New Statistical Treatment of Ball Indentation Data to Determine Distribution of Flaws in Glass

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Abstract
Ring fractures generated by a steel ball indenting a flat glass plate occur outside the contact circumference, not at the circumference as theory predicts. It has been proposed by others, and is accepted as a basis for the present work, that the position of ring fracture is not determined by the locus of maximum stress but by the presence of a flaw which is severe enough to initiate fracture under the local condition of stress. The ring fracture radii thus locate flaws of various sizes at various distances from the center of contact. A new statistical method is introduced for calculating the distribution of such flaws with respect to both sizes of flaw and surface density of flaws. Application of this analysis to data taken from indentations of HF‐etched surfaces shows that flaw densities range from 15 to 30 per mm2per 5 A depth interval (150 to 300 flaws per mm2over the range detected by the indenter). Since continued removal of the surface did not change this density distribution, it is concluded that these flaws are due to inhomogeneities in the glass structure rather than to surface flaws which are accidental in origin. The limitation of the strength of flat glass to 300,000 psi is due to these inhomogeneities.

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