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� � � ����� � �� � � � ��� � � ��� �
Crack Growth and Pattern Formation
Induced by Desiccation in Paste
��� �So Kitsunezaki∗
���The method of using a spring network model with a breaking threshold is suc-
cessful for the pattern formation of cracks in the drying process, in which paste isassumed as an elastic material. However recent researches reveal that the porousand rheological properties of paste influence the fracture process. After reviewingthe formation of a crack pattern both in a thin layer of uniformly dried paste and ina directionally dried system, we describe the memory effect found by Nakahara andthe drying-rate dependence of crack growth, which are distinctive features differentfrom those in normal solids.
Key Words: Mud crack pattern, Drying fracture, Paste rheology, Wet granular
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Fig. 1: Typical mud crack patternin a thin layer of calcium carbonate(CaCO3) paste. The thickness wasabout 4 mm after drying. The width ofthis photograph corresponds to 10 cm.
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Fig. 2: 1-dimensional springnetwork model.
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Fig. 3: Schematicpicture of the di-vision process of athin layer of paste.
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Fig. 4: The shrinking rate at the first break-ing is plotted for the system size.3) Arrows in-dicate the change of the system size in a divi-sion process as in Fig. 3. • and ◦ are the break-ing points for the fixed bottom and a slipperybottom, respectively.
Fig. 5: Schematic picture of a 2-d springnetwork model. The 2-d elastic layer is dis-cretized to a random lattice composed of tri-angular tiles, which are removed if their elas-tic energy exceeds a breaking threshold. Weintroduced the viscous relaxation equivalentto adopting Voigt elements (springs and dash-pots), as shown in the bottom of the figure.
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Fig. 6: Crack pattern obtained froma numerical simulation.3) Broken tilesare indicated with black color, and slipoccurs in the dotted region of each cell.
Fig. 7: Columnar structure of cracksdeveloped in cornstarch paste. Thissample was dried from the top surfacein a cylindrical container, and then bro-ken by hand in the middle of drying.
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Fig. 8: Typical crack pattern obtainedfrom a numerical simulation by Nishimotousing a spring network model with non-linear water transportation.11) A columnarstructure of cracks develops with dryingfrom the front surface.
Fig. 9: Nakahara effect for a thin layerof CaCO3 paste. Before drying, thesample was shaken for about 2 min at140 rpm in the direction indicated bythe arrow. The size and the drying con-dition were approximately the same asthose in Fig. 1.
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Fig. 10: Measure-ment of stress.
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(1/min)
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Fig. 11: Stresses arising in alayer of paste for two drying con-ditions are plotted with respectto (a) time and (b) the volumefraction of water.16) Cracks firstappear near the peak of stress.
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)
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nent
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Fig. 12: Dependence of crack speed onthe drying rate. A thin layer of CaCO3paste was dried at 40 ± 1◦C for variousdrying conditions.16)
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