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

Layered ceramics have been proposed as an alternative choice for the design of structural ceramics with improved fracture toughness, strength and reliability. The use of residual compressive stresses, either at the surface or in the internal layers, may improve the strength as well as the crack resistance of the material during crack growth. In this work, two alumina–zirconia laminates designed with external (ECS-laminates) and internal (ICS-laminates) compressive stresses have been investigated using a fracture mechanics weight function analysis. An optimal architecture that maximises material toughness and strength has been found for each design as a function of geometry. From a flaw tolerant viewpoint, ECS-laminates are suitable for ceramic components with small cracks or flaws which are embedded in or near the potential tensile surface of the piece. On the other hand, the existence of large cracks or defects suggests the use of ICS-laminates to attain a more reliable response.

Optimal strength and toughness of Al2O3–ZrO2 laminates designed with external or internal compressive layers

Prediction of the fracture toughness of a ceramic multilayer composite – Modeling and experiments

: In this paper the axisymmetric crack problem for a nonhomogeneous medium is considered. It is assumed that the shear modulus is a function of z approximated by mu = mu (sub 0) e to the alpha z power. This is a simple simulation of materials and interfacial zones with intentionally or naturally graded properties. The problem is a mixed mode problem and is formulated in terms of a pair of singular integral equations. With fracture mechanics applications in mind, the main results given are the stress intensity factors as a functions of the nonhomogeneity parameter alpha for various loading conditions. Also given are some sample results showing the crack opening displacements.

The axisymmetric crack problem in a nonhomogeneous medium

During the processing of laminar ceramics, biaxial residual stresses can arise due to the thermal mismatch between different layers. For ceramic multilayers, the beneficial consequences of compressive stresses at the surface are well known: increase in strength, apparent toughness and reliability. Nevertheless, the resulting tensile stresses may induce a negative influence in the effective fracture toughness if the tensile stresses are high. The weight function technique is used to assess the stress intensity factor corresponding to the residual stresses field. The influence of geometrical parameters such as thickness, number of layers and tension/compression thickness ratio is analyzed. For different multilayers (Al 2 O 3  −  x Al 2 O 3 /(1 −  x )ZrO 2 ), effective R -curves are presented. The existence of an optimal architecture that maximizes the toughening is exposed as well as two tendencies on the apparent R -curve that define different fracture patterns: brittle failure or layer-by-layer fracture.

https://pure.unileoben.ac.at/portal/files/555737/ISFK_Publikation_2007_08_EffectiveToughnessAZA_tlu_JECS_OA.pdf

D. Munz

Papers

Applicability of the extended Petroski–Achenbach weight function procedure to graded materials