Theoretical and Applied Fracture Mechanics最新文献

{"title":"Beyond classical fracture mechanics: A micromechanics-informed non-local fracture onset criterion for mixed-mode loading of orthotropic materials","authors":"Farnoush Nodoumi,&nbsp;Mahdi Fakoor","doi":"10.1016/j.tafmec.2025.105186","DOIUrl":"10.1016/j.tafmec.2025.105186","url":null,"abstract":"<div><div>Non-local micromechanics-informed mixed-mode fracture onset criteria are proposed for isotropic and orthotropic materials. First, a general framework for a non-local mixed-mode fracture criterion is developed based on a non-local stress condition. Subsequently, a novel micromechanics-based damage parameter is introduced to capture micromechanical interactions ahead of the crack tip within a characteristic length of the fracture process zone (FPZ) for isotropic materials. This parameter is then extended to account for orthotropic materials. The fracture limit curve (FLC) of the proposed orthotropic criterion is compared to established classical fracture criteria and experimental data for Eastern red spruce and Scots pine, both considered as orthotropic materials. The impact of microcrack density on the proposed damage parameter and material fracture limit curve is studied, and a prediction band is presented that captures the interplay between FPZ influence and LEFM conservative criteria, offering a more accurate prediction. Furthermore, a valuable methodology for estimating critical material microcrack density based on experimental data and fracture limit curves is provided.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"140 ","pages":"Article 105186"},"PeriodicalIF":5.6,"publicationDate":"2025-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144902232","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Design-oriented fracture criteria for orthotropic composites based on minimum strain energy density theory","authors":"Mohamadmahdi Ebrahimi,&nbsp;Mahdi Fakoor","doi":"10.1016/j.tafmec.2025.105182","DOIUrl":"10.1016/j.tafmec.2025.105182","url":null,"abstract":"<div><div>Accurately and efficiently predicting the fracture behavior of composite materials under mixed-mode loading I/II remains a significant challenge. This study presents novel design-oriented fracture criteria based on the Minimum Strain Energy Density Theory (MSEDT) to effectively address these challenges. To improve the accuracy of predictions for the critical stress intensity factor (CSIF) related to fiber-aligned cracks, the classical Strain Energy Density (SED) criterion is enhanced by including micromechanical crack initiation angles. Subsequently, a statistically averaged initiation angle, derived from forty-two highly orthotropic materials, is used to significantly reduce computational costs while maintaining acceptable accuracy. This approach achieves a balance between precision and simplicity. Furthermore, to account for the variability observed in experimental results due to T-stress effects at arbitrary crack-fiber orientations, two complementary criteria based on micromechanical and macromechanical assumptions are proposed. The micromechanical version offers a high-risk estimate, whereas the macromechanical variant provides a conservative prediction. Additionally, a semi-empirical criterion that explicitly considers T-stress effects is introduced for the frequently encountered case of cracks that are perpendicular to fibers. All proposed criteria show strong agreement with experimental data, proving reliable for preliminary design and structural assessments. Therefore, these criteria can support effective design decisions and structural integrity evaluations in aerospace, automotive, and other composite-utilizing industries.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"140 ","pages":"Article 105182"},"PeriodicalIF":5.6,"publicationDate":"2025-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144902233","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Failure mechanism of rock-like specimens under uniaxial compression: Effects of hole-crack spatial relationship and crack number","authors":"Faxin Li ,&nbsp;Zhi Li ,&nbsp;Qianqian Xue ,&nbsp;Sheng Wang","doi":"10.1016/j.tafmec.2025.105185","DOIUrl":"10.1016/j.tafmec.2025.105185","url":null,"abstract":"<div><div>The geometric characteristics of cracks exert a significant influence on the stability and failure behavior of rock masses, particularly in underground engineering contexts. This study integrated uniaxial compression experiments with numerical simulations using the Particle Flow Code in Two Dimensions (PFC^2D) to systematically investigate the failure modes, acoustic emission (AE) characteristics, and stress distribution patterns of rock-like specimens with varying hole-crack distances and crack numbers. The results indicated that the hole-crack distance had a pronounced impact on the specimen’s peak strength and failure mode. When the distance was 20 mm, the coupling effect between the hole and the crack was most prominent, often triggering boundary-crack-hole penetration failure. As the distance increased, the failure mode transitioned into asymmetric failure. An increase in crack number enhanced crack dominance, driving the failure zone from the specimen boundary toward the central zone, while intensifying stress field disturbance and localized instability. AE analysis showed that when the hole-crack distance was 15–20 mm and the crack number was two, energy release was abrupt and concentrated, frequently leading to severe instability. When the crack number increased to three, the failure process became more gradual, accompanied by greater energy consumption. Stress monitoring and numerical results further revealed that the spatial configuration between holes and cracks, combined with crack quantity, jointly altered stress transmission paths, induced localized stress redistribution, and promoted the development of asymmetric failure zones. These findings contribute to a deeper understanding of the failure mechanisms of fractured rock masses and offer theoretical guidance for the prevention and mitigation of crack-induced hazards in underground engineering.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"140 ","pages":"Article 105185"},"PeriodicalIF":5.6,"publicationDate":"2025-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144890817","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Crack propagation analysis of angled surface-crack clay under compressive loading","authors":"Wei Wang,&nbsp;Jibin Shang,&nbsp;Deheng Zhang,&nbsp;Aiyu Hu","doi":"10.1016/j.tafmec.2025.105183","DOIUrl":"10.1016/j.tafmec.2025.105183","url":null,"abstract":"<div><div>This study develops a dual-criterion framework integrating maximum circumferential stress (MCS) and maximum shear stress (MSS) theories to characterize fracture initiation in angled surface-crack clay under axial compression, systematically incorporating the complete <em>T</em>-stress tensor components (<span><math><mrow><msub><mi>T</mi><mi>x</mi></msub><mo>,</mo><msub><mi>T</mi><mi>y</mi></msub></mrow></math></span> and <span><math><mrow><msub><mi>T</mi><mrow><mi>xy</mi></mrow></msub></mrow></math></span>) to establish predictive models for critical fracture process zone (FPZ) sizes and crack initiation angles. Comparative analysis reveals that the MCS criterion incorporating <span><math><mrow><msub><mi>T</mi><mi>x</mi></msub></mrow></math></span> and <span><math><mrow><msub><mi>T</mi><mi>y</mi></msub></mrow></math></span> provides optimal predictive capability for the initiation of new fractures in clay specimens containing mid-upper surface cracks, while the <em>T</em>-stress-excluded MCS criterion yields better agreement for right-upper and top-right cracks, with MSS-based predictions consistently showing significant deviations regardless of crack locations. The results demonstrate that the <em>T</em>-stress exerts a relatively limited influence on crack initiation angles in clay specimens containing angled surface cracks under axial compression. Concurrently, the critical FPZ size of 1.28 mm for mid-upper surface cracks is revealed. These findings provide a significant theoretical basis for fracture mechanics analysis of geomaterials and predictive modeling in geotechnical engineering applications.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"140 ","pages":"Article 105183"},"PeriodicalIF":5.6,"publicationDate":"2025-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144913919","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Frost heaving pressure in fractured rock under different freezing paths: Multiphysics analysis","authors":"Fengqi Shen,&nbsp;Wenliang Qiu","doi":"10.1016/j.tafmec.2025.105184","DOIUrl":"10.1016/j.tafmec.2025.105184","url":null,"abstract":"<div><div>Accurate prediction of frost heaving pressure in fractured rock remains challenging for cold-region engineering due to oversimplified models neglecting seepage and freezing-path effects. This study establishes a thermal–hydraulic-mechanical (THM) coupling model for fractured rock, introducing an equivalent water expansion method to simulate ice-water phase change, seepage, and frost heaving pressure distribution. Validated through laboratory tests on crack propagation and pressure evolution, the model quantifies how freezing paths govern frost damage. Simulations demonstrate that uniform freezing (Case B) generates 16.8 % higher peak pressure than unidirectional freezing (Case A) in low-permeability sandstone, primarily due to restricted seepage pathways inhibiting pressure dissipation. Rock permeability critically modulates this effect: frost heaving pressure increases by 3.91 MPa in Case A but only 1.29 MPa in Case B when permeability drops from 10⁻¹⁶ to 10⁻¹⁹ m². Furthermore, higher elastic modulus (5–30 GPa) increases frost heaving pressure by 111.9 %–125.3 % by constraining volumetric deformation. These findings underscore the necessity of integrating freezing path effects and seepage dynamics into frost damage predictions for cold-region geotechnical engineering.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"140 ","pages":"Article 105184"},"PeriodicalIF":5.6,"publicationDate":"2025-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144902234","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Examining crack nucleation under spatially uniform stress states with a complete phase-field model for fracture","authors":"Bo Zeng,&nbsp;Johann Guilleminot,&nbsp;John E. Dolbow","doi":"10.1016/j.tafmec.2025.105170","DOIUrl":"10.1016/j.tafmec.2025.105170","url":null,"abstract":"<div><div>This work concerns crack nucleation problems in elastic brittle materials subjected to stress states that are spatially uniform or nearly so. Such conditions arise under a wide range of settings, including standard tests of material strength. This class of problems presents challenges from both modeling and computational standpoints, as the localization of fracture occurs as the strength is violated, and naturally represents a bifurcation from a state of uniform stress. In this work, these problems are examined using a complete phase-field model for fracture. In contrast to classical phase-field models, the complete model provides a formulation that can account for the elasticity, the strength, and the toughness of elastic brittle materials, whatever these material properties may be. We consider problems ranging from the fracture of thin films bonded to substrates to crack nucleation during thermal quenching. Where appropriate, we provide comparisons to both experimental observations and results provided by classical phase-field models for fracture. We also explore the introduction of stochastic aspects, using random field models for strength parameters. The material strength fields are represented either through a translation model with controlled correlation lengths, or with a simple random mosaic field (without spatial correlations). The results illustrate the utility of models employing arbitrary strength surfaces and spatial perturbation for simulations of fracture nucleation under near uniform stress states.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"140 ","pages":"Article 105170"},"PeriodicalIF":5.6,"publicationDate":"2025-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144906896","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Numerical investigation of constraint-dependent crack growth in X70 pipeline steel using XFEM-based cohesive segments approach with surface strain-based J-integral evaluation","authors":"Amirhossein Iranmehr ,&nbsp;Mohammad Kheirkhah Gilde ,&nbsp;Haoyang Li ,&nbsp;Benjamin Hanna ,&nbsp;Lyndon Lamborn ,&nbsp;Arman Hemmati ,&nbsp;Samer Adeeb ,&nbsp;James Hogan","doi":"10.1016/j.tafmec.2025.105175","DOIUrl":"10.1016/j.tafmec.2025.105175","url":null,"abstract":"<div><div>This study employs the Extended Finite Element Method-based cohesive segments approach to investigate the constraint-dependent fracture behavior of API X70 pipeline steel. The Single Edge Notched Tension (SENT) geometry is used for numerical analysis within the <em>Abaqus</em> software since it closely replicates the tip constraint of the surface flaws typically observed on steel pipelines. The primary focus is to derive J-integral and Crack Tip Opening Displacement (CTOD) resistance curves for plain-sided and side-grooved specimens with varying initial crack depths. Before post-processing the XFEM models, validation occurred against experimental data. Then, three J-integral calculation methods were systematically compared, including incremental unloading compliance, CTOD conversion, and the surface strain-based XFEM method. Accordingly, a path-independency analysis of the surface strain-based XFEM method, which overcomes limitations for J-integral evaluation during crack growth, was conducted to assess the influence of the plastic zone. Results indicate that side-grooved specimens yield 3%–10% lower CTOD values than plain-sided counterparts due to enhanced crack-tip constraint while reducing variability in resistance curves. Among the J-integral calculation methods, the surface strain-based XFEM approach yielded results similar to standardized methods for crack extensions lower than 1 mm. However, the incremental unloading compliance-based method underestimates J-integral relative to the other two methods beyond 1 mm. It is also found that shallow cracks may exhibit up to 13% higher J-integral values than deep cracks, highlighting the constraint dependence of fracture toughness. This study’s outcomes show the efficacy of XFEM in simulating low-constraint fracture conditions and provide invaluable insights for pipeline integrity assessments.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"140 ","pages":"Article 105175"},"PeriodicalIF":5.6,"publicationDate":"2025-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144887395","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Damage-fracture evolution mechanism of rock bridge structures in flawed sandstone under cyclic disturbance: Insights from DIC-AE","authors":"Jun Wang ,&nbsp;Xingxing Xie ,&nbsp;Wenpu Li ,&nbsp;Xianhui Chen ,&nbsp;Xiaodong Zhang ,&nbsp;Nan Fan ,&nbsp;Tao Wang ,&nbsp;Huan Zhang","doi":"10.1016/j.tafmec.2025.105180","DOIUrl":"10.1016/j.tafmec.2025.105180","url":null,"abstract":"<div><div>In deep mining engineering, the geological-mining interaction (repeated disturbance from mining activities leading to stress field reconstruction) results in significant roof instability and failure. This study uses combined Acoustic Emission (AE) and Digital Image Correlation (DIC) techniques to monitor and conduct cyclic loading tests on double-fractured sandstone specimens with different rock bridge angles. The study systematically analyzes the impact of rock bridge angle on the dynamic response and damage-fracture mechanisms of sandstone under cyclic loading. The results show that cyclic loading hardens sandstone, but the weakening effect of initial defects is more dominant. The 60° rock bridge angle specimen exhibits the lowest D_ed, with most of the energy stored elastically. Furthermore, the evolution of AE parameters characterizes the progressive damage under cyclic loading. For the 60° sample, the rapid crack propagation results in AE energy concentrating at the peak release stage, consistent with the macroscopic energy release characteristics. The RA-AF plot indicates that microscopic damage is primarily driven by the propagation of tensile cracks, with their proportion first increasing and then decreasing as the rock bridge angle changes. Based on DIC displacement fields, two types of single-mode cracks and six types of mixed-mode cracks were identified. The evolution of macroscopic crack types is associated with the trend of tensile cracks in the RA-AF plot, with the proportion of tensile cracks being highest in the 60° rock bridge specimen. Finally, through analyzing the RA-AF values and the surface strain field characteristics captured via DIC at distinct loading stages, the disaster-causing mechanisms induced by varied rock bridge angles under cyclic loading were elucidated. Based on these findings, a dual-control theory of rock damage evolution under cyclic loading, comprising an energy dissipation-driven mechanism (the competition between tensile and shear energy efficiencies) and a spatial configuration-regulated mechanism (rock bridge angles governing crack propagation directions), was proposed. This theoretical framework provides a robust foundation and quantitative criteria for evaluating surrounding rock stability and preemptively mitigating hazards under high-intensity disturbance conditions in practical engineering contexts.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"140 ","pages":"Article 105180"},"PeriodicalIF":5.6,"publicationDate":"2025-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144887291","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The influence of horizontal borehole spacing on the interaction of two dynamic cracks propagating towards each other under unequal biaxial confining pressure","authors":"Shengnan Xu ,&nbsp;Zhongwen Yue ,&nbsp;Xingyuan Zhou ,&nbsp;Jun Zhou ,&nbsp;Peng Wang ,&nbsp;Kejun Xue","doi":"10.1016/j.tafmec.2025.105181","DOIUrl":"10.1016/j.tafmec.2025.105181","url":null,"abstract":"<div><div>As resource extraction depth increases, deep rock engineering often encounters geostress environments where horizontal stress significantly exceeds vertical stress, sometimes by factors up to three. This distinctive stress state critically impacts the propagation paths and interaction mechanisms of blasting cracks. This study establishes an experimental system for blasting photoelasticity under unequal biaxial confining pressure (9 MPa horizontal, 3 MPa vertical). It investigates the propagation behavior of opposing cracks and the effects of explosive stress waves and crack-tip stress fields on nearby cracks at various horizontal spacings (8–14 cm). Results indicate that under unequal biaxial confining pressure, the shaped charge shows a marked directional effect, with the optimal horizontal spacing between boreholes being 11 cm. At this spacing, the main cracks between the two boreholes have longer propagation lengths and better connectivity. As horizontal spacing increases, both wave-crack and crack-crack interactions weaken, with crack-crack interactions attenuating faster than wave-crack interactions. When the spacing exceeds 11 cm, the influence of crack-crack interactions on the mode II stress intensity factor at the crack tip rapidly diminishes. Under dynamic-static loading, predictions of crack deflection angle prediction using the Maximum Tangential Stress (MTS) and Generalized Maximum Tangential Stress (GMTS) criteria align closely with experimental trends, particularly regarding the timing of inflection points. However, predictions are consistently larger than actual values, and T-stress has minimal effect on crack deflection. Thus, the simpler MTS criterion is preferable for practical applications. These findings provide key insights into the interaction of opposing dynamic cracks at varying horizontal spacings and strengthen the theoretical foundation for optimizing perimeter-hole blasting parameters in horizontal stress-dominated environments.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"140 ","pages":"Article 105181"},"PeriodicalIF":5.6,"publicationDate":"2025-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144880021","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Fracture mechanical properties of shale and macro-meso-micro multi-scale fracture surface characteristics","authors":"Zhuo Dong ,&nbsp;Xiaoyan Zhai ,&nbsp;Yingxian Lang ,&nbsp;Bin Gong ,&nbsp;Ruifu Yuan ,&nbsp;Zhuli Ren","doi":"10.1016/j.tafmec.2025.105179","DOIUrl":"10.1016/j.tafmec.2025.105179","url":null,"abstract":"<div><div>The presence of bedding planes imparts pronounced anisotropy to the mechanical behavior of shale, fundamentally influencing its response to external stress. This anisotropic behavior is critical in determining the fracturing characteristics and overall mechanical performance of shale in engineering applications, particularly in resource extraction and stability evaluations. In this study, fracture tests were conducted on shale specimens with varying bedding angles (0°, 30°, 60°, and 90°) using the notched semi-circular bend (NSCB) method. The influence of the bedding angle on fracture toughness and failure pattern was systematically investigated. Additionally, multi-scale fracture surface morphology characteristics were analyzed through 3D optical scanning, ultra-depth field microscopy, and scanning electron microscope (SEM), enabling a comprehensive evaluation of the structural effects of bedding angles. The results indicate that fracture toughness decreases with increasing bedding angle, crack propagation becomes more stable, and the dispersion of fracture toughness diminishes. The failure pattern observed can be categorized as follows: tensile failure across the bedding plane (0°), shear failure along the bedding plane with mixed failure across the bedding plane (30°), shear failure along the bedding plane or tensile failure across the bedding plane (60°), and tensile failure along the bedding plane with mixed failure across the bedding plane (90°). These distinct failure patterns underscore the critical influence of bedding angle on fracture mechanisms. Moreover, the multi-scale failure characteristics exhibit significant correlation and consistency. The fractal dimension and joint roughness coefficient (JRC) initially increase and decrease with increasing bedding angle. Based on parameters such as asperity height, slope angle, and aspect direction, quantitative morphology characterization confirms that 30° specimens exhibit the highest surface complexity. A strong correlation is observed between the fractal dimension and the standard deviation of morphology descriptors, indicating robust geometric consistency across scales. These findings provide compelling evidence for the intrinsic link between macroscopic mechanical response and microscopic fracture surface morphology, offering critical insights into the multi-scale evolution of shale failure mechanisms and furnishing a theoretical foundation for designing and optimizing fracturing strategies in anisotropic shale formations.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"140 ","pages":"Article 105179"},"PeriodicalIF":5.6,"publicationDate":"2025-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144902235","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}