Desiccation cracks on different substrates: simulation by a spring network model

Abstract

Crack patterns formed due to desiccation of clay or similar materials showdistinctive reproducible patterns. If one measures the cumulative areaAcum covered by thecracks with widths ≥Wmin, then Acum plottedagainst Wmin shows a typical reproducible shape. In a log–log plot, this curve has two roughly linearregions with different slopes. For a polypropylene (PP) substrate, there is a sharp changefrom a nearly horizontal line to a very steep line, whereas for a glass substrate,which is smoother, there is a gradual changeover between the two regions. Wepropose a simple one-dimensional spring chain model, in which reducing the naturallength of the springs corresponds to the desiccation process. Springs may break, orslip against the substrate to accommodate strain beyond a specified threshold.The model successfully reproduces the successive stages of crack formation andbehaviour of the cumulative area curve, as observed in experiments. The difference inthe qualitative nature of the patterns on smooth and rougher substrates is alsoobtained.