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Plastic zone evolution in Al–2 wt% Si metal films on silicon and sapphire substrateswas studied using nanoindentation and atomic force microscopy (AFM). AFM wasused to measure the extent of plastic pileup, which is a measure of the plastic zoneradius in the film. It was found that the plastic zone size develops in a self-similarfashion with increasing indenter penetration when normalized by the contact radius,regardless of film hardness or underlying substrate properties. This behavior was usedto develop a hardness model that uses the extent of the plastic zone radius to calculatea core region within the indenter contact that is subject to an elevated contact pressure.AFM measurements also indicated that as film thickness decreases, constraint imposedby the indenter and substrate traps the film thereby reducing the pileup volume.I. INTRODUCTIONThe popularity of nanoindentation is due in large partto its ability to probe the mechanical properties of ma-terials in a nondestructive fashion without extensivesample preparation. However, it is often difficult tomeasure film properties independent of the substrateproperties. Several solutions to this problem have beenproposed with varying degrees of success, the simplestbeing the “10% rule,” by which it is proposed that thefilm properties can be measured for indentation depthsless than 10% of the total film thickness.However, this “rule of thumb” has several deficien-cies. The rule is too restrictive for soft coatings onhard substrates;

Substrate effects on indentation plastic zone development in thin soft films