In 1881 and 1882 Hertz first gave a scientific description of the cone-shaped crack that forms in a brittle solid critically loaded with a spherical indenter. A decade later Auerbach (1891) put forward an empirical relationship (Auerbach's law) for Hertzian fractures, which has since aroused increased interest, (i) because it has deep implications concerning the validity of certain widely accepted brittle fracture criteria and (ii) because it has potential application as a means for measuring

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... acture strength. Consequently, theoretical justification of Auerbach's law ii has been the target of many treatments. From these, two main schools of thought, (i) flaw statistical and (ii) energy balance, have evolved. More recently Frank and Lawn (1967) derived Auerbach's law from the first law of thermodynamics and Griffith's (1920) energy balance criterion. This explanation of Auerbach's law was questioned by proponents of the flaw statistical approach. This issue provided the motivation for the present study. In 1969 Langitan and Lawn partially resolved the issue by verifying one of the predictions based on the energy balance theory. However, no evidence to substantiate the second prediction -that the cone crack should grow in the form of a stable ring crack -was found. Thus the aim of this thesis is to look at the second prediction in detail. A powerful dislocation-revealing technique, the section-and-etch method, is developed and applied to systematic measurements of cone-crack extension. Results show that within a certain range of indenter load iii the cone crack grows in the form of a shallow surface ring prior to full development. This directly confirms the second prediction -a salient feature of the energy balance theory. Other tests, designed to complete the Langitan and Lawn experiments are also described in Chapter 4 of this thesis. These tests make use of new vacuum equipment recently constructed in this laboratory and highlight the part played by environment in the fracture strength of solids.