Crack Patterns Research Articles

Fracture mechanism and ductility performances of fiber reinforced shotcrete under flexural loading insights from digital image correlation (DIC)

This paper investigates the fracture mechanism and ductility performance of fiber-reinforced shotcrete (FRS) under flexural loading through digital image correlation (DIC) analysis. The focus is on determining the optimal mix design, utilizing recycled and manufactured fibers in shotcrete through four-point bending tests. These tests reveal significant improvements in flexural strength and ductility, as well as crack resistance, attributed to the synergistic effect of both types of fiber in hybrid fiber reinforcement. Notably, the inclusion of recycled fibers from automobile tires enhances mechanical characteristics and impact resistance, contributing to environmental sustainability and cost reduction. DIC analysis offers crucial insights into crack initiation and propagation in shotcrete, highlighting the impact of fiber reinforcement on crack patterns. Manufactured fibers delay crack onset effectively, while hybridization enhances fracture characteristics, offering improved crack control and flexural strength. The study underscores the potential of hybrid fiber mixes for enhancing structural performance in tunnel support applications, emphasizing the synergistic effect of hybrid of different fiber types. Overall, the research contributes to advancing understanding of fracture behavior in fiber-reinforced shotcrete and provides practical insights for optimizing mix designs to achieve superior mechanical properties and durability.

Shear behavior of reinforced concrete walls under variable axial tension‐compression and cyclic lateral loads

AbstractUnder a strong earthquake, the axial force of shear walls in tall buildings may vary from compression to tension, but few studies have been conducted on this. Three low‐aspect‐ratio reinforced concrete (RC) wall specimens subjected to coupled variable axial tension‐compression and lateral load were tested in this study, to investigate the effect of the fluctuating range of axial force and loading histories on the shear behavior of RC walls. The test results indicated that shear‐compression failure occurred under the compressive‐shear loading for all test wall specimens, and no obvious post‐peak strength degradation in tension‐shear loading. The hysteretic curves of test wall specimens were strongly affected by the loading histories; the shear strength and deformation capacity were mainly affected by the fluctuation of axial forces, especially for tension‐shear strength. The equation of ACI 318‐19 and JGJ 3‐2010 conservatively predicted the shear strength of RC walls under the variable axial force, while the equation of ASCE/SEI 43‐05 accurately predicted the shear strength with the mean values of the VTest/VASCE of 0.97 and 0.94 for compression‐shear and tension‐shear strength, respectively. Comparison with an RC wall under constant axial tension revealed that the failure modes of RC walls were strongly dependent on the initial cracking patterns. Finally, a finite element (FE) model was developed, and parametric analyses were carried out to further estimate the effect of variable axial force on the cyclic shear behavior of RC walls.

Crack Growth Patterns of Aluminum Tubular Specimens Subjected to Cyclic Tensile Loads

This study presents a detailed analysis of a fatigue test campaign in order to identify different crack patterns. It was conducted on 6061-T6 aluminum tubular specimens featuring an internal diameter of 10 mm and different thicknesses (2, 3 and 4 mm). These specimens were subjected to cyclic tensile loads with a load ratio of R = 0.1, utilizing a sinusoidal load function at a frequency of 3 Hz. The investigation examines the crack growth rates, the stress intensity factor, and the final and intermediate fracture zones by applying overloads in some cases. The differences with two-dimensional specimens and the importance of this study for the interpretation of results with biaxial loading states are highlighted. The different states of crack growth detected are analyzed using artificial vision techniques. The differences between the exterior and interior faces of the specimen are revealed, and a series of states prior to the formation of the radial crack front expected in these specimens are identified.

Mechanism of initiation and propagation of surface cracks in gun bore under thermomechanical coupling impact

Surface cracks in gun bore may exacerbate rifling ablation and wear and in turn shorten barrel life. Thermomechanical coupling finite element (FE) models of bore are established and the dynamic responses of the bore under high-temperature and high-pressure are numerically simulated. The stress distribution characteristics on the inner surface are analyzed and the effects of autofrettage, number of firings and harden layer on the stress distribution are discussed. Based on the stress distribution characteristics, FE models with two initial cracks on the ledge of land surface are set up and the propagation, interaction and intersection of the cracks are numerically simulated, considering the effect of the distance between the two cracks. Based on simulation results, the initiation and propagation pattern and mechanism of the cracks on the inner surface are analyzed. An ablation test system was designed and produced, and used to experimentally verify the initiation and propagation mechanism of the cracks. The observed crack patterns on the inner surface of a real gun bore are also used to illustrate the mechanism obtained in this work. Understanding of the initiation and propagation mechanism of cracks in gun bore can be applied to improve and optimize the design of barrels.

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.

Coupling effect of concrete cracks and stray current on chloride-induced corrosion of rebar

Either concrete cracking or stray current promotes the corrosion of rebars; however, the coupling effects of concrete cracking and stray current on the rebar corrosion are still unknown. In this work, the effect of concrete cracking patterns coupled with stray current on rebar corrosion is presented by both experimental and finite element simulation. Specifically, there is a strong coupling effect when crack width is less than 100 μm, which manifests that ion concentration and electric field intensity increase pronouncedly with decreasing crack width. Simulation shows that the coupling effect leads to an asymmetric distribution of ions and electric fields at the crack tip, which in turn causes the asymmetric corrosion of rebars. Under the coupling effect, the highest corrosion rate reaches 3 μA/cm2 and is more than three times higher than that in a natural environment. Our findings contribute to understanding and evaluating accurately rebar corrosion in practical application.

Effect mechanism of low-velocity impact loading rate on the failure modes transition of steel-UHPC-steel composite plates

This study delved into the transition mechanism of loading rate on the failure mode transition in steel-ultra-high performance concrete-steel (SUHPCS) composite plates under concentrated low-velocity impact loads. A series of drop-weight tests elucidated that, as impact velocity escalated, the composite plate shifts from local punching failure, characterized by circumferential cracks, to overall flexural failure, marked by radial cracks resembling yield lines. Given the constraints in capturing strain data in drop-weight test, a 3D nonlinear structural analysis using Abaqus software was conducted. This numerical simulation method was validated by drop-weight test results in terms of crack patterns and impact force time histories. Moreover, structural dynamic punching and flexural loads at a specific loading rate were obtained with the assistance of the dynamic increase factor (DIF). Failure mode could be judged through comparison between the two critical loads. The discrepancy in strain sensitivity exhibited by steel plates and UHPC accounted for the transition in failure modes of the SUHPCS composite plates. DIFs for UHPC compressive strength and steel plate strength were lower than DIF for UHPC tensile strength, as these factors were around 1.5, 1.7 and 2.6, respectively. Parameter analysis showed that the critical transition impact velocity for a composite plate with a core thickness of 80 mm was 11 m/s, surpassing the 13 m/s threshold for a composite plate with a 100 mm-thick core. Moreover, changes in DIFs of UHPC and steel strengths were less than 2 % with various impact masses and the composite plate maintained the same failure mode.

Enhancing structural damage evaluation of PC girder bridges through digital twinning Bayesian model updating

Developing a unified analytical framework to assess the structural performance of deteriorated prestressed concrete (PC) girder bridges is important for their maintenance. This study aims to construct a physics-based digital twin framework for PC girder bridges incorporating Bayesian model selection and updating, a high-fidelity three-dimensional (3D) finite element (FE) model, and a method for simulating prestressed tendon damage. In this study, three PC girder specimens were designed and tested to evaluate the effects of tendon rupture near the anchorage region on structural performance. Bayesian model selection was used to determine the most plausible model class based on the estimated model evidence. The most probable values (MPVs) of the model parameters, derived from the estimated posterior probability density functions (PDFs), were then used to calibrate the FE model, which reflects a healthy state of the PC girder bridge. This updated FE model serves as the baseline for conducting what-if scenario simulations. Subsequently, nonlinear segments of the constitutive model, obtained from coupon tests, and a simulation method for tendon rupture were incorporated into the updated FE model. Nonlinear static simulation results obtained through the updated model were found to be consistent with both the observed crack pattern and the load–deflection curve. The reliability of the digital twinning FE model for assessing tendon damage and for predicting the residual load-bearing capacity was verified through comparison with measured data. Therefore, the digital twinning Bayesian model updating approach shows potential applications in continuous structural health monitoring (SHM) of PC bridges.

Experimental investigation of the compressive and shear resistance of laminated steel-reinforced glass beams

This paper presents an experimental investigation into the compressive and shear resistance of triple-layered laminated steel-reinforced glass beams. Two types of tests are performed: (a) local compressive tests (force over a support) and (b) bending tests (force close to a support). In total, six local compressive tests and eight bending tests are performed. Overall, beams with a shear span-to-effective depth ratio (a/d) approximately equal to 0, 0.63, and 1.0 are tested. Two different types of flexural reinforcement are used separately: solid (S) and hollow (H) reinforcement. The behaviour of the outer glass panes, and top and bottom reinforcement is monitored using strain gauges and Digital Image Correlation (DIC). The test results are elaborated in terms of load-displacement curves, the evolution of strains and crack patterns. Three failure modes are observed: yielding of the reinforcement (PF), crushing of glass (CF), and rupture of the reinforcement (RR). Shear failure occurred due to the crushing of glass in the compressed diagonal strut in the shear span. It was found that the shear resistance increases with a smaller shear span-to-effective depth ratio and stronger reinforcement. The dominant shear transfer mechanism was the direct strut action. It was found that the post-fracture capacity had a relatively constant value for all the tests with a slight increase for smaller a/d. The actual tensile strains in the bottom reinforcement measured by DIC are compared with the calculated strains based on the curvature of uncracked and cracked cross-sections, assuming plane section behaviour. It was observed that the actual strains are systematically larger than the calculated ones because, in reality, the section does not remain plane. After the appearance of the first crack, the beams essentially behave like strut-and-tie systems, where the strut is the diagonally compressed laminated glass and the tie is the bottom reinforcement.

Investigating the impact of corrosion on behavior and failure modes of reinforced concrete slabs: An experimental and analytical study

Corrosion of steel reinforcement significantly reduces the load-carrying capacity of reinforced concrete (RC) flat slabs, making them more vulnerable to punching shear failure. This type of failure can lead to sudden and catastrophic collapse of the structure. Despite its critical implications, research on this topic remains limited, and a mechanical model to estimate the load-displacement behavior of RC flat slabs with corroded reinforcements is currently lacking. In this paper, experimental work on corroded RC slabs under punching shear loading was conducted. To investigate the impact of corrosion on the structural behavior of reinforced concrete (RC) flat slabs, eight specimens, including both corroded and uncorroded controls, were subjected to load testing. The study focused on key performance indicators including punching shear strength, stiffness, crack patterns, failure modes, and energy dissipation capacity. Additionally, an analytical study based on the newly developed Critical Shear Crack Theory (CSCT) was conducted to understand the behavior of corroded RC slabs. Experimental results indicated a significant reduction in the punching shear strength of corroded slabs. Moreover, as corrosion progressed, a notable shift in failure mode from punching shear to flexural failure was observed. The proposed CSCT model demonstrated good agreement between the experimentally obtained and analytically predicted load-displacement curves.

Numerical Simulation of Effects of Previous PVD Treatment on Second Vacuum-PVD Improvement

The influence of the initial improvement through prefabricated vertical drains (PVD) and surcharge embankment on the second improvement by vacuum PVD has not been comprehensively explored in the existing literature. The expansion of the Second Bangkok International Airport (Suvarnabhumi Airport) underwent initial treatment with PVD and surcharge, followed by further soft ground improvement with vacuum PVD, which serves as a valuable case study for understanding the impact of the initial PVD improvement. This study highlights the effects of the initial PVD improvement through a comparison of two case studies: the first improvement by vacuum PVD on Taxiway Extension D at Zone 27 and the second vacuum PVD improvement on the Third Extension North at Zone 7. Extensive back analysis results reveal significantly higher flow parameters and reduced settlements for the second improvement at Zone 7 compared to the first improvement at Zone 27. The water contents, void ratios, and compression indices decreased while the undrained shear strengths and maximum past pressures increased. These results demonstrated the effectiveness of the vacuum PVD improvement with a modified field-distributed air-water separation system. Numerical studies further corroborated these findings and confirmed the observed crack patterns at the surface resulting from inward lateral movement.

Flexural Behaviour of Reinforced Shotcrete beams Comprehending Waste Plastic Fiber

Abstract Wet-mix shotcrete is often used as a placement method in tunnelling and ground support. However, to date, only a limited number of studies have been identified the roles of waste plastic fiber (WPF) on wet-mix shotcrete mixtures. This experimental study show the flexural performance of reinforced shotcrete concrete members (beams) having waste plastic fiber, which may be considered as a new study. In order to achieve that, a manufacturing of wet-mix shotcrete machine has been developed to product special wet-mix shotcrete that will be used to cast reinforced shotcrete concrete members containing waste plastic fiber. Extensive attempts were done in this project to generate a special wet-mix shotcrete combinations using locally sourced waste materials like beverage bottles. The qualities of WPF shotcrete concrete (SC) were investigated in terms of fresh, hardened, mechanical, and bending behaviour, with extensive results analysis. Five SC formulations (0.25, 0.5, 0.75, 1.0, and 1.25) percent WPF content, as well as the control shotcrete (SC0.00), were used in the experiments. In addition, the flexural behaviour of SC beams casted from the same waste materials was investigated. The results revealed that all SC beams had almost similar flexural behaviour when compared to the creation of crack patterns, as well as the ductility index and stiffness. The maximum ductility index was 2.29 for SC0.25, while the minimum stiffness was 1.31 for SC 1.25 beam. The flexural resistance of SC beams show in beams deflection state, the primary crack with presence the waste plastic fibers was small, because of the resistance of plastic fibers to tensile stresses happening at a moment of growth the crack. It also shows that adding WPFs to SC up to (Vf=1%) results in a rise in the loads that cause initial cracks when compared to beams made with reference mix.

CRACKING PATTERN ANALYSIS OF THE TURNING BAND METHOD (TBM) APPLICATION ON A SINGLE-REINFORCEMENT BAR CONCRETE BEAM MODELLING USING THE MAZARS DAMAGE

The development of crack patterns in reinforced concrete structures is a randomly stochastic process influenced by the heterogeneous nature of concrete materials, which impacts the sensitivity to damage and variability in mechanical properties. The numerical simulation of damage pattern appearance on the reinforced concrete for special building structures needs a realistic result, especially in terms of crack distribution. The Turning Band Method (TBM) serves as a tool for assessing the variability of concrete heterogeneity, functioning as an operator to generate a random variable for each specific field. In this study, the investigation of crack patterns in reinforced concrete structures involves using a simple concrete beam sample, measuring 10x10x50 cm3, with a single longitudinal reinforcement cast in the centre. This beam is subjected to an axial tensile loading, while the Mazar Damage Model is employed as the concrete behaviour law. Through the implementation of The Turning Band Method (TBM) and the variation of the random field parameters, distinct crack patterns are observed, not only the number but also the locations of cracks. The use of a smaller correlation length showed 2 cracks while the larger size had around 1 to 3 cracks, with the first crack localizations of each sample generally occurring in the middle surface, in which a noticeable contrast to non-TBM modelling just displays 1 crack. Furthermore, the resulting probability of cracks for ten random draws demonstrates similarity to experimental tests and numerical simulation of the previous study, both at global and local levels.

Thermally-induced fracture in the oxide scale of T91 ferritic/martensitic steel after exposure to oxygen-saturated liquid lead–bismuth eutectic

Ensuring the continuity and stability of the oxide scale to separate T91 steel from lead-bismuth eutectic (LBE) is an effective method for limiting corrosion in the lead-based fast reactor system. In this study, we specifically investigated the impact of cooling thermal stress on the stability and damage of the oxide scales of T91 steel when exposed to oxygen-saturated liquid lead–bismuth eutectic at high temperatures. A corrosion test was conducted on T91 steels exposed to stagnant oxygen-saturated LBE at 500 °C. Experimental results indicated that oxide damage exists without any external force, including interface cracks and through-scale cracks perpendicular to the interface. We developed a three-layer peridynamic model of T91-(Fe,Cr)3O4-Fe3O4 to simulate the deformation and failure of oxides under a cooling process from high temperature to room temperature. The simulation results show that a temperature drop of about 200 °C from 500 °C can cause through-oxide cracks in the oxide scale, and subsequent cooling can lead to the propagation of interfacial cracks. Additional modifications were introduced in the model to account for the porosity of the oxide scale. Parametric investigations illustrate the effects of oxide scale thickness and porosity on the resulting crack patterns.

Evaluation of retrofitting effect of concrete filling in hollow RC columns using XFEM

Hollow RC columns are widely utilized in the construction of high piers in mountainous regions. Recently, precast hollow RC columns have been increasingly used to enhance transportability and ease of handling, aiding Accelerated Bridge Construction. This paper evaluated the effectiveness of concrete-filling retrofitting measures for hollow RC columns using eXtended Finite Element Method (X-FEM). Our focus was particularly on instances where original hollow sections and post-filled concrete sections don't behave as unified structures. The proposed X-FEM model's reliability was validated through simulations replicating compressive strength tests on molded concrete specimens and previous static loading tests on hollow RC columns conducted to evaluate the efficacy of concrete-filling retrofitting for hollow RC columns. The proposed X-FEM model successfully represents the compressive softening and fracture behavior of concrete under uniaxial compression. It also successfully replicated the lateral load capacity and the crack patterns of hollow RC columns observed in the previous experiments. When comparing the component ratios of bending and shear deformation of the columns, the shear deformation component of the hollow RC column retrofitted with the concrete filling was about 1.5 times larger than that of the solid RC column at each displacement. This result indicates that concrete-filling retrofitting might not enhance the shear capacity of hollow RC columns to the anticipated level in scenarios where the pre-existing hollow portion and the post-filled concrete portion fail to function as unified structures. Based on these findings, this study investigated the efficacy of anchor reinforcement in hollow RC columns filled with concrete to enhance the structural unity of existing and filled portions. The results indicate that anchor reinforcement improved the shear resistance properties by enhancing the structural unity between the pre-existing hollow portion and the post-filled concrete portion.

Enhanced pavement crack segmentation with minimal labeled data: a triplet attention teacher-student framework

ABSTRACT Effective crack detection is critical for pavement maintenance, yet existing methods face significant challenges. Deep learning has become a popular solution due to its superior accuracy and automation capabilities, but supervised methods require extensive labelled data, making it costly and time-intensive. Unsupervised methods, while less data-reliant, struggle with feature extraction, especially for indistinct crack edges. Semi-supervised methods attempt to bridge this gap by using minimal labelled data, enhancing accuracy while reducing manual labelling efforts. However, accurate segmentation remains difficult, particularly with sparse labelled data or complex crack patterns. These limitations highlight the need for a more effective approach. To address these challenges, we propose a novel framework based on a teacher-student model enhanced with triplet attention. Leveraging the Unet architecture, this approach enables efficient feature extraction with minimal labelled data. The teacher model refines predictions using an exponential moving average of the student model’s weights, while the student model is trained with supervised and uncertainty losses. Evaluations on three benchmark datasets demonstrate our framework outperforms fully supervised models, achieving higher intersection-over-union and dice scores with just 2% labelled data. This approach overcomes the limitations of existing methods, enabling accurate crack segmentation with minimal labelled data.

Influence of reinforcement reductions on the response of reinforced concrete half-joints

Reinforced concrete half-joints are susceptible to deterioration mechanisms primarily due to the leakage of surface water, often contaminated with chlorides from de-icing salts, through the expansion joint. Due to the joint geometric form, favourable conditions can be created inside the joint for the corrosion of steel reinforcement. To this end, seven reinforced concrete half-joints were tested to failure under three-point bending to investigate the effect of reinforcement reductions that simulate common deterioration scenarios arising from the corrosion of reinforcement. The results were then compared to the predictions of nonlinear finite element analyses and the strut-and-tie method. The results demonstrated that a reduction in the amount of reinforcement close to the re-entrant corner has major influence on the load-deflection response of reinforced concrete half-joints. The largest reductions in load-carrying capacity were obtained from the half-joints with a full removal of diagonal bars and a combined removal of diagonal and U-bars, both showing reductions in load capacity of more than 50 %. The failure mode in each case of simulated deterioration scenarios involved a shear failure at the nib, except one case which displayed a shear failure in the full depth section due to the reduced anchorage of the bottom reinforcement. Furthermore, it was shown that nonlinear finite element analyses provide accurate predictions of the load-deflection response and failure crack patterns. The strut-and-tie method was found to result in overly conservative predictions, with an average observed-to-predicted load ratio of 1.48 and a coefficient of variation (COV) of 10.2 %. This is considerably higher than an average load ratio of 1.05 and a COV of only 3.1 % obtained from the nonlinear finite element analyses.

In and out of plane behaviour of TRM strengthened heritage masonry elements

This paper presents detailed experimental and analytical investigations into the influence of textile-reinforced mortar (TRM) strengthening on the in-plane and out-of-plane response of unreinforced heritage masonry (URM) elements. The URM wall elements consist of hydraulic lime mortar and fired-clay bricks, and the TRM reinforcement employs mortar-embedded layers of alkali age-resistant glass meshes. Apart from the material characterisation tests on mortars, bricks, and TRM coupons, the experimental programme includes axial compression tests on wallettes, diagonal compression tests on square panels, as well as four-point bending tests on rectangular panels. In the latter, the bending loads are applied either parallel or perpendicular to the bed joints in order to assess the joint layout effect on the behaviour. With the aid of digital image correlation, the in-plane and out-of-plane enhancement in stiffness, strength, and ductility of the masonry elements due to the TRM strengthening is quantified, while the TRM influence on the crack patterns and failure modes is also examined. The results show that the number of mesh layers has a significant influence on the behaviour for the out-of-plane bending tests but plays a less pronounced role in the in-plane shear cases. Modified analytical models for the in-plane shear and out-of-plane bending capacities of reinforced masonry elements, of the type examined in this study, are also proposed and assessed alongside existing codified procedures. The application of current code provisions results in overly conservative estimates. In contrast, the proposed analytical approaches for determining the in-plane and out-of-plane strength provide close prediction of the experimental capacities from this study as well as those from a wider collated database of previous tests, and are therefore suitable for implementation in practical assessment and rehabilitation guidelines.

Numerical study on flexural behaviour of sulphate corroded RC beams strengthened with ultra-high-performance concrete

Ultra-high-performance concrete (UHPC) has found extensive application in the strengthening of existing reinforced concrete (RC) structures; however, limited knowledge exists regarding its use in RC structures exposed to sulphate attacks. This study developed a non-linear finite element analysis (FEA) model to predict the flexural behaviour of sulphate corroded RC beams strengthened with UHPC jackets. The FEA model, validated with experimental results, was extended to examine UHPC configurations and thicknesses. Evaluation included ultimate load capacity, serviceability state, and stiffness. Crack patterns, load-deflection behaviour, and strain distribution were analysed for strengthened beams at their respective ultimate loads along the mid-span cross-section height. FEA results showed diverse configurations significantly enhanced the load-carrying capacity of sulphate corroded RC beams by 54.5-88.6%. Strengthened beams exhibited a 64% increase in flexural moment capacity, with notable improvements in cracking and post-cracking stiffness. Strain distribution analysis revealed UHPC strengthening increased strain values, emphasising UHPC jackets’ substantial role in resisting stresses and enhancing flexural behaviour. As expected, the three-sided UHPC configuration outperformed two-sided and bottom-side ones. Increasing UHPC thickness proved most effective in bottom-side strengthening, followed by three-sided, with a lesser effect in two-sided strengthening. Theoretical predictions from the suggested flexural moment capacity calculation aligned well with FEA results.

Formation mechanism of radial and circular cracks promoted by delamination in drying silica colloidal deposits.

Cracks with radial and circular patterns are appealing in nature and industry. Although morphologies and propagation conditions of cracks are extensively studied, the formation mechanism of crack pattern by the interaction of channel fracture and interfacial delamination remains elusive. Here, we present the transition of radial to coexisting radial and circular crack patterns when the thickness of colloidal deposits on both hard and soft substrates exceeds a critical value, through the colloidal volume fraction dependence. In addition, a thickness-dependent phase diagram from radial crack to coexistence of radial and circular cracks was constructed with respect to the radius and the volume fractions of silica colloidal deposits. A phase-field fracture model is developed to elucidate how the formation of radial cracks is facilitated by simultaneous delamination. The warping-induced radial tensile stress at the bottom surface of the striped deposit is proportional to the thickness. It leads to subsequent nucleation and growth of circular cracks in thick deposits. This work provides insight into the formation mechanism of complex crack patterns in drying colloidal deposits and revolutionizes the design space of crack-based micro-nano structures.