Dynamic fragmentation of ice spheres: Two specific fracture patterns

Abstract

Although ice materials are commonly found not only in our daily life on the earth but also in space, e.g. in the rings of Saturn, their fracture mechanisms, especially those in a dynamic range, have not been fully clarified. In our previous investigation, therefore, collision of a brittle ice sphere (diameter 25, 50 or 60 mm) that is free falling against a fixed plate of ice or polycarbonate has been experimentally observed using high-speed digital video cameras at a frame rate of up to 150,000 frames per second. It has been recognized that there exist basically only two specific fracture patterns generated by this dynamic impact: (i) “Top”-type fracture, normally at a relatively smaller impact speed, where only the bottom surface areas of a sphere are fragmented into small pieces by the impact at bottom and a relatively large top-shaped portion is left unbroken; and (ii) “orange segments”-type in which rather flat fracture planes extend approximately along the central axis of the sphere and split the sphere into three or four larger segments of comparable size. Preliminary comparison of the experimental findings with linear elastic wave fields obtained numerically by three-dimensional finite difference calculations suggests two distinct spatiotemporal scales: (1) The “top” fracture pattern is induced by the propagation of surface waves with relatively shorter wavelengths from the bottom along the free surface of the sphere, quickly producing fracture only near the bottom; (2) In the “orange segments”-type fracture, a longer contact time makes largely stressed regions enlarge more slowly and widely (quasi-statically-like) and larger fracture planes develop along the axis of the sphere. The above speculations seem to be supported by recent computations adopting the Discontinuous Galerkin (DG) method that treat more rigorously the mechanics of dynamic contact between the sphere and plate.