Fracture and tearing in oriented polyethylene

Measurements of energy for crack propagation (fracture surface energy) have been made on low-density and high-density polythenes both in the undrawn state and in different states of orientation produced by drawing under various conditions. Both cleavage and tear tests were employed. For the unoriented materials the values of fracture surface energies were in the range 10⁴ to 10⁵ J m^–2.With increasing orientation (represented by birefringence) the energy for crack propagation parallel to the direction of orientation fell by a factor of approximately 100. The differences between the low-density and high-density polymers, and between the different types of low-density polymers examined, were comparatively slight.Measurements of crack tip diameter showed a direct relation between this quantity and fracture surface energy. From their comparable studies of the tearing of rubbers Rivlin and Thomas have interpreted such a relationship as implying that the high values of fracture surface energy arise from the work required to deform the material in the crack tip up to the point of rupture. On this basis the reduction in fracture surface energy with increase in orientation is a direct result of the reduction in the diameter of the crack tip.     

Apparent interfacial failure in mixed-mode adhesive fracture

Aluminium-epoxy adhesive specimens constructed with the bond at 45? to the direction of loading appear to fail very close to the interface. The actual locus of failure was investigated by¹⁴C labelling of the epoxy polymer and also by Auger spectroscopy profile analysis. Both techniques indicated a residual film of polymer a few hundred angstroms thick on the aluminium surface. The fracture energy of these specimens was determined and found to be affected by the surface roughness of the aluminium. The mixed-mode fracture energy (G _{I,II) C} ^45° of these specimens in the absence of any surface roughness effect (polished surfaces) was 140 J m^?2 compared to 136 J m^?2 for the same polymer in simple opening-modeG _{I C} adhesive fracture. The “interfacial” failure and the effect of surface finish on fracture are discussed in terms of the applied stress directing the failure toward the interface but the approach of the crack to the boundary being limited by the size of the crack tip deformation zone.     

Isotactic polypropylene/EPDM blends: Effect of testing temperature and rubber content on fracture

Charpy impact tests in the temperature range ?100 to +20° C have been carried out on two isotactic polypropylenes (PP) having different molecular weight and their blends containing as rubbery phase an ethylene-propylene-diene terpolymer (EPDM). For fractures of brittle nature the impact data were analysed in terms of the linear elastic fracture mechanics andK _c andG _c were determined. This behaviour was observed for the homopolymers over the temperature range investigated, and for the blends only up to ?20° C. At higher temperatures such materials showed fracture of a semiductile type with visible evidence of craze whitening around the crack tip, followed by brittle type fracture. In this case the results were analysed in terms of a ductile contribution (energy required to form the crazed area) and of a brittle one (relative to the crack propagation area) from whichG _c could be derived according to a procedure proposed in the literature. Tentative interpretations of the results also on a molecular and structural basis have been given. A critical discussion of the elaboration of the semiductile fracture data proposed in the literature has also been provided.     

Time-temperature dependent fracture toughness of PMMA

Some observations are made on the fractography of surfaces obtained by cracking “compact tension” profile testpieces of PMMA over a range of temperatures and crack speeds, both stably and unstably. To a first approximation, it was possible to group and “shift” (as in visco-elastic transformations) characteristic surface markings at various fracture toughness/temperature/crack velocity combinations, particularly in the range where a toughness-biased Ree-Eyring relationship described the experimental toughness data.     

Crack patterns in cylinders explosively loaded at an hemispherical end

The final crack and fracture damage found in hemispherically-ended ‘Perspex’ (PMMA) rods loaded explosively by electrical detonators at their hemispherical end is described. The mechanisms of the formation of the major features are also considered. The most significant feature observed occurs as a Hertzian cone crack which develops to form a completely closed crack surface in the shape of a cardioid (heart-shape) solid of revolution. Also associated with these features are small areas of crazing and spalling generated by stress wave reflections.     

Static and energetic fracture parameters for rocks and concretes

The object of the paper is to determine the fracture toughness parameters K_1C,G _1C and J_1C for some aggregative materials. Values of the J-integral are calculated from load-displacement curves, following the procedure suggested by Begley and Landes for steel alloys. Some recurring experimental incoherences are explained applying Buckingham's Theorem for physical similitude and scale modeling to Fracture Mechanics. Thus a non-dimensional parameter can be defined (the test brittleness number), which governs the fracture-sensitivity phenomenon. The fracture parameters K_1C and J_1C are connected by a fictitious Young's modulus E^*, which is lower than the real modulus E and represents the stiffness of the damaged material near the crack tip before the extension. When the specimen sizes are so small that the material becomes fracture insensitive, then E^* appears higher than E.     

Craze formation and growth in anisotropic polymers

Craze formation and craze growth in anisotropic polymers has been studied as a function of the degree of anisotropy and the relation between the testing direction and the primary orientation direction. Tests on PMMA and PC indicate that both the morphology and orientation of the crazes are senstivie functions of testing direction. Crazes form in directions which arenot orthogonal to the principal tensile stress, and the data clearly show that craze growth occurs in directions governed by the major principal strain. The fracture process is identical in nature to that in isotropic polymers, i.e. craze formation, crack nucleation within the craze and subsequent crack propagation through the craze. Thus, the angle of fracture coincides with the craze angle rather than occurring perpendicular to the principal tensile stress.     

Predicting stress corrosion crack growth rates when linear elastic fracture mechanics conditions are not operative

The growth rate of a stress corrosion crack in situations where linear elastic fracture mechanics (LEFM) conditions are not operative is predicted on the basis that the crack tip opening angle (CTOA) is related to the growth rate dc/dt, the functional relation between the CTOA and dc/dt being obtained by coupling theoretical results for crack growth under small-scale yielding conditions in an inert environment, with the experimentally determined power law relation between the crack tip stress intensity K and dc/dt for environmentally-assisted crack growth under LEFM conditions. Then, by assuming that the same CTOA-dc/dt relation applies to non-LEFM conditions, and by determining the CTOA under these conditions, it is in principle possible to predict the stress corrosion crack growth rate under non-LEFM conditions. A specific model: the plane strain deformation of a solid with two symmetrically situated deep cracks, and with tension of the small remaining ligament, is analyzed in detail, and the effects of the extent of plastic deformation and loading pattern (i.e., displacement or load control), on the predicted stress corrosion crack growth rate, are examined in detail. The results are compared with those obtained via application of the K versus dc/dt relation, its conversion to a J versus dc/dt correlation and then the determination of J, and also with those obtained on the assumption that a K approach is derectly applicable. The extent to which these latter approaches give conservative or non-conservative growth rate predictions when compared with the present paper's predictions, is discussed in relation to the extent of plastic deformation and loading pattern.     

Carbon fibre composites with rubber toughened matrices

In carbon fibre reinforced plastics (CFRP), the initial resistance to crack propagation parallel to fibres is determined largely by the matrix toughness. The fracture toughness (G _IC) of an epoxide resin can be increased considerably by the addition of butadieneacrylonitrile co-polymers (CTBN). These cause the precipitation of small spheres of a second phase and, for example, increaseG _IC from ～ 300 to ～ 3000 J m^?2 on the addition of 9 wt% CTBN. The large increases obtained in bulk resins are not obtained in CFRP, instead significant but modest increases are achieved. The suppression of toughness is related to the thickness of resin film through which the crack propagates.     

The temperature wave method of determining fracture toughness values due to crack propagation

A method is presented of determining fracture toughness by measurement of the amount of heat emitted at the tip of a propagating crack. Two thermojunctions placed adjacent to the crack were used to monitor the temperature wave produced at fracture. An electromagnetic fluxmeter was used to integrate the thermojunction output with respect to time and was calibrated to give a direct reading in terms of strain energy release rate G. The temperature wave method is independent of initial crack length and fracture surface area and can be readily used for specimens having complex sections. Values obtained by this method compare favourably with toughness values determined by a linear elastic fracture mechanics analysis. Results of static and dynamic three-point bending tests on specimens at different temperatures within the range ?40 to 60° C are reported.     

The validity of various fracture mechanics methods at creep temperatures

The application of stress intensity factors derived from linear elastic fracture mechanics (LEFM) to fracture at creep temperatures has been considered. From tensile creep rupture tests on single edge notched and notched centre hole specimens of solution treated A.I.S.I. type 316 stainless steel, it is shown that a LEFM approach is inapplicable to predicting creep crack growth rates, whilst the net section stress is found to correlate well with the crack growth rates. These observations have been explained by considering the creep relaxation that takes place at the notch root, smoothing out the local stresses and thus making the LEFM stress distribution inapplicable. The resulting stress distribution supports the observation that the net section stress is a successful criterion on which to predict creep rupture in stainless steel. The limitations as a fracture mechanics method are explored and it is found that a criterion based on the amount of creep rather than stress would have advantages in some respects. In this context the “crack opening displacement” and the “fracture angle” criteria are considered and their use is found to hinge upon the development of suitable methods for relating the local displacement to the applied stress.     

Effect of residual stress on crack propagation in MDPE pipes

Crack propagation behaviour in single edge notched specimens prepared from medium-density polyethylene (MDPE) pipe is examined under creep condition. The crack grown from an exterior notch (inbound) initiated faster than that grown from an interior notch (outbound). Subsequently, the outbound crack propagated monotonically to ultimate failure. The inbound crack showed anomalous behaviour involving two arrest stages prior to ultimate failure. The pipe is found to possess substantial residual stresses. The energy release rate for each case was calculated taking into account the respective residual stream distribution. The fact that the rates of crack propagation are not a unique function of the energy release rate indicates that the fracture is also influenced by morphological gradients imposed by processing conditions.     

On the small crack fracture mechanics

The limit of validity of linear fracture mechanics is specified by the minimum allowable crack length through an ASTM convention. Extension into the non-linear region ought to imply an extension towards smaller allowable cracks. In order to elucidate the question “How short is the smallest crack that fits the methods of fracture mechanics, and how do shorter cracks than that behave?” a pilot investigation is carried out. The process region is modelled as a Barenblatt line region and plastic flow off-side the process region is neglected. Results show that instability occurs before the process region is fully developed (as at large cracks) if the crack is short. This implies large deviations from the large crack fracture mechanics if the crack is very small. Even cracks of infinitesimal length are included in the study.     

Basic issues in the mechanics of high cycle metal fatigue

Mechanics issues related to the formation and growth of cracks ranging from subgrain dimension to up to the order of one mm are considered under high cycle fatigue (HCF) conditions for metallic materials. Further efforts to improve the accuracy of life estimation in the HCF regime must consider various factors that are not presently addressed by traditional linear elastic fracture mechanics (LEFM) approaches, nor by conventional HCF design tools such as the S-N curve, modified Goodman diagram and fatigue limit. A fundamental consideration is that a threshold level for ΔK for small/short cracks may be considerably lower than that for long cracks, leading to non-conservative life predictions using the traditional LEFM approach. Extension of damage tolerance concepts to lower length scales and small cracks relies critically on deeper understanding of (a) small crack behavior including interactions with microstructure, (b) heterogeneity and anisotropy of cyclic slip processes associated with the orientation distribution of grains, and (c) development of reliable small crack monitoring techniques. The basic technology is not yet sufficiently advanced in any of these areas to implement damage tolerant design for HCF. The lack of consistency of existing crack initiation and fracture mechanics approaches for HCF leads to significant reservations concerning application of existing technology to damage tolerant design of aircraft gas turbine engines, for example. The intent of this paper is to focus on various aspects of the propagation of small cracks which merit further research to enhance the accuracy of HCF life prediction. Predominant concern will rest with polycrystalline metals, and most of the issues pertain to wide classes of alloys.     

Optical properties of Er3+–Ag co-doped ZnO nanocrystals prepared by combustions method

The Er³⁺–Ag co-doped ZnO nanocrystals have been synthesized by citric acid-assisted combustions method. The effect of different concentration of silver nanoparticles (NPs) on Er³⁺ doped ZnO nanocrystals and the optical behaviors are explored. The nanocrystals were characterized by X-ray diffractions, scanning electron microscopy, UV–Vis–NIR absorption spectra, X-ray photoelectron spectroscopy, and photoluminescence, respectively. The luminous intensity of Er³⁺ doped ZnO nanocrystals was significantly influenced by the concentration of silver NPs. A large enhancement in up-conversion intensity has been observed when the concentration of silver NPs was 0.10 mol%. The effect of localized surface plasmon resonance of silver NPs and the energy transfer between the silver NPs and Er³⁺ ions (²H_11/2 → ⁴I_15/2, ⁴S_3/2 → ⁴I_15/2, and ⁴F_9/2 → ⁴I_15/2) are discussed as the sources of enhancement or quenching.     

Hertzian indentation of thorium dioxide,ThO2

The Hertzian indentation technique was used to study the fracture properties of ThO₂ and to measure the fracture surface energy, , of sintered ThO₂. Optical microscopy and acoustic emission were employed to detect ring crack formation. Perfect cracks were always formed and no indication of permanent plastic deformation was observed. From the observed crack behaviour, a fracture surface energy, , of 2.5±0.2 J m^–2 at room temperature and a fracture toughness, K _Ic, of 1.07 MN m^–3/2 were deduced.     

Highly oriented single-phase blend films of high- and low-density polyethylene

The microstructures of highly oriented drawn films of blends of high-density polyethylene (HDPE) and low-density polyethylene (LDPE) were investigated by transmission electron microscopy, electron diffraction, X-ray diffraction, and differential scanning calorimetry (DSC). The average crystal size, as well as long period, crystalline content, and melting endotherm peak, decreased as LDPE was added to the blend. When the LDPE content exceeded ～ 50%, the film texture changed from a single crystal texture to fibre symmetric. Segregation of the two polyethylenes was not detected at low LDPE contents in as-drawn or melted and recrystallized films. In the as-drawn films, a low temperature tail began to appear on endotherm melting peaks at LDPE contents ?70%, indicating the onset of segregation. In meltcrystallized films, however, two distinct melting endotherm peaks were visible for LDPE contents ?50%. An equilibrium melting point of 141° C and end surface free energy of 101 erg cm^?2 (101 × 10^?7 J cm^?2) were determined by use of the Thomson equation. The close agreement between these values and literature values for HDPE suggested that the crystals present in HDPE/LDPE blends were thermodynamically equivalent to HDPE crystals of equal size, implying that branches were excluded from the crystalline phase.     

The disentanglement time of the craze fibrils in polymethylmethacrylate

A breaking time has been defined for the fibrils in the craze at the tip of a steady-state moving crack. It has been shown that, for polymethylmethacrylate above the critical temperature of ?20° C, the fibrils of the craze at the crack tip break due to a thermally activated process. The activation energy is equal to 23 kcal mol^?1, which corresponds fairly closely to the activation energy of theΒ relaxation. Then, the breaking time is probably a disentanglement time rather than a breaking time of chains, and this may be used to explain the time-temperature behaviour of the macroscopic fracture toughness.     

Crack resistance behavior of particulate reinforced composites at various test speeds and temperatures

In this study, the fracture behavior and characteristics of particulate-reinforced composite materials were evaluated by performing wedge splitting tests. The crack resistance of the materials was evaluated using the crack tip opening displacement and crack tip opening angle. The composites were tested under various temperatures and test speeds. The digital image correlation method was used to analyze the strain field at the crack tip. The fracture surface under test conditions was observed using a scanning electron microscope. The test results showed that the fracture energy increased with decreasing temperature, and the crack resistance increased with increasing test speed. The crack tip opening angle is divided into an unstable region and stable region. The critical crack tip opening angle can be defined as the fracture mechanics parameter measured in a stable region. The surface strain fields obtained by digital image correlation method are distributed in the range from 1.5 % to 4.5 % at the initiation of the crack. A crack grows with dewetting phenomenon at the temperature range from 60 °C to −40 °C, and the crack propagates with fracture of ammonium perchlorate oxidizer particles at the glass transition temperature of −70 °C.     

Interfacial energetics in the TD-nickel and TD-nichrome systems

The absolute (mean) interfacial free energies are measured in thoria-dispersed (2 vol %) (TD)-nickel and the TD-nichrome (Ni-20% Cr) systems at 1200° C utilizing techniques of scanning electron and transmission electron microscopy. Values of particle/matrix interfacial energies for TD-NiCr and TD-Ni were measured at 2300 and 2000 erg cm^?2 respectively based upon measured values of 2040 and 2200 erg cm^?2 for the surface free energies for nichrome (80∶20 NiCr) and pure nickel respectively, by the method of zero creep and the measurement of grain-boundary groove angles in the electron microscope. Values of 900 erg cm^?2 and 1040 erg cm^?2 were measured for the surface and grain-boundary free energies for thoria (ThO₂). The particle/matrix adhesive energy for TD-nichrome was measured to be roughly half that for the TD-nickel system based upon the classical interfacial adhesion concept. It is concluded that the apparent difference in particle/matrix interfacial strength between TD-nickel and TD-nichrome results by a more complex mechanism than simple interfacial decohesion involving phase separation.