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

Crack patterns formed due to desiccation of clay or similar materials show distinctive reproducible patterns. If one measures the cumulative area Acum covered by the cracks with widths > =Wmin, then Acum plotted against Wmin shows a typical reproducible shape. In a log-log plot, this curve has two roughly linear regions with different slopes. For a polypropylene (PP) substrate, there is a sharp change from 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. We propose a simple one-dimensional spring chain model, in which reducing the natural length of the springs corresponds to the desiccation process. Springs may break, or slip against the substrate to accommodate strain beyond a specified threshold. The model successfully reproduces the successive stages of crack formation and behaviour of the cumulative area curve, as observed in experiments. The difference in the qualitative nature of the patterns on smooth and rougher substrates is also obtained.