Modeling of contact-induced radial cracking in ceramic bilayer coatings on compliant substrates
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Pedro Miranda Departamento Electrónica e Ingeniería Electromecánica, Escuela de Ingenierías Industriales, Universidad de Extremadura, 06071 Badajoz, Spain (Received 22 December 2002; accepted 6 March 2003)
Contact-induced radial cracking in ceramic coatings on compliant substrates was analyzed recently. Radial cracks initiate at the coating/substrate interface beneath the contact where maximum flexural tension occurs, and an analytical expression for the onset of radial cracking in monolayer coatings was formulated on the basis of the classical solution for flexing plates on elastic foundation. In the present study, the analytical expression was derived for the case of ceramic bilayer coatings on compliant substrates, which have significant applications in the structure of dental crowns. It was found that the analytical solution for bilayer-coating/substrate systems can be obtained from that of monolayer-coating/substrate systems by replacing the neutral surface position and the flexural rigidity of monolayer coating with those of bilayer coating. The predicted critical loads for initiating radial cracking were found to be in good agreement with existing measurements and finite element results for glass/alumina, glass/glass–ceramic, and glass/Y2O3-stabilized ZrO2 polycrystal bilayers on polycarbonate substrates. Limitations of the present analysis are discussed.
I. INTRODUCTION
Ceramic coatings on compliant substrates have extensive applications in microelectronic, structural, optical, and biological components.1–3 Whereas hard coatings provide enhanced electrical, wear, thermal, and corrosion resistance, compliant substrates provide stress redistribution and damage tolerance. To maintain the functionality and reliability of ceramic coating systems, it is essential to understand the geometrical and material factors that limit their lifetime. Among various loading modes applied on ceramic coating systems, contact loading presents a worst case,4,5 and it is also a practical loading mode in studying failure of dental crowns.5–14 It has been concluded that cone cracks or quasiplasticity at the top surface and radial cracks at the lower surface beneath the contact can be competing damage modes in ceramic coatings.5–14 Whereas studies of cone cracking and quasiplasticity have been well documented, studies of lower surface radial cracking have only recently been considered.9–14 Hence, contact-induced radial cracking is our interest in this study. Stress fields resulting from contact loading of ceramic coatings on compliant substrates are complex, especially when the coating consists of more than one layer. Finite element analysis (FEA) provides a powerful means for analyzing stress fields in complex multilayer systems. J. Mater. Res., Vol. 18, No. 5, May 2003
However, it suffers from the drawback that it is a caseby-case study and computation needs to be performed for each change in geometrical parameters and material properties. On the other hand, the closed-form analytical solution is more desirable because it descr
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