Creep crack growth in power plant materials

Economic considerations have made it desirable to extend the 30 to 40 year operating life of power plants by another 10 to 20 years. Crack growth at elevated temperatures is an important consideration in estimating the remaining life, determining operating conditions and deciding inspection criteria and intervals for power plant materials. This paper presents an overview of high-temperature crack growth phenomenon in such materials. The focus is on various techniques used for characterizing creep crack growth (CCG) and creep-fatigue crack growth (CFCG) in high-temperature materials. The collection of data, their analysis and the interpretation of results is discussed in detail, especially for CFCG laboratory testing. The discussion is primarily focussed on creep-ductile materials such as those used in power plant applications. Special considerations for elevated temperature crack growth in weldments are also presented. Finally, the application of these concepts to the life prediction of power plant components is also discussed.     

Analysis of smooth crack growth in brittle materials

When a fault in the crust extends, earthquake faults appear as a set of displacement discontinuities on the ground surface and cause strong motion and large deformation. For the prediction of such earthquake faults, one needs to analyze the propagation of smoothly growing cracks. This paper develops an analysis method based on a new formulation of growing crack problems. In this method, the change in the stress intensity factors due to a small extension is explicitly related to the curvature and length of the extension, and these geometrical parameters can be determined from assumed fracture criteria, without taking any trial-and-error routes of the extension geometry. The validity of the proposed method is numerically examined; in particular, the predicted stress intensity factor changes coincide with numerically computed ones. The proposed method is applied to reproduce two experimental observations. It is shown that in both cases, the configuration of the simulated crack is in good agreement with the observed one.     

Slow crack growth in brittle materials under dynamic loading conditions

The failure of materials due to slow crack growth, under dynamic loading conditions, is analyzed in terms of crack velocity, stress intensity relationships. It is shown that this type of analysis can fully describe the failure characteristics for both constant strain-rate and constant stress-rate loading. The analysis is used to predict the variations of strength and subcritical crack growth with strain-rate and stress-rate. Application of the analysis to several ceramic systems give data which are entirely consistent with available experimental data.

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Zusammenfassung Der Bruch von Material durch langsame Rißausdehnung, unter dynamischer Beanspruchung wird in Hinsicht der Beziehung zwischen der Rißausdehnungsgeschwindigkeit und der Spannungsintensität untersucht. Man zeigt daß diese Form von Untersuchung die Bruchbegebenheiten vollständig beschreiben kann sowohl für eine Belastung, sowohl unter konstantem Verformungsgrad, als unter konstantem Spannungsgrad. Die Untersuchung wird zur Voraussagung der Änderungen der Festigkeit und des subkritischen Rißwachstums mit dem Verformungs- und dem Spannungsgard. Die Anwendung der Untersuchung auf verschiedene Keramiksysteme ergibt Ergebnisse die vorzüglich mit bestehenden Versuchsergebnissen übereinstimmen.

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Résumé La rupture des matériaux due à une propagation lente d'une fissure sous des charges dynamiques est analysée en termes de relations entre la vitesse de propagation et l'intensité des contraintes.On montre que le type d'analyse envisagé peut complètement décrire les caractéristiques d'une rupture sous charges caracterisées par une vitesse constante de déformation, ou par une vitesse constante de tension.On utilise l'analyse pour prédire les variations de la résistance et la propagation subcritique de la fissure en fonction de la vitesse de déformation ou de mise sous tension.L'application de l'analyse à divers systèmes céramiques fournit des données qui satisfont entièrement les données expérimentales disponibles.

     

A simple method for evaluating slow crack growth in brittle materials

A simple method for evaluating stress intensity factor, crack velocity (K, V) diagrams is described. The method enables K and V to be obtained from the load relaxation at constant displacement. There are no additional requirements for monitoring crack growth. The method is evaluated for the glass/water system and is shown to generate data that is entirely consistent with data obtained on the same system using other techniques. The method is applied to the alumina/water system and the K, V diagrams are used to predict times to failure (). The calculated are in excellent agreement with available data.

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Zusammenfassung Eine einfache Methode zur Aufstellung der Diagramme Intensitätsfaktore Rißgeschwindigkeit (K.V.) wird beschrieben. Diese Methode ermöglicht die Ableitung von K und V von der Lastrelaxation bei konstanter Fortbewegung. Keine andere Mittel sind nötig zum Überwachen der Rissausbereitung. Die vorgeschlagene Methode wird für das Glasswassersystem erprobt und es ergibt sich dass die Resultate mit denen von anderen Methoden für das selbe System übereinstimmen.Die Methode wird auf das Aluminal Wasser System angewendet und die erhaltene K.V. Diagramme wurde ausgenützt um die Zeit bis zum Bruch () vorauszusagen. Die errechnete Werte von stimmen ganz gut mit denen zur Zeit zu Verfügung stehenden Resultate überein.

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Résumé On décrit une méthode simple pour déterminer les diagrammes facteurs d'intensité des contraintes/vitesse de fissuration (K. V.).Par cette méthode, on obtient K et V en mesurant la relaxation de la charge sous déplacement constant. Il n'est pas nécessaire de recourir à un moniteur de propagation de fissure.La méthode proposée est sujette à vérifications sur un système verre/eau et conduit à des données absolument identiques à celles obtenues sur le même système à l'aide d'autres techniques.On applique ensuite la méthode à un système alumine/eau, et on utilise les diagrammes K.V. obtenus à la prédiction des durées à la rupture ().Ces durées calculées sont en excellent accord avec les données actuellement disponibles.

     

Numerical simulation of multiple crack growth in brittle materials with adaptive remeshing

In this paper, an automated adaptive remeshing procedure is presented for simulation of arbitrary shape crack growth in multiple cracked bodies. The Zienkiewicz–Zhu error estimator is employed in conjunction with the modified superconvergent patch recovery (SPR) technique to obtain more accurate estimation of error. A stability analysis is performed to determine active cracks from a set of competitive cracks. Various crack growth criteria together with the respective crack trajectory prediction are compared. Several numerical examples are illustrated to demonstrate the efficiency, robustness and accuracy of computational algorithm in the simulation of multiple crack growth. Copyright © 2010 John Wiley & Sons, Ltd.     

Theory of dynamic crack branching in brittle materials

The problem of dynamic symmetric branching of a tensile crack propagating in a brittle material is studied within Linear Elastic Fracture Mechanics theory. The Griffith energy criterion and the principle of local symmetry provide necessary conditions for the onset of dynamic branching instability and for the subsequent paths of the branches. The theory predicts a critical velocity for branching and a well defined shape described by a branching angle and a curvature of the side branches. The model rests on a scenario of crack branching based on reasonable assumptions and on exact dynamic results for the anti-plane branching problem. Our results reproduce within a simplified 2D continuum mechanics approach the main experimental features of the branching instability of fast cracks in brittle materials.     

Three-dimensional simulation of crack extension in brittle polycrystalline materials

Crack extension resistance in brittle polycrystals was investigated from the viewpoint of three-dimensional microcrack evolution. Even in the case of macroscopically two-dimensional cracks, inhomogeneous distribution of microscopic stress along the crack front gives rise to three-dimensional structures of extended crack surfaces. Numerical simulations of macroscopic crack extension were carried out, which showed that three-dimensional distribution of grain-by-grain thermal stress leads to a significant increase in the crack extension resistance. It was concluded that three-dimensional interpretation on the microscopic inhomogeneity is necessary for the correct comprehension of macroscopic crack extension behavior in brittle polycrystals.     

Creep crack growth in internally pressurised tubes

This work was conducted as a small part of BRITE-EURAM Project BE 7463. In order to relate results from laboratory sized specimens to those on actual tubular components, test pieces from straight and cold bent carbon manganese steel tubing were tested under internal pressurisation at 360°C. Project work had previously indicated significant residual stress relaxation in cold bent material at 360°C, hence this was also investigated, it being anticipated that such stresses would play a role in the crack growth. Increased time at 360°C before pressurisation increased failure times on both bends and straight tubing. The latter was found also to contain high residual stresses. Such effects must be taken into consideration both during testing and when applying results to plant situations. Preliminary data analysis indicates that crack growth in tubular materials is faster than crack growth rates in both compact tension and three point bend specimens for equivalent K or C* values. Therefore both geometry and size effects have a significant influence on creep crack growth behaviour.     

Creep crack growth laws in heat-resistant steels

The conditions of various fundamental fields' domination at the creep crack tip have been considered. The creep crack growth properties and criteria are discussed. The relation between the creep crack growth kinetics and mechanisms have been studied for heat-resistant turbine steels over a wide test temperature and load range. In recent years much attention has been paid to the theoretical analysis of creep crack growth, though experimental investigations were generally performed for a comparatively narrow temperature and test time interval. The paper is concerned with the criteria and basic laws of creep crack growth. The results of our experimental investigation of the crack kinetics and crack growth mechanisms in heat-resistant steels in wide temperature and test time ranges are also presented.     

Creep crack growth under history-dependent loading

We discuss the influence of loading history on creep crack growth. Our attention is mainly focused on the following three aspects of this problem: (i) principal laws of history-dependent creep strain of materials; (ii) creep behavior of cracks, including the choice of suitable fracture parameters that may help to predict cracking; (iii) the importance of taking the history-dependent response of the material into account. We performed numerical calculations based on the use of an appropriate constitutive model and fracture theory for (1) and (2), respectively, to analyze results of tests for (3).Battelle, Columbus, Ohio. UES Incorporated, Dayton, Ohio. Published in Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 30, No. 4, pp. 37–45, July – Augus, 1994.     

Analysis of stable crack growth in brittle materials Part I: A process zone model

The phenomenon of stable crack growth in brittle materials is considered where stable crack growth is modeled as the formation of an elongated process zone of microcracks and isolated intact ligaments ahead of a stationary main crack. The role of residual stress in protecting the intact ligaments is explored via the hypothesis that compressive zones sorrounding isolated ligaments under residual tension protect these ligaments and result in stable crack growth and toughening of the microcracked material. The dependence of process zone behavior on either a plane strain or an axisymmetric representation of microcrack distribution is considered. Numerical results based on the above hypothesis indicate that interaction between residual stress and microcracking can lead to stable crack growth with attendant toughness enhancement.     

Multiple cohesive crack growth in brittle materials by the extended Voronoi cell finite element model

This paper is aimed at modeling the propagation of multiple cohesive cracks by the extended Voronoi cell finite element model or X-VCFEM. In addition to polynomial terms, the stress functions in X-VCFEM include branch functions in conjunction with level set methods and multi-resolution wavelet functions in the vicinity of crack tips. The wavelet basis functions are adaptively enriched to accurately capture crack-tip stress concentrations. Cracks are modeled by an extrinsic cohesive zone model in this paper. The incremental crack propagation direction and length are adaptively determined by a cohesive fracture energy based criterion. Numerical examples are solved and compared with existing solutions in the literature to validate the effectiveness of X-VCFEM. The effect of cohesive zone parameters on crack propagation is studied. Additionally, the effects of morphological distributions such as length, orientation and dispersion on crack propagation are studied.     

High speed fracture in brittle materials: Supersonic crack propagation

Microcircuit resistance grids were deposited on the surface of glass and glass-ceramic single edge notched beam (SENB) specimens. The individual strips were as small as ~ 10 μm in width. The specimens were broken in bending and the signal from the grids was captured using a waveform recorder. It was observed that the crack began to propagate with a nonzero initial velocity provided the initial notch was blunt. With continued crack propagation, the crack velocity decreased. In specimens with sharp notches, the crack began propagating with a near zero velocity and the velocity increased with increasing crack length. In some glass specimens with blunt notches, the initial crack velocity was found to be considerably greater than the sound velocity thereby showing that supersonic crack propagation can occur.