Failure of curved brittle layer systems from radial cracking in concentrated surface loading
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Brian R. Lawna) Materials Science and Engineering Laboratory, National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8500 (Received 6 June 2005; accepted 14 July 2005)
A study was made of radial crack evolution in curved brittle layers on compliant support substrates. Three-dimensional boundary element analysis was used to compute the stepwise growth of radial cracks that initiate at the bottom surfaces of glass on polymeric support layers, from initiation to final failure. The algorithm calculates reconstituted displacement fields in the near-tip region of the extending cracks, enabling direct evaluation of stress-intensity factors. Available experimental data on the same material systems with prescribed surface curvatures were used to validate the essential features of the predicted crack evolution, particularly the stability conditions prior to ultimate failure. It was shown that the critical loads to failure diminish with increasing surface curvature. Generalization of the ensuing fracture mechanics to include alternative brittle-layer/polymer-substrate systems enabled an explicit expression for the critical load to failure in terms of material properties and layer thicknesses. Implications concerning practical layer systems, particularly dental crowns, are briefly discussed. I. INTRODUCTION
Brittle layers on compliant substrates are relevant to a wide range of engineering coating and film applications. It has been well documented that radial cracks induced at brittle layer undersurfaces by contact-induced flexure are highly dangerous.1–11 A photograph of such a radial crack in a glass plate on a polycarbonate base is shown in Fig. 1.5 Such cracks form directly below the indentation center and propagate radially outward on median planes containing the indentation axis. Usually more than one such crack forms, in a regular star pattern. The crack fronts resemble contours of tensile hoop stresses in the flexing plate.12 In some layer systems, the surfaces may be curved, as in biomechanical structures like dental crowns on dentin13,14 or polyethylene-backed acetabular ceramic liners in total hip replacements,15,16 as well as in some coated tool and engine components. Whereas curvature may have little effect on the critical load to initiate radial cracks, it can have a considerable effect on the “failure” load to propagate these same cracks to the edges of the specimen.17,18 In crowns, the layers are basically (but not exclusively) convex, which can substantially exacerbate a)
Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/JMR.2005.0343 2812
http://journals.cambridge.org
J. Mater. Res., Vol. 20, No. 10, Oct 2005 Downloaded: 02 Apr 2015
unstable propagation. In acetabular cups, the articulating surface is concave, which tends to restrain crack extension.17 Other, top-surface, near-contact cracks can occur in brittle layer systems and may even dominate in some structures, especially in thicker brittle layers; such alternative crack systems have been adeq
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