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

A methodology, based on sintering-induced stiffening, for prediction of the spallation lifetime of plasma-sprayed coatings

This paper gives a bibliographical review of the finite element methods applied to the analysis and simulation of coatings, their mechanical and material properties from the theoretical and application points of view. The surface modification technologies in the context of coatings are also included. The added bibliography at the end of this paper contains 1032 references to papers and conference proceedings on the subject that were published in 1995–2005. The following topics are included: coating property simulations; surface modification process simulations and practical coating applications.

https://iopscience.iop.org/article/10.1088/0965-0393/13/6/011/pdf

Coatings and surface modification technologies: a finite element bibliography (1995–2005)

The fracture behaviour of volcanic glass and relevance to quench fragmentation during formation of hyaloclastite and phreatomagmatism

The adherence of plasma sprayed NiCrAlY bond coats can be improved by an appropriate substrate surface finish. The interface fracture energy for crack propagation along the coating/substrate interface has been measured for different surface roughness by means of a specially designed four-point bending test. An increase of the interface fracture energy of about 15% was observed for a three times higher surface roughness. In addition, four-point bending tests with the coating on the side face of bending specimens were performed to analyze the fracture and spalling behavior of the coatings both under large tensile and compressive substrate deformations.

Effect of substrate surface roughness on the adherence of NiCrAlY thermal spray coatings

Rapid quenching of brittle materials gives rise to hierarchically ordered crack patterns. A scenario of thermal shock crack propagation can be derived: unstable propagation of several out of a great number of preexisting surface flaws leads to a transient state of cracks of nearly equal lengths and spacing. In the further process of stable multiple propagation, the progressive unloading among the cracks results in the formation of hierarchical patterns.

Multiple Crack Propagation under Thermal Load

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.

H.-J. Weiß

Papers

Multiple Crack Propagation under Thermal Load

Fracture mechanical damage modelling of thermal barrier coatings