The influence of punch blunting on the elastic indentation response

Elastic solutions of a family of axisymmetric problems concerning frictionl ess contact between a rigid punch and a semi-infinite substrate are conside red using the method of Green and Zerna and of Collins. The analysis is rel evant to the interpretation of experimental results in materials indentatio n testing, e.g. when substrate properties need to be determined from load-d isplacement traces, and precise information about the indenter tip shape is crucial. Commonly used solutions for ideal punch shapes, e.g. those having spherical or conical tips, may only be viewed as approximations since, in practice, indenter tips are neither perfectly round nor infinitely sharp. In order to illustrate the influence that small variations in punch shape may have on the contact behaviour, analytical solutions for a blunted Hertzian indenter and a rounded cone are obtained in parametric form, and their asymptotic b ehaviour at the extremes of low and high loads is investigated. A smooth pu nch is then considered of a general shape, given by a power series, and the resulting general solution is used as a basis for developing an inverse pr oblem formulation of the tip shape calibration procedure. The method allows the best match between the measured and predicted load-displacement depend encies to be established. An example of the application of this procedure t o the analysis of some nanoindentation data is presented.