Stress singularity at the vertex of a flat wedge-shaped crack by variational method

Three-dimensional elasticity problems are generally complex. In this paper we present the analysis for the stress singularity at the apex of a 3-dimensional, flat, wedge-shaped crack under general loadings. The problem is reduced to a set of coupled dual integral equations. Because of the complexity they are not amenable to a closed form solution. A variational method is developed to handle such problems. The physical interpretation of the results are also presented.     

Detection of general yielding in a516 steel by acoustic emission

A study of the acoustic emission behaviour of A516-70 steel has shown that acoustic emission is well suited to the detection of general yielding. The acoustic emission parameters studied were the count rate and the total count as well as a quantitative analysis of the frequency spectrum of acoustic emission signals obtained during the fracture tests. It was found that the major acoustic emission activity occurs during the process of formation of the plastic zone and ends at the load corresponding to general yielding of the untorn ligament. The frequency analysis of the acoustic signals, however, was found to overestimate the onset of unstable crack growth. Ductile crack propagation mechanisms for this material did not exhibit a high activity of acoustic emission.     

Acoustic emission monitoring of corrosion fatigue crack growth in offshore steel

A research and development programme has been carried out to establish relationships between corrosion fatigue crack growth in offshore steel qualities and acoustic emission. Laboratory experiments on small-scale specimens and wide plates have shown that when a certain combination of crack size and crack surface corrosion deposit thickness has been reached, high acoustic emission event rates, in the range of 10–40 events per fatigue cycle, are recorded. The main activity is recorded on rising load, generated from crack surface activity, eg secondary emission. On the basis of the results from this programme general AE equipment can now be modified for offshore applications, and a research and development strategy to implement these modifications is presented,     

Characterisation of fatigue crack extension by quantitative acoustic emission

A calibrated four-channel elastic wave recording system has been used to detect and characterise acoustic emission events associated with the growth of a fatigue crack in a compact tension specimen of 7010 aluminium alloy. The transducers sampled the elastic wave field in four independent directions in a plane perpendicular to the crack. The 2-D force dipole representation of each event, assumed to be a point source, was deduced by inversion of the Green's tensor. Each emission event was then characterised in terms of source type (e.g. microfracture, slip), orientation relative to fatigue crack and size (e.g. crack volume).All of the events (other than clearly distinguishable signals due to fretting at the loading pins) were located within 0.5 mm of the crack tip. 80% of the recorded events had the character of fracture, and were mostly oriented approximately parallel to the fatigue crack. The typical event size was 2,000 m³. It is believed that the principal source of emission was brittle inclusion fracture at, or close to, the crack tip. The largest inclusions ( 10 m) were much smaller than the deduced emission sources, implying that the fatigue crack modifies the elastic wave radiation from the inclusions and amplifies the apparent source strengths. Nevertheless the point-source model fitted most of the data reasonably well, with residual errors < 10%.

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Résumé On a utilisé un système étalonné d'enregistrement à quatre canaux d'ondes élastiques pour détecter et caractériser les zones d'émission acoustiques associées à la croissance d'une fissure de fatigue dans une éprouvette compacte de traction d'un alliage d'aluminium 7010. Les transducteurs captent le champ d'onde élastique dans quatre directions indépendantes d'un plan perpendiculaire à la fissure. Par une inversion du tenseur de Green, on déduit une représentation de chaque émission supposée être ponctuelle par un dipole de forces à deux dimensions. On caractérise ensuite chaque émission par le type de source d'émission (micro-rupture, glissement, etc.), par son orientation par rapport à la fissure de fatigue, et par son importance (par ex. volume de la fissure).On a pu établir que toutes les émissions-à l'exception de celles dont il était clair qu'elles provenaient des efforts dus aux tenons de mise en charge-étaient localisées dans une zone de 0,5 mm en avant de la pointe de la fissure. On a constaté également que 80% des zones d'émission détectées étaient caractéristiques d'une rupture, et se trouvaient le plus souvent orientées parallèlement à la fissure de fatigue. La taille typique de ces zones est de 2000· microns cubes. On pense que la principale émission d'onde est la rupture fragile d'une inclusion à l'extrémité d'une fissure ou en son voisinnage immédiat.Let inclusions les plus grandes ( 10 microns) se sont révélées beaucoup plus petites que la taille des sources d'émission telle que déduite des mesures, ce qui implique que la fissure de fatigue modifie l'irradiation d'onde élastique en provenance des inclusions, et accroit la puissance apparente d'émission.Toutefois, le modèle de source ponctuelle s'est révélé le mieux correspondre à la plupart des résultats, avec des erreurs résiduelles de moins de 10%.

     

Slow crack growth and acoustic emission characteristics in COD test

Brittle material fractures at a critical value of stress intensity factor or crack opening displacement (COD) without any prior crack growth. In the ductile materials, however unstable fracture initiation may be preceded by a period of slow crack growth from the notch tip. Such slow crack growth may be an essential prelude to unstable fast fracture and thus COD at the start of slow crack growth can also be regarded as a critical value of the fracture characteristics. We have tried to apply the acoustic emission techniques to the COD test. Acoustic emission techniques can be used to detect the onset of slow crack growth and to obtain a relation between COD and AE characteristics in the COD test.     

Analysis of acoustic emission during sliding friction of manganese steel

The process of acoustic emission during the sliding friction of X120Mn12 (DIN EN Standard) manganese steel has been studied. The coefficient of sliding friction has been determined in the absence of lubricants and the parameters of generated sound have been measured. A relationship between the acoustic emission spectrum and the friction coefficient is established.     

Investigation of debonding processes in particle-filled polymer materials by acoustic emission: Part I Acoustic emission and debonding stress

Debonding processes in model composites under tensile deformation were investigated by acoustic emission analysis. The composites were prepared from epoxy and polyethylene matrix filled with glass beads of various sizes and with different coatings. The detected acoustic emission signals were identified as debonding processes at the filler–matrix interphase, and are discussed as a rupture process on the basis of the Weibull probability distribution function. For the model composites, the effect of the filler size is discussed using a theory based on Griffith’s criterion of rupture. This revised version was published online in November 2006 with corrections to the Cover Date.     

Using acoustic emission for the analysis of wear processes during sliding friction

The acoustic response of two friction pairs, in which brittle fracture and intense plastic deformation take place during friction, has been studied. The acoustic signals have been analyzed by calculating median frequencies using the window Fourier transform technique.     

Monitoring of thermal shock induced crack growth in a feed water nozzle corner of a reactor pressure vessel by acoustic emission

In the framework of a reactor safety research programme, thermal shocking of a clad feed water nozzle has been carried out during simulated operating conditions (temperature = 300°C, pressure = 11 MPa). The objective of these trials is to contribute to the understanding of crack initation and propagation under realistic thermal shock conditions, and to monitor crack initiation and growth by NDT on-line as well as off-line. Up to now the nozzle corner has been shocked 5200 times. The shocked area was monitored by acoustic emission (AE). During the last 800 thermal shocks new AE equipment with optimized capabilities for detection, location of AE sources and interpretation of AE signals has been used. This AE system and the results obtained during the last 800 shocks will be described. One important result is that it is possible to separate crack-growth signals from friction noise of the cracks by signal analysis when the AE signals are received with broad-band transducers.     

Acoustic emission behaviour during stage II fatigue crack growth in an AISI type 316 austenitic stainless steel

Acoustic emission (AE) behaviour during fatigue crack growth (FCG) in a ductile AISI type 316 austenitic stainless steel is reported. The two substages in the stage II Paris regime of FCG could be distinguished by a change in the rate of acoustic activity with increase in crack growth rate. The transition point in the cumulative ringdown count plot coincides with that in the da/dn plot. The AE activity increases with increase in ΔK during stage IIa and decreases during stage IIb. The major source of AE during stage IIa is found to be the plastic deformation within the cyclic plastic zone (CPZ) as compared to the phenomena such as monotonic plastic zone (MPZ) expansion, ductile crack growth, crack closure, etc. The increase in AE activity with increase in ΔK during stage IIa is attributed to the increase in the size of the CPZ which is generated and developed only under plane strain conditions. The decrease in AE activity during stage IIb is attributed to the decrease in the size of the CPZ under plane stress condition. The high acoustic activity during the substage IIa is attributed to irreversible cyclic plasticity with extensive multiplication and rearrangement of dislocations taking place within the CPZ. The AE activity is found to strongly depend on the optimum combination of the volume of the CPZ, average plastic strain range and the number of cycles before each crack extension. Based on this, an empirical relationship between the cumulative RDC and ΔK has been proposed and is found to agree well with experimentally observed values.     

Application of the critical load assessment method for stable crack growth analysis

A new systematic procedure has been developed for analyzing stable crack growth. In this method, the crack instability point can be predicted from a single J-l record, which is developed from a given material J_r-curve and the J-integral-related solutions resulting from stress analysis of a flawed structure. Here l represents the physical load applied to the structure. The development of the J-l relation that satisfies the equilibrium state of crack growth is so simple that hand calculator analysis is possible for complex structural geometries with available j-related stress analysis results.

The advantage of the new method over existing ones, such as the failure assessment diagram approach or the tearing instability theory, is that it can predict the critical physical load level and the crack instability point at the same time without resorting to the use of a fixed diagram or evaluating tearing modulus. The validity of the procedure has been demonstrated by solving a center-cracked tensioned panel with various loading mechanisms (displacement-controlled, load-controlled and mixed loading systems) and a pressure vessel geometry under internal pressure.     

Investigation of the basic creep of concrete by acoustic emission

The physical origins of the basic creep of concrete are still poorly understood even though some researchers have proposed hypotheses concrening the physical mechanisms that govern this delayed behaviour of concrete. A very complete summing up of these hypotheses was produced, in the past, by, Neville; he shows that none of them, provides a satisfactory explanation of the bulk of basic creep. More recently, Rossi has proposed a new hypothesis, which has been the subject of several articles. This article concerns the use of the acoustic emission technique as a ‘tool’ to provide information on the pertinence of the physical hypothesis advanced by Rossi. The counting of the total number of acoustic events together with a frequency analysis of the acoustic emission signals indicate that there is a strong correlation between the basic creep of concrete and the creation of microcracks in the material.     

On the calculation of plastic energy dissipation rate during stable crack growth

An approximate analysis is presented for the calculation of the plastic energy dissipation rate during stable growth of a centrally located through crack. in a sheet subjected to gradually increasing uniaxial tension normal to the crack plane.It is shown that the plastic energy dissipation rate is a function of the slow growth parameter (_p/)·(d/da)+(_p/a), where _p is the plastic enclave width in the plane of the crack and d/da is the rate of increase of the gross stress with respect to stable growth. At the point of instability this parameter becomes equal to _p/a. By assuming that this parameter is zero at the point of instability, a simple expression is obtained for the plastic energy dissipation rate.The analysis excludes the energy dissipation rate resulting from energy changes in an inner fracture zone in the immediate neighborhood of the crack tip in which it is presumed that fracture processes such as vacancy formation, crack initiation by dislocation pile ups etc., are active. The analysis is not applicable in this inner zone as deformation is not homogeneous.

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Zusammenfassung Es wurde eine mehr oder weniger genaue Analyse für die Kalkulation eines plastischen Energiezerstreuungsverhältnisses während stabilem Wachstums eines zentral lokalisierten Durchrißes in einer einfachen Anspannungsplatte präsentiert.Man zeigte, daß das plastische Energiezerstreuungsverhältnis eine Funktion des langsam wachsenden Parameters ist, wobei _p die eingeschlossene, plastische Weite in der Rißebene und d/da das Wachstumsverhältnis des Rohdruckes mit Rücksicht auf das stabile Wachstum, darstellt.Diese Analyse schließt das Energiezerstreuungsverhältnis vom Energiewechsel in einer inneren Bruchzone in der unmittelbaren Nähe der Rißspitze aus. Man nahm nicht an, daß these Veränderung homogen, sondern auf Vakanzen, Verschiebungen, etc. begründet sei.

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Résumé On présente une analyse approchée pour le calcul de la vitesse de dissipation de l'érgie de déformation plastique au cours de l'extension stable d'une fissure située au centre d'une tôle et traversant celle-ci de part en part, lorsque cette tôle est sujette à une contrainte uniaxiale, normale au plan de la fissure, et graduellement croissante.On montre que cette vitesse de dissipation est fonction du paramètre d'extension lente: où _p est la largeur de l'enclave de déformation plastique dans le plan de la fissure, et d/da le taux d'accroissement de la tension nominale par rapport à l'extension de la fissure dans des conditions stables.Au point d'instabilité, ce paramètre devient égal à _p/a, en supposant que sa valeur soit nulle, on aboutit à une expression simple de la vitesse de dissipation de 1'énergie de déformation plastique.L'analyse ne considère pas la vitesse de dissipation qui résulte de modifications de l'énergie au sein d'une zone de rupture interne, et située dans le voisinage immédiat de la pointe de la fissure. Dans cette zone, l'on présume que les processus de fissuration tels que la formation de lacunes, ou l'amorçage d'une fissure par empilements de dislocations, etc., sont particulièrement actifs. L'analyse n'est pas applicable dans cette zone interne, car les déformations n'y sont pas homogènes.

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Notations 2a Crack length - t Thickness of sheet - W Width of sheet - Gross stress applied at infinity normal to the crack plane - A, ₀, n Parameters in a Ramburg-Osgood representation of the octahedral shear stresss-hear strain curve - _oct Octahedral shear stress at any point near the crack tip - _oct Octahedral shear strain at any point near the crack tip. - _infoct ^supel Octahedral shear stress at any point near the crack tip given by elastic analysis - _oli Octahedral shear stress at yield - _oli/₀ - _infoct ^supel /_oli - \5m _oct/_oli - E Young's modulus - E _s Secant modulus - G Shear modulus - G _s Secant modulus of the octahedral stress-strain curve - u _p Plastic energy density at any point inside the plastic enclave at the crack tip - U _p Plastic energy dissipated in the plastic enclave per unit thickness - v Poisson's ratio - r, Polar co-ordinates with the crack tip as origin - K Stress intensity factor - _p Plastic enclave width given by Irwin's formula - f ₁, f ₂, f ₃ Functions of , defining the stress field near the crack tip - f _e f _inf1 ^sup2 –f ₁ f ₂+f _inf2 ^sup2 +3f _inf3 ^sup2 - _oct Limiting octahedral shear stress beyond which homogeneous plastic deformation is not possible since fracture processes such as vacancy formation etc., become active. - \5m_{0 infoct} ^supu /_oli - C (_p/)·(d/da)+(_p/da); slow growth parameter - B (G·A/_o1i)· ⁿ      

Characteristics of an acoustic emission source from a thermal crack in glass

Thermal cracks of mode I type oriented normal to the surface along an initial scratch were generated by blowing cold nitrogen gas through a small nozzle onto the surface of a glass plate. Acoustic emission (AE) signals emitted from the thermal cracks were detected on the opposite side of the plate, both at epicentral and at off-epicentral positions with a nine-channel AE system. AE source characteristics, such as moment tensor components, source-time function, radiation pattern, and dipole strength, were obtained from the detected waveforms. The strength of dipoles associated with the thermal cracks was determined from comparing the crack signals to those generated when a glass capillary was broken at the crack site prior to crack formation. It is shown that the AE source-time function, together with the dipole strength, can provide valuable information on the dynamic behavior of fracture.

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Résumé On a créé des fissures thermiques de Mode I orientées normalement à une surface en projetant de l'azote froid par un petit ajustage sur une rainure initiale à la surface d'une plaque de verre. Les signaux d'émission acoustique émis par la fissure thermique ont été détectés sur la face opposée de la plaque, à l'épicentre et en d'autres positions par rapport à la fissure, en utilisant un système de captation à neux canaux. Les formes d'ondes détectées fournissent les caractéristiques de la source acoustique, telles que les composantes du tenseur de moment, la fonction sourcetemps, la répartition de la radiation et la puissance du dipole. Cette dernière grandeur a été déterminée, lorsqu'elle est associée aux fissures thermiques, en comparant les signaux obtenus à ceux que produit un capillaire de verre rompu à l'endroit de la fissure, avant que celle-ci se forme. On montre que la fonction d'émission acoustique source-temps ainsi que la puissance dipole peuvent fournir des informations valables sur le comportement dynamique d'une rupture.