Formation Of Crack Patterns Research Articles

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.

Mechanisms of Anisotropy in Salt Rock Upon Microcrack Propagation

Salt rock is a polycrystalline material of interest for geostorage because of its low permeability and potential to self-heal by pressure solution at favorable stress and temperature conditions. It is often assumed that microcrack propagation and healing lead to isotropic stiffness changes. The goal of this study is to check this assumption and to gain a fundamental understanding of the mechanisms that control the accumulation of damage and irreversible deformation. Cyclic axial loading tests are performed under a confining pressure of 1 MPa on synthetic salt rock generated by thermal consolidation. The stress–strain curves and the microstructure images taken at key stages of the cycles reveal the formation of a complex system of sliding and wing microcracks, the orientation of which is loading dependent. We interpret the mechanisms that control the coupled evolution of crack families by a discrete wing crack elastoplastic damage (DWCPD) model. Crack propagation is controlled by Mode I and Mode II fracture mechanics criteria. Sliding “main” cracks grow if a cohesive frictional criterion is met, while the wing cracks propagate in tension. Displacement jumps at crack faces are related to the deformation of the rock representative elementary volume (REV). The DWCPD model can capture the nonlinear stress–strain relationship and the degradation of stiffness during the loading cycles. Simulations show that microcracks occur following two stages: (1) wing cracks initiate and main cracks do not propagate; (2) wing cracks and main cracks then propagate simultaneously. Higher friction at the crack faces leads to higher strength. With a larger cohesion, salt rock strength increases, damage development is delayed and exhibits a stick-slip evolution. At higher confinement, the initiation of wing cracks is delayed, which results in an increase of strength. The damage rate is higher in specimens that are damaged prior to compression than in the ones that are not. The proposed DWCPD model can be extended to any polycrystalline semi-brittle material, and can be applied to understand the formation of crack patterns in geostorage facilities.

Hierarchical crack patterns of metal films sputter deposited on soft elastic substrates.

Controlled cracks are useful in a wide range of applications, including stretchable electronics, microfluidics, sensors, templates, biomimics, and surface engineering. Here we report on the spontaneous formation of hierarchical crack patterns in metal (nickel) films sputter deposited on soft elastic polydimethylsiloxane (PDMS) substrates. The experiment shows that the nickel film generates a high tensile stress during deposition, which is relieved by the formation of disordered crack networks (called primary cracks). Due to the strong interfacial adhesion and soft substrate, the cracks can penetrate into the PDMS substrate deeply. The width and depth of the primary cracks both increase with increasing film thickness, whereas the crack spacing is insensitive to the film thickness. The film pieces dividing by the primary cracks can fracture further when they are triggered by an external disturbance due to the residual tensile stress, resulting in the formation of fine crack networks (called secondary cracks). The width and spacing of the secondary cracks show different behaviors in comparison to the primary cracks. The morphological characteristics, growth behaviors, and formation mechanisms of the primary and secondary cracking modes have been discussed in detail. The report in this work could provide better understanding of two distinct cracking modes with different sizes and morphologies.

Application of electrical resistivity method in the characterization of 2D desiccation cracking process of clayey soil

Electrical resistivity method (ERM) is an attractive approach in the assessment of soil physical properties (water content, void ratio, density, etc.), which are closely related to electrical resistivity distribution. ERM performance in the detecting and mapping of cracks initiation, propagation, and coalescence processes in the 2D/3D scale needs to be studied to provide the technical support for its field application. An evaporation test of a clayey soil specimen with an integrated experimental configuration is performed to analyze the performance of ERM in the characterization of the 2D desiccation cracking process. The evolutions of ambient temperature, relative humidity, average water content, crack morphology, and apparent electrical resistivity of the studied sample are well captured during continuous drying. Image processing allows the quantitative geometrical description of the crack pattern formation. The consistency between the start-to-increase point of measured electrical resistivity, electrical resistivity anomalies, and the cracks propagations presents the good performance of ERM in crack characterization and reveals its potential to map the cracks before possible visualization. A better understanding of the fundamental mechanisms of desiccation cracking is also obtained based on the experiment results. This study provides an insight to apply ERM for engineering purposes involving crack monitoring and early crack detection.

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'.

Boundary Effects in the Desiccation of Soil Layers with Controlled Environmental Conditions

This article presents the results of an experimental research carried to investigate the mechanics of cracking of soil layers under drying conditions. The tests were conducted under controlled laboratory conditions and in an environmental chamber with circular and rectangular specimens to investigate the effect of the boundary conditions (size, shape, and aspect ratio of the specimens and containers) on the process of initiation and propagation of cracks and on the final crack pattern at the end of desiccation. The tests in the environmental chamber were conducted with imposed temperature and relative humidity and provided new insight into the mechanics of the formation of cracks in a drying soil, and they showed that cracks can initiate either at the top, bottom, or at both surfaces of the drying specimen. The results also reveal how the crack patterns are controlled by the existing mechanical and hydraulic boundary conditions. The cracks seem to form sequentially in patterns that can be explained by three key factors: stresses higher than the tensile strength, the direction of the generated stresses, and the stress redistribution in the vicinity or inside the newly formed domain. In order to substantiate the sequential nature of the crack pattern formation, experimental evidences showing the existence of a cracking sequence during the laboratory desiccation experiments are presented and analyzed.

Crack Patterns in Drying Laponite-NaCl Suspension: Role of the Substrate and a Static Electric Field.

We report the formation of crack patterns in drying films of Laponite-NaCl solution. Crack patterns that develop upon drying aqueous Laponite-NaCl solution change drastically as the amount of NaCl is varied in the solution. In this work, we have investigated the effect of NaCl on drying films of aqueous solution of Laponite under two conditions: (i) when the film is bounded by a wall, as in Petri dish experiments and (ii) when the film does not have any boundary, as in experiments with droplets. In order to obtain insights into the effect of the substrate, the experiments have been done with two different substrates of different hydrophobicities, polypropylene and glass. The formation of crack patterns has been explained on the basis of the wetting and spreading properties of the solution on these substrates and the effect of salt on colloidal aggregation. In this work, we have shown that the presence of salt in aqueous Laponite solution can induce crack patterns depending on the nature of the substrate. Another important aspect of this work is the role of NaCl in crack inhibition in desiccating films of aqueous Laponite, in the presence of static electric field. This effect can be utilized to suppress undesirable crack formation in many applications.

Mechanics of Periodic Film Cracking in Bilayer Structures Under Stretching

In a bilayer structure consisting of a stiff film bonded to a soft substrate, the stress in the film is much larger when the rigidity of the film is much higher than that of the substrate so that film cracking is a common phenomenon in bilayer structures such as flexible electronics and biological tissues. In this paper, a theoretical model is developed to analyze the normal stress distribution in the structure to explain the mechanism of the formation of periodic crack patterns. The effects of geometrical and material parameters are systematically discussed. The analytical result agrees well with finite element analysis, and the prediction of spacing between cracks agrees with experiments from the literature.

Periodic cracks and temperature-dependent stress in Mo/Si multilayers on Si substrates

This work examines formation of the peculiar periodic crack patterns observed in the thermally loaded Mo/Si multilayers. Using the substrate curvature measurements, the macroscopic film stress evolution during thermal cycling was investigated. Then high-speed microscopic observation of crack propagation in the annealed Mo/Si multilayers was presented providing experimental evidence of the mechanism underlying formation of the periodic crack patterns. The origin of the peculiar periodic crack patterns was determined. They were observed to form by the slow crack propagation under quasi-static conditions as a result of the interaction between the channelling crack propagation and the advance of the delamination front.

Theoretical analysis of desiccation crack spacing of a thin, long soil layer

Soil desiccation cracking is important for a range of engineering applications, but the theoretical advancement of this process is less than satisfactory. In particular, it is not well understood how the crack spacing-to-depth ratio depends on soil material behaviour. In the past, two approaches, namely stress relief and energy balance, have been used to predict the crack spacing-to-depth ratio. The current paper utilises these two approaches to predict the approximate spacing-to-depth ratio of parallel cracks that form in long desiccating soil layers subjected to uniform tensile stress (or suction profile) while resting on a hard base. The theoretical developments have examined the formation of simultaneous and sequential crack patterns and have identified an important relationship between the stress relief and energy approaches. In agreement with experimental observations, it was shown that the spacing-to-depth ratio decreases with layer depth, and crack spacing generally increases with layer depth. The influence of the stiffness at the base interface indicated that decreasing the basal interface stiffness makes the crack spacing to increase in sequential crack formation. The experimental observations also show a decrease in cracking water content with the decrease in layer thickness, and this behaviour was explained on the basis of a critical depth concept.

Comparative Phenomenological Study of Fracture Behavior of Ceramic and Glass Foams under Compressive Stress Using In Situ X‐Ray Microtomography

This contribution is dealing with the phenomenological characterization of the cracking and damage of two different brittle foam materials (ceramic foams and glass foams) under compressive load. The compression tests were performed in situ in X‐ray microtomograph in order to visualize the formation of single crack and crack patterns in 3D. Successive microtomographic scans at different levels of compression strain provide an insight into the stressed microstructure of the ceramic and glass foams. The linked evaluation of the microtomographic scans and registered load‐displacement curves clarify the different mechanical response of ceramic and glass foams. Both, ceramic and glass foams show in the early stages of load nearly elastic response. The compressive loading above the elastic region induces different behavior. Ceramic foams response with local failure of single struts and edges to increasing loading. In case of glass foams, the response is depending on whether the cells are predominantly open or close. Predominantly open cell glass foams features very brittle behavior whereas close cell glass foams show pseudo‐ductile behavior with a formation of a crushing band transversal to the loading direction.

Modeling of thermomechanical fracture of functionally graded materials with respect to multiple crack interaction

Different aspects of thermomechanical fracture of functionally graded materials (FGMs) are considered. Among them are the crack interaction problems in a functionally graded coating on a homogeneous substrate (FGM/H). The interaction between systems of edge cracks is investigated, as well as, how this mutual interaction influences the fracture process and the formation of crack patterns. The problem is formulated with respect to singular integral equations which are referred to the boundary equation methods. The FGM properties are modeled by exponential functions. The main fracture characteristics are calculated, namely, the stress intensity factors, the angles of deviation of the cracks from their initial propagation direction and the critical stresses when the crack starts to propagate. The last two characteristics are calculated using an appropriate fracture criterion. The problem contains different parameters, such as the geometry (location and orientation of cracks, their lengths, and the width of the FGM layer) and material parameters, i.e. the inhomogeneity parameters of elastic and thermal coefficients of the functionally graded material. The influence of these parameters on the thermo-mechanical fracture of FGM/H is investigated. As examples the following real material combinations are discussed: TiC/SiC, Al2O3/MoSi2, MoSi2/SiC, ZrO2/nickel and ZrO2/steel.

Crack Patterns under Mechanical Loading

The fracture with the formation of crack patterns instead of a single main crack may occur in the structures for several reasons. The main factor is always the presence of high gradients through the depth of a structure at almost constant stresses near the surface. In this case a growing crack can get into the zone of low stresses and stop, and the fracture will continue by formation of new cracks. Such fracture type is typical for heat-stressed structures, but can also occur under mechanical loading. This paper discusses the possible mechanisms of the crack pattern formation. It is shown that in addition to the form of stress field, the fracture type depends on material properties - in particular, its creep. The considered fracture by crack pattern formation could be characteristic of not only the metallic structural elements, but also for the natural formations, for instance rock or ice massives.

Analysis of localized fracture in 3D reinforced concrete structures using volume averaging technique

In this paper, the propagation of localized damage in reinforced concrete structures is investigated in three dimensional domain. A mesoscale approach is employed whereby the material is perceived as a composite medium comprising two constituents, i.e. concrete matrix and steel reinforcement. The response at the macroscale is obtained via a homogenization procedure that incorporates the volume averaging. After the onset of cracking in concrete, a traction-separation law is introduced for the fractured zone, in which the Timoshenko beam theory is used to assess the stiffness characteristics in the presence of reinforcement. A general 3D scheme for tracing the crack geometry is incorporated, which employs a smoothening algorithm. The mathematical formulation is implemented in Abaqus user subroutine UMAT to verify the performance of the proposed methodology against the available experimental data. A number of numerical examples are given that examine the crack pattern formation and the associated fracture mechanism in concrete beams at different intensity of reinforcement.

Early age fracture properties of microstructurally-designed mortars

This paper compares the fracture properties as well as crack initiation and propagation of real and equivalent mortars. The development of the elastic modulus, tensile strength, and fracture energy at different hydration stages were determined by inverse analysis of load-displacement curves obtained by the compact tension test (CTT). Further, the impact of the moisture content on the aforementioned material properties was also tested on oven-dried equivalent mortars. Digital image correlation (DIC) was used to follow the crack initiation and propagation.The elastic modulus, tensile strength, and fracture energy support the validity of the equivalent mortars approach. The load-displacement curves obtained by the CTT were also compared to those simulated by finite element method showing excellent correlations. DIC revealed the formation of similar crack patterns at comparable load levels between the two mortars. At early age, the moisture content has a considerable influence on the tensile strength and the fracture energy.

Influence of manufacturing parameters on the crackling process of ancient Chinese glazed ceramics

Abstract Guan and Ge wares, produced during the Song Dynasty (960–1279 AD), hold a very special position in Chinese ceramic history because of their aesthetical qualities with a prominent crackle as their only decorative feature. The aim of this inter-disciplinary research is to understand the formation of crack patterns in ancient Chinese glazed ceramics in order to gain knowledge on the manufacturing process. We propose a new approach based on a time-scale investigation of the crackling process and of the cracks morphology obtained on glazed ceramic model systems synthesized under controlled conditions. In order to establish a link between macroscopic and microscopic properties, EDXRF, XRD and SEM-EDX analyses have been performed. Our results show that the relative glaze-body thickness and the firing temperature and atmosphere are key factors to control the crack patterns morphology.

Experiments and numerical simulations of thermal shock crack patterns in thin circular ceramic specimens

An attempt was made to explore the formation mechanism of thermal shock crack patterns in ceramics and to develop quantitative numerical simulations. A set of experiments on thin circular ceramic specimens yielded two-dimensional readings of thermal shock crack patterns with periodical and hierarchical characteristics. The numerical simulations of the thermal shock crack patterns are based on the minimum potential energy principle, where the convective heat transfer coefficient at high temperatures, which is difficult to measure, was inversely estimated by the crack spacing, which is easy to measure. Numerical simulation results were in good agreement with the experimental data. Several interesting thermal shock crack evolution phenomena were found. Two stability criteria of crack propagation, i.e. the minimum potential energy principle and the fracture mechanics bifurcation theory, were compared. It was found that the two criteria verify and complement each other. The present study leads to an improved understanding of the formation and evolution of thermal shock crack patterns in ceramics and can help engineers to assess the thermal shock failure of practical ceramic components.

Bending induced self-organized switchable gratings on polymeric substrates.

We present a straightforward procedure of self-surface patterning with potential applications as large area gratings, invisible labeling, optomechanical transducers, or smart windows. The methodology is based in the formation of parallel micrometric crack patterns when polydimethylsiloxane foils coated with tilted nanocolumnar SiO2 thin films are manually bent. The SiO2 thin films are grown by glancing angle deposition at room temperature. The results indicate that crack spacing is controlled by the film nanostructure independently of the film thickness and bending curvature. They also show that the in-plane microstructural anisotropy of the SiO2 films due to column association perpendicular to the growth direction determines the anisotropic formation of parallel cracks along two main axes. These self-organized patterned foils are completely transparent and work as customized reversible diffraction gratings under mechanical activation.

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.

On the Comprehension of Mechanical, Thermal and Chemical Evolution of Exhaust Gases after Treatment Catalysts

The stricter environmental regulations impose a drastic reduction of vehicles emissions and a longer durability of the automotive catalyst. The studies of the catalyst evolution in real conditions are very expensive. It is interesting to elaborate an ageing process to well simulate the real conditions of the automotive catalyst ageing at the laboratory scale. Thermal, chemical and mechanical effects can cause degradations of the catalytic performances. Thermal ageing is the result of high temperature that surges in the catalytic converters. Chemical ageing is due to phosphorus, zinc, magnesium, calcium or sulfur originating from either engine oil additives or fuel contaminants. Mechanical ageing (cracks and detachment) is the consequence of thermal and chemical ageing (thermal and textural stresses). Understanding the formation of crack patterns and spalling of thin films is challenging in fracture mechanics. The need for two conditions, one involving energy and the other one stresses, has recently been shown. The stress condition defines a threshold below which the pattern formation is inhibited. As this threshold is not reached, the energy accumulates. Then, at onset, depending on the strength and toughness of the material, the amount of energy can be sufficiently large to give rise to a more or less dense lattice of cracks. Following, after initiation, when the crack tips are close to the support, the newly created small cells tend to separate from it, thicker the film and more harmful the debonding.