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Indentation of Ceramics with Spheres: A Century After Hertz



Brian R. Lawn


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 like glasses, single crystals, fine-grain ceramics [tensile, brittle mode]; 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 micromechanical models of the quasi-plasticity 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 contact-induced damage on the ensuing strength properties of both brittle and 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], due to 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.
Journal of the American Ceramic Society


ceramics, cone crack, contact fatigue, Hertzian contact, quasi-plastic damage, strength degradation


Lawn, B. (1998), Indentation of Ceramics with Spheres: A Century After Hertz, Journal of the American Ceramic Society, [online], (Accessed June 12, 2024)


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Created May 4, 1998, Updated February 19, 2017