The virtual crack extension method for evaluation of J- and

The equation for evaluating the nonlinear fracture mechanics parameters J- and Ĵ-integrals are derived using the virtual crack extension method. The validity of the equations derived here are checked by solving several numerical examples, that is, the J-integral analyses of compact tension specimen and three-point bend specimen, and the Ĵ-integral analysis of centrally cracked plate. Reasonably good agreement is found between the virtual crack extension method and the line integral method.     

Classification of environmentally assisted fatigue crack growth behavior

Fatigue crack growth is represented using fracture mechanics parameters, ΔK and K_max. Environmental effects that depend on time and stress affect the fatigue behavior predominantly through K_max parameter. The superimposed effects of environment and stress are seemingly complex. We have developed a methodology for classifying and separating the effects of environment on fatigue crack growth. A “crack growth trajectory map” is constructed from the behavior of ΔK versus K_max for various constant crack growth rate curves. A “pure fatigue” behavior is defined, in terms of environment-free behavior, such as in high vacuum. Deviation from this “pure fatigue” reference of the trajectory map is associated with either monotonic mode of fracture or to the superimposed environmental effects on crack growth. Using such an approach, called “Unified Damage Approach”, we classify the environmental effects in almost all materials into only five types. Each of these types shows the combination of time and stress affecting the crack tip driving force, and thus ΔK and K_max. The trajectory map depicts the changing material resistance due to the changing crack growth mechanisms with increasing crack growth rate, as reflected in terms of the applied stress intensities, ΔK and K_max. Thus the trajectory map provides a useful tool to separate the contributions from pure fatigue and superimposed monotonic modes and the governing crack growth mechanisms as a function of load-ratio, crack growth rate and environment. Understanding and quantification of the governing mechanisms would help in developing a more fundamental and reliable life prediction method.     

Nature of the Chemical Bond in Uranium Dioxide UO<Subscript>2</Subscript>

Fine structure of the X-ray photoelectron and conversion spectra of low-energy (0–40 eV) electrons of uranium dioxide UO₂ was analyzed based on the electronic structure calculations for the UO ₈ ¹²⁻ cluster with O _h symmetry, simulating the nearest surrounding of uranium in UO₂, by the relativistic X _α discrete variation method. It was predicted theoretically and validated experimentally that, in UO₂, the U5f electrons (∼1 U5f electron) can directly participate in chemical bonding: ∼2 U5f electrons weakly contributing to chemical bonding are localized at −1.9 eV; ∼1 U5f electron participating in chemical bonding is delocalized in the range of outer valence molecular orbital energies from −4 to −9 eV; and unfilled U5f states are localized mostly at low (from 0 to 5 eV above zero) energies. It was shown experimentally that the U6p electrons actively participate in formation of not only inner valence but also outer valence (0.6 U6p electron) molecular orbitals. The density of the U6p states in UO₂ was estimated experimentally. The composition and sequence of the inner valence molecular orbitals at energies within 13–40 eV were also elucidated.__________Translated from Radiokhimiya, Vol. 47, No. 3, 2005, pp. 193–202.Original Russian Text Copyright © 2005 by Yu. Teterin, Maslakov, Ryzhkov, Traparic, Vukcevic, A. Teterin, Panov.     

The mechanics of self-similar and self-affine fractal cracks

In this paper we study the mechanical attributes of the fractal nature of fracture surfaces. The structure of stress and strain singularity at the tip of a fractal crack, which can be self-similar or self-affine, is studied. The three classical modes of fracture and the fourth mode of fracture are discussed for fractal cracks in two-dimensional and three- dimensional solid bodies. It is discovered that there are six modes of fracture in fractal fracture mechanics. The J-integral is shown to be path-dependent. It is explained that the proposed modified J-integrals in the literature that are argued to be path-independent are only locally path-independent and have no physical meaning. It is conjectured that a fractal J-integral should be the rate of potential energy release per unit of a fractal measure of crack growth. The powers of stress and strain singularities at the tip of a fractal crack in a strain-hardening material are calculated. It is shown that stresses and strains have weaker singularities at the tip of a fractal crack than they do at the tip of a smooth crack.     

Future balloon experiments for electron and positron measurements at high energy

A large interest has been triggered by the recent direct measurements of cosmic positrons and electrons. They include: the anomalous positron abundance reported by PAMELA; the spectral “feature” suggested by the analysis of the inclusive electron and positron data of the ATIC balloon experiment; the results of FERMI and H.E.S.S. experiments. Further accurate measurements, with smaller systematic errors, might clarify the present experimental scenario. While measurements of dipole asymmetries and of the electron spectrum above 1 TeV may require a space mission to provide a sufficient exposure, balloons can investigate the spectral shape below 1 TeV and contribute to the clarification of the, so-called, “ATIC anomaly”. A concise review will be presented of the main balloon missions that have been specifically designed to provide new electron measurements in the near future.     

The effect of the loading rate on the fracture toughness of Poly(methyl methacrylate), Polyacetal,Polyetheretherketone and modified PVC

The mode-l-plane-strain fracture toughness at initiation of various engineering plastics was determined for test speeds between 10^–4ms^–1 and 1.0 ms^–1, using a high-speed, servohydraulic testing apparatus. At high rates of testing, the transient acceleration of the specimen was reduced by the use of a damping technique aimed at overcoming dynamic effects. The results obtained are correlated with fractographic analysis performed by scanning electron microscopy (SEM) and by digital image analysis of macroscopic fracture surfaces. The results show that for some materials the high values of K _lc measured at low testing rates are associated with deformation detectable by either method. The extent of such deformation tends to be reduced as the testing velocity is increased and the fracture toughness drops.     

Experimental and numerical investigation of cracked chevron notched Brazilian disc specimen for fracture toughness testing of rock

The cracked chevron notched Brazilian disc (CCNBD) specimen has been suggested by the International Society for Rock Mechanics to quantify mode I fracture toughness (K_Ic) of rock, and it has also been applied to mode II fracture toughness (K_IIc) testing in some research on the basis of some assumptions about the crack growth process in the specimen. However, the K_Ic value measured using the CCNBD specimen is usually conservative, and the assumptions made in the mode II test are rarely assessed. In this study, both laboratory experiments and numerical modeling are performed to study the modes I and II CCNBD tests, and an acoustic emission technique is used to monitor the fracture processes of the specimens. A large fracture process zone and a length of subcritical crack growth are found to be key factors affecting the K_Ic measurement using the CCNBD specimen. For the mode II CCNBD test, the crack growth process is actually quite different from the assumptions often made for determining the fracture toughness. The experimental and numerical results call for more attention on the realistic crack growth processes in rock fracture toughness specimens.     

Analysis of the curve of cyclic elastoplastic fracture of a specimen with a crack. Report no. 2

A new method is used to experimentally establish the laws governing the cyclic and quasistatic final fracture of compact specimens of steels 30 and 45. Specimen thicknesses are 10, 20, and 40 mm. It is proposed that the curve describing the cyclic elastoplastic fracture of a specimen be constructed with allowance for the actual load acting on the specimen during final fracture (the CEPFSC Q-curve). Q-curves are analyzed for specimens of different thicknesses and a method is described for constructing a curve that generalizes (for specimens of different sizes) both types of CEPFSC curves for the given steels on the basis of suitable similarity transformations.Translated from Problemy Prochnosti, Nos. 5–6, pp. 52–61, May–June, 1995.     

A review of the J and I integrals and their implications for crack growth resistance and toughness in ductile fracture

The application of the J and the I-integrals to ductile fracture are discussed. It is shown that, because of the finite size of the fracture process zone (FPZ), the initiation value of the J-integral is specimen dependent even if the plastic constraint conditions are constant. The paradox that the I-integral for steady state elasto-plastic crack growth is apparently zero is examined. It is shown that, if the FPZ at the crack tip is modelled, the I-integral is equal to the work performed in its fracture. Thus it is essential to model the fracture process zone in ductile fracture. The I-integral is then used to demonstrate that the breakdown in applicability of the J-integral to crack growth in ductile fracture is as much due to the inclusion in the J-integral of progressively more work performed in the plastic zone as it is to non-proportional deformation during unloading behind the crack tip. Thus J _R -curves combine the essential work of fracture performed in the FPZ with the plastic work performed outside of the FPZ. These two work terms scale differently and produce size and geometry dependence. It is suggested that the future direction of modelling in ductile fracture should be to include the FPZ. Strides have already been made in this direction.     

Mode II fracture testing method for highly orthotropic materials like wood

In this paper a mode II fracture testing method has been developed for wood from analytical, experimental and numerical investigations. Analytical results obtained by other researchers showed that the specimen geometry and loading type used for the proposed mode II testing method results in only mode II stress intensity and no mode I stress intensity at the crack tip. Experiments have been carried out to determine mode II fracture toughness K _IIC and fracture energy G _IIF from the test data collected from both spruce (pice abies) and poplar (populus nigra) specimens. It was found that there existed a very good relation between fracture toughness K_IIC and fracture energy G _IIF when the influence of orthotropic stiffness E _II ^* in mode II was taken into account. It verified that for this mode II testing method the formula of LEFM can be employed for calculating mode II fracture toughness even for highly orthotropic materials like wood. In the numerical studies for the tested spruce specimen, the crack propagation process, stress and strain fields in front of crack tips and the stress distributions along the ligament have been investigated in detail. It can be seen that the simulated crack propagating process along the ligament is a typical shear cracking pattern and the development of cracks along the ligament is due to shear stress concentrations at the crack tips of the specimen. It has been shown that this mode II fracture testing method is suitable for measuring mode II fracture toughness K _IIC for highly orthotropic materials like wood.     

Crack path selection in adhesively bonded joints: the roles of external loads and speciment geometry

This paper investigates the roles of external loads and specimen geometry on crack path selection in adhesively bonded joints. First, the effect of mixed mode fracture on crack path selection is studied. Using epoxy as an adhesive and aluminum as the adherends, double cantilever beam (DCB) specimens with various T-stress levels are prepared and tested under mixed mode fracture loading. Post-failure analyses on the failure surfaces using X-ray photoelectron spectroscopy (XPS) suggest that the failure tends to be more interfacial as the mode II fracture component in the loading increases. This fracture mode dependence of the locus of failure demonstrates that the locus of failure is closely related to the direction of crack propagation in adhesive bonds. Through analyzing the crack trajectories in failed specimens, the effect of mixed mode fracture on the directional stability of cracks is also investigated. The results indicate that the direction of the crack propagation is mostly stabilized when more than 3% of mode II fracture component is present at the crack tip regardless of the T-stress levels in the specimens for the material system studied. Second, using a high-speed camera to monitor the fracture sequence in both quasi-static and low-speed impact tests, the effect of debond rate on the locus of failure and directional stability of cracks is investigated. Post-failure analyses including XPS, Auger electron spectroscopic depth profile, and scanning electron microscopy indicate that as the crack propagation rate increases, the failure tends to be more cohesive and the cracks tend to be directionally unstable. Last, as indicated by the finite element analyses results, the T-stresses, and therefore the directional stability of cracks in adhesive bonds, are closely related to the thickness of the adhesive layer and also the thickness of adherend. This specimen geometry dependence of crack path selection is studied analytically and is verified experimentally.     

Mechanical failure of a Thompson’s hemiarthoplasty stem 28 years post-implantation: an investigation with electron microscopy

Τhe authors would like to report a mechanical failure of a Thompson’s prosthesis, 28 years post-implantation. A detailed examination of the specimen revealed no defects in the prosthesis and a dominating ‘brittle component’ fracture of the stem. In this context the detailed fractographic study by scanning electron microscopy (SEM) revealed no detrimental manufactural defects that may have produced microcracks and consequently risked initiating the fracture propagation. In contrast, the fracture was mainly a fatigue one with a mixed mode of microscopic trans- and intergranular crack propagation. To the best of our knowledge, such a mechanism of implant failure in a cementless stem has never before reached 28 years neither in a Thompson’s nor any other type of prosthesis, and in the already reported case, it exceeded 30 years [N. Wolson and J. P. Waadell, Can. J. Surg. 38(6) (1995) 542], however the stem’s ultrastructure has never been investigated under electron microscopy, which arguably can provide a useful assessment of a fatigue fracture. Τhe authors introduce the question of revising our standards when evaluating the newly designed and expensive implants and propose re-focusing on surgical technique, rather than purely on implant properties.     

Comparison of mode I and mode II elastic-plastic fracture toughness for two low alloyed high strength steels

In the present work, mode I and mode II tests were carried out on two low alloyed high strength steels. An asymmetrical four point bend specimen and J _II-integral vs. crack growth resistance curve technique were used for determining the mode II elastic-plastic fracture toughness, J _IIc · J _II-integral expression of the specimen was calibrated by finite element method. The results indicate that the present procedure for determining the J _IIc values is easy to use. Moreover, the mode I fracture toughness J _Ic is very sensitive to the rolling direction of the test steels, but the mode II fracture toughness J _IIc is completely insensitive to the rolling direction of the steels, and the J _IIc /J _Ic ratio is not a constant for the two steels, including the same steel with different orientations. Finally, the difference of the fracture toughness between the mode I and mode II is discussed with consideration of the different fracture mechanisms.     

Influence of temperature and strain rate on cohesive properties of a structural epoxy adhesive

Effects of temperature and strain rate on the cohesive relation for an engineering epoxy adhesive are studied experimentally. Two parameters of the cohesive laws are given special attention: the fracture energy and the peak stress. Temperature experiments are performed in peel mode using the double cantilever beam specimen. The temperature varies from −40 to + 80°C. The temperature experiments show monotonically decreasing peak stress with increasing temperature from about 50 MPa at −40°C to about 10 MPa at + 80°C. The fracture energy is shown to be relatively insensitive to the variation in temperature. Strain rate experiments are performed in peel mode using the double cantilever beam specimen and in shear mode, using the end notch flexure specimen. The strain rates vary; for peel loading from about 10⁻⁴ to 10 s⁻¹ and for shear loading from 10⁻³ to 1 s⁻¹. In the peel mode, the fracture energy increases slightly with increasing strain rate; in shear mode, the fracture energy decreases. The peak stresses in the peel and shear mode both increase with increasing strain rate. In peel mode, only minor effects of plasticity are expected while in shear mode, the adhesive experiences large dissipation through plasticity. Rate dependent plasticity, may explain the differences in influence of strain rate on fracture energy between the peel mode and the shear mode.     

Procedure for measuring the sensitivity of precision detectors of visible and infrared synchrotron radiation

A procedure is described for measuring the total sensitivity of photodetectors used in precision measurements of the number of low-energy (E<20 MeV) relativistic electrons from the intensity of their synchrotron radiation in the visible and infrared regions of the spectrum. The calibration constants of two types of uncooled photodetectors (a lead selenide photoresistor and a silicon photodiode) are measured, and the measurement errors are analyzed.Translated from Izmeritel'naya Tekhnika, No. 10, pp. 67–69, October, 1995.     

Features of the splitting fracture of copper in the submicrosecond range of life

A laser Doppler method of continuous recording of velocity is used for measurement of the fracture stresses in copper. It is shown that dynamic deformation and fracture of materials occur under conditions of significant distribution of particles by velocities. In the experiments the average velocity of the particles and the dispersion of the velocity and also the development of fracture in the cross section of the specimen are recorded.Translated from Problemy Prochnosti, No. 12, pp. 62–66, December, 1992.     

Combination of finite element and reliability methods in nonlinear fracture mechanics

This paper presents a probabilistic methodology for nonlinear fracture analysis in order to get decisive help for the reparation and functioning optimization of general cracked structures. It involves nonlinear finite element analysis. Two methods are studied for the coupling of finite element with reliability software: the direct method and the quadratic response surface method. To ensure the response surface efficiency, we introduce new quality measures in the convergence scheme. An example of a cracked pipe is presented to illustrate the proposed methodology. The results show that the methodology is able to give accurate probabilistic characterization of the J-integral in elastic–plastic fracture mechanics without obvious time consumption. By introducing an “analysis re-using” technique, we show how the response surface method becomes cost attractive in case of incremental finite element analysis.     

Dynamic crack propagation in large steel specimens

Dynamic fracture experiments on crack initiation and crack growth in single edge bend specimens are performed. The impact velocity is in the range of 14 to 50 m/s and the specimen size is 320×75 mm with a thickness varying from 18 to 40 mm. The experiments are recorded by high speed photography.Two different steel qualities are investigated and their constitutive characterisation are obtained from uni-axial tension tests and shear tests with strain rates in the range 10⁻⁴ to 10³ s⁻¹ and tension tests at temperatures between −196 and 600°C.One of the materials exhibits a transition from a ductile dimple fracture to a brittle cleavage fracture as the loading velocity increases and as the specimen thickness increases. Scanning electron microscope fractographs show that the density of plastic bridges within cleavage ligaments decreases with increasing impact velocity and with increasing specimen thickness. It is also noted that the local crack propagation direction deflects from the global one in cleavage fracture areas with a high density of plastic bridges.The other material fails in a ductile mode in all the investigated cases.     

The de Haas-van Alphen effect in Sb(Sn) and Sb(Te) alloys

Measurements have been made of the de Haas-van Alphen effect in Sb(Sn) alloys containing up to 0.58 at % Sn and Sb(Te) alloys with up to 0.26 at % Te. The maximum electron period in the bisectrix-trigonal plane increased from 14.66 × 10^–7 G^–1 in pure Sb to 68.0 × 10^–7 G^–1 in the most concentrated Sn-doped sample, whereas the maximum hole period decreased from 16.33 × 10^–7 to 7.4 × 10^–7 G^–1 . The Te doping had the opposite effect—increasing the number of electrons and decreasing the number of holes. The results of measurements of effective mass and Fermi surface area are found to be consistent with a rigid-band model of these dilute alloys. Both electron and hole bands are strongly nonparabolic and a two-band model is used to estimate that the gap below the electron pocket at L is 110 ± 25 meV. The Fermi levels of electrons and holes in Sb are estimated to be 150 ± 10 and 180 ± 40 meV, respectively. It is predicted that the electron pockets will be completely emptied for an alloy with 0.78 ± 0.07 at % Sn. Pseudopotential calculations suggest that the rigid-band model is a reasonable approximation in these dilute alloys.     

The observation of compliance change in the transition from hydrogen to air environment during the fatigue test

A compliance change was observed during fatigue testing of ASTM A710 HSLA steel using constant “K” CDCB specimen. The compliance decreased from 1.296 × 10⁻⁵ mm/N to 1.235× 10⁻⁵ mm/N when the environment was changed from hydrogen to air under the fatigue test conditions of f = 0.2 Hz, R = 0.1 and Δ K = 10 MPa✓m. The compliance change was observed in all fatigue testing while changing the environment from hydrogen to air. This compliance change can be explained numerically using the differential method for the design factors of the CDCB specimen. It was found from the calculation that the compliance change corresponded to a 6.3% change in Young’s modulus. It is proposed that the increased compliance resulted from the decreased Young’s modulus, the reduced Young’s modulus resulted from the increased lattice dilation which in turn resulted from a significantly increased hydrogen concentration at the crack tip region. The increased hydrogen concentration at the crack tip resulted from stress-induced hydrogen diffusion at the crack tip region.This work was conducted at Illinois institute of Technology (IIT).