The Auerbach Range in the Hertzian Fracture of Glass

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Abstract
Several workers have reported the somewhat curious phenomenon that in ball‐indentation fracture experiments on glass plates, the average fracture load is directly proportional to the indenter radius for a wide range of small indenters. As a part of the present investigation, similar experiments have been performed and confirm these observations. That such a definite relation (known as Auerbach's Law) should exist serves as one of the more puzzling barriers to nearly universal acceptance of statistical theories of glass fracture. This paper discusses such behavior from a probabilistic view in the content of the Hertz solution of classical elasticity. In particular a statistical solution is demonstrated, which, based on the hypothesis that there is a distribution of flaws with a density which varies inversely as the cube of the flaw severity, not only yields the linear range for average fracture loads, but also gives good agreement with other detailed characteristics of experimental fracture load‐frequency data.

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