The determination of film hardness from the composite response of film and substrate to nanometer scale indentations

Abstract

Two equations for determining the hardness of thin films from depth-sensing indentation data are examined. The first equation is based on an empirical fit of hardness versus indenter displacement data obtained from finite element calculations on a variety of hypothetical films. The second equation is based on a model which assumes that measured hardness is determined by the weighted average of the volume of plastically deformed material in the coating and that in the substrate. The equations are evaluated by fitting the predicted hardness versus contact depth to data obtained from titanium coatings on a sapphire substrate. Only the volume fractions model allows the data to be fitted with a single adjustable parameter, the film hardness; the finite element equation requires two thickness-dependent parameters to obtain acceptable fits. It is argued that the difficulty in applying the finite element model lies in the use of an unrealistic area function for the indenter. For real indenters, which have finite radii, the area function must appear explicitly in the final equation. This is difficult to do with the finite element approach, but is naturally incorporated into the volume fractions equation. Finally, using the volume fractions approach the hardnesses of the titanium films are found to be relatively insensitive to film thickness. Thus, the apparent increase in hardness with decreasing film thickness for the titanium films is most likely due to increased interactions between the film and substrate for the thinner films rather than to a change in the basic structure of the titanium films.

Synthesis and mechanical wear studies of ultra smooth nanostructured diamond (USND) coatings deposited by microwave plasma chemical vapor deposition with He/H2/CH4/N2 mixtures

“…The hardness and Young's modulus of the diamond films was measured using a Nanoindenter XP (MTS Systems, Oak Ridge TN) system with a continuous stiffness (CSM) attachment which provided continuous hardness/modulus measurements with increasing depth into the film [11,12]. The system was calibrated by using silica samples for a range of operating conditions.…”

Surface hydration and nanoindentation of silicate glasses

“…Mechanical properties of the hydrated layer were measured only for SKMB1, SKMB2 (0-30 nm) and SS (20-40 nm) low durability compositions where thickness of the hydrated layer was suitably thick to minimise the contribution of substrate effect. [24][25][26][27] Mechanical properties for hydrated SLS1, SLSM1 and SLSM2 high durability glasses are given to show that hydration has little effect on their near-surface mechanical properties. For SS sample mechanical properties of hydrated layer are given for samples hydrated for 5 and 10 min respectively.…”

“…[24][25][26][27] To exclude contribution of the substrate empirical or semi-empirical models have been proposed. 31,32 When considering comparatively thick films, the Bückle rule is often employed which states that substrate effect can be negligible if the indentation depth is less than 10% of film thickness.…”

Determining the elastic modulus and hardness of an ultra-thin film on a substrate using nanoindentation

“…The accuracy of such a measurement depends on the film and substrate properties and on the indentation depth as a fraction of the total film thickness. In general, the error due to the substrate effect increases with increasing indentation depth and with increasing elastic mismatch between film and substrate [3][4][5][6][7]. To m i n i m i z e t h e effect of the substrate on the measurement, the indentation depth is often limited to less than 10% of the film thickness [5].…”