Crack propagation behavior in rubber materials

Within the linear viscoelastic theory, crack tip fields are calculated at various crack tip velocities. A transition from rubbery to glassy material behavior in the vicinity of the crack tip can be observed. Shear and bulk behavior is analyzed separately. Whereas the increase of tearing energy at higher crack tip velocities can be ascribed to the shear behavior, bulk behavior influences the fracture mechanism. The results support experimental investigations that the instability separating stable from unstable crack propagation is related to a change in the fracture mechanism. At low crack tip velocities, material separation is the result of formation, growth, and coalescence of cavities. At high crack tip velocities, cavitation is suppressed and fracture is driven by a rather brittle mechanism resulting in a decreased amount of energy to propagate the fracture process zone. Published in Russian in Vysokomolekulyarnye Soedineniya, Ser. A, 2008, Vol. 50, No. 5, pp. 882–891. This article was submitted by the authors in English.     

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.     

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     

On the thermodynamic theory of the strength of solids: 3. Thermodynamic linear tension of a crack in solid with dispersion forces

Th thermodynamic linear tension of rectilinear and curvilinear cracks in a solid with dispersion forces is calculated at the arbitrary value of the opening angle of a crack. The dependence of linear tension on the depth of the crack at depth and conformal mechanisms of its growth is analyzed. The effect of linear tension on the ultimate strength of a solid is evaluated and the known Griffith formula is generalized to the ultimate strength. It is shown that, in the case of rectilinear crack, the effect of linear tension on the ultimate strength is related to changes in linear tension during the growth of the crack, which is typical for a depth mechanism. For a curvilinear crack, this effect becomes twofold greater due to additional changes in the length of the frontal line of the crack in the course of its growth. The contribution of linear tension is negligible for macroscopic cracks, but can be equal to tens of percentage points for nanocracks demonstrating the beginning of the fracture of solids.     

Measurement of rapid crack propagation in pressure pipes: A static S4 approach

A method for creating rapid crack propagation in pressurized pipes under slow static loading using modified S4 apparatus is described. In the development of the method a complexity involved with dynamic loading in the S4 test (ISO 13477) is eliminated by the use of a displacement controlled static loading machine. The experimental system consisted of an universal testing machine, a low compliance wedge loading device, notch tip quenching apparatus and a pipe specimen where a through thickness hole is drilled to accommodate the wedge loading device. The pipe specimen is made in such a way that a section containing a hole is free from the internal pressure, while the rest of the specimen is made to carry the internal pressure which would eventually drive the unstable crack along the pipe axis. The idea of such rapid crack initiation under static loading was derived from the concept of time-temperature equivalence, where impact loading may in part be simulated by lowering the temperature at the site of rapid crack initiation. The details of the method for rapid crack propagation under static loading are described and the correlation of the results to rapid crack propagation obtained by ISO 13477 is illustrated. The two methods were shown to compare quite well in terms of critical pressure determination and the details regarding normalized rapid crack length versus the internal pressure curve as well as the crack propagation pattern.     

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.     

Crack growth in medical-grade silicone and polyurethane ether elastomers

One major problem with ball and socket artificial discs is the migration of wear particles to the surrounding tissues. This debris can cause inflammation that can lead to implant loosening. Encapsulating the artificial disc with an elastomer sheath could prevent this problem by retaining the wear particles within the disc. The encapsulation sheath will face millions of tensile cycles during the implant life and, therefore, it must have the ability to withstand large strains without fracture. Using cyclic displacement, crack nucleation was applied on dumbbell specimens and crack growth was applied on rectangular specimens with an initial crack. Both tests were performed on Silex silicone and polyurethane ether elastomer specimens, both with a Shore durometer hardness of 40 shore A. No samples completely failed during the crack nucleation tests after five million cycles. The polyurethane ether elastomer showed a slower rate of crack growth life (421 k cycles to reach 70 mm crack length) than silicone elastomer (221 k cycles to reach the same crack length) in the control group. Accelerated ageing decreased the hardness and the crack growth rate of the polyurethane elastomer but had the opposite effect for the silicone elastomer. Gamma sterilization increased the crack growth rate and did not affect the hardness of the polyurethane elastomer. The hardness and the crack growth rate of the silicone elastomer were increased after gamma sterilization.     

Effect of fibril arrangement on crack trapping in a film‐terminated fibrillar interface

We present a three‐dimensional (3D) model for adhesion enhancement due to crack trapping in a film‐terminated fibrillar structure. Adhesion enhancement occurs due to trapping of the interfacial crack in the region between fibrils. Energy release to the crack tip is attenuated because, between fibrils, it has to pass through the compliant terminal film. Using perturbation theory and a finite element method, we solve for the shape of crack front, which is unknown. Our model thus also allows us to study how adhesion enhancement depends on the arrangement of fibrils. For example, our model explains why, for a fixed area density of fibrils and for similar crack orientations, hexagonal arrays have higher adhesion than square arrays. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 2368–2384, 2009     

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     

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.     

On the thermodynamic theory of the strength of solids: 4. Capillary condensation and capillary evaporation in wedge-shaped crack

The processes of capillary condensation and capillary evaporation in a wedge-shaped crack are considered. Capillary evaporation is a comparatively new phenomenon that is opposite to capillary condensation and occurs upon the cleavage of a solid in a nonwetting liquid. For both cases, the positions of a meniscus inside a wedge-shaped crack have been calculated as functions of the meniscus curvature radius, liquid-contact angle, and crack-opening angle. The effect of temperature on the meniscus position has been analyzed; it has been established that the meniscus shifts from the gaseous toward the liquid phase as temperature rises. The regularities of meniscus displacements in the course of crack growth have been established: under the conformal mechanism of crack growth, the absolute position of the meniscus remains unchanged (i.e., the meniscus and the crack frontal line move at the same velocity), while, under the depth mechanism of growth, the relative position of the meniscus is retained.     

Solvent-induced crack growth in rubbery block polymers

The rapid cracking of lightly stressed rubbery block polymers of styrene and isoprene in certain liquids and vapors has been examined experimentally, by using model test pieces containing a single crack. Solvents which preferentially dissolve the rigid molecular end blocks rather than the rubbery center blocks are efficient cracking agents. The stress required for crack growth to occur is shown to be in accord with a simple energy criterion: the stored elastic energy must be sufficient to provide a characteristic energy for the newly formed surface. This characteristic energy ranges from values close to the surface energy of simple liquids up to about 100 times this value for thicker test pieces or slowly diffusing vapors, when some tearing of an incompletely swollen core is inferred. “Induction times,” before the initial crack starts to grow, are shown to be due to a progressive increase in stored energy under a constant stress as the material absorbs solvent and softens until the critical energy criterion is met. Thus, a timedependent fracture process is shown to be in accord with a constant energy criterion. Above the critical condition the rate of crack growth depends strongly upon stress, like tearing of amorphous elastomers, and the crack then accelerates rapidly.     

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.     

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.     

Automated monitoring of the crack propagation in mode I testing of thermoplastic composites by means of digital image correlation

One of the main challenges of the mode I double cantilever beam (DCB) test is the simultaneous determination of the applied load and displacement with the developing delamination length. The present work addresses this issue by side-view tracking the crack propagation by means of digital image correlation (DIC). Two different reduction methods were developed to determine the crack length from the DIC data. On the one hand, the crack tip position was defined by the high strain concentration in the immediate vicinity of the crack tip, and on the other hand, by crack tip opening displacement (CTOD). The data obtained enabled the calculation of the energy release rate of carbon fibre reinforced thermoplastic specimens with either run-arrest or stable crack extension. For reasons of comparability, top surface analysis (TSA), as recently reported, was also carried out. Following this approach, the crack propagation was tracked applying DIC to the top specimen surface. The methods developed showed a good correlation with both the standardised procedure and TSA. It was shown that DIC can be used as an alternative to the conventional optical measuring tools to follow the crack propagation in the mode I DCB test.     

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.     

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.     

Crack propagation from a preexisting flaw at a notch root

We study crack kinking from a preexisting crack initiated at a notch root. This makes it necessary to evaluate the stress intensity factors at the tip of the initial crack, as a function of the “stress intensity factor of the notch” (the multiplicative coefficient of the singular stress field at the notch root in the absence of the crack), the length of the crack, the aperture angle of the notch and the angle between its bisecting line and the direction of the crack. Applying Goldstein and Salganik's well-known principle of local symmetry yields then the prediction of the kink angle of the crack extension. It is found that although the notch is always predominantly loaded in “mode I”, this angle is generally not large enough for the crack tip to get closer to the bisecting line of the notch.     

Carbon tetrachloride-induced crack healing in polycarbonate

Crack healing induced by carbon tetrachloride in polycarbonate has been studied at temperatures in the range of 40–60°C. The carbon tetrachloride treatment reduces the glass transition temperature of polycarbonate. Crack healing is observed because the effective glass transition temperature in polycarbonate is reduced to below the test temperature by the carbon tetrachloride treatment. Two distinctive stages of crack healing are divided based on the recovery of mechanical strength and fractograph. The first stage corresponds to the progressive healing due to the convolution of wetting and self-diffusion, which has a constant crack closure rate. Immediately following the first stage, the second stage, corresponding to the self-diffusion of polymer chain, enhances the quality of healing behavior. The transport of carbon tetrachloride in polycarbonate consists of case I (concentration gradient controlled) and case II (relaxation controlled) behaviors. The direction of case II is opposite to that of case I. The solubility decreases with increasing temperature, but diffusivity and velocity for mass transfer, crack closure rate, and diffusion coefficient for the diffusion front have the opposite trend. The first stage of crack healing is controlled by case II transport. The transport of carbon tetrachloride changes the fracture behavior of polycarbonate from ductile to brittle. A comparison of crack healing in polycarbonate and poly (methyl methacrylate) is made. © 1994 John Wiley & Sons, Inc.