The extended Hertzian theory and its uses in analyzing indentation experiments

Abstract

Since the presentation of the complete elastic field of an extended Hertzian approach [J. Phys. D 37 2761 (2004).] (treating the problem of mechanical contact of two bodies with shape functions of symmetry of revolution of the type z(r) = r ²/d ₀ + r ⁴/d ₂ + r ⁶/d ₄ + r ⁸/d ₆ + ···), a number of publications have appeared showing useful applications of the new theory. They are mainly dedicated to the problem of parameter identification in nanoindentation experiments. In this paper, these new analysis techniques are summarized and further applications concerning indentation testing are proposed. Thus, the main topics of the paper are: (1) purely elastic indentation experiments: (a) two spheres in contact → revised (with the new theoretical results, the limits of the classical Hertzian approach are investigated), (b) arbitrarily shaped indenters of symmetry of revolution and their resulting elastic field at each point within the either monolithic or layered sample material, and (c) the determination of the surface pressure distribution in the case of layered materials. (2) Elasto-plastic indentation experiments: (a) the concept of the effectively shaped indenter, (b) identification of Young's modulus, hardness and yield strength for monolithic and layered materials, (c) about the determination of intrinsic stresses via indentation experiments → an in principle feasibility study, and (d) about pile-up and sink-in (does the new mathematical tool also help in analyzing and detecting indents where pile-up or sink-in has occurred?). The new techniques are in parts demonstrated on real nanoindentation data. The results are discussed and, wherever possible, compared with the outcome of other analyzing procedures.

Notes

†For one, there is no proper Nanoindenter with a sufficiently sensitive lateral force unit available yet. Though the author knows of some efforts, it still seems to be a long way until the “next generation of Nanoindenters” can be used in order to tackle problems like those ones described here.