Flaw length distribution measurement in brittle materials

A technique was developed in an experiment of fractured soda-lime glass which yielded a wide mist zone. This technique enabled us to measure the lengths of a large number (≈ 12 000) of secondary cracks (SC) in this zone. Statistical analysis of these lengths across the mist as a function of distance from fracture origin revealed some unexpected results. (a) The total number of SC remains constant for ≈ 40% of the width of the mist zone and subsequently decreases monotonically down to ≈ 50% of the initial number towards the end of this zone. (b) The length distribution of SC can be interpreted as constituting of two populations: (1) A nucleated SC population which remains unchanged across the whole mist. This distribution consists of two subpopulations: (i) half Gaussian (around 84%), and (ii) decaying exponential (around 16%). (2) A rather small portion of the nucleated population of SC (≈ 9% throughout) which grow monotonically by a factor of up to 40 with distance across the mist. (c) This factor agrees well with our theoretical calculation of the growth mode, and yields a reasonable estimate of the radius of the initial critical flaw (1.85 mm).