Spiral cracks without twisting

A fascinating class of patterns, often encountered in nature as wiggling cracks on rocks, dried out fields and tectonic plates, is produced by the fracture of solids 1. Here we report the observation and modeling of an unusual type of patterns consisting of spiral cracks within fragments of a thin layer of drying precipitate. We find that this symmetry-breaking cracking mode arises naturally not from twisting forces, but from a propagating stress front induced by the fold-up of the fragments. Many recent studies have analysed the morphology of fractured surfaces and lines 2-6 , which typically show a cellular and hierarchical pattern. When twisting forces are applied, spiral-like of fracture is naturally expected. An example is the helical fracture of the tibia suffered in ski accidents 7. However, spiral cracks are not restricted to those situations, as we illustrate with a very simple experiment of the drying of a fine aqueous suspension of precipitate. As generally expected, during drying the suspension solidifies and later fragments into isolated parts (Fig. 1a). Surprisingly, for very fine precipitates and solidified layer thickness between 0.2 to 0.5 mm, regular spiral as well as circular crack paths show up inside the fragments (Fig. 1b). Depending on the grain size, precipitate type and layer thickness, the size of the spirals vary widely from several hundred microns to a few mm. With naked eye they might look as small dots, but their full beauty is revealed under a microscope (Fig. 1c). The spiral cracks are not limited to one peculiar material, since we managed to produce them in three different precipitates: Ni 3 (PO 4) 2 , Fe 4 [Fe(CN) 6)] 3 and Fe(OH) 3. Careful in-situ observations suggested the following mechanism. The spirals and circle-shaped structures form only after the fragmentation process is over. Due to the humidity gradient across the thickness, the fragments gradually fold up and detach from the substrate, generating large tensile stresses in the radial direction, at and normal to the front of