Spacing of crack patterns driven by steady-state cooling or drying and influenced by a solidification boundary

Evolution of Tiling-like Crack Patterns in Maturing Columnar Joints

Fracture or cracking essentially involves the formation of new interfaces. These patterns are usually studied as two-dimensional mosaics. The new surface that opens up is in the third dimension, along the thickness of the sample. The thickness is usually very small compared to the lateral dimensions of the pattern. A spectacular and distinctive departure from these everyday examples of cracks are columnar joints. Here, molten volcanic lava, by the sea, cools and cracks under appropriate thermal and elastic conditions, causing the crack system to grow downward, creating long, vertical columns with polygonal cross-section. The focus of this paper is the study of the elongated interfaces of these columns: how the cross-section of their outlines gradually undergoes a metamorphosis from a disordered-looking Gilbert tessellation to a well-ordered hexagonal Voronoi pattern. As the columns grow downward to lengths of several meters (in natural systems), their outline continuously changes, the center may shift, causing the column to twist. For the first time, the evolution of these crack mosaics has been simulated and mapped as a trajectory of a 4-vector tuple in a geometry-topology domain. The trajectory of the columnar joint systems is found to depend on the crack seed distribution and crack orientation. An empirical relationship between the system energy and the crack mosaic shape parameter λ has been proposed on the basis of principles of fracture mechanics. The total system energy shows a power-law dependence on λ with the exponent β ∼ 0.3 and λ ≈ 0.75 at crack maturation. The parameter values are validated by matching the proposed relation with energy estimates existing in the literature. The relation not only matches the visible changes in geometry but also provides a feasible measure of the energy of the system. The geometric energy for the polygonal mosaics in the transverse section has also been estimated as a function of time. The geometric energy moves toward a minimum as the mosaic becomes more Voronoi-like at maturation.

Universal fluctuation of polygonal crack geometry in solidified lava

Outcrops of columnar joints made of solidified lava flows are often covered by semiordered polygonal cracks. The polygon diameters are fairly uniform at each outcrop, but their shapes largely vary in the number of sides and internal angles. Herein, we unveil that the statistical variation in the polygon shape follows an extreme value distribution class: the Gumbel distribution. The Gumbel law was found to hold for different columnar joints, regardless of the locality, lithologic composition, and typical diameter. A common distribution for columnar joints implies a universal class that may integrate the polygonal crack networks observed on the surface of various fractured brittle materials.

Drying colloidal systems: Laboratory models for a wide range of applications

The drying of complex fluids provides a powerful insight into phenomena that take place on time and length scales not normally accessible. An important feature of complex fluids, colloidal dispersions and polymer solutions is their high sensitivity to weak external actions. Thus, the drying of complex fluids involves a large number of physical and chemical processes. The scope of this review is the capacity to tune such systems to reproduce and explore specific properties in a physics laboratory. A wide variety of systems are presented, ranging from functional coatings, food science, cosmetology, medical diagnostics and forensics to geophysics and art.

Why Hexagonal Basalt Columns?

Basalt columns with their preferably hexagonal cross sections are a fascinating example of pattern formation by crack propagation. Junctions of three propagating crack faces rearrange such that the initial right angles between them tend to approach 120°, which enables the cracks to form a pattern of regular hexagons. To promote understanding of the path on which the ideal configuration can be reached, two periodically repeatable models are presented here involving linear elastic fracture mechanics and applying the principle of maximum energy release rate. They describe the evolution of the crack pattern as a transition from rectangular start configuration to the hexagonal pattern. This is done analytically and by means of three-dimensional finite element simulation. The latter technique reproduces the curved crack path involved in this transition.

Self-similarity and scaling of thermal shock fractures

The problem of crack pattern formation due to thermal shock loading at the surface of half space is solved numerically using the two-dimensional boundary element method. The results of numerical simulations with 100-200 random simultaneously growing and interacting cracks are used to obtain scaling relations for crack length and spacing. The numerical results predict that such a process of pattern formation with quasistatic crack growth is not stable and at some point the excess energy leads to unstable propagation of one of the longest cracks. This single-crack scenario should be understood in a local sense. There could be other unstable cracks far away that together can form a new pattern. The onset of instability has also been determined from numerical results.