The failure of ceramic materials is caused by the extension of small flaws. Therefore, linear-elastic fracture mechanics can be applied to describe the failure behaviour. The main problem in the application of the simple fracture mechanics relation is the existence of a rising crack growth resistance curve, which is caused by crack bridging forces behind the advancing crack tip or by transformations in front of the crack tip. The increasing crack growth resistance leads to problems in the transformation of results from specimens with macrocracks to components with natural cracks.

Fracture Mechanics of Ceramics

Universal features of weight functions for cracks in mode I

Weight functions for a surface semi-elliptical crack in a finite thickness plate

The weight function method is described to analyze the crack growth behavior in functionally graded materials and in particular materials with a rising crack growth resistance curve. Further, failure of graded thermal barrier coatings (TBCs) under cyclic surface heating by laser irradiation is modeled on the basis of fracture mechanics. The damage of both graded and non-graded TBCs is found to develop in several distinct stages: vertical cracking → delamination → blistering → spalling . This sequence can be understood as an effect of progressive shrinkage due to sintering and high-temperature creep during thermal cycling, which increases the energy-release rate for vertical cracks which subsequently turn into delamination cracks. The results of finite element modeling, taking into account the TBC damage mechanisms, are compatible with experimental data. An increase of interface fracture toughness due to grading and a decrease due to ageing have been measured in a four-point bending test modified by a stiffening layer. Correlation with the damage observed in cyclic heating is discussed. It is explained in which way grading is able to reduce the damage.

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Cracks in functionally graded materials

Determination of weight functions from reference stress intensity factors

On the calculation of crack opening displacement from the stress intensity factor

The weight function method is an important procedure to determine stress intensity factors for complex stress distributions. This approach is based on the knowledge of the crack opening displacement field for a reference load case. The approximate analytical determination of the crack opening field from the reference stress intensity factor is outlined in detail. In the absence of a reference solution the FE-method is used in some special applications. The general treatment is illustrated by a number of examples, which have been obtained by the authors in the last years.

Approximate weight function for 2D and 3D-problems

The Cruse-Besuner method for calculating energy release rates or weighted stress intensity factors for semi-elliptical surface cracks is based on some assumptions. To check the accuracy of this method an internal elliptical crack under roof-shaped stress distribution is considered. The deviations from the exact solution are in the order of about 3%. From these results also for surface cracks in bending the same accuracies can be expected.

C. Mattheck

Papers

On the calculation of crack opening displacement from the stress intensity factor

Approximate weight function for 2D and 3D-problems

On the accuracy of the Cruse-Besuner weight function approximation for two-dimensional cracks

Averaged stress intensity factors for embedded elliptical cracks