Cascadating fracture in a laminated tempered safety glass panel

Abstract

The macrofracture pattern of a laminated, tempered safety plate glass panel in which failure was initiated by a sharp object was statistically analyzed. The crack density decreased linearly with distance from the fracture origin as did the average distance between successive crack branching events. The average bifurcation half angle, however, remained at about 21°, independent of distance from the fracture origin. This half angle is very similar to that reported for the branching of an individual primary crack in a fracture mechanics specimen. The two branching half-angles are negatively correlated, approaching a maximum of 45° in the extreme.

The curvatures of the new crack paths after bifurcation were also observed to be independent of the distance from the fracture origin and followed the general expression where the coefficient α is a random variable and β is a constant equal to 0.035. It was possible to describe the repetitive crack branching through the concept of a fractal tree with a fractal dimension of 2.58, a value similar to some geological processes. Applying the fractal tree concept, the multiple cascadation phenomenon was reproduced for the range of fractal dusts of z ≤ 4, beyond which degeneration related to excessive selfoverlapping occurred.

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