This paper presents a review of the principal developments in functionally graded materials (FGMs) with an emphasis on the recent work published since 2000. Diverse areas relevant to various aspects of theory and applications of FGM are reflected in this paper. They include homogenization of particulate FGM, heat transfer issues, stress, stability and dynamic analyses, testing, manufacturing and design, applications, and fracture. The critical areas where further research is needed for a successful implementation of FGM in design are outlined in the conclusions. DOI: 10.1115/1.2777164

https://web.mst.edu/~vbirman/papers/Modeling%20and%20Analysis%20of%20FGM_Review_2007.pdf

Modeling and Analysis of Functionally Graded Materials and Structures

http://user.engineering.uiowa.edu/~rahman/efm_fgm.pdf

Mesh-free analysis of cracks in isotropic functionally graded materials

Mixed-mode fracture of orthotropic functionally graded materials using finite elements and the modified crack closure method

The interaction integral for fracture of orthotropic functionally graded materials: Evaluation of stress intensity factors

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

In order to find ways of suppressing damage of thermal barrier coatings, a few well-defined partial problems have been investigated experimentally and theoretically: crack formation due to high temperature creep, measurement of creep properties by laser shock, formation of layer and spalling cracks, and fracture mechanics analysis of the normal/spalling transition. The creep parameters of the material are derived from the residual surface uplift after local heating. It is shown how the numerical effort for solving the involved creep problems can be reduced by applying suitable approximations. The expected depth of spalling fracture is estimated by considering the stress intensity factor K II .

Laser induced creep and fracture in ceramics

The fracture and damage behaviour of high temperature materials can be modified by realizing well-defined property gradients. The damage characterization of thermal barrier coatings (TBCs) by means of laser irradiation shows that crack propagation perpendicular and parallel to the heated surface are the crucial phenomena. Crack propagation parallel to the surface leads to delamination and spalling. In terms of fracture mechanics, optimizing gradients means minimization of the ratio between the energy release rate G for delamination and its critical value G c . The aim is to allow maximum load at large TBC thickness. Two effects are discussed by means of an example. One is the reduction of G for stationary heat flow and the other one is the higher G c through a gradient towards a more ductile material. A method for measurement of G c for thin, brittle layers is presented. Cyclic surface heating by laser irradiation enables us to quantitatively evaluate the damage resistance of non-graded and graded TBCs.

Fracture Mechanical Modelling and Damage Characterization of Functionally Graded Thermal Barrier Coatings by Means of Laser Irradiation

The problem of how to avoid damage of TBCs has been approached by calculating the energy release rate of two crack configurations under thermal loading. This has been done for the limiting cases of perfect and lacking heat transfer across the crack. Suitable grading of TBCs is a means of suppressing the tendency to delamination and damage by both decreasing the energy release rate G and increasing its critical value Gc. TBCs can be graded such that delamination cracks would be deflected into depth where Gc is sufficiently high to avoid crack propagation.

Fracture mechanical damage modelling of thermal barrier coatings

By suitably scanning a circular sample with a beam from a 1 kW-Nd-YAG laser, steep temperature gradients and high stresses can be generated. Ceramics with outstanding high temperature strength have been tested, such as silicon nitride. Thermal shock figures-of-merit have been calculated from the measured temperature field at the instant of fracture. By means of repeated thermal loading, the number of cycles to failure and the parameter of subcritical crack growth have been determined for unnotched samples. In addition to elastic effects, damage due to tensile stresses arising after stress relaxation by creep has been demonstrated.

G. Kirchhoff

Papers

Cracks in functionally graded materials

Laser induced creep and fracture in ceramics

Fracture Mechanical Modelling and Damage Characterization of Functionally Graded Thermal Barrier Coatings by Means of Laser Irradiation

Fracture mechanical damage modelling of thermal barrier coatings

Fracture mechanical characterization of thermal damage of ceramics by means of laser irradiation