Numerical study of oscillatory crack propagation through a two-dimensional crystal

Assisting and eliminating memory effects of paste by adding polysaccharides

A densely packed colloidal suspension, called a paste, is known to remember the direction of its motion because of its plasticity. Because the memory in the paste determines the preferential direction for crack propagation, the desiccation crack pattern morphology depends on memory of its motions (memory effect of paste). Two types of memory effects are memory of vibration and memory of flow. When a paste is dried, it usually shows an "isotropic and random cellular" desiccation crack pattern. However, when a paste is vibrated before drying and it remembers the direction of its vibrational motion, primary desiccation cracks propagate in a direction perpendicular to its vibrational motion before drying (memory of vibration). Once it flows and remembers the direction of its flow motion, primary desiccation cracks propagate in the direction parallel to its flow motion (memory of flow). Anisotropic network formation via interparticle attraction among colloidal particles in a suspension is the dominant factor affecting a paste's memory of its motion. Calcium carbonate (CaCO_{3}) paste remembers the direction of its vibrational motion, but not its own flow direction because Coulombic repulsion among charged CaCO_{3} colloidal particles prevents the formation of a network structure in a flow. For this study, we strove to assist and eliminate CaCO_{3} paste memory effects by adding polysaccharides. First, to characterize memory in paste, we propose a method of image analysis to quantify the strength and the direction of the anisotropy of desiccation crack patterns using Shannon's information entropy. Next, we conduct experiments to add polysaccharide to CaCO_{3} paste, revealing that the addition of a small amount of polysaccharide to CaCO_{3} paste assists the paste in remembering its own flow motion. Findings also indicate that the addition of a large amount of polysaccharide prevents the formation of both memories of its flow and vibrational motion and eliminates the memory effects of paste. We then perform "flocculation and sedimentation" experiments to investigate the interaction among CaCO_{3} colloidal particles in a solution. Results show that, in an aqueous solution with low polysaccharide concentration, CaCO_{3} colloidal particles flocculate each other and quickly form a sediment in a short time, whereas, in an aqueous solution with high polysaccharide concentration, a longer time is necessary for flocculation and sedimentation. Because the addition of small amounts of polysaccharides to CaCO_{3} paste induces polymer bridging between colloidal particles as interparticle attraction, it helps to produce a macroscopic network structure which retains memory of its flow motion and thereby assists the formation of memory of flow, whereas the addition of large amounts of polysaccharides induces interparticle repulsion, which prevents the formation of memory effects of all types.

Recent progress in controlled nano/micro cracking as an alternative nano-patterning method for functional applications

Generally, cracking occurs for many reasons connected to uncertainties and to the non-uniformity resulting from intrinsic deficiencies in materials or the non-linearity of applied external (thermal, mechanical, etc.) stresses. However, recently, an increased level of effort has gone into analyzing the phenomenon of cracking and also into methods for controlling it. Sophisticated manipulation of cracking has yielded various cutting-edge technologies such as transparent conductors, mechanical sensors, microfluidics, and energy devices. In this paper, we present some of the recent progress that has been made in controlling cracking by giving an overview of the fabrication methods and working mechanisms used for various mediums. In addition, we discuss recent progress in the various applications of methods that use controlled cracking as an alternative to patterning tools.

Position control of desiccation cracks by memory effect and Faraday waves

Pattern formation of desiccation cracks on a layer of a calcium carbonate paste is studied experimentally. This paste is known to exhibit a memory effect, which means that a short-time application of horizontal vibration to the fresh paste predetermines the direction of the cracks that are formed after the paste is dried. While the position of the cracks (as opposed to their direction) is still stochastic in the case of horizontal vibration, the present work reports that their positioning is also controllable, at least to some extent, by applying vertical vibration to the paste and imprinting the pattern of Faraday waves, thus breaking the translational symmetry of the system. The experiments show that the cracks tend to appear in the node zones of the Faraday waves: in the case of stripe-patterned Faraday waves, the cracks are formed twice more frequently in the node zones than in the anti-node zones, presumably due to the localized horizontal motion. As a result of this preference of the cracks to the node zones, the memory of the square lattice pattern of Faraday waves makes the cracks run in the oblique direction differing by 45 degrees from the intuitive lattice direction of the Faraday waves.

Global bifurcation criterion for oscillatory crack path instability

A bifurcation criterion for the transition from straight to oscillatory quasistatic crack propagation in an isotropic material is derived from the requirement of pure mode I stress fields at the crack tip (K_{II}=0) on the entire crack path, henceforth called global bifurcation criterion. For a small-amplitude sine-shaped crack path which is observed in experiments at the transition, it is shown to be sufficient to postulate K_{II}=0 only for two phases of the crack path instead, which simplifies calculations. By using the measured temperature fields to solve the thermoelastic problem of dipping a hot thin glass slab into cold water, critical wavelengths of the oscillating crack growth obtained with the derived global bifurcation criterion agree remarkably well with those observed in experiments by Ronsin and Perrin. It is also shown that local bifurcation criteria, which do not take into account K_{II}=0 on the entire crack path, lead to incorrect results for the oscillatory crack path instability.

Transition in the pattern of cracks resulting from memory effects in paste

Experiments involving vibrating pastes before drying were performed for the purposes of controlling the crack patterns that appear in the drying process. These experiments revealed a transition in the direction of lamellar cracks from perpendicular to parallel when compared with the direction of the initial external vibration as the solid volume fraction of the paste is decreased. This result suggests a transition in the memory in paste, which is visually represented as morphological changes in the crack pattern. Given that the memory in paste represents the flow pattern induced by the initial external vibration, it should then be possible to control and design various crack patterns, such as cellular, lamellar, radial, ring, spiral, and others.

Development and geometry of isotropic and directional shrinkage-crack patterns

We have studied shrinkage-crack patterns which form when a thin layer of an alumina/water slurry dries. Both isotropic and directional drying were studied. The dynamics of the pattern formation process and the geometric properties of the isotropic crack patterns are similar to what is expected from recent models, assuming weak disorder. There is some evidence of a gradual increase in disorder as the drying layer become thinner, but no sudden transition, in contrast to what has been seen in previous experiments. The morphology of the crack patterns is influenced by drying gradients and front propagation effects, with sharp gradients having a strong orienting and ordering effect.

Fracture patterns induced by desiccation in a thin layer

We study a theoretical model of mud cracks, that is, the fracture patterns resulting from the contraction with drying in a thin layer of a mixture of granules and water. In this model, we consider the slip on the bottom of this layer and the relaxation of the elastic field that represents deformation of the layer. Analysis of the one-dimensional model gives results for the crack size that are consistent with experiments. We propose an analytical method of estimation for the growth velocity of a simple straight crack to explain the very slow propagation observed in actual experiments. Numerical simulations reveal the dependence of qualitative nature of the formation of crack patterns on material properties.