and in the dynamic mechanical data. The present data, together with the data obtained on polystyrene and on high impact polystyrene, are used to show the strong influence of rubber content on various mechanical properties, such as the tensile craze yielding stress, ductility, compression yield strength, degree of strain softening, and fatigue durability.     

Mechanism of craze thickening during craze growth in polycarbonate

It has been shown previously that dry craze growth kinetics in bisphenol-A polycarbonate (PC) subjected to creep are compatible with a model in which craze growth occurs at constant aspect ratio, the rate-controlling process being craze thickening due to homogeneous creep of craze material. In the present work, craze thickening during growth was investigated by electron microscopy and by an optical interference method in order to check this hypothesis. Results indicate that thickening occurs by drawing in fresh material from the craze—matrix interface. The previous model is modified in order to take these findings into account.     

Craze initiation,crack growth,and lifetime trends in fatigue of poly(vinylchloride)

The fatigue behavior of pure poly (vinylchloride) (PVC) and a PVC pipe compound has been investigated. Unnotched S-N lifetime, fatigue-crack growth, and craze/crack-initiation data are presented. The data trends, coupled with direct-microscopic observation, suggest that the unnotched-specimen lifetime in fatigue is dominated by the craze/crack-initiation process. This differs from the observed consistency of crack propagation and specimen-lifetime trends in several other polymers, whose failure can be traced to the initiation and growth to instability of a single dominant craze/crack.     

Craze morphology and molecular orientation in the slow crack growth failure of polyethylene

An optical microscopy study and a micro‐Raman spectroscopy study were carried out on polyethylene samples subjected to an environmental stress crack resistance (ESCR) test. The aim was to elucidate the molecular deformation mechanisms associated with the failure process. It has been shown that in the early stages of the ESCR test, in a regime of low local stress, failure in the craze occurs via a brittle process with limited ductility and with molecular orientation being detected. As the experiment progresses, however, extensive fibrillation takes place. The molecular orientation in these fibrils was found to be comparable to that measured in cold‐drawn samples. Moreover, the fibril molecular orientation decreased from the crack to craze tip and was found to be higher in the midrib part of the fibril (fibril failure point). As a consequence, fibril creep is the most likely mechanism of failure in the craze. Microscopy and Raman measurements showed that the extent of the brittle process is molecular weight‐dependent, that is, the brittle process seems to operate longer at higher molecular weights. These observations are in agreement with a previous work which showed that the molecular stress per macroscopic strain/stress decreases with increasing molecular weight, therefore holding the high molecular weight craze in a regime of low local stress for longer testing times. Fibrils spanning the craze are envisaged as the anchor points that hold the structure during the process of failure. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 77: 283–296, 2000     

Time-dependent craze zone growth at a crack tip in polymer solids

By considering the polymer bulk as a linear viscoelastic body and the craze zone at crack tip as a nonlinear damage zone, the control equation for craze zone growth has been derived. It is shown that for a time-independent craze-zone stress, the craze zone would grow only if the crack-tip stress intensity factor is changed. If the crack-tip stress intensity factor remains constant during loading, the growth rate of the craze zone length will be interrelated to the crack-tip stress, the craze zone length and the rate of change of the craze-zone stress. If both the craze-zone stress and the crack-tip stress intensity factor are time-independent, the craze zone length will be constant during the crack growth, which is the case of self-similar crack growth. Moreover, a new stress distribution model in craze zone is presented based on the constructed damage evolution law, and the lengthening and thickening of the craze zone at the crack tip are also formulated. The numerical calculations from the proposed model agree well with the published experimental data.     

Craze initiation and growth in high-impact polystyrene

Quantitative transmission electron microscopy and optical microscopy is used to study craze initiation and growth in thin films of high-impact polystyrene (HIPS). Dilution of the HIPS with unmodified polystyrene reduces the craze–craze interactions, permitting equilibrium growth and craze micromechanics to be studied. It is found that the equilibrium craze length depends on the size of the nucleating rubber particle, but not the internal structure; no short crazes less than a particle diameter are observed. The long crazes can be adequately modelled by the Dugdale model for crazes grown from crack tips. The effects of particle size and particle internal occlusion structure on craze nucleation have been separated. Craze nucleation is only slightly enhanced at highly occluded particles relative to craze nucleation at solid rubber particles of the same size. There is a strong size effect, however, which is independent of particle internal structure. Crazes are rarely nucleated from particles smaller than ～1 μm in diameter, even though these make up about half the total number. These craze nucleation and growth effects may be understood in terms of two hypotheses for craze nucleation: (1) the initial elastic stress enhancement at the rubber particle must exceed the stress concentration at a static craze tip and (2) the region of this enhanced stress must extend at least three fibril spacings from the particle into the glassy matrix. Since the spatial extent of the stress enhancement scales with the particle diameter, the second hypothesis accounts in a natural way for the inability of small rubber particles to nucleate crazes.     

The interpretation of electron microscope images and scattering patterns from crazes

Images and small-angle diffraction patterns of crazes obtainable in the transmission electron microscope have been calculated from model structures using a single theory of interaction of electrons with the sample. The model was of a relatively thick craze so that many fibrils overlapped. The calculated defocused images of this model showed little obvious relationship to the original model showing that it is very hard to estimate craze fibril diameters from craze images. The calculated scattering pattern normal to the craze showed both the refraction and diffraction effects observed previously and so is in excellent accord with experiment.     

The effects of stress cracking on the fracture toughness of polycarbonate

The growth of crazes from a sharp crack in extruded polycarbonate sheets immersed in ethanol was measured. Below a critical level of the stress intensity factor craze growth was controlled by solvent diffusion through the end of the notch and fracture was prevented by craze arrest. Above a critical level, growth was controlled by either end diffusion or a combination of end diffusion and diffusion through the faces of the extruded sheet, and in both cases the final result was brittle fracture. The effects of annealing and quenching was studied at various sheet thicknesses. In thin specimens annealing and/or quenching had a significant effect on crack growth rate, which was predictable in terms of the state of stress. As the specimen thickness increased, causing a transition from plane stress to plane strain conditions, the previous thermal history had a diminishing effect on craze growth rate. The effects of thermal history and thickness on the fracture toughness of polycarbonate was also investigated. It was found that thickness was the more important variable and that at a ½ in. thickness the effects of thermal history were statistically insignificant. The effect of ethanol exposure on fracture toughness was studied. It was found that exposure to solvent initially caused an increase in k_IC with time to a maximum value, followed by a substantial decrease with time which eventually led to brittle fracture. This behavior was explained as a competition between plasticization of the crack tip and coalescence of crazes to form microcracks.     

Measurement of the residual mechanical properties of crazed polycarbonate. I: Qualitative analysis

A new technique to quantify the bulk craze density of transparent plates was used to characterize the craze growth behavior of polycarbonate at various stress levels. The craze growth rates were found to exponentially increase with an increase in stress, obeying the Eyring equation for thermally activated processes in the presence of an applied stress. The residual mechanical properties of crazed polycarbonate were then correlated to the crazing stress, relative craze density and strain rate. The results show that increasing the bulk craze density does not affect the yield stress but decreases both the failure stress and ductility of polycarbonate. Also, a crazing stress of 40 MPa was found to cause a much larger degree of degradation of failure properties than a crazing stress of 45 MPa. Correlating the crazing stress to the craze microstructure revealed that fewer, larger crazes form at the lower crazing stress. Therefore, flaw size has a greater effect on the failure properties of polycarbonate than flaw quantity.     

Measurement of cohesive zone parameters in tough polyethylene

The initiation, growth and final failure of the craze ahead of a crack tip generally controls the onset of crack growth in polyethylene, particularly in slow crack growth. In this research, circumferentially deep notched tensile specimens are used to analyze the evolution and failure of crazes in polyethylene under plane strain conditions. An experimental method is used wherein the traction‐separation behavior of the craze structure is measured directly in‐situ. Results yield a cohesive zone type analysis in which a two parameter traction curve, containing within it all information pertaining to local decohesion, fully describes the separation of the interface. Experimentally measured rate dependent trends in the work of separation (I) provide good discrimination between different grades of tough polyethylene at both high and quasi‐static test speeds, and highlight the exceptional long term behavior of one particular grade. The method also allows for the quantification of the long term behavior of each grade by more traditional stress‐time analysis.     

A study of the fracture behaviour of polyethersulphone

The fracture behaviour of polyethersulphone has been studied by combining fracture toughness measurements with optical examination of the craze and shear lips at the tip of the crack. It is shown that the behaviour can be very well described by a mixed mode fracture model in which the total strain energy release rate contains a plane strain term from the craze and a plane stress term from the shear lips. In unannealed samples the craze shape was well approximated by the Dugdale plastic zone model, but this was not so for annealed samples. The effect of annealing on the fracture behaviour is discussed in qualitative terms.     

The craze initiation response of a polystyrene and a styrene-acrylonitrile copolymer during physical aging

The influence of structural recovery or physical aging on the craze initiation of amorphous polystyrene and a styrene-acrylonitrile copolymer has been examined in two states of stress/deformation and at different temperatures. Studies of craze initiation in equibiaxial creep were performed using a “bubble” inflation test geometry while uniaxial elongation in stress relaxation conditions was studied by bending the specimen over a variable radius of a curvature test jig. All tests were performed by aging the specimen and testing it at the same temperature subsequent to a quench from above the glass transition to below it. The results are compared with expectations from three craze models: Sternstein and Ongchin (1), Argon (2), and Kambour (3). The results are most consistent with the model of Kambour, but discrepancies arise because, e.g., the impact of aging on the stress for crazing in the equibiaxial tests is different for the polystyrene than for the styrene-acrylonitrile copolymer. The results also suggest that there are two regimes of behavior for craze initiation under equibiaxial stresses, a behavior not manifested in the uniaxial stress relaxation experiments.     

Tensile deformation and failure processes of amine-cured epoxies

Evidence is reviewed for the occurrence of microscopic flow under tensile loads in a variety of amine-cured epoxies. The nature of the deformation and failure processes involved in these flow processes are discussed. The slow-crack growth fracture topographies of these epoxies, fractured as a function of temperature and strain-rate, are reviewed, and consist of a rough initiation region, that can contain microvoids and/or fractured fibrils, surrounded by a smooth temperature and strain-rate dependent region. These topographical features are explained by initial course craze formation followed by crack propagation through the craze midrib. The crack then imposes a higher stress field on the craze tip which produces a small plastic zone that results in a smooth fracture topography. Fracture topographies also indicate that shear band propagation can occur in the fracture initiation process. The ductile mechanical response of many of these epoxies together with direct experimental observations from transmission electron microscopy and birefringence studies produce further evidence that flow can occur in these glasses. Both plastic, homogeneous and inhomogeneous deformations can occur. The inhomogeneous deformations can evolve into macroscopic shear bands. The ability of these crosslinked glasses to undergo microscopic flow is discussed in terms of (i) our understanding of their chemical and physical structure and (ii) covalent bond scission.     

Effects of residual stress and orientation on the fatigue of injection molded polysulfone

The tensile fatigue behavior of unnotched injection molded polysulfone specimens has been investigated. The effects of orientation and residual stress were studied by comparing asmolded specimens with annealed or annealed and quenched specimens with a known residual stress pattern. The treatments are shown to have differing effects at high stresses, where failure is by shear yielding and necking, and at intermediate stresses, where failure is by fatigue crack propagation. The geometries of fatigue cracks are described for each case. An attempt is made to separate the effects of crack and craze initiation from crack propagation, and cyclic loading from cumulative time under load.     

Stress and displacement fields at the tip of a craze containing a crack

Plane elasticity theory is utilized to obtain expressions for the stress and displacement fields at the tip of a craze containing a crack. The craze is modeled as a very thin elliptical inclusion with different elastic properties from hat of the surrounding bulk polymer. Problem is solved by superimposing the solution of a crack problem onto the solution for a uniformly loaded homogeneous craze. Invoking stress free boundary conditions on the crack surface provides a singular integral equation of Hilbert type with a unique solution. Contour lines of constant hydrostatic stress and constant maximum shear stress around the craze tip are shown graphically. These two stress combinations have played prominent roles in a number of proposed craze growth criteria. Results show that even for relatively long cracks within the craze, very little stress enhancement at the craze tip occurs. Only as the crack tip approaches the craze tip does the enhancement become significant, tending to drive the craze region ahead of the crack.     

The effects of physical aging on the brittle fracture behavior of polymers

The effects of physical aging on the failure behavior of a typical brittle polymer, polystyrene, have been studied. Properties examined were creep rupture lifetimes, fatigue lifetimes, and environmental stress cracking in ethanol. Fractured samples were examined both optically and by scanning electron microscopy to determine the degree of crazing. It was found that a longer physical aging time produced shorter lifetimes in all cases. The main reason for this is the reduction in craze strength caused by a reduced toughness due to physical aging. A long aging time was found to delay craze formation, but once formed, these crazes were much less stable than those formed with a short aging time. The effects of aging are important on failure prediction criteria and on testing methodologies, and the implications are discussed.     

Polymer fatigue fracture diagrams: BPA polycarbonate

A fatigue fracture diagram for BPA polycarbonate has been created from fatigue lifetime data obtained from knit line notched samples. This fatigue fracture diagram maps out stress-temperature zones where fatigue fracture is dominated by crack growth through leading crazes and zones where fatigue fracture occurs through shear fracture at 45 degrees to the load direction. Both craze and shear planes coexist in the fatigue crack tip plastic zone, and both compete to determine the ultimate crack growth behavior. The shear planes preferentially develop (and fracture) at higher temperatures and stresses, but this fracture process is quite slow. Consequently, an inversion in the fatigue lifetime curve is observed, with longer lifetimes at higher stresses. This inversion is easily understood as a transition between a craze branch and a shear branch on the fatigue lifetime plot. When the fatigue lifetime curve is plotted for data at different temperatures, with the stresses normalized to the yield stress at the respective test temperatures, the craze branch data from different temperatures overlap. This overlap can be explained by the N = 2 power law dependence of crack growth in the discontinuous crack growth regime.     

Relaxation of stresses in crazes at crack tips and rate of craze extension

The Barenblatt theory of cohesive stresses at crack tips is used to investigate the effect of the relaxation of craze stresses at crack tips on the rate of craze extension. The craze stresses are equated to the cohesive stresses of the Barenblatt theory. The cancellation by the cohesive/craze stress of the singularity that would exist at the crack tip in their absence is assumed to hold for an extending craze. With this assumption, relaxation of the craze stresses produces craze extension, an effect which has been called ‘relaxation controlled growth’ by Williams and Marshall. A general equation relating the rate of change of craze length to the rate of change of stress intensity factor (K₁) and the rate of change of the craze stress is derived. It is argued from this equation that uniform crack growth with a constant craze length can occur only at constant K₁. Using plausibility arguments for the behaviour of the craze stress with time and position in the craze, and assuming a generalized Dugdale model, differential equations for the rate of craze extension with no crack growth are derived for the constant load and constant K₁ cases. These equations relate the rate of change of craze length to the craze stress at the tip of the crack. Assuming a specific form for the time dependence of this stress, the equation for the constant K₁ case is solved to yield an expression for the craze length as a function of time.