The development of polygonal fractures due to contraction: A disorder to order transition

The formation of three-dimensional polygonal fractures in two-layered materials during surface cooling is numerically investigated to study the disorder to order transition mechanism of such fractures. The heterogeneity of the breakdown threshold in a brittle solid is modeled using a probability distribution at the mesoscopic level, and the cracking behavior of meso-elements is modeled using continuum damage mechanics. A finite element method (FEM) is used to obtain the thermal stress distribution. Then, the damage threshold is determined based on the maximum tensile stress criterion. The polygonal fracture behavior, including the initiation and propagation of microcracks and the formation of approximately equal-area surface cracks, are captured well by the numerical results. The impact of thermal conductivity on cracking patterns is discussed. The quantitative results indicate that the polygon sizes and fracture spacing are independent of the material heterogeneity while the thermal conductivity significantly affects the failure patterns of layered materials subjected to thermal shrinkage. Furthermore, the effect of the bond strength between the overlay and substrate is studied. For a high bond strength, the cracks initiate in the overlay and propagate into the interface. However, for a low bond strength, debonding is observed. The modeling results shows that heterogeneity of the brittle solid is the main reason for disordered initiation of cracks and that local energy minimization at a location and time is the key factor affecting polygonal fracture failure patterns.