ANALYSIS OF NANOINDENTATION LOAD-DISPLACEMENT LOADING CURVES

Nanoindentation load-displacement curves provide a ''mechanical finger print'' of a materials response to contact deformation. Over the last few years, much attention has been focused on understanding the factor s controlling the detailed shape of unloading curves so that parameter s such as true contact area, Young's modulus, and an indentation hardn ess number can be derived. When the unloading curve is well behaved (b y which we mean approximating to linear behavior, or alternatively, fi tting a power-law relationship), then this approach can be very succes sful. However, when the test volume displays considerable elastic reco very as the load is removed [e.g., for many stiff hard materials and m any inhomogeneous systems (e.g., those employing thin hard coatings)], then the unloading curve fits no existing model particularly well. Th is results in considerable difficulty in obtaining valid mechanical pr operty data for these types of materials. An alternative approach, des cribed here, is to attempt to understand the shapes of nanoindentation loading curve and thus quantitatively model the relationship between Young's modulus, indentation hardness, indenter geometry, and the resu ltant maximum displacement for a given load. This paper describes the development and refinement of a previous approach by Loubet et al.(1) originally suggested for a Vickers indenter, but applied here to under stand the factors that control the shape of the loading curve during n anoindentation experiments with a pointed, trigonal (Berkovich) indent er. For a range of materials, the relationship P = K-m delta(2) was fo und to describe the indenter displacement, delta, in terms of the appl ied load P. For each material, K-m can be predicted from the Young's m odulus (E) and the hardness (H). The result is that if either E or H i s known, then the other may be calculated from the experimental loadin g curve. This approach provides an attractive alternative to finite el ement modeling and is a tractable approach for those cases where analy sis of unloading curves is infeasible.