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.     

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     

Fatigue crack propagation in high-density polyethylene

An investigation of the influence of crystalline microstructure on fatigue crack propagation (FCP) in high-density polyethylene (HDPE) is reported. Various thermal histories were used to generate samples with the same crystallinity and supermolecular structure for three different molecular weight HDPEs. Estimation of tie chain densities were obtained from measurements of brittle fracture stress and predicted from the estimated chain dimensions of the polymers using the modified version of the approach originally taken by Huang and Brown. A significant decrease in FCP resistance and a clear transition to a more brittle fracture surface was observed with decreasing molecular weight. Detailed studies of damaged zones preceding the growing crack show a transition to a more highly branched crack structure for those samples associated with a higher FCP resistance. These results strongly suggest that the branched damaged zone structure improves the FCP resistance by enlarging and blunting the crack tip and, therefore, consuming more energy during the fatigue crack propagation. Additional efforts were made to prepare samples with the same crystallinity and tie chain density, but different supermolecular structure. However, in contrast to reports in the literature, no significant difference in FCP resistance was observed for specimens with different average spherulite sizes. This is probably because the propagating crack front is preceded by a significant zone of plastic deformation and is not expected to directly encounter the spherulites.     

Slow-brittle-fracture transition in polymethylmethacrylate

A slow crack growth was achieved in initially edge-cracked specimens made of a high-molecular weight PMMA by regulating the cross-head speed of loading by a computer-driven testing machine. The strain rate \(\dot \varepsilon \) used during the tests varied between \(\dot \varepsilon \) =1× l0^?6 s^?1 and 1×10^?4 s^?1. It was shown that, in this zone of slow quasi-static loading of brittle polymethylmethacrylate specimens under conditions of plane stress, the crack initiated for a critical value of loading, at some characteristic zone of strain-rate variation at the crack tip. It was established that for strain rate between \(\dot \varepsilon \) =0.18×10^?5 s^?1 and \(\dot \varepsilon \) =0.45×10^?4 s^?1 brittle cracks were propagating always slowly with velocities in the range ofc=3 to 5×10^?2 m/s. For values ofv _s outside this transition zone fracture was typically brittle with high crack-propagation velocities. As the strain rate was varying beyond the stable low-velocity region, a two-step crack velocity pattern was operative, where the one step took always low values, and the other step corresponded to crack-propagation velocities significantly higher than these limits, tending to typical brittle-fracture velocities of the material. Oscillations of the velocityc at the transition zones, or, in many cases all over the zone of slow propagation of the crack, indicated the unstable character of crack propagation, influenced by different stress raisers and especially by the opposite longitudinal boundary of the specimen. Stress intensity factor values during crack propagation, evaluated from the front (cuspoid) and the rear (external) caustic, which remained alwaysk _g-dominant, were following similar trends as the variation of the crack propagation velocity.     

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     

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.     

Nonequilibrium statistical theory of damage and fracture for glassy polymers, 1. The statistical distribution and evolution of microcracks in glassy polymers

The purpose of this paper is to construct a unified theoretical framework to link micro to macro-mechanical properties of glassy polymers. Starting from a model of microcrack propagation in craze on a mesoscale, the kinetic process of microcrack propagation resulting from fibril breakdown in the crack tip zone is mathematically formulated by a combination of fracture mechanics and fracture kinetics. A microcrack evolution equation involving both the geometric structure parameters of craze and the meso-mechanical quantities is obtained. After solving this evolution equation, a statistical distribution function of microcrack size which evolves with time and the moment generating function of microcrack size are derived. Any-order averaged damage functions can be therefore deduced. Specifically, the analytical expressions of the first-order averaged damage function and its damage rate are presented, which correspond to a similar definition of damage mechanics.     

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.     

‘Tail’ phenomenon and fatigue crack propagation of PC/ABS alloy

The fatigue crack propagation (FCP) behavior of the alloy of polycarbonate (PC) and acrylonitrile-butadiene-styrene (PC/ABS) is experimentally investigated in this paper. An improved compliance method is employed to measure the fatigue crack length and optical and scanning electron microscopes (SEM) are used to observe the features of crack tip deformation in situ. ‘Tail’ phenomenon has been observed at the initial stage of fatigue for each specimen, which is regarded as a reflection of the transition process of accumulation of damage and plastic deformation during FCP. The law of FCP from low to high crack growth rate (10⁻⁶-10⁻³ mm/cycle) is obtained and described with Paris law. Porous or dimple features govern the fatigue crack surfaces and coarse features have been seen on the crack surfaces with higher crack growth rate, while smooth features have been observed on the crack surfaces with lower crack growth rate. A stretched band appears when the crack growth transforms from lower to higher region of FCP rate.     

Effects of molecular weight,rubber toughening,and environment on fatigue crack propagation behavior of block amide copolymers

The Fatigue Crack Propagation (FCP) behavior of block amide copolymers is investigated as a function of molecular weight, rubber toughening as well as environmental conditions. The enhancement of FCP resistance with increasing average molecular weight is shown and correlated to features observed on the fracture surface. Particular attention is paid to hysteretic heating, measured with an infrared camera, in the crack tip zone of different average molecular weight copolymers and rubber-toughened copolymer. A FCP approach of stress-cracking in an aqueous solution of zinc chloride is proposed here. An improvement in FCP resistance as the average molecular weight increases, similar to that exhibited in normal environment, appears. The shift in da/dN values over the tested range of can be approximated by an exponential function:      

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.     

Nanocavitation around a crack tip in a soft nanocomposite: A scanning microbeam small angle X‐ray scattering study

We explore nanocavitation around the crack tip region in a styrene‐butadiene random copolymer filled with typical carbon black (CB) particles used in the rubber industry for toughening the rubber. Using quasistatic loading conditions and a highly collimated X‐ray microbeam scanned around the crack tip, we demonstrate the existence of a damage zone consisting of nanovoids in a filled elastomer matrix. The existence of voids near the crack tip is demonstrated by a significant increase of the scattering invariant Q/Q₀ in front of both fatigued and fresh cracks. The size of the zone where cavities are present critically depends on the macroscopic strain ε_m, the loading history, and the maximum energy release rate G applied to accommodate the crack. Our findings show that nanovoiding occurs before fracture in typical CB‐filled elastomers and that realistic crack propagation models for such elastomers should take into account a certain level of compressibility near the crack tip. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 422–429     

Yielding of a notched poly(vinyl chloride) sheet

The development of plastic deformation around the crack tip of poly(vinyl chloride), a ductile glassy polymer, has been studied in relation to the Dugdale–Barenblatt model of ductile yielding. Three-dimensional observations reveal that the plastic deformation ahead of the crack tip consists of crazes, shear bands, and their intersections. The formation of the craze is due to a state of plane strain at the immediate vicinity of the crack tip and restricted to early steps of loading. The size and shape of the fully developed plastic zone can be described by the model. The influence of strain hardening beyond the yield point is discussed on the basis of comparison of the plastic zone lengths of poly(vinyl chloride) with those of polycarbonate which always shows shorter lengths than the model predicts.     

The effects of annealing on fatigue crack propagation in polyethylene

Fatigue crack propagation tests on annealed and quenched medium-density polyethylene showed the annealed specimens to have much lower resistance to crack initiation and subsequent propagation. Although the same fracture mechanism, in which the brittle crack gradually becomes more ductile, prevailed in both cases, the voided and fibrillated crack tip root craze in the annealed material was much weaker that the nonfibrillated quenched root craze. Microstructural analyses indicate that the annealed material had separate crystallite populations, whereas the quenched material had a more homogeneous morphology. The highest melting fraction of the annealed material was composed of lamellae that were about 270 Å thick, and the quenched lamellae were estimated to be 160 Å thick. The reduced fatigue crack propagation resistance of the annealed material was suggested to be a result of a lower concentration of tie molecules and its reduced damping capability, compared to the quenched material. © 1995 John Wiley & Sons, Inc.     

Plane-strain fracture energy instability and mixed mode crack propagation in polycarbonate at room temperature

A study of crack propagation in double cantilever beam specimens of polycarbonate has revealed a large velocity-dependent instability in the plane-strain fracture energy G_Ic. At a crack velocity of 10^?2 in./min, G_Ic accords with published values obtained from tensile studies of precracked specimens. Crack propagation in doubly grooved double cantilever beam specimens is unstable at higher velocities. The G_Ic's during crack jumping and at crack arrest are estimated to be 0.2 and 2%, respectively, of the low crack speed value, based on the amounts of crazing produced at the various crack speeds. Evidence of plane-strain shear deformation at the low speed crack tip is presented. The G_Ic instability is suggested to arise from differences in the kinetics of shear failure and craze breakdown.     

光学显微镜研究交联有机玻璃断面上的肋状形态

用光学显微镜观察了交联有机玻璃断面上的肋状形态。发现断面形态、裂纹路径以及肋状区裂端簇射状银纹群之间有直接联系。每一肋条由一细砂带和一粗破带构成。前者对应于裂端楔形银纹/固体聚合物之间界面的剥离;后者对应于剥离后锐化裂端银纹群之间的剪切;这两个交替过程可以用“滑-粘”模型来解释。在不稳定肋状区发现到裂纹在霉纹区和肋状区的扩展机理是可以相互转化的。     

Effect of molecular relaxations on the fracture behavior of poly(vinyl chloride)

The fracture toughness of PVC has been measured by using three-point bend specimens tested over a wide range of strain rate and temperature. A method has been described of deriving fracture load indirectly by measurement of stiffness from a preliminary “low blow” test in instrumented impact testing. Some limitations of the method, when used with semi-ductile material of low stiffness, have been discussed. Fracture toughness results have also been evaluated by an alternative energy method, which is however more suitably applied to the lower speed impact test. The curves of K_1c versus temperature for PVC contain a weak maximum at a temperature below T_g, the location of which varies with testing speed. The position of the maximum in the time–temperature field has been compared with the locus of the β damping peak derived from mechanical (flexural vibrations, torsion pendulum) and dielectric loss measurements, with reasonable agreement. Static toughness was higher than dynamic, and this correlated with fracture surface appearance, thereby indicating a real difference in toughness probably associated with crack tip craze development.     

Crack growth in a pipe grade PVC material under static and cyclic loading conditions

The creep crack growth (CCG) and the fatigue crack growth (FCG) behavior of a commercial pipe grade PVC material was studied based on a linear elastic fracture mechanics (LEFM) methodology. The FCG tests were performed under sinusoidal load control at a frequency of 5 Hz and at R-ratios (F_min/F_max) of 0.1, 0.3 and 0.5; the test temperatures were 23°C and 60°C. The creep crack growth behavior (corresponding to R = 1) was studied at a test temperature of 60°C. The results of the FCG tests revealed that fatigue crack propagation is primarily controlled by the cyclic component of the crack tip stress field rather than by the mean stress level. Comparing FCG and CCG data in terms of K_Imax and K_I, respectively, also confirmed the deteriorating effect of the fatigue loading on the crack growth resistance. Fracture surface investigations for both fatigue and static loading were performed to gain insight into the micromechanisms of crack advance.     

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.

     

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.