Topology of desiccation crack patterns in clay and invariance of crack interface area with thickness

Combinatorial topology and geometry of fracture networks

A map is proposed from the space of planar surface fracture networks to a four-parameter mathematical space, summarizing the average topological connectivity and geometrical properties of a network idealized as a convex polygonal mesh. The four parameters are identified as the average number of nodes and edges, the angular defect with respect to regular polygons, and the isoperimetric ratio. The map serves as a low-dimensional signature of the fracture network and is visually presented as a pair of three-dimensional graphs. A systematic study is made of a wide collection of real crack networks for various materials, collected from different sources. To identify the characteristics of the real materials, several well-known mathematical models of convex polygonal networks are presented and worked out. These geometric models may correspond to different physical fracturing processes. The proposed map is shown to be discriminative, and the points corresponding to materials of similar properties are found to form closely spaced groups in the parameter space. Results for the real and simulated systems are compared in an attempt to identify crack networks of unknown materials.

Time Evolution and Spatial Hierarchy of Crack Patterns

Cracks generated due to desiccation of wet colloidal systems are ubiquitous, examples being nanomaterial films, painted walls, cemented floors, mud fields, river beds, and even giant rocks. In all such cases, crack patterns are often appreciably similar but for the length and time scales, which can be widely differing. In this work, we have examined the crack formation more closely to see if there exists some generality with regard to the length scale of parameters and the formation time. Specifically, using a commonly used colloidal dispersion and optimized conditions to form polygonal network patterns rather than isolated cracks (films of subcritical thickness), we have studied the time evolution of the pattern parameters, the area occupied by the cracks, their lengths, and the widths. As is well known, initially, a network of cracks forms, which we term as the primary generation, followed by interconnecting cracks inside the polygonal regions (secondary) and, later, cracks spreading in local regions (tertiary). We find that the area and the width increase nearly linearly with time with the change in the slope corresponding to the change in the generation. When normalized with respect to the final values, the trends obtained for different film thicknesses overlap, the only exception being the pattern containing unconnected cracks. Thus, the time evolution of cracks is shown to be predictable based on width filtering. Including the angle between cracks as further input into the recursive model, the possibility of identifying the hierarchy of crack segments is also shown. The approach may be useful in determining the age, authenticity, and details of old paintings, understanding the stress profile of geological rocks, and analyzing various natural and manmade hierarchical structures.

The Effects of Fiber Inclusion on the Evolution of Desiccation Cracking in Soil-Cement

Desiccation cracking frequently occurs in mud, clay, and pavement. Understanding the evolution of desiccation cracking may facilitate the development of techniques to mitigate cracking and even prevent it from developing altogether. In this study, experimental investigations were performed focusing on the effects of fibers on the evolution of desiccation cracking in soil-cement. Varied types of fibers (i.e., jute fiber and polyvinyl alcohol fiber (PVA)) and fiber contents (i.e., 0%, 0.25%, 0.5%, and 1%) were involved. The digital image correlation (DIC) method was employed to capture the evolution and propagation of cracks in the soil-cement specimens when subjected to desiccation. The results show that the presence of fibers imposes significant effects on the crack propagation pattern as well as the area and length of the cracks in the soil-cement during shrinkage. The addition of fibers, however, insignificantly affects the evaporation rate of the specimens. The crack area and crack length of the specimens decreased significantly when more fibers were included. There were no macroscopic cracks observed in the specimens where the fiber content was 1%. The DIC method effectively helped to determine the evolution of displacement and strain field on the specimens’ surface during the drying process. The DIC method is therefore useful for crack monitoring.

Cracking to curling transition in drying colloidal films

Drying-induced cracking is widely encountered in nature and is of fundamental interest in industrial applications. During desiccation, the evolution of water content is nonlinear. Considering the inhomogeneous procedure of desiccation, it is worth considering whether water content will affect the crack pattern formation. To address this concern, in this paper, we report an experimental investigation on the effect of water content on the failure mode in drying colloidal films. A distinct failure transition from random cracking to curling is found when the initial water content increases gradually. When the water content is below a critical value for given film thickness, random desiccation cracking driven by shrinkage is observed. Beyond this critical water content, the film curls with the advent of several main cracks. It is also found that the critical water content corresponding to the transition point depends on the film thickness. In order to qualitatively interpret the experimental observation, a theoretical model is established by adopting the fracture mechanics based on the energy method. The model is found to agree well with the experimental results, elucidating the effects of initial water content on the crack patterns and the transition of failure modes.

Formation of desiccation crack patterns in electric fields: a review

Desiccation crack formation is an important and interesting part of the broad area of fracture mechanics. Generation of cracks due to drying depends on ambient conditions, which may include externally applied fields. In this review, we discuss the effect of both direct and alternating electrical fields on desiccation crack formation. After a brief introduction to materials which crack on drying, e.g. colloids, clay and ceramics we discuss how they respond to an electric field. Following that, we present an account of experiments and modelling studies performed on granular pastes or clays drying while exposed to an electric field. Specific patterns formed under different geometries, strengths and frequencies of the electric field are described and explained. The review includes work on cracks formed in clay droplets, where a memory effect has been observed and analysed using a generalized calculus formalism.This article is part of the theme issue 'Statistical physics of fracture and earthquakes'.

Tailoring crack morphology in coffee-ring deposits via substrate heating

The drying of a sessile drop consisting of colloidal particles and the formation of particulate deposits with spatially periodic cracks were ubiquitous. The drying induced stress, which is generated during the evaporation of a colloidal drop, is released by the formation of cracks. We find that the morphology of cracks formed in particulate films dried at substrate temperature, T_sub = 25 °C is markedly different from that of cracks formed at T_sub > 45 °C. The cracks are disordered in the former case, but ordered and periodic in the latter. The disorderedness of cracks observed at T_sub = 25 °C is mainly due to the formation of a coffee-ring like particle deposit that exhibits a larger height gradient. The ultimate deposit pattern after complete drying is observed to be different for colloidal dispersion drops evaporated at different substrate temperatures. This is attributed to temperature-dependent solvent flow mechanisms and capillary-driven flow, which occur inside the colloidal drop during the course of drying. In addition, for the coffee-ring-like particulate deposit obtained at T_sub ≤ 45 °C, the ratio between the width of the deposit w and the radius of the ring R scales with the volume fraction of the colloids φ, w/R ∼ φ^0.5, in the range of volume fractions studied in this work. The deposited patterns obtained at temperature T_sub > 45 °C are largely dominated by the capture of particles by the receding liquid-vapor interface. This is due to the faster rate of decrease of the liquid-vapor interface position with an increase in substrate temperature.

Morphometric analysis of polygonal cracking patterns in desiccated starch slurries

We investigate the geometry of two-dimensional polygonal cracking that forms on the air-exposed surface of dried starch slurries. Two different kinds of starches, made from potato and corn, exhibited distinguished crack evolution, and there were contrasting effects of slurry thickness on the probability distribution of the polygonal cell area. The experimental findings are believed to result from the difference in the shape and size of starch grains, which strongly influence the capillary transport of water and tensile stress field that drives the polygonal cracking.