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

Abstract

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.

Morphometric analysis of polygonal cracking patterns in desiccated starch slurries

“…Below the stress-concentrated intermediate zone having a finite thickness, the interior of the slurry is more moist, so it can be considered as a different medium trying to hold the upper dried layer together and providing adhesion. Under this condition, the intercrack spacing on the two dried surfaces should be proportional to the thickness of the layer under tensile stress 46,47 , as a direct consequence of the theory of fracture mechanics; the validity of the proportionality relation has been experimentally confirmed for many kinds of desiccated slurries 7,13,14,16 . Eventually, the vertical limits of the stress-concentrated region determine the horizontal spacing between adjacent secondary cracks, or equivalently, they determine the area of the polygonal cells surrounded by secondary cracks Our experimental results indicate that for the potato starch, the vertical limits of the stress-concentrated region, which is denoted by L φ , is comparable to or exceeds 11 mm, which is the maximum of the slurry thickness that we used in the experiments.…”

“…Examples include those that develop in dried mud [1][2][3] , old paintings 4,5 , ceramic glaze 6,7 , and so on. These cracks usually exhibit a specific network structure, splitting the entire surface of the fractured media into many polygonal cells.…”

Evolution of mud-crack patterns during repeated drying cycles

“…1(a,b). This behavior has been reported in many materials, including clay, 1,2 colloidal alumina, 3 corn starch, [4][5][6] and coffee grounds.…”

Tearing of thin sheets: Cracks interacting through an elastic ridge

“…They are observed during the desiccation of films made of colloidal suspensions, like bentonite clay or cornstarch [5][6][7][8][9][10][11], in sol-gel films [12,13], in broken objects like windows [14][15][16], or in sea ice [17,18] and ice floes collisions [19,20].…”