Cracks In Materials Research Articles

Interaction between microcapsules and crack using XFEM and data-driven fracture toughness predictive model

The interaction mechanism between microstructures of materials, including microcrack, inclusion and interface defect, is crucial for studying the microscopic damage of materials. The interaction between microcapsules and cracks in self-healing material is examined using a combination of the extended finite element method (XFEM) and the interaction integral method, which is implemented by a program written in Fortran language. The non-dimensional stress intensity factors (SIFs) of a crack with a single microcapsule, a pair of microcapsules and a cluster of microcapsules are investigated. Moreover, the data-driven fracture toughness predictive model using a genetic programming-based symbolic regression (SR) technique is proposed by training the data from the XFEM program. Results reveal that the non-dimensional SIFs are related to the mechanical property, geometry and interface defect of microcapsule. The influence of microcapsule on the SIF is limited within a distance of five times the microcapsule radius. The predictive model quantifies the contribution of microscopic structures on the macroscopic fracture parameter, highlighting the potential of machine learning in guiding the quantitative design and discovery of high-performance smart materials.

Characterization of self-healing in cement-based materials with a low water-to-cement ratio during subsequent hydration

This study explores the role of subsequent hydration in healing cracks in cement-based materials, focusing on a water-cement ratio of 0.20 and aging up to 1260 days. A novel bond strength testing method and backscattered electron imaging (BSE) analyzed the relationship between bond strength and unhydrated cement. Techniques like X-ray diffraction (XRD), scanning electron microscopy (SEM), and mercury intrusion porosimetry (MIP) helped investigate crystal phase content and microstructural changes. Key findings reveal that subsequent hydration primarily produces calcium hydroxide (CH), calcium carbonate (CaCO3), and C–S–H gel. Bond strength notably increased to 36.08 % at 394 days, with a significant reduction in C3S and C2S phases and increases in CH and CaCO3. The calcium-silicon ratio varied across hydration products, with external products containing the highest ratio. The study demonstrates the transformation of C–S–H gel from low to high density and highlights the cohesive structure formation of CH and C–S–H gel, crucial for crack healing. Porosity showed an initial decrease followed by an increase, peaking at 54.14 % above the initial value. These findings underscore the importance of controlling unhydrated cement content for optimizing self-healing in cement-based materials.

Strip electro-mechanical yield model for three equal straight collinear cracks in piezoelectric materials

This paper is devoted to the development of a model to study three straight collinear cracks in piezoelectric materials under the influence of combined electrical and mechanical loading conditions. Mathematical relationships for the size of yield zones with mechanical yielding conditions and the saturation zone sizes to applied electrical field has been established. To make this plausible, two different cases are considered: first when the electrical saturation zones are bigger than the mechanical yield zones while other case in which situation is just opposite. Closed-form analytic expressions are derived for various fracture parameters with the help of well known complex variable method. Numerical results are presented to study the multiple cracks in different piezoelectric materials. Results obtained are reported graphically, analyzed and concluded.

Improvement of drilled holes quality by voice-activated ultrasonic vibration assisted drilling process of different orientation

Ultrasonic drilling enables drilling in difficult-to-machine materials, including ceramics and composites, with greater accuracy and precision. The localized and controlled energy application of ultrasonic frequency minimizes the risk of material fracture, cracks, or delamination. This capability ensures that the drilled hole maintains its intended dimensions, shape, and integrity, resulting in improved hole accuracy and overall drilled hole condition. Ultrasonic drilling is an advanced machining technique that utilizes high-frequency vibrations to improve the drilling process. In this designed voice-activated module, electrical energy has been converted into mechanical vibrations through piezoelectric transducers, generating ultrasonic waves in the range of 20 kHz to 80 kHz. Experiments has been conducted considering different process parameters with the changing different orientations of the emitters-horizontal and vertical positions and comparison was done with no vibration conditions. It has been observed that with the application ultrasonic vibration frequency the surface roughness improved by 45% in horizontal position, 28% in vertical position compared with no vibration conditions-conventional techniques. It has also been observed that the circularity index of the drilled holes also improved by 31% for horizontal and 7.6% for vertical position.

A novel thermal-tailored strategy to mitigate thermal cracking of cement-based materials by carbon fibers and liquid-metal-based microencapsulated phase change materials

Massive concrete structures are susceptible to thermal cracking due to the large surface-to-internal temperature gradients induced by the exothermic cement hydration, threatening their durability and safety. This study explored a novel thermal-tailored strategy to mitigate thermal cracking of cement-based materials by incorporating carbon fibers (CF) and liquid-metal-based microencapsulated phase change materials (MEPCM). Specifically, spherical MEPCM composed of In-Bi-Sn alloy cores coated by polyvinyl alcohol shells was prepared through a high-speed liquid-phase dispersion method, with average diameters of 36.26 μm and a high volumetric latent heat of 214 MJ/m3. The synergistic effect of CF and MEPCM on the microstructure, mechanical and thermal properties of cement mortars was further investigated. Upon adding 0.3 wt% of CF and 3.2 vol.% of MEPCM, the flexural strength of cement mortars exhibited a significant increase of 30.3 %. Microanalysis revealed that the molten MEPCM could flow to fill the pores and microcracks within its surrounding matrix and form a network skeleton with well-dispersed CF, imparting flexibility to the typically rigid cement hydrates. By this way, the thermal conductivity of cement mortars was increased by 21.7 % and internal temperature rise was decreased by 12 ℃ by adding 4.8 vol.% of MEPCM, contributing to the mitigation of risks associated with thermal cracking. The research outcomes will provide valuable insights into the development of thermal cracking-resistant cement-based materials in a highly efficient way.

Influence of basalt fiber and polypropylene fiber on the mechanical and durability properties of cement-based composite materials

To boost the mechanical strength and endurance quality of cement-based composites, basalt fiber and polypropylene fiber have been included cement-based composites in a single-doped and mixed manner, respectively. Through the tests of flexural strength, compressive strength, drying shrinkage and freeze-thaw cycle, the mechanics properties and endurance quality of cement-based composites with different fiber contents were analyzed. Scanning electron microscopy and a mercury intrusion test were used to compare and study the microstructure and pore structure properties of cement-based composites. The results indicate that the improvement of compressive strength for cement-based composites by single adding basalt, polypropylene fiber and mixed addition of two kinds of fibers is not obvious, but improving the flexural strength of composites by single addition of fiber and 1:1 mixing in a certain dosage range is effective. Among them, 1:1 mixed fiber shows a better advantage superposition effect, which shows better enhancement and toughening effect on composites. Fiber single doping and 1:1 mixing can reduce the Drying shrinkage and mass loss rate of the composites within a certain range, and enhance the composites' ability to resist Drying shrinkage and freezing. Based on the comprehensive mechanical properties and durability tests, it is recommended that the content range of the two fibers mixed with 1:1 is 0.4 %–0.6 %. Both basalt fiber and polypropylene fiber can be closely combined with the cement matrix, and randomly distributed in the composite material to form a network structure, which has the function of series skeleton, effectively inhibits the generation and expansion of cracks in the composite material, and improves the microstructure of the composite material. Both basalt fiber and polypropylene fiber can reduce the harmful pores and multi-harmful pores of the composite material, and transform them into harmless pores and less harmful pores, refine the internal pore structure of the composite material, and improve its compactness. The two kinds of fibers are randomly distributed to form a network structure, which refines the large pore size inside the composite material and blocks the connected pores, and the basalt fiber is refined to fill the interface between the polypropylene fiber and the cement matrix, so that the composite material is more compact, thereby significantly improving the mechanical properties and durability of the composite material.

Mastering the art: Proficient finite element implementation and robust evaluation of a strain-hardening porous ductile material crack growth prediction model at finite strain

Accurate prediction of crack extension is crucial for ensuring the structural integrity of metal components exposed to diverse loads. While the Gurson model and its extensions are widely accepted for delineating ductile fracture stages, especially in porous materials with a rigid-perfectly plastic matrix, their efficacy diminishes in the presence of strain-hardening matrices. To address this limitation, our study introduces a robust numerical implementation and assessment of Perrin's model. In contrast to Gurson's approach, Perrin's model incorporates two distinct strain-hardening parameters derived from an intricate analysis of a strain-hardening hollow sphere subjected to axisymmetric loading.Moving beyond theoretical discussions, this paper actively engages in the rigorous evaluation of Perrin's model under various scenarios, encompassing isotropic, kinematic, and mixed isotropic-kinematic hardening conditions. The model's effectiveness is convincingly demonstrated through meticulous comparisons between numerical simulations and real-world experimental observations conducted on pre-cracked specimens.Facing challenges related to achieving global elastic-plastic convergence in large-scale simulations, our research introduces a sophisticated approach. Leveraging stiffness tangent moduli ensure the maintenance of quadratic convergence in global Newton method iterations. This not only enhances the reliability of our simulations but also underscores the practical applicability of our findings.The study also focuses on the necking and crack propagation of a cylindrical specimen through meticulous computational modeling. Our mesh captures intricate details and addresses stress gradients, revealing coplanar crack propagation contrary to prior beliefs. The confirmation of the cup-cone fracture effect challenges previous interpretations, emphasizing the critical role of void nucleation. This reinforces the credibility and applicability of our approach in advancing the understanding of material fracture behavior.In summary, this study significantly contributes to existing knowledge in fracture prediction models, offering a robust framework for predicting ductile fracture under substantial deformations. The presented findings pave the way for advancements in structural engineering, providing invaluable insights for optimizing the performance and resilience of metal structures in real-world applications.

Performance of Engineered Cementitious Composites (ECC) in shield tunnel segmental joints: A comparative study with ordinary reinforced concrete

Shield tunnel segmental joints are traditionally vulnerable, limited by their tensile capacity and susceptibility to cracking. Engineered Cementitious Composites (ECC) offer a promising solution due to their superior tensile strength, exceptional crack resistance, and remarkable toughness. However, the application of ECC in tunnel segment joints remains unexplored. To address this gap, this paper conducted comprehensive full-scale tests of ECC segmental joints versus ordinary reinforced concrete (RC) segmental joints. It investigated mechanical responses including material behavior, deflection, joint action, bolt strain, crack development, and failure modes. Results revealed that: (1) ECC joints provided a 33.97 % higher stable bearing capacity and a 50 % increase in initial cracking strength compared to RC joints. (2) ECC joints excelled in crack control, maintaining crack widths below 0.2 mm, while RC joints experienced significant cracking with widths exceeding 1 mm. (3) In terms of toughness, ECC joints surpassed RC by 66 % in the elastic stage and 123 % in the normal serviceability stage, with 96 % higher ductility. (4) ECC joints significantly outperformed RC joints in bolt stress uniformity and concentration, achieving a 43.21 % reduction in average bolt stress. (5) Regarding multi-scale mechanical effects, ECC joints increased the toughness and strength advantage over RC by more than 45 % in the elastic phase. These results reveal the potential of ECC in significantly enhancing the durability and resilience of shield tunnels, particularly in harsh environments subjected to high ground stress or seismic activities.

Interface crack analysis in 2D bounded dissimilar materials using an enriched physics-informed neural networks

This study explores the application of physics-informed neural networks (PINNs) to analyze interface crack problems within the context of elastic bimaterial fracture mechanics. Bimaterial interface cracks exhibit a distinct behavior compared to cracks in homogeneous materials, and this behavior often involves oscillatory phenomena that can pose challenges in numerical modeling. By employing neural networks for solution approximation, PINNs are meshless and are trained using batches of collocation points, which may be randomly or strategically sampled across the computational domain. To effectively capture the oscillatory singular behavior in the crack-tip regions, this paper introduces an enhanced PINNs formulation that enables the modeling of interface cracks without requiring any refinement near the crack-tip. The trainable parameters of the current PINNs are dynamically optimized throughout the training process to fulfill both the underlying differential equations and the associated initial/boundary conditions. One of the significant advantages of the present PINNs is that it uses enrichment functions to capture the behavior around the crack region, allowing for greater flexibility in handling irregular or complex crack paths. The method's accuracy and stability are validated across several benchmark examples.

Novel microbial synthesis of titania nanoparticles using probiotic Bacillus coagulans and its role in enhancing the microhardness of glass ionomer restorative materials

Dental caries is a commonly occurring non-communicable disease throughout the world that might compromise the quality of any individual’s life. Glass ionomer cements (GIC) are the most acceptable restorative materials due to their ease of manipulation, minimal tooth loss and least invasive strategy; however, they lack mechanical stability that has become a point of concern. Nanoparticles (NPs) are an outstanding option for modifying and enhancing the properties of dental materials. The focus of this study was to prepare novel, biocompatible titania dioxide (TiO2) NPs as a dental-restorative material using an efficient probiotic Bacillus coagulans. The prepared NPs were incorporated into glass ionomer restorative material at varying concentrations and investigated for cell viability percentage, microhardness and surface morphology. Results indicated that pure 100% anatase phase TiO2 NPs with particle size of 21.84 nm arranged in smooth, spherical agglomerates and clusters forms. These NPs depicted cell viability > 90%, thus confirming their non-cytotoxic behavior. GIC restorative materials reinforced by 5% titania (TiO2) NPs demonstrated the highest microhardness in comparison to the control group and other experimental groups of the study. Surface morphology analysis revealed a reduction in cracks in this novel dental-restorative material supporting its compatible biological nature with better hardness strength and negligible crack propagation. Overall, these results indicated that TiO2 NPs produced using a biological approach could be easily used as restorative materials in dental applications.Graphical

An application of machine learning for material crack diagnosis using nonlinear ultrasonics

Crack diagnosis in non-destructive testing often requires reference data from the structure before damage or a considerable amount of response data. Also, detecting compression cracks is challenging. In this study, a machine learning-based method is proposed for diagnosing cracks in structures under compression. The method consists of convolutional neural networks (CNN) and fully connected networks (FCN). The CNN extracts features from nonlinear ultrasonic signal data, and the features determine the occurrence of fatigue cracks in a target specimen. Four types of input data are defined in accordance with the number of input frequency combinations. The performance of the proposed method is investigated using each data type to secure efficiency and accuracy in diagnosing aluminum specimens under various compression conditions. As a result, the F1 score, a measure of accuracy, of the proposed method depends on the number of input frequency combinations. The method detects high-compression cracks with high accuracy compared to the present technology specialized for compression cracks in a certain data type. A high accuracy of more than 96% is achieved with less computation time. The proposed method will provide an accurate crack diagnosis for compression cracks with reduced time and effort.

The Review of Research on Fatigue Crack Propagation in Metallic Materials

In recent years, with the development of industry and scientific technology, the demand for materials has been increasing. Fatigue crack propagation is an important issue in the field of materials, and developing relevant theories and methods, understanding the mechanisms of fatigue cracks, and making scientific predictions on fatigue crack propagation are hot topics both domestically and internationally. Fracture mechanics, as a discipline studying the strength and propagation of cracks in materials, has developed a relatively complete theoretical system and engineering application methods over more than 100 years of continuous development. This article focuses on the effects of factors such as temperature, stress ratio, and load frequency on the fatigue crack propagation characteristics of metallic materials, and summarizes the common theories and methods of fatigue crack propagation.

The intrinsic relationship of the thermal stress intensity factor and the temperature difference at the crack surface

The intrinsic relationship of the thermal stress intensity factor and temperature difference between the upper and lower surface of the crack have been studied in this paper. The results show the thermal stress intensity factor is always proportional to the temperature difference between the upper and lower crack surface, and the ratio depends only on material parameters and crack length, but is independent of loading condition. For a finite medium problem, the above conclusion is still valid by simply adding a size related correction factor. When the size of medium is 10 times larger than the crack size, the size related correction factor is less than 1.019, that is, the error is less than 2%. Our conclusion provides a theoretical basis to estimate the localization thermal stress intensity factor simply by measuring the temperature difference of the crack surface.

The synergistic effect of microorganisms and multiple admixtures on improving the self-healing of cracks in biogenic mortar exposed to different marine environments

Existing research has inadequately addressed the synergistic effects of microorganisms and admixtures in promoting self-healing behavior and mechanisms of cracks in marine environments, including the atmospheric zone, tidal-splash zone, and submerged zone. This study primarily involved the incorporation of multiple admixtures and microorganisms into cement to prepare two types of biogenic mortars: Bacillus pasteurii-based mortar (BPM) and Bacillus subtilis-based mortar (BSM), with ordinary mortar (OM) serving as the control group. The mechanical properties, electrical flux, and pore structure of the mortars were investigated. Additionally, the self-healing behavior and mechanisms of cracks were studied under atmospheric, tidal-splash, and submerged conditions. The results indicate that with increasing curing age, the synergistic effect of admixtures and microorganisms continuously refined the pore structure of the specimens and enhanced their flexural strength, compressive strength, and resistance to chloride ion penetration. The atmospheric environment was found to be unfavorable for the self-healing of cracks in the specimens. However, in the submerged and tidal-splash zones, the combined action of microorganisms and admixtures led to more pronounced self-healing phenomena in the biogenic mortars compared to OM. Particularly, the self-healing effect of BSM cracks was more pronounced in the tidal-splash zone, with a 100% self-healing efficiency observed after 53 days. This was attributed to the ability of microorganisms in the tidal-splash zone to induce calcium carbonate precipitation on the surface of cracks in admixture-modified cementitious materials, thereby reducing the penetration of seawater, CO2, and O2 into the cracks, lowering the carbonation reaction of Ca(OH)2 crystals, and reducing the formation of brucite crystals inside the cracks, consequently enhancing the water permeability resistance of the specimens. These research findings hold significant engineering implications for improving the durability and service life of coastal self-healing concrete structures.

Analytical solution of the stress field and plastic zone at the tip of a closed crack

The investigation of stress field and plastic zone distribution at the closed crack tip provides a fundamental basis for failure analysis and life prediction of geotechnical materials. Closed crack is a common crack in geotechnical materials. Studying the distribution of stress field and plastic zone at the tip of closed crack can provide theoretical basis for stability evaluation of geotechnical structures. In this study, we employ the superposition principle to obtain complex function solutions for the stress field and displacement field at the crack tip. Furthermore, we analyze the plastic zone distribution at the crack tip based on the Mohr Coulombs criterion. We investigate how factors such as crack angle, confining pressure, and material properties influence the stress field, displacement field, plastic zone size, and crack propagation direction. Our results demonstrate that this method effectively characterizes the distribution of stress field and displacement field at closed crack tips. Moreover, we elucidate that wing cracks are primarily formed due to tension-shear coupling effects. The solutions for the stress field and displacement field at the crack tip are obtained using the superposition principle. The distribution of the plastic zone at the crack tip is analyzed based on the M-C (Mohr-Coulomb) criterion. Subsequently, an analysis is conducted to investigate the influence of crack angle, confining pressure, and material properties on stress field, displacement field, plastic zone, and crack propagation direction. Lower crack angles and higher confining pressures effectively suppress slip between crack surfaces by reducing tension-shear coupling effects and inhibiting wing foil crack development. The results further indicate that the rock cohesion and internal friction angle exert negligible influence on the stress field, displacement field, plastic zone shape at the crack tip, as well as the growth direction of new cracks. The results demonstrate the effective representation of stress field and displacement field at the closed crack tip using this method. The stress distribution at the crack tip reveals that the tension-shear coupling effect primarily contributes to wing crack formation. Lower crack angles and higher confining pressures effectively suppress surface slip, reduce tension-shear coupling effects, and inhibit wing crack propagation. Furthermore, material properties do not influence the crack propagation angle, stress field, or displacement field.

New approach for determining the fracture parameters by electromagnetic-mechanical coupling

This paper introduces a novel method for assessing fracture mechanics parameters such as Stress Intensity Factor (SIF), Energy Release Rate (J) and Crack Tip Opening Displacement (CTOD). An electromagnetic–mechanical coupling (EMC) approach is employed to evaluate and to measure these fracture parameters by monitoring the variation of impedance using eddy currents. This approach relies on the eddy current signal obtained from a sensor, which calculates and verifies SIF parameters along with the J-integral and CTOD through changing the sensor impedance. To ensure theoretical consistency, the magnetic field is theoretically used, formulated and verified. Additionally, a numerical simulation method employing the finite element method is used to analyze and identify cracks in structures and assess their propagation. The quantification of SIF and J-integral parameters is demonstrated using two sensors based on a differential probe. This research paper demonstrates that the proposed method is the most efficient approach for exploring and detecting cracks in materials, as well as understanding their propagation behavior.

Influence of Recycled High-Density Polyethylene Fibers on the Mechanical and Electrochemical Properties of Reinforced Concrete

The quantity of different plastics generated after consumption is an impact factor affecting the environment, and the lack of recycling generates solid waste. The purpose of this work is to incorporate high-density recycled polyethylene fibers (HDPE) for possible use as concrete reinforcement. Physical and mechanical properties from recycled fibers were analyzed, such as density, absorption, and stress resistance, as well as workability, air content, porosity, concrete compression, and flexural strength properties. Samples were prepared with a low fiber content of 0.2% and 0.4%, as a substitution for sand weight, and lengths of 10 and 30 mm. To study corrosion phenomena, the specimens were exposed to a saline environment containing 3% sodium chloride for 365 days, and the electrochemical techniques including half-cell potential (HCP), electrochemical noise (EN), linear polarization resistance (LPR), and electrochemical impedance spectroscopy (EIS) were applied. The results showed a 4.8% increase in compressive strength with a low fiber percentage and short geometries, while flexural strength increased marginally by 2.3% with small quantities of HDPE fibers. All these factors contribute to greater material durability, less permeability, and crack control. A positive effect of fibers with short dimensions on the corrosion processes of a steel bar was observed, with the fibers acting as a physical barrier against the diffusion of chloride ions.

Study of the inhibition mechanism of sapphire subsurface damage by tangential ultrasonic vibration

Ultrasonic vibration has a certain effect on the crack propagation tendency during sapphire grinding, but the mechanism of the effect on the crack propagation tendency has not yet been elucidated. In this study, tangential ultrasonic vibratory scratching and normal scratching sapphire processes were simulated using the discrete element method, and the expansion tendency of sub-surface cracks in the scratching sapphire process was analyzed in terms of cutting forces and stresses. The results of the study show that the crack depth decreases with increasing scratch speed and increases with increasing scratch depth; The greater the variation in cutting force, the greater the number of cracks formed and the crack propagation is mainly distributed near the maximum residual tensile stress; The introduction of tangential ultrasonic vibration induces a decrease in residual tensile stresses and an increase in residual compressive stresses, thus inhibiting subsurface crack propagation; The suppression of subsurface cracks becomes more pronounced as the amplitude increases. Finally, tangential ultrasonic vibratory scratching and normal scratching sapphire experiments were comparatively studied and the experimental results were in agreement with the simulation results. This study provides some theoretical guidance for the suppression of subsurface cracks in sapphire materials during the grinding process.

Mg/Al Double-Pillared LiNiO2 as a Co-Free Ternary Cathode Material Ensuring Stable Cycling at 4.6 V.

Cobalt-free (Co-free) and nickel-rich (Ni-rich) cathode materials have attracted significant attention and undergone extensive studies due to their affordability and superior energy density. However, the commercialization of these Co-free materials is hindered by challenges such as cation disorder, irreversible phase changes, and inadequate high-voltage performance. To overcome these challenges, a Co-free ternary cathode material of Mg/Al double-pillared LiNiO2 (NMA) synthesized via a wet-coating and lithiation-sintering technique is proposed. Fundamental studies reveal that Mg and Al have the potential to form a distinctive double-pillar structure within the layered cathode, enhancing its structural stability. To be specific, the strategic placement of Mg and Al in Li and Ni layers, respectively, effectively reduces Li+/Ni2+ disorder and prevents irreversible phase transitions. Additionally, the inclusion of Mg and Al refines the primary grains and compacts the secondary grains in the cathode material, reducing stress from cyclic usage and preventing material cracking, thereby mitigating electrolyte erosion. As a result, NMA demonstrates exceptional electrochemical performance under a high charge cutoff voltage of 4.6 V. It maintains 70% of initial specific capacity after 500 cycles at 1 C and exhibits excellent rate performance, with a capacity of 162 mAh g-1 at 5 C and 149 mAh g-1 at 10 C. As a whole, the produced NMA achieves a high structural stability in cases of excessive delithiation, providing a groundbreaking solution for the development of cost-effective and high-energy-density cathode materials for lithium-ion batteries.

State-of-the-art review on meshless methods in the application of crack problems

Meshless or meshfree methods (MMs) are practical and excellent numerical techniques for solving crack problems. With the inherent limitations of mesh-based methods such as the finite element method (FEM) in modeling cracks, MMs have captivated the attention of researchers worldwide because of their conspicuous merits, including mesh independence and higher-order continuity. However, the most recent review literature on MMs in crack problems is only available until 2018, and no relevant analyses have been reported in detail since then. To fill this gap, this state-of-the-art review explores the novel potential and advancements of MMs in crack problems. Generally, eight approaches are implemented with MMs to reproduce crack behaviors. To improve efficiency and stability, the existing strategies are explored in terms of numerical integration, method coupling, and adaptive analysis. Based on these techniques, 82 highly cited and influential articles are analyzed to determine the specific MMs, simulation techniques, and the enhanced strategies that have been adopted. According to existing studies, various novel MMs have been proposed to analyze cracks. Furthermore, flexible coupling of multiple techniques to simulate cracks can be applied to different forms of cracks in various materials. However, adaptive analysis still needs to be widely performed in the MMs for crack problems due to the absence of a solid mathematical foundation for error estimators. This paper presents the research gaps and the future prospect of MMs in the application of crack problems. It should be stated that significant works on numerical methods for modeling cracks predating 1994 are not cited in this paper, a decision considered by the authors to be non-essential to its scope and objectives.