Deformation and failure of a film/substrate system subjected to spherical indentation: Part II. Prediction of failure mo
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V. Jayaram Department of Metallurgy, Indian Institute of Science, Bangalore–560012, India
S.K. Biswasa) Department of Mechanical Engineering, Indian Institute of Science, Bangalore–560012, India (Received 27 June 2005; accepted 19 December 2005)
We have demonstrated previously, using nanoindentation, that the film thickness and substrate plasticity, the important two external variables in the film layer, control the failure of the film in a mutually exclusive way. In this work, we used a non-iterative Hankel transform method to analyze the stresses in an elastic film bound to an elastic substrate by a no-slip boundary condition and subjected to a Hertzian traction. We vary the substrate compliance by two orders of magnitude to generate interfacial mismatch stresses, which mimic the corresponding changes found in a real-life elastic film on an elastic-plastic substrate when the hardness of the substrate is changed. The analysis is found to reproduce faithfully the experimental trends, which showed that normal load and interfacial stresses generated by strain mismatch drive different modes of fracture depending on the film thickness in a mutually exclusive way. This validation paves the way for this theoretical technique to be used to design multilayered film structures.
I. INTRODUCTION
It has recently been shown that thin columnar films of TiN on metallic substrates can accommodate contact loads in one of two ways. Thin films on hard substrates deform together by means of slippage of TiN columns into the substrate along inter-columnar boundaries.1,2 A good fit can be obtained to the load–displacement behavior of such a system by assuming that the two phases suffer the same displacement and support loads that scale with their respective stiffnesses, which are based on an expanding cavity (substrate) and elastic loading up to a critical shear stress (film). In contrast, thick films on soft substrates predominantly display cracking with little or no sign of column slippage.3,4 The modes of cracking during loading are principally: (i) inclined transcolumnar shear cracks that begin just below the contact surface and proceed at an angle towards, but without reaching, the interface, and (ii) bending cracks that nucleate from the edge of the contact and move down, as well
a)
Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/JMR.2006.0095 J. Mater. Res., Vol. 21, No. 3, Mar 2006
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as those that nucleate from the interface and move upward toward the free surface until they experience the compressive field of an elastically bent film. Three of these modes of slippage/cracking are shown in Figs. 1(a)–1(c). Other cracks present include the lateral cracks immediately below the contact that have been attributed to the unloading cycle and the ubiquitous nested cracks that run parallel to the indenter circumference and have been shown to be shallow4,5 in depth. It has been argued3 that these grosser forms of fracture (inclined, bendi
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