Fracture of Brittle Solids. II. Distribution Function for Fragment Size in Single Fracture (Experimental)

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Abstract
The theoretical results of Gilvarry for the size distribution of the fragments in single fracture have been verified experimentally by fracturing spherical glass specimens under compression. The fragments were contained by a gelatin matrix to inhibit secondary fracture and thus make conditions conform as closely as possible to single fracture. Experimental values of the probability of fracture as obtained by sieve analysis show the predicted linear variation with the mean dimension x of the particles, over reasonably large intermediate ranges of the variables. It is shown that a logarithmic‐normal distribution does not represent the experimental results. The over‐all data exhibit three local maxima in the differential probability of fracture as a function of x, whereas the theory permits only two. Agreement in the number of peaks is obtained by subtracting the contribution to the over‐all probability of those fragments containing original surface of the specimen, which yields the true probability considered in the theory. In this manner, reasonably complete agreement between theory and experiment for single fracture is obtained. For plural fracture (carried out without use of gelatin), two additional peaks exist in the curve of the over‐all differential probability vs x, as compared to the case for single fracture. The theory of Gilvarry is confirmed down to a fragment dimension of at least 1 μ by means of an electrical counting instrument, and checked by direct microscopic sizing to 5 μ. The results yield numerical values of internal flaw densities, and thus provide a tool to study the distribution of Griffith flaws existing internally in a solid.

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