Formation Of Crack Patterns Research Articles

Deciphering the Benefits of Coordinated Binders in Si‐Based Anodes by Combined Operando/In Situ and Ex Situ X‐Ray Micro‐ and Nano‐Tomographies

AbstractThe simple addition of a Zn(II) precursor to a preoptimized poly(carboxylic acid) binder solution enhances the electrochemical performance and cycle life of silicon‐based electrodes. The binder/cation couple forms a cross‐linked coordinated binder that plays a key role in enhancing the mechanical and chemical stability of the electrode microstructure. The impact of the addition of the Zn precursor on the microstructural evolution of the electrode during cycling is investigated at different scales (from cell/electrode to silicon particle scale) using complementary operando, in situ, and ex situ X‐ray tomography techniques. Comparative analyses conducted on the reference and with Zn electrode formulations using operando and in situ X‐ray micro‐tomography allow for monitoring of the electrode morphological deformations along with the crack pattern formation and evolution during cycling. The benefits of the precursor addition include enhancing the mechanical stability of the electrode through a strengthened microstructure more apt to maintaining its integrity, as well as a better anchoring to the current collector leading to decreased electrical disconnections and capacity fade. Moreover, complementary ex situ X‐ray nano‐tomography measurements highlight the benefits of the precursor addition in terms of chemical stability with mitigated solid electrolyte interface (SEI) formation over the electrode cycling.

Multiple kinking of a tensile crack in the brittle multilayered media abundant with closely-parallel weak interfaces

Crack kinking is a basic way to form a complex crack trajectory in a multilayered solid abundant with weak interfaces. However, it remains unclear that under which condition a multi-kinked crack emerges with the influence of closely-parallel weak interfaces. According to a basic crack kink criterion, here we consider a brittle multilayered plate with a tensile edge crack to seek the occurrence condition of the multi-kinking behavior. The strain energy release rate ratio of the crack during its propagation is examined based on finite element simulations. We find a value domain of intersection angle and fracture toughness ratio, where the fracture toughness anisotropy competes with the load anisotropy to orient the crack propagation direction. We obtain the continual kinking condition of the tensile edge crack, including the intersection angle range about 0∼38° and the closed form upper and lower bounds of the fracture toughness ratio range. Our multi-kinking results for the tensile crack are helpful to understand the formation of complex crack patterns in the multilayered materials under complicated loads.

Deep generative spatiotemporal learning for integrating fracture mechanics in composite materials: inverse design, discovery, and optimization.

The trade-off between strength and toughness presents a fundamental challenge in engineering material design. Composite materials (CMs) can strategically arrange different materials to enhance both strength and toughness by optimizing the distribution of loads and increasing resistance to crack propagation. However, current data-driven computational modeling approaches for CM configuration optimization suffer from limitations of "substantial computational cost" and "poor predictive power over extrapolation spaces", making it difficult to integrate with global optimization algorithms, and ultimately limiting the discovery of materials with optimal tradeoffs. As a breakthrough, we propose a data-driven design framework with a multi-task DL architecture capable of accurately predicting local fields' spatiotemporal behavior, including stress evolution and crack propagation, alongside homogenized mechanical properties. Our model, trained on datasets generated from crack phase fields simulations of random configurations, demonstrated exceptional predictive performance even for unseen configurations with well organized patterns exploiting nature-inspired morphological features. Importantly, solely from composite material (CM) configurations, our model effectively predicts long-term spatiotemporal fields with an accuracy comparable to FEM but with a substantial reduction in computational time. By coupling the model's predictive power with genetic optimization algorithms, we demonstrated the framework's applicability in two representative inverse design tasks: devising CM configurations with mechanical properties beyond the training set and guiding desired crack pattern formation. Our research highlights the potential of artificial intelligence as a feasible alternative to conventional computational approaches for straightforward configurational and structural optimization.

Flexural response of UHPC beams post-tensioned with internal unbonded tendons: Experimental study

This paper presents the results of an experimental study that deals with the characterization of the complete flexural response of post-tensioned (PT) ultra-high-performance concrete (UHPC) beams with internal unbonded tendons. A total of 6 PT UHPC beams were monotonically loaded to failure. The variables investigated include volumetric fiber content, non-prestressed reinforcement ratio, and loading configuration. Flexural response is characterized in terms of crack pattern formation, propagation, and localization as well as failure mode identification. The influence of the investigated variables on change in: strand strain, UHPC compressive and tensile strains, strand stress, moment capacity, curvature ductility and member level ductility is presented including explanations of observed phenomena. The measured flexural response and capacity are compared with the predicted response using two mechanics-based methods and a numerical method. Prestress losses are quantified and used to obtain the predicted response. UHPC material characterization is conducted to obtain the necessary inputs for the prediction models. The measured to predicted ratio of flexural capacity and the corresponding COV for the considered prediction methods vary from 0.95 to 1.02, and from 6% to 11% suggesting good predictive capabilities. The use of nonprestressed flexural reinforcement in PT UHPC flexural members is recommended from the perspective of crack distribution, delay in the precipitation of flexural failure through crack localization and subsequent hinging, and member level ductility.

Universal shielding effect of curvature on two interacting cracks

The interaction of approaching cracks plays a crucial role in the formation of complex crack patterns in the mechanics and physics of materials defects. While curvature has been shown to be important in the growth, interaction, and ordering of various defects, its influence on the interactions of multiple cracks remains poorly understood. In this study, we investigate how two approaching cracks interact in curved sheets using an integrated mechanical framework combing experiments, fracture phase-field simulations, and theoretical analysis. Our findings demonstrate that the repulsive and attractive interactions between the two initially parallel cracks are significantly shielded by curvature. This shielding effect arises because curvature alters the stress fields at the crack tips and reduces the initial deflection angle of the crack tips. We observe this effect under different initial crack positions, material properties, and curved configurations, indicating a general role of curvature in controlling the paths and interactions of cracks. This study provides insights into understanding the interaction of approaching cracks, which has implications for fracture and fatigue control.

The physics of desiccation cracks 1: Ductile fracturing and dependence on relative humidity

Ductile deformation is ubiquitously found in the shrinkage of geomaterials. The existence of ductility requires elastoplastic mechanics when analyzing the structure deformation under external stress. In this work, we explore the physics of ductile fracturing based on the results from desiccation experiments and triaxial tests. By using the digital image correlation (DIC) method to generate the strain maps of samples undergoing desiccation cracking under different relative humidities, we obtain results showing the previously postulated Cnoidal Wave ductile failure patterns propagating under atmospheric condition-controlled crack velocities. We then correlate these observations with rate-dependent plasticity models calibrated through triaxial tests undergoing several unloading–reloading cycles and velocity stepping. This work demonstrates the necessity to consider ductility in soil cracking, indicating that the formation of crack patterns in soil desiccation is a slow and predictable process.

Desiccation cracking of polymer-bentonite mixtures: An experimental investigation

Despite some evidence that polymer addition may enhance the resistance of clay to desiccation cracking, the topic remains under-researched. This study evaluated the effect of sodium carboxymethyl cellulose (Na-CMC) additive on the formation of crack patterns in bentonite clay undergoing dehydration. Thirteen groups of amended and unamended mixtures, prepared with two different mixing methods and several Na-CMC types and dosages, were exposed to air dehydration in petri dishes under different environmental conditions of temperature, humidity and friction. Moisture loss was tracked in real-time and surface cracking was recorded with a digital camera at regular intervals. Captured photos were analyzed by image processing to quantify crack ratio and surface area of soil clods. The results indicated that polymer-modified samples consistently exhibited reduced levels of desiccation cracking compared to unmodified ones under different environmental conditions. Na-CMC with a degree of substitution (DS) of 0.9, corresponding to peak viscosity of polymer, generated a higher resistance to cracking than DS of 0.7 or 1.2. In addition, dry mixing seemed to be more effective than wet mixing in increasing mixture resistance to desiccation cracking.

A Penalty Method for Coupling of Finite‐Element and Peridynamic Models

AbstractA classical continuum mechanics model no longer fulfills its basic assumptions, when the deformations are not smooth or discontinuous. Peridynamics (PD) as an integral formulation could better overcome these issues. Therefore, it is better suited to solve fracture problems such as crack initiation, its growth and formation of crack patterns. In PD the magnitudes of internal forces at a material point depend on the collective interaction of all material points within a subdomain called horizon. To take advances from the formulation, typically it is implemented in a mesh‐free form. In that case, it is easy to separate interactions between different material points. As consequence, a relatively high resolution is required to describe continuous deformation functions and, consequently computationally expensive. Therefore, the application of mesh‐free PD in undamaged regions requires an unnecessary high effort for receiving sufficient accurate results. In contrast, the finite element method (FEM) as a classical continuum mechanics‐based approach, is very efficient, if continuous stress distributions can be assumed. Consequently, a computational cost reduction can be achieved, if the PD is applied in the local damaged zone only and the remaining area is modeled and analyzed with the classical FEM. Realization of such an approach requires a sufficient accurate coupling of the PD and the FEM subdomains.A brief overview about different coupling approaches is given. Then the general approach of an Arlequin based method is presented. Here the coupling is achieved via an overlapping of PD and FEM areas. The coupling equations are developed and realized with help of the Penalty method. The Penalty method is considered as an alternative procedure to the Lagrange multiplier strategy without creating new unknowns, which essentially simplifies the coupled PD‐FEM approach. The validity and limits of the proposed technique are demonstrated through analysis, where the choice of the Penalty number is discussed as well as artificial wave oscillations, caused by the coupling area.

Simulation of Crack Pattern Formation Due to Shrinkage in a Drying Material

Crack patterns observed in nature have attracted the interest of researchers in various fields, and the mechanism of the pattern formation has been investigated. However, the phenomenon is very complicated, and many factors affect the process. Therefore, we are motivated to construct a general simulation code with a simple algorithm. In this study, crack pattern formation due to shrinkage caused by the drying of a wet material was simulated. The process was simplified as follows: tensile force is generated in the model, and a crack is generated when the tension exceeds a critical value. The tensile forces in the x and y directions are independently evaluated. A crack propagates perpendicular to the tension until it reaches another crack or a boundary. Based on this modeling, simulations with a two-dimensional square domain were performed. Consequently, a cross-divided pattern was generated. Assuming zigzag crack propagation, more realistic patterns were obtained. The effects of the boundary and domain size were also considered, and various characteristic patterns were obtained. Furthermore, the orientation dependency was simulated, and 45&#730 declined patterns and rectangularly divided patterns were generated. The model presented in this study is very simplified and is expected to be applicable to various objects.

Interplay of Consolidation Fronts and Cracks in Drying Colloidal Coatings and Its Application in Controlling Crack Pattern Formation

Cracks are frequently observed in drying colloidal coatings. Although a rich collection of crack patterns has been reported, the systematic study on how cracks grow into the final morphology during the drying process remains elusive. In this work, we use directional drying channels with wedge-shaped edges of different angles to study the interplay of advancing consolidation fronts and propagating cracks. We found that although the shape of the advancing consolidation fronts is altered by the drying edge, the growth direction of the following cracks remains perpendicular to the consolidation fronts during the whole drying process, resulting in cracks with a large curvature. We rationalize the evolution of consolidation fronts with the distribution of capillary pressure revealed by a Laplace model. Further, the growth direction of cracks can be explained by the fracture mechanics mechanism that the main orientation of internal tensile stresses developed during the consolidation determines the crack growth direction. Utilizing this understanding, wavy crack patterns are generated in rectangular drying channels with an alternating temperature field, demonstrating a feasible method of designing and controlling drying-induced crack patterns for micro-/nano-fabrication applications.

Simulation of crack patterns in quasi-brittle materials under thermal shock using phase field and cohesive zone models

Complex crack patterns are usually formed on the surface of brittle and quasi-brittle solids under thermal shock. In this paper, the phase field coupled cohesive zone model is established to simulate the brittle and quasi-brittle fracture processes in three-dimensional solids, especially to reproduce the complex crack patterns under thermal shock. Several examples are given to illustrate the effectiveness of the model to complex fracture problems under thermal shock: from uniaxial tensile and thermal shrinkage fracture of a one-dimensional rod to nucleation, propagation, and crack pattern formation of thermal shock crack of a three-dimensional ceramic bottle. In addition, the formation mechanism of crack patterns in ceramic bottle is discussed, especially the dominant role of the difference in thermal expansion coefficients between the ceramic matrix layer and the glaze layer in the formation of crack patterns and the final crack density.

The continuous Airy-based for stress-singularities (CASS) method: an energy-based numerical formulation for unilateral materials

Unreinforced masonry buildings represent a large part of the world's architectural heritage. Despite their significant diffusion, their mechanical behaviour is still subjected to increasing scientific investigations as modelling difficulties arise from the negligible tensile strength in tension. Because of this unilateral response, masonry constructions can flexibly accommodate different loading and displacement-like boundary conditions in a new deformed configuration through the formation of crack patterns. The internal stress state changes accordingly and can be represented through stress singularities. Defining the internal stress states compatible with general boundary conditions is primarily essential from an engineering perspective.This paper presents the Continuous Airy-based for Stress-Singularities (CASS) method, a new numerical strategy to model the internal stress state in unilateral materials, whose main peculiarity is the ability in describing singular stress fields independently of the discretisation. The internal equilibrium is guaranteed using the Airy stress potential discretising the domain with plate-type finite elements. The compatibility with boundary displacements is satisfied through a variational formulation based on the minimum of the Total Complementary Energy. The boundary value problem is then reduced to a second-order cone programming where the linear objective function represents the work of the emerging stress for the boundary displacements, and the constraints enforce the boundary equilibrium and the material compatibility. The CASS method is benchmarked against analytical solutions and other numerical strategies on several 2D problems, also used to illustrate and discuss its main features. Lastly, a real masonry façade is considered to show the method's effectiveness clearly.

Shrinkage Crack Detection in Expansive Soil using Deep Convolutional Neural Network and Transfer Learning

The formation of shrinkage cracks is a natural phenomenon in expansive soils. The development of these cracks affects both the physical and mechanical properties of the soil. This paper proposes new procedures for predicting and detecting the formation of crack patterns in expansive soils, based on customized Convolution Neural Network (CNN) and transfer learning. A total of four different deep learning models are developed to detect the soil crack pattern by changing the convolution layers and hyper-parameters in the analysis. The novelty of the proposed detection methods lies in the use of customized CNN models in shrinkage crack detection for expansive soils. The customized CNN models are constructed by varying the number of convolution layers and the hyperparameters. The results show that the proposed CNN models provide very accurate results and are capable of detecting the presence of cracks in the soil with great accuracy. The best results are from one of the customized CNN models namely the Customized CNN Model 2 which consists of five convolution layers, three activation layers, one pooling layer, two fully connected layers, and a softmax layer. The results from this model are compared with other well-known approaches from the literature and are shown to provide improved results. Overall, the proposed deep learning methods developed in this paper produce excellent results in terms of the accurate detection of shrinkage soil cracks and can also be applied to other types of soil cracks.

Modeling approach to estimate the bending strength and failure mechanisms of glued laminated timber beams

The numerical simulation of four-point bending tests on glued laminated timber (GLT) beams requires an adequate description of the material behavior and of relevant failure mechanisms. The wooden lamellas, building up the GLT element, include knots, as a result of the natural tree growth process, which significantly affect the mechanical behavior. The variability of the morphology and arrangement of these knots lead to a large fluctuation, especially of strength properties, along the wooden lamellas. This leads to complex and, in general, quite brittle structural failure mechanisms of the GLT element. Such failure mechanisms can numerically be described with discrete cracks, using the framework of the extended finite element method (XFEM) for cracks without predefined positions or cohesive surfaces for cracks with predefined positions. In this work, a modeling approach to reliably estimate the bending strength and failure mechanisms of GLT beams subjected to four-point bending tests is proposed. Herein, the approach is validated by simulating replications of experimentally tested GLT beams of two beam sizes and strength classes, where each knot group is considered as a section with reduced individual stiffness and strength in exactly the same position as in the real beam. The results show that the application of quasi-brittle material failure may still result in a brittle global failure of GLT beams. The present study exemplarily shows how valuable insight into progressive failure processes can be gained by allowing the formation of continuous crack patterns. Moreover, a refined consideration of the knot geometries with such sophisticated realizations of discrete cracks may be able to simulate the actual failure mechanisms even more precisely.

Recent progress on crack pattern formation in thin films.

Fascinating pattern formation by quasi-static crack growth in thin films has received increasing interest in both interdisciplinary science and engineering applications. The paper mainly reviews recent experimental and theoretical progress on the morphogenesis and propagation of various quasi-static crack patterns in thin films. Several key factors due to changes in loading types and substrate confinement for choosing crack paths toward different patterns are summarized. Moreover, the effect of crack propagation coupled to other competing or coexisting stress-relaxation processes in thin films, such as interface debonding/delamination and buckling instability, on the formation and transition of crack patterns is discussed. Discussions on the sources and changes in the driving force that determine crack pattern evolution may provide guidelines for the reliability and failure mechanism of thin film structures by cracking and for controllable fabrication of various crack patterns in thin films.

Simulation of Crack-Pattern Formation Caused by Shrinkage due to Drying

When a wet materials dries up, cracks are generated due to the volumetric shrinkage, and curious complicated pattern is generated. The formation mechanism is difficult to completely understand because various factors are related, for example, the circumstantial conditions such as humidity and temperature, mechanical conditions as static or dynamic, and materials condition like the uniformity and homogeneity. The simulation of the crack-pattern formation is consequently not straightforward, and many kinds of difficulty is raised. In this study, therefore, we are trying to construct a simple and widely applicable simulation model for the phenomena. As a first step, the prototype was constructed, and the basic process was successfully regenerated. In this model, volumetric shrinkage generates a single crack and the crack progresses straightly to the boundary. This process occurs successively, and various patterns were obtained depending on the difference in the parameters corresponding to the drying condition.

Rock Strain Prediction Using Deep Neural Network and Hybrid Models of ANFIS and Meta-Heuristic Optimization Algorithms

The majority of natural ground vibrations are caused by the release of strain energy accumulated in the rock strata. The strain reacts to the formation of crack patterns and rock stratum failure. Rock strain prediction is one of the significant works for the assessment of the failure of rock material. The purpose of this paper is to investigate the development of a new strain prediction approach in rock samples utilizing deep neural network (DNN) and hybrid ANFIS (adaptive neuro-fuzzy inference system) models. Four optimization algorithms, namely particle swarm optimization (PSO), Fireflies algorithm (FF), genetic algorithm (GA), and grey wolf optimizer (GWO), were used to optimize the learning parameters of ANFIS and ANFIS-PSO, ANFIS-FF, ANFIS-GA, and ANFIS-GWO were constructed. For this purpose, the necessary datasets were obtained from an experimental setup of an unconfined compression test of rocks in lateral and longitudinal directions. Various statistical parameters were used to investigate the accuracy of the proposed prediction models. In addition, rank analysis was performed to select the most robust model for accurate rock sample prediction. Based on the experimental results, the constructed DNN is very potential to be a new alternative to assist engineers to estimate the rock strain in the design phase of many engineering projects.

A comprehensive nonlinear finite element modelling and parametric analysis of reinforced concrete beams

PurposeThis study aims to present comprehensive nonlinear material modelling techniques and simulations of reinforced concrete (RC) beams subjected to short-term monotonic static load using the robust and reliable general-purpose finite element (FE) software ANSYS. A parametric study is carried out to analyse the flexural and ductility behaviour of RC beams under various influencing parameters.Design/methodology/approachTo develop and validate the numerical FE models, a total of four experimentally tested simply supported RC beams are taken from the available literature and two beams are selected from each author. The concrete, steel reinforcements, bond-slip mechanism, loading and supporting plates are modelled using SOLID65, LINK180, COMBIN39 and SOLID185 elements, respectively. The validated models are then used to conduct parametric FE analysis to investigate the effect of concrete compressive strength, percentage of tensile reinforcement, compression reinforcement ratio, transverse shear reinforcement, bond-slip mechanism, concrete compressive stress-strain constitutive models, beam symmetry and varying overall depth of beam on the ultimate load-carrying capacity and ductility behaviour of RC beams.FindingsThe developed three-dimensional FE models can able to capture the load and midspan deflections at critical points, the accurate yield point of steel reinforcements, the formation of initial and progressive concrete crack patterns and the complete load-deflection curves of RC beams up to ultimate failure. From the numerical results, it can be concluded that the FE model considering the bond-slip effect with Thorenfeldt’s concrete compressive stress-strain model exhibits a better correlation with the experimental data.Originality/valueThe ultimate load and deflection results of validated FE models show a maximum deviation of less than 10% and 15%, respectively, as compared to the experimental results. The developed model is also capable of capturing concrete failure modes accurately. Overall, the FE analysis results were found quite acceptable and compared well with the experimental data at all loading stages. It is suggested that the proposed FE model is a practical and reliable tool for analyzing the flexural behaviour of RC members and can be used for performing parametric studies.

Drying silica-nanofluid droplets

Exsiccation of suspension droplets generates characteristic ring-like stains. The homogeneity of such coffee rings is disturbed by subsequent cracking. Placing silica droplets on copper and stainless steel substrates, the ensuing drying and cracking chronology is investigated. The formation of the coffee ring and its cracking are visualised through microscopic imaging and videotaping. Based on the cracking chronology, three crack generations are identified. The evolution of the 1st crack generation is studied in detail. Two fracture types – logarithmic spiral and straight radially oriented – characterise these initial cracks. While the first type is due to deposition delamination, the straight cracks are induced by the interplay of capillary pressure and shear stress between coating and substrate. Most noteworthy is our finding that the cracking speed of the straight cracks is one order of magnitude larger than that of the spiral cracks. The pattern of the 1st generation cracks defines the final crack network. Our findings provide a comprehensive understanding of the crack pattern formation following the desiccation of silica droplets. This study offers details on nanofluid exsiccation on metal substrates, thereby opening routes for depositing nanoparticles on heated and non-heated surfaces for various engineering applications.

Thermo-elasto-plastic phase-field modelling of mechanical behaviours of sintered nano-silver with randomly distributed micro-pores

Nano-silver paste is an emerging lead-free bonding material in power electronics, and has excellent mechanical properties, thermal conductivity and long-term reliability. However, it is extremely challenging to model the mechanical and failure behaviours of sintered nano-silver paste due to its random micro-porous structures and the coupled thermomechanical loading conditions. In this study, a novel computational framework was proposed to generate the random micro-porous structures and simulate their effects on mechanical properties and fracture behaviour based on the one-cut gaussian random field model and the thermo-elasto-plastic phase-field model. The elastic modulus, ultimate tensile strength and strain to failure are computed statistically, showing good agreement with the experimental results. Further, the framework was applied to model the fracture of sintered nano-silver paste under thermal cyclic conditions, demonstrating the formation of distinctive crack patterns and complex crack networks. The cracking behaviours observed in the experiments and simulations are remarkably similar to each other. The framework was implemented within Abaqus via a combination of subroutines and Python scripts, automating the process of model generation and subsequent computation. This study provides an efficient and reliable approach to simulate the mechanical and failure behaviours of sintered nano-silver paste with random micro-porous structures.