Constructing critical stress diagrams for anisotropic brittle materials

The problem of critical equilibrium in a plate with a crack in biaxial tension/compression was analyzed for the case in which the plate material is brittle and anisotropic with respect to its breaking stress. The obtained solutions were used to construct critical state diagrams for brittle solids of this kind. Strength diagrams for orthotropic materials were constructed.     

Construction of strength diagrams for a brittle body with defects of elliptical shape

Diagrams of the critical stressed state (strength diagrams) of a brittle body with elliptical defects were constructed on the basis of the first theory of strength. In the case for which the smaller axis of the ellipse is infinitely small, a diagram previously constructed by Griffith [1] was obtained.     

Work-of-fracture of brittle materials with microcracking and crack bridging

The fracture mechanics basis of fracture energies is considered through micromechanical phenomena in the crack tip frontal process zone, the following crack wake and crack bridging regions of brittle materials, such as cement-based materials, rocks, ceramics, and ceramic composites. The discussion is mainly focused on the work-of-fracture parameter ({ie65-1}) as a material characteristic for representing the resistance to crack extension. Theoretical considerations of the dependence of {ie65-2} on the unnotched remaining ligament length of the fracture test specimen lead to the concept of the essential work-of-fracture, {ie65-3}. The experimental results obtained for three different types of ceramic materials support the theoretical predictions.     

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.     

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.     

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.     

基于定长裂缝试件的脆性材料尺寸效应实验方法

由于脆性或准脆性材料内各类微缺陷的影响,材料的力学性能,如名义破坏应力,　刚度以及断裂韧性等随试件的大小而改变,具有明显的尺寸效应。通常情况下,描述材料尺寸效应的Ｂａｚａｎｔ尺寸效应律是建立在一系列相似试件的基础上通过实验方法确定的。　本文提出了一种新的用含固定长度裂缝试件测定断裂韧性和有效断裂过程区大小的实验方法和计算公式。与相似试件测定方法相比,实验结果吻合很好。根据本文提出的定长裂缝试件实验方法,在保证与相似试件相同脆性指数范围的前提下,可以用小试件进行测量。     

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.     

An XFEM method for modeling geometrically elaborate crack propagation in brittle materials

We present a method for simulating quasistatic crack propagation in 2‐D which combines the extended finite element method (XFEM) with a general algorithm for cutting triangulated domains, and introduce a simple yet general and flexible quadrature rule based on the same geometric algorithm. The combination of these methods gives several advantages. First, the cutting algorithm provides a flexible and systematic way of determining material connectivity, which is required by the XFEM enrichment functions. Also, our integration scheme is straightforward to implement and accurate, without requiring a triangulation that incorporates the new crack edges or the addition of new degrees of freedom to the system. The use of this cutting algorithm and integration rule allows for geometrically complicated domains and complex crack patterns. Copyright © 2011 John Wiley & Sons, Ltd.