Hierarchical crack pattern as formed by successive domain divisions. II. From disordered to deterministic behavior.

Hierarchical crack patterns, such as those formed in the glaze of ceramics or in desiccated layers of mud or gel, can be understood as a successive division of two-dimensional domains. We present an experimental study of the division of a single rectangular domain in drying starch and show that the dividing fracture essentially depends on the domain size, rescaled by the thickness of the cracking layer e. Utilizing basic assumptions regarding the conditions of crack nucleation, we show that the experimental results can be directly inferred from the equations of linear elasticity. Finally, we discuss the impact of these results on hierarchical crack patterns, and in particular the existence of a transition from disordered cracks at large scales--the first ones--to a deterministic behavior at small scales--the last cracks.