Error estimation of nanoindentation mechanical properties near a dissimilar interface via finite element analysis and an
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Nanoindentation methods are well suited for probing the mechanical properties of a heterogeneous surface, since the probe size and contact volumes are small and localized. However, the nanoindentation method may introduce errors in the computed mechanical properties when indenting near the interface between two materials having significantly different mechanical properties. Here we examine the case where a soft material is loaded in close proximity to an interface of higher modulus, such as the case when indenting bone near a metallic implant. The results are derived from both an approximate analytical quarter space solution and a finite element model, and used to estimate the error in indentation-determined elastic modulus as a function of the distance from the apex of contact to the dissimilar interface, for both Berkovich and spherical indenter geometries. Sample data reveal the potential errors in mechanical property determination that can occur when indenting near an interface having higher stiffness, or when characterizing strongly heterogeneous materials. The results suggest that caution should be used when interpreting results in the near-interfacial region. I. INTRODUCTION
Determination of the elastic modulus and hardness of materials during the nanoindentation test relies on the use of the load versus indentation depth curve,1–5 and is based on the mathematical solutions for contact of the semi-infinite half space. However, it is expected that the results may not reflect the true mechanical properties when the indentation test is conducted near a dissimilar interface. An example of this is the case where one desires to determine the mechanical properties of bone near a metallic implant, such as titanium (as in the case of a threadless dental implant6–8), or typical cobaltchrome alloys used in orthopedic implants.9,10 Since bone remodels itself and adapts to applied loads,11–13 its properties in close proximity to the implant interface may be considerably different from its properties further away. Nonetheless, the mechanical properties at the (load-bearing) bone-implant interface are important for proper implant fixation and performance. Discrepancies in properties in the region of a dissimilar interface are the result of partial development of the displacement field that would normally occur in the half space contact problem. One method proposed to solve this is to experimentally account for structural compliance introduced by the Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/JMR.2010.0295
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II. METHODOLOGY A. Analytical solutions
Three-dimensional (point load) contact solutions for both (rigid) spherical and Berkovich (approximated as a 140.6 axisymmetric cone) indenters were used to model
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transition across a dissimilar interface.14 Another method is to solve the quarter space problem. However, due to the complexity of the boundary conditions and the nonaxisymmetry of typical three-dimensional (point contact) indentation probe
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