Numerical study of drying process and columnar fracture process in granule-water mixtures

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.

Elastic plastic fracture mechanics investigation of toughness of wet colloidal particulate materials: Influence of saturation

HYPOTHESIS

Previous use of linear elastic fracture mechanics to estimate toughness of wet particulate materials underestimates the toughness because it does not account for plastic deformation as a dissipation mechanism. Plastic deformation is responsible for the majority of energy dissipated during the fracture of wet colloidal particulate materials. Plastic deformation around the crack tip increases with saturation of the particulate body. The toughness of the body increases with increasing saturation.

EXPERIMENTS

Elastic plastic fracture mechanics using the J-integral approach was used for the first time to measure the fracture toughness (J_IC) of wet micron sized alumina powder bodies as a function of saturation. The samples were prepared by slip casting. The saturation was controlled by treatment in a humidity chamber. The elastic modulus (E) and the energy dissipated by plastic flow (A_pl) were measured in uniaxial compression. The critical stress intensity factor (K_IC) was measured using a diametral compression sample with a flaw of known size. The fracture toughness (J_IC) was calculated from these measured quantities and the geometry of the specimen.

FINDINGS

Elastic plastic fracture mechanics was used for the first time to quantitively account for plastic deformation of wet particulate materials. The linear elastic fracture mechanics approach previously used accounted for less than 1% of the total energy dissipated in fracture. Toughness (J_IC) was found to increase with increasing saturation due to plastic deformation that increased with saturation level. The improved understanding of toughness as a function of saturation will aid in providing quantitative analysis of cracking in drying colloidal films and bodies.

Locally-curved geometry generates bending cracks in the African elephant skin

An intricate network of crevices adorns the skin surface of the African bush elephant, Loxodonta africana. These micrometre-wide channels enhance the effectiveness of thermal regulation (by water retention) as well as protection against parasites and intense solar radiation (by mud adherence). While the adaptive value of these structures is well established, their morphological characterisation and generative mechanism are unknown. Using microscopy, computed tomography and a custom physics-based lattice model, we show that African elephant skin channels are fractures of the animal brittle and desquamation-deficient skin outermost layer. We suggest that the progressive thickening of the hyperkeratinised stratum corneum causes its fracture due to local bending mechanical stress in the troughs of a lattice of skin millimetric elevations. The African elephant skin channels are therefore generated by thickening of a brittle material on a locally-curved substrate rather than by a canonical tensile cracking process caused by frustrated shrinkage.

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.

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.

Evolving fracture patterns: columnar joints, mud cracks and polygonal terrain

When cracks form in a thin contracting layer, they sequentially break the layer into smaller and smaller pieces. A rectilinear crack pattern encodes information about the order of crack formation, as later cracks tend to intersect with earlier cracks at right angles. In a hexagonal pattern, in contrast, the angles between all cracks at a vertex are near 120°. Hexagonal crack patterns are typically seen when a crack network opens and heals repeatedly, in a thin layer, or advances by many intermittent steps into a thick layer. Here, it is shown how both types of pattern can arise from identical forces, and how a rectilinear crack pattern can evolve towards a hexagonal one. Such an evolution is expected when cracks undergo many opening cycles, where the cracks in any cycle are guided by the positions of cracks in the previous cycle but when they can slightly vary their position and order of opening. The general features of this evolution are outlined and compared with a review of the specific patterns of contraction cracks in dried mud, polygonal terrain, columnar joints and eroding gypsum-sand cements.

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

Regular columnar joints that originate from networklike crack patterns can be observed in basalt and, on a much smaller scale, in dried starch slurry. Here, the basalt columns are idealized by a periodic array of parallel cracks driven by steady-state cooling. By means of a bifurcation analysis, the minimal possible crack spacing for sustained propagation of the crack array is calculated. It can be shown qualitatively that the minimal possible crack spacing for sustained propagation increases with decreasing velocity. This is confirmed by numerical calculations. The latent heat released at the solidification front is taken into account in the thermomechanical linear-elastic model of propagating shrinkage. Our calculations show that the solidification front is positioned not far ahead of the crack tips, which influences the result considerably. The results agree reasonably well with new measured data of basalt columns. By use of the analogy between contraction due to cooling and that due to drying the model is applied for columns in dried cornstarch, too, showing good agreement with recent experimental data.

Drying and cracking mechanisms in a starch slurry

Starch-water slurries are commonly used to study fracture dynamics. Drying starch cakes benefit from being simple, economical, and reproducible systems, and have been used to model desiccation fracture in soils, thin-film fracture in paint, and columnar joints in lava. In this paper, the physical properties of starch-water mixtures are studied, and used to interpret and develop a multiphase transport model of drying. Starch cakes are observed to have a nonlinear elastic modulus, and a desiccation strain that is comparable to that generated by their maximum achievable capillary pressure. It is shown that a large material porosity is divided between pore spaces between starch grains, and pores within starch grains. This division of pore space leads to two distinct drying regimes, controlled by liquid and vapor transport of water, respectively. The relatively unique ability for drying starch to generate columnar fracture patterns is shown to be linked to the unusually strong separation of these two transport mechanisms.

Diameter of basalt columns derived from fracture mechanics bifurcation analysis

The diameter of columnar joints forming in cooling basalt and drying starch increases with decreasing growth rate. This observation can be reproduced with a linear-elastic three-dimensional fracture mechanics bifurcation analysis, which has been done for a periodic array of hexagonal columnar joints by considering a bifurcation mode compatible with observations on drying starch. In order to be applicable to basalt columns, the analysis has been carried out with simplified stationary temperature fields. The critical diameter differs from the one derived with a two-dimensional model by a mere factor of 1/2. By taking into account the latent heat released at the solidification front, the results agree fairly well with observed column diameters.