Scale-free bursting activity in shrinkage induced cracking.

Based on computer simulations of a realistic discrete element model we demonstrate that shrinkage induced cracking of thin layers of heterogeneous materials, generating spectacular crack patterns, proceeds in bursts. These crackling pulses are characterized by scale free distributions of size and duration, however, with non-universal exponents depending on the system size and shrinking rate. On the contrary, local avalanches composed of micro-cracking events with temporal and spatial correlation are found to obey a universal power law statistics. Most notably, we demonstrate that the observed non-universality of the integrated signal is the consequence of the temporal superposition of the underlying local avalanches, which pop up in an uncorrelated way in homogeneous systems. Our results provide an explanation of recent acoustic emission measurements on drying induced shrinkage cracking and may have relevance for the acoustic monitoring of the electro-mechanical degradation of battery electrodes.

X-ray computerized tomography observation of Lycopodium paste incorporating memory of shaking.

In a uniform layer consisting of a mixture of granular material and liquid, it is known that desiccation cracks exhibit various anisotropic patterns that depend on the nature of the shaking that the layer experienced before drying. The existence of this effect implies that information regarding the direction of shaking is retained as a kind of memory in the arrangements of granular particles. In this work we make measurements in paste composed of Lycopodium powder using microfocus x-ray computerized tomography (µCT) in order to investigate the three-dimensional arrangements of particles. We find shaking-induced anisotropic arrangements of neighboring particles and density fluctuations forming interstices mainly in the lower part of the layer. We compare the observed properties of these arrangements with numerical results obtained in the study of a model of non-Brownian particles under shear deformation. In the experimental system, we also observe crack tips in the µCT images and confirm that these cracks grow along interstices in the direction perpendicular to the initial shaking.

Evolution of anisotropic crack patterns in shrinking material layers.

Anisotropic crack patterns emerging in desiccating layers of pastes on a substrate can be exploited for controlled cracking with potential applications in microelectronic manufacturing. We investigate such possibilities of crack patterning in the framework of a discrete element model focusing on the temporal and spatial evolution of anisotropic crack patterns as a thin material layer gradually shrinks. In the model a homogeneous material is considered with an inherent structural disorder where anisotropy is captured by the directional dependence of the local cohesive strength. We demonstrate that there exists a threshold anisotropy below which crack initiation and propagation is determined by the disordered micro-structure, giving rise to cellular crack patterns. When the strength of anisotropy is sufficiently high, cracking is found to evolve through three distinct phases of aligned cracking which slices the sample, secondary cracking in the perpendicular direction, and finally binary fragmentation following the formation of a connected crack network. The anisotropic crack pattern results in fragments with a shape anisotropy which gradually gets reduced as binary fragmentation proceeds. The statistics of fragment masses exhibits a high degree of robustness described by a log-normal functional form at all anisotropies.

Mechanism of memory effect of paste which dominates desiccation crack patterns.

When a densely packed colloidal suspension, called a paste, behaves as plastic fluid, it can remember the direction of its motion it has experienced, such as vibrational motion and flow. These memories kept in paste can be visualized as the morphology of crack patterns that appear when the paste is dried. For example, when a paste remembers the direction of vibrational motion, all primary desiccation cracks propagate in the direction perpendicular to the direction of the vibrational motion that the paste has experienced. On the other hand, when a paste remembers the direction of flow motion, all primary cracks propagate along the flow direction. To find out the mechanism of memory effect of vibration, we perform experiments to rewrite memory in paste by applying additional vibration to the paste along a different direction before the paste is dried. By investigating the process of rewriting memory in paste, we find the competitive phenomena between quasi-linear effect and nonlinear effect, which were studied in each theoretical model based on residual tension theories. That is, at the initial stage of the memory-imprinting process of the vibrational motion, the mechanism predicted by the quasi-linear analysis based on residual tension theory holds, but, as the paste is vibrated repeatedly, the mechanism shown by the nonlinear analysis gradually come to play a dominant role in the memory effect.This article is part of the theme issue 'Statistical physics of fracture and earthquakes'.

Memory effect and anisotropy of particle arrangements in granular paste.

It is known that pastes of fine powder, for example those of clay, retain memory of shaking applied early in a drying process. This memory results in the appearance of anisotropic patterns of desiccation cracks after drying. In this work, we find a similar behavior in pastes consisting of large granular particles, specifically cornstarch and Lycopodium spores. Because of the large particle size, we were able to observe particle arrangements in Lycopodium paste with micro-focus X-ray computerized tomography ( µ CT). We prepared pastes consisting of Lycopodium particles and water. Agar was added to the paste in order to allow for solidification during a drying process. In these samples, we found statistical anisotropy induced by shaking applied early in the drying process. This anisotropy possesses a feature that was predicted on the basis of results obtained in previous experimental and theoretical studies.

Effect of disorder on shrinkage-induced fragmentation of a thin brittle layer.

We investigate the effect of the amount of disorder on the shrinkage-induced cracking of a thin brittle layer attached to a substrate. Based on a discrete element model we study how the dynamics of cracking and the size of fragments evolve when the amount of disorder is varied. In the model a thin layer is discretized on a random lattice of Voronoi polygons attached to a substrate. Two sources of disorder are considered: structural disorder captured by the local variation of the stiffness and strength disorder represented by the random strength of cohesive elements between polygons. Increasing the amount of strength disorder, our calculations reveal a transition from a cellular crack pattern, generated by the sequential branching and merging of cracks, to a disordered ensemble of cracks where the merging of randomly nucleated microcracks dominate. In the limit of low disorder, the statistics of fragment size is described by a log-normal distribution; however, in the limit of high disorder, a power-law distribution is obtained.

Cracking condition of cohesionless porous materials in drying processes.

The invasion of air into porous systems in drying processes is often localized in soft materials, such as colloidal suspensions and granular pastes, and it typically develops in the form of cracks before ordinary drying begins. To investigate such processes, we construct an invasion percolation model on a deformable lattice for cohesionless elastic systems, and with this model we derive the condition under which cracking occurs. A Griffith-like condition characterized by a dimensionless parameter is proposed, and its validity is checked numerically. This condition indicates that the ease with which cracking occurs increases as the particles composing the material become smaller, as the rigidity of the system increases and as the degree of heterogeneity characterizing the drying processes decreases.

Bioconvection and front formation of Paramecium tetraurelia.

We have investigated the bioconvection of Paramecium tetraurelia in high-density suspensions made by centrifugal concentration. When a suspension is kept at rest in a Hele-Shaw cell, a crowded front of paramecia is formed in the vicinity of the bottom and it propagates gradually toward the water-air interface. Fluid convection occurs under this front, and it is driven persistently by the upward swimming of paramecia. The roll structures of the bioconvection become turbulent with an increase in the depth of the suspension; they also change rapidly as the density of paramecia increases. Our experimental results suggest that lack of oxygen in the suspension causes the active individual motions of paramecia to induce the formation of this front.

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

The formation of three-dimensional prismatic cracks in the drying process of starch-water mixtures is investigated numerically. We assume that the mixture is an elastic porous medium which possesses a stress field and a water content field. The evolution of both fields is represented by a spring network and a phenomenological model with the water potential, respectively. We find that the water content distribution has a propagating front which is not explained by a simple diffusion process. The prismatic structure of cracks driven by the water content field is observed. The depth dependence and the coarsening process of the columnar structure are also studied. The particle diameter dependence of the scale of the columns and the effect of the crack networks on the dynamics of the water content field are also discussed.

Directional crack propagation of granular water systems.

Pattern dynamics of directional crack propagation phenomena observed in drying process of starch-water mixture is investigated. To visualize the three-dimensional structure of the drying-fracture process two kinds of experiments are performed, i.e., resin solidification planing method and real-time measurement of water content distribution with MR instruments. A cross section with polygonal structure is visualized in both experiments. The depth dependency of cell size is measured. The phenomenological model for water transportation is also discussed.