Indentation of Ceramics with Spheres: A Century after Hertz

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Abstract
In this article we review the nature and mechanics of damage induced in ceramics by spherical indenters, from the classical studies of Hertz over a century ago to the present day. Basic descriptions of continuum elastic and elastic–plastic contact stress fields are first given. Two distinct modes of damage are then identified: Hertzian cone cracks, in relatively hard, homogeneous materials, such as glasses, single crystals, fine‐grain ceramics (tensile, “brittle” mode); and diffuse subsurface damage zones, in relatively tough ceramics with heterogeneous microstructures (shear, “quasi‐plastic” mode). Ceramographic evidence is presented for the two damage types in a broad range of materials, illustrating how an effective brittle–ductile transition can be engineered by coarsening and weakening the grain structure. Continuum analyses for cone fracture and quasi plasticity, using Griffith–Irwin fracture mechanics and yield theory, respectively, are surveyed. Recent micro‐mechanical models of the quasi‐plastic mode are also considered, in terms of grain‐localized “shear faults” with extensile “wing cracks.” The effect of contact‐induced damage on the ensuing strength properties of both brittle and quasi‐plastic ceramics is examined. Whereas cone cracking causes abrupt losses in strength, the effect of quasi‐plastic damage is more gradual—so that more heterogeneous ceramics are more damage tolerant. On the other hand, quasi‐plastic ceramics are subject to accelerated strength losses in extreme cyclic conditions (“contact fatigue”), because of coalescence of attendant microcracks, with implications concerning wear resistance and machinability. Extension of Hertzian contact testing to novel layer structures with hard, brittle outer layers and soft, tough underlayers, designed to impart high toughness while preserving wear resistance, is described.

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