On the extreme depth dependence of the hardness of PDMS rubber: A problem of false surface detection

There is significant interest in nanoindentation of materials yet mixed results for material properties have been reported, including modest depth dependence of the surface stiffness in metals and other crystalline materials and polymer glasses, as well as stiffening of several orders of magnitude in some studies of soft materials such as poly(dimethylsiloxane) (PDMS) rubber. At the same time, there are reports that suggest that the observed extreme stiffening in soft materials might be an artifact, and that such materials at most exhibit only mild stiffening. Unfortunately, a quantitative model of potential artifacts has not been provided. In the present work, we examine the problem of one potential artifact in the testing of soft materials, that of the difficulty of detecting the surface or “true zero” in the indentation test. We provide a quantitative estimate of the effect of error in surface detection on the measured force–displacement curves for the Berkovich tip geometry and find that the observed apparent stiffening is in agreement with our analysis. The significance of the results for testing of soft materials by nanoindentation is discussed. It is also shown that for hard/stiff materials the induced errors are smaller, but may still be significant in some circumstances.