Thin-coating contact mechanics with adhesion
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An elementary theory for a rigid spherical indenter contacting a thin, linear elastic coating that is bonded to a rigid substrate was developed. This theory predicts that contact area varies as the square root of the compressive load in contrast to Hertz theory where contact area varies as the two-thirds power of the compressive load. Finite element analysis confirmed an approximate square root dependence of contact area on compressive load when the coating thickness-to-indenter radius ratio is less than 0.1 and when the coating Poisson’s ratio is less than 0.45. Thin-coating contact mechanics theories that use either the Derjaguin-Muller-Toporov (DMT) approximation or the Johnson-Kendall-Roberts (JKR) approximation were also developed. In addition, a finite element simulation capability that includes adhesion was developed and verified. Illustrative finite element simulations that include adhesion were then performed for a thin elastic coating (rigid indenter/substrate). Results were compared with the thin-coating contact theories and the transition from DMT-like to JKR-like response was examined. I. INTRODUCTION
There is a continuing interest in the application of contact mechanics to thin elastic coatings and multilayers. Fields of application include pressure-sensitive adhesives, anti-wear coatings, microelectronics, optical systems, and microelectromechanical systems (MEMS). Such applications have generated a need for accurate methods for determining the mechanical properties of thin coatings. These measurements typically require the use of a contact mechanics model to isolate coating properties from composite data that includes the constraint imposed by the substrate. This has motivated recent work aimed at the development of a contact analysis for coated substrates that enables a more accurate interpretation of indentation test results.1–3 Much current work is aimed at developing analyses that can be used in the interpretation of tests that include the effect of adhesion. Analyses that include adhesion are of particular interest when the coating is a soft, rubbery material or when interpreting results of tests using nanoscale probes. Examples of work that allows for adhesion and are aimed at a thin, soft, incompressible coating include a study that considered both rigid spherical and conical indenters4 as well as a study that considered a rigid flat cylindrical indenter.5 As the size of a probe becomes smaller, adhesion effects can become important. Indeed the atomic force microscope (AFM) can be a)
Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/JMR.2006.0327 2660 http://journals.cambridge.org
used to characterize nanoscale adhesion and friction interactions between solids.6 One set of recent studies, which assumed Johnson-Kendall-Roberts (JKR)-like behavior, was specifically aimed at providing a contact analysis for AFM tests on coated substrates.7,8 In one interesting study, finite element and molecular dynamic analyses were used to estimate the properties of a 2.5– n
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