Brittle fracture in rounded-tip V-shaped notches

Two failure criteria are proposed in this paper for brittle fracture in rounded-tip V-shaped notches under pure mode I loading. One of these criteria is developed based on the mean stress criterion and the other based on the point stress criterion which both are well known failure criteria for investigating brittle fracture in elements containing a sharp crack or a sharp V-notch. To verify the validity of the proposed criteria, first the experimental data reported by other authors from three-point bend (TPB) and four-point bend (FPB) tests on PMMA at −60 °C and Alumina–7% Zirconia ceramic are used. Additionally, some new fracture tests are also carried out on the rounded-tip V-notched semi-circular bend (RV-SCB) specimens made of PMMA for various notch opening angles and different notch tip radii. A very good agreement is shown to exist between the results of the mean stress criterion and the experimental data.     

Brittle fracture of pipes under the effect of external influences

Investigations were carried out into the mechanisms, kinetics, and dynamics of the physicomechanical factors determining damage and brittle fracture of pipes of low-alloy steel of the ferritic-pearlitic grade. The results show that due to hydrogen charging at high pressures and temperatures, the subsequent interaction of similar effects, and loading with internal pressure at room temperature the brittle fracture of pipes takes place at stress intensity factor values several times lower than the cracking resistance of the metal in the initial condition and in the period of the effect of external factors. The rate of crack growth, and the form and size of cracks are determined technological heredity. The results were used to improve the accuracy of the methods and the test, conditions of metals and components and also improve the calculation method.Translated from Problemy Prochnosti, No. 2, pp. 40–45, February, 1993.     

Brittle fracture assessment of engineering components in the presence of notches: a review

Brittle fracture of notched components has been widely investigated in recent decades both experimentally and theoretically. This is because of designers' concern about catastrophic failure in notched engineering components made of brittle or quasi‐brittle materials. Up to now, extensive studies have been performed on brittle fracture analysis of engineering components weakened by notches of various features under mode I, mode II, mode III and mixed mode loading conditions. In the present paper, the attempt is made to review the research articles published in the open literature on brittle fracture assessment of notched components by means of notch fracture mechanics concepts. The main focus of this paper is on the stress‐based fracture criteria, which are the basis of authors' experience in recent years.     

Brittle fracture of rocks under impulse loads

Brittle fracture of Tennessee Marble, Charcoal Granite and sandstone was studied using the Hopkinson split bar method. The study of the actual fracture behaviour of the rock was possible as no transducers were attached to the specimens themselves. The degree of brittleness of rock was determined by using the attenuation of the first wavefront in a fracturing specimen. There existed a maximum limit to the stress amplitude which could be transmitted through a rock specimen. Fracture is initiated in rock at the same stress under both static and dynamic loads.     

Failure of composite cylinders under combined external pressure and axial loading

An experimental and theoretical investigation was carried out into the collapse behaviour of filament wound glass fibre/epoxy cylinders under combinations of external pressure and axial loading in the third quadrant of the stress plane. Samples were tested with length-to-diameter ratios from 2·5 to 20 and diameter-to-thickness ratios in the approximate range of 20 to 40. Four ratios of hoop to axial stress were employed: ∞, 2, 1 and 0·5. The theoretical study employed a special purpose finite element program to calculate first ply failure (FPF) and buckling loads for shells of revolution made from multi-layered orthotropic materials. In all cases the experimental collapse pressure was strongly influenced by the predicted buckling failure mode. For those samples predicted to fail by buckling, agreement between the model and the experimental results was excellent. With the samples predicted to undergo FPF prior to buckling it was found that the residual strength was often sufficient to permit the buckling load to be approached.     

Brittle fracture and fatigue propagation paths of 3D plane cracks under uniform remote tensile loading

Fatigue and brittle fracture propagation paths of arbitrary plane cracks, loaded in mode I, embedded in an infinite isotropic elastic body, are investigated. The crack advance is supposed to be governed by the stress intensity factor, for instance through Paris' law in fatigue or Irwin's criterion in brittle fracture. The method used is based on successive iterations of the three-dimensional weight-function theory of Bueckner-Rice, that gives the variation of the stress intensity factor along the crack front arising from some small arbitrary coplanar perturbation of the front. Its main advantage is that only one dimensional integrals along the crack front are involved so that only the one dimensional meshing of the crack front is needed, and not the 3D meshing of the whole body as in the finite-element method. It is closely linked to previous works of Bower and Ortiz (1990, 1991, 1993). The differences lie on the one hand, in the simplified numerical implementation; on the other hand, in the simplified treatment of brittle fracture, Irwin's criterion being regularized by Paris' law by a procedure analogous to the `viscoplastic regularization' in plasticity; and finally in the applications studied: propagation paths of an initially elliptical, rectangular or heart shaped crack in an homogeneous media and of a penny shape crack in an heterogeneous one.     

Brittle fracture propagation in rock under compression

The results of studies ot the initiation and propagation of fracture front a single Grifith crack in a biaxial Compressive stress field are reported. In is concluded that Griffith's theory of brittle fracture offers a reliable prediction of the fracture initiation stress but that the resulting fracture propagation froth a single crack cannot account for the macroscopic fracture of a specimen. Some preliminary results of studies on crack arrays and on the effects of crack closure iii compression are presented. The applicability of these results to the prediction of rock fracture in predominantly compressive stress fields is discussed.[/p]

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Zusammenfassung Die Versuchergebnisse über die Bildung und Fortpflanzung von Brüchen, die von einem einzelnen Griffith-Riss in einem zweiachsigen Spannungsfeld ausgehen, werden beschrieben. Die Folgerung ist, dass die Theorie von Griffith über Sprödbrüche eine sichere Voransage von der Spannung bei Bruchbildung ist. Aber dass die darauffolgende Fortpflanzung vom Bruch, von einem einzelnen Riss aus, nicht verantwortlich sein kann für den Gesamtbruch der Probe. Ein paar vorläufige Forschungsergebnisse über Rissanordnungen und die Auswirkung der Schliessung von Rissen durch Druck, werden gegeben. Die Anwendung von diesen Ergebnissen für das Voraussagen vom Versagen des Gesteins bei vorwiegenden Druckspannungsfeldern werden besprochen.[/p]

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Résumé Un rapport a été fait des résultats d'études de l'amorçage et de la propagation d'une fracture, partant d'une seule fissure genre Griffith et se développant dans un champ de contrainte de compression biaxiale. On peut en conclure que la théorie Griffith de fraction de fragilité offre une prédiction sûre de la contrainte de départ de la fracture, mais que la propagation de la fracture, qui en résulte -partant d'une seule fissure-ne justifie pas la fracture macroscopique du spécimen. Quelques résultats préliminaires d'études sur des rangées de fissures et l'effet de fermeture des fentes sous compression sont soumis. L'application de ces résultats sur la prédiction de la fracture du massif sous des champs de tension prédominants compressifs est discutée.[/p]

     

Brittle fracture propagation in rock under compression

The results of studies of the initiation and propagation of fracture from a single Griffith crack in a biaxial compressive stress field are reported. It is concluded that Griffith's theory of brittle fracture offers a reliable prediction of the fracture initiation stress but that the resulting fracture propagation from a single crack cannot account for the macroscopic fracture of a specimen. Some preliminary results of studies on crack arrays and on the effects of crack closure in compression are presented. The applicability of these results to the prediction of rock fracture in predominantly compressive stress fields is discussed.

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Zusammenfassung Die Versuchergebnisse über die Bildung und Fortpflanzung von Brüchen, die von einem einzelnen Griffith-Riss in einem zweiachsigen Spannungsfeld ausgehen, werden beschrieben. Die Folgerung ist, dass die Theorie von Griffith über Sproödbrüche eine sichere Voransage von der Spannung bei Bruchbildung ist. Aber dass die darauffolgende Fortpflanzung vom Bruch, von einem einzelnen Riss aus, nicht verantwortlich sein kann für den Gesamtbruch der Probe. Ein paar vorläufige Forschungsergebnisse über Rissanordnungen und die Auswirkung der Schliessung von Rissen dutch Druck, werden gegeben. Die Anwendung von diesen Ergebnissen für das Voraussagen vom Versagen des Gesteins bei vorwiegenden Druckspannungsfeldern werden besprochen.

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Résumé Un rapport a été fait des résultats d'études de l'amorçage et de la propagation d'une fracture, partant d'une seule fissure genre Griffith et se développant dans un champ de contrainte de compression biaxiale. On peut en conclure que la théorie Griffith de fraction de fragilité offre une prédiction sûre de la contrainte de départ de la fracture, mais que la propagation de la fracture, qui en résuite -partant d'une seule fissure- ne justifie pas la fracture macroscopique du spécimen. Quelques résultats préliminaires d'études sur des rangées de fissures et: l'effet de fermeture des fentes sous compression sont soumis. L'application de ces résultats sur la prédiction de la fracture du massif sous des champs de tension prédominants compressifs est discutée.

     

Damage and fracture mechanism of aluminium alloy thick-walled cylinder under external explosive loading

The damage and failure mechanism of aluminium alloy were investigated by means of the radial collapse of a thick-walled cylinder under high-strain-rate deformation. Adiabatic shear bands (ASBs) initiated at the inner surface of the aluminium alloy cylinder, and most of them were in spiral form along the cross-section of the cylinder towards counterclockwise direction. Tip of a shear band propagated along the direction of the maximum shear stress. The propagating trajectory of small shear band rather than developed shear band could be affected by grain boundary. The morphologies of ASBs such as bifurcation, crossing and annihilation were observed, and the evolution of ASBs was affected to a great extent by stress state. The nucleation of microcrack was mostly observed at the weak microstructure in ASBs. The coalescence of microcracks formed the crack within ASBs, and when the critical crack length is reached catastrophic fracture occurs.     

Calculation of elasto-plastic strains and stresses in notches under multiaxial loading

A method for calculating elasto-plastic notch tip strains and stresses in bodies subjected to multiaxial loading has been presented. The method has been formulated in terms of strain energy density relationships. Two approximate formulae are derived based on the analysis of strain energy density in the notch tip region. The two formulae represent the lower and upper limits of the band within which the actual elasto-plastic notch tip strains can be found. All necessary relationships are derived for a general multiaxial stress state. The calculated notch tip strain and stress components are compared with experimental and finite element data obtained for a variety of loading conditions and materials. This method may be particularly useful for stress/strain analysis of notched components subjected to lengthy multiaxial cyclic loading histories.On leave from Warsaw University of Technology.     

Mixed-mode fracture of ductile thin-sheet materials under combined in-plane and out-of-plane loading

Cracks in thin structures often are subjected to combined in-plane and out-of-plane loading conditions leading to complex mixed mode conditions in the crack tip region. When applied to ductile materials, large out-of-plane displacements make both experimentation and modeling difficult. In this work, the mixed-mode behavior of thin, ductile materials containing cracks undergoing combined in-plane tension (mode I) and out-of-plane shear (mode III) deformation is investigated experimentally. Mixed-mode fracture experiments are performed and full, three-dimensional (3D) surface deformations of thin-sheet specimens from aluminum alloy and steel are acquired using 3D digital image correlation. General characteristics of the fracture process are described and quantitative results are presented, including (a) the fracture surface, (b) crack path, (c) load-displacement response, (d) 3D full-field surface displacement and strain fields prior to crack growth, (e) radial and angular distributions of the crack-tip strain fields prior to crack growth and (f) singularity analysis of the crack-tip strains prior to crack growth. Results indicate that the introduction of a mode III component to the loading process (a) alters the crack tip fields relative to those measured during nominally mode I loading and (b) significantly increases the initial and stable critical crack-opening-displacement. The data on strain fields in both AL6061-T6 aluminum and GM6208 steel consistently show that for a given strain component, the normalized angular and radial strains at all load levels can be reasonably represented by a single functional form over the range of loading considered, confirming that the strain fields in highly ductile, thin-sheet material undergoing combined in-plane tension and out-of-plane shear loading can be expressed in terms of separable angular and radial functions. For both materials, the displacement and strain fields are (a) similar for both mixed-mode loading angles Φ = 30° and Φ = 60° and (b) different from the fields measured for Mode I loading angle Φ = 0°. Relative to the radial distribution, results indicate that the in-plane strain components do not uniformly exhibit the singularity trends implicit in the HRR theory.     

Brittle fracture of a rod under a longitudinal impact

In this paper a model of a rigid-fractured body is introduced. It is applied to the rod of variable cross-section area and of limited length striking a rigid wall. A simple approximate solution of the problem of brittle fracture of such a rod is given here. The limit stress on the fracture front is supposed to be a function of the impact velocity. Some examples are considered in Section 3.     

A numerical study of two integral type elasto-plastic fracture parameters under cyclic loading

This paper examines the behaviour of two elasto-plastic fracture parameters which characterise the severity of a crack-tip field under large scale yielding. One may be regarded as a local crack-tip parameter which associates closely to the stress/strain fields at the crack-tip whilst the other may be considered as a far-field parameter. Several centre-cracked and edge-cracked plates were analysed under various loading and unloading sequences, and it was found that such parameters can be of significant use in explaining the effects of prior plastic deformation in fracture problems.     

Dynamic fracture under plane wave loading

A new plate impact experiment is presented for studying dynamic fracture processes that occur under sub-microsecond loading. The experiment is designed to provide comparatively straightforward interpretation within the framework of fracture mechanics. A disc containing a mid-plane, pre-fatigued, edge crack that has been propagated halfway across the diameter is impacted by a thin flyer plate of the same material. A compressive pulse propagates through the specimen and reflects from the rear surface as a step, tensile pulse with a duration of 1s. This plane wave loads the crack and causes initiation and propagation of the crack. The motion of the rear surface is monitored during this event using a laser interferometer system. The location of the crack front is mapped before and after the experiment using a focussed ultrasonic transducer.Experiments have been conducted on a hardened 4340 VAR steel at temperatures ranging from room temperature to — 100°C. Crack advance increases monotonically with increasing impact velocity and with decreasing temperature. Critical values of the stress intensity factorK _Ic are inferred from known elastodynamic solutions and the assumption that the measured crack advance occurs at a constant energy release rate. Fracture modes are characterized by means of scanning electron microscopy of the fracture surfaces.A finite difference method is used for numerical simulation of the experiments. The loading is modelled as that of a plane, square, tensile pulse impinging at normal incidence on a semi-infinite crack. Crack advance is assumed to initiate when the crack-tip stress intensity factor reaches the critical valueK _Ic. Crack velocities are prescribed corresponding to various fracture models. The predicted motion of the rear surface is found to be in good agreement with the measured motion when the crack velocity is taken to be a constant.

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Résumé On présente un nouvel essai de choc sur plaque pour l'étude du processus de rupture dynamique qui se produit sous des charges inférieures à la micro-seconde. L'essai est conçu de manière à fournir une interprétation comparativement directe dans le cas de las mécanique de la rupture. L'essai consiste à soumettre à un choc un disque comportant une fissure du bord suivi un plan médian, préfatiguée et propagée sur la moitié du diamètre du disque, à l'aide d'une plaque mince mobile du même matériau. Une impulsion de compression se propage au travers de l'echantillon, se réfléchit sur la surface arrière comme sur un seuil, entraînant une impulsion de traction avec une durée d'une micro-seconde. Cette onde plane soumet la fissure à la sollicitation et provoque l'amorçage de la propagation de la fissure. On enregistre le mouvement de la surface arrière au cours du phénomène en utilisant un système d'interférométrie à laser. La localisation du front de fissure est tracée avant et après l'essai, en utilisant un transducteur ultrasonique focalisé.Des essais ont été conduits sur un acier 4340 Var durci, à des températures comprises entre la température ambiante et — 100°C. L'avancement de la fissure augmente de manière monotone avec les vitesses croissantes de choc et avec l'abaissement de la température. Des valeurs critiques des facteurs d'intensité de contrainteK _lc, sont déduites à partir des solutions élasto-dynamiques connues et de l'hypothése que l'avancement de la fissure mesurée se produit suivant une vitesse de relaxation en énergie constante. Les modes de rupture sont caractérisés au moyen de la microscopie électronique à balayage des surfaces de rupture.Une méthode finie différentielle est utilisée pour l'assimiliation numérique des essais. La mise en charge est modélisée comme celle d'une impulsion de traction plane et carrée agissant suivant une incidence normale sur une fissure semi-infinie. L'avancement de la fissure est supposé commencer lorsque le facteur d'intensité de contrainte à son extrémité atteint la valeur critiqueK _Ic. Les vitesses de fissuration sont établies en correspondance avec différents modèles de rupture. On trouve que le mouvement prévu de la surface arrière est en bon accord avec les mouvements mesurés, lorsque la vitesse de fissuration est considérée comme constante.

     

Generalised stress intensity factors for rounded notches in plates under in-plane shear loading

The Notch Stress Intensity Factors (NSIFs) quantify the intensities of the asymptotic linear elastic stress distributions of sharp (zero radius) V-shaped notches. When the notch tip radius is different from zero, the singular sharp-notch field diverges from the rounded-notch solution in the close neighborhood of the notch tip. Nevertheless the NSIFs might continue to be parameters governing fracture if the notch root radius is small enough. Otherwise they can be seen simply as stress field parameters useful in quantifying the stress distributions ahead of the specific notch. Taking advantage of some analytical formulations which are able to describe stress distributions ahead of parabolic, hyperbolic and V-shaped notches with end holes, the paper discusses the form and the significance of the NSIFs with reference to in-plane shear loading, considering explicitly the role played by the notch opening angle and the notch tip radius. These parameters quantify the stress redistribution due to the root radius with respect to the sharp notch case to which they should naturally tend for decreasing values of the notch radius.     

Probability of stress-corrosion fracture under random loading

A method is developed for predicting the probability of stress-corrosion fracture of structures under random loadings. The formulation is based on the cumulative damage hypothesis and the experimentally determined stress-corrosion characteristics. Under both stationary and nonstationary random loadings, the mean value and the variance of the cumulative damage are obtained. The probability of stress-corrosion fracture is then evaluated using the principle of maximum entropy. It is shown that, under stationary random loadings, the standard deviation of the cumulative damage increases in proportion to the square root of time, while the coefficient of variation (dispersion) decreases in inversed proportion to the square root of time. Numerical examples are worked out to illustrate the general results.     

The fracture of wood under impact loading

High speed motion picture photography was used to study the fracture, under impact loading, of wood beams. Photographs were taken at the rate of 500 frames per second, which permitted the crack development during the fracture event to be monitored. Load vs. time data during the test were also recorded. This paper presents a photographic record of the crack patterns which developed when the beams were tested in an instrumented impact machine.