Crack patterns on uneven substrates

Abstract

Cracks patterns are influenced by the substrates beneath them. From buried craters to crocodile skin, crack patterns are found over an enormous range of length scales. Regardless of their scale, substrates can impart geometry and symmetry to a crack pattern. There are two central problems discussed in this thesis -how does an uneven substrate affect a crack pattern? how can crack patterns be quantified? To answer these questions, crack patterns are generated by drying mud slurries over sinusoidal and radially sinusoidal substrates. It is observed that as the thickness of the cracking layer increases, the crack patterns transition from wavy to ladder-like to isotropic. Four main measures of the crack pattern are introduced to quantify the observations -one parameter which measures the relative alignment of these crack networks, one parameter that measures the orientation of cracked regions, one parameter which measures uses the Manhattan metric to compare crack patterns and Fourier methods which are used to characterise the transitions between crack pattern types. These results are explained these results with a model, based on the Griffith criteria of fracture. This model suggests that there is a transition region between wavy to ladder-like cracks. The metrics developed here and results can be adapted to any connected networks of cracks.