Theoretical and Applied Fracture Mechanics最新文献

{"title":"Investigating the impact of freezing and thawing cycles on the dynamic fracture properties of red sandstone subjected to impact loading","authors":"Barkat Ullah ,&nbsp;Zilong Zhou ,&nbsp;Dagan Lin ,&nbsp;Fushen Liu","doi":"10.1016/j.tafmec.2025.105006","DOIUrl":"10.1016/j.tafmec.2025.105006","url":null,"abstract":"<div><div>Comprehending the dynamic fracture behaviour of rocks exposed to freeze–thaw cycles (FTCs) is essential for warranting the safety and stability of construction projects and rock engineering activities in frigid regions. In this study, the split Hopkinson pressure bar (SHPB) and nuclear magnetic resonance techniques (NMR) methods are adapted to reveal the dynamic fracture and porosity characteristics of sandstone influenced by FTCs. The dynamic fracture tests were conducted under different impact pressures and the effect of loading rate <span><math><mrow><mover><mrow><mo>(</mo><mi>K</mi></mrow><mo>̇</mo></mover><mrow><mo>)</mo></mrow></mrow></math></span> on dynamic fracture characteristics is elucidated. The results revealed that there is a non-linearly declining trend between the average dynamic fracture toughness (<em>K_IC(d)</em>) and the number of FTCs. As the number of FTCs increases, the mean values of <em>K_IC(d)</em> decrease, and this loss after each cycle becomes more pronounced. Amongst the FTCs, the <em>K_IC(d)</em> decreased drastically from 0 to 20 FTCs, then stabilized at 40 cycles. As the number of FTCs approaches 80, the <em>K_IC(d)</em> has significantly decreased. The <em>K_IC(d)</em> demonstrated a gradual increase corresponding to the loading rate <span><math><mrow><mover><mrow><mo>(</mo><mi>K</mi></mrow><mo>̇</mo></mover><mrow><mo>)</mo></mrow></mrow></math></span> during different FTCs. The analysis conducted through NMR revealed a correlation between the total porosity of rock specimens and the number of FTCs, indicating an increase in porosity with each cycle. The number of micropores fluctuates with FTCs, showing no obvious trend. However, macropores consistently increase throughout the freezing and thawing process, indicating that the rock’s microstructural impairment primarily arises from the increase in macropore porosity. Based on the variation law in porosity, the damage characteristics of sandstone under FTCs are demonstrated by introducing a damage factor (<em>D_ft</em>). It has been unveiled from the correlation analysis, that under a specific loading rate <span><math><mrow><mover><mrow><mo>(</mo><mi>K</mi></mrow><mo>̇</mo></mover><mrow><mo>)</mo></mrow></mrow></math></span> range, the <em>K_IC(d)</em> exponentially declines with an increase of <em>D_ft</em> revealing a good correlation. The results of this research will contribute to the formulation of guidelines aimed at enhancing the safety and stability of rock slope engineering in cold climates.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"139 ","pages":"Article 105006"},"PeriodicalIF":5.0,"publicationDate":"2025-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144123483","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":"Study on mixed-mode I+Ⅱ fracture properties of red sandstone under thermal-acid conditions","authors":"Longlong Mao,&nbsp;Yilei Yuan,&nbsp;Chaolin Wang,&nbsp;Jing Bi","doi":"10.1016/j.tafmec.2025.105005","DOIUrl":"10.1016/j.tafmec.2025.105005","url":null,"abstract":"<div><div>This study aims to explore the influence of sulfuric acid solution under different conditions of temperature (25 °C, 60 °C) and pH value (1, 3) on the mechanical properties and deterioration mechanism of sandstone. The apparent change characteristics of sandstone under diverse treatment conditions were delineated through systematic analysis, and a thorough exploration was conducted into the evolution patterns of peak load and the degree of deterioration in fracture toughness within the sandstone. The digital image correlation (DIC) technique was employed to determine the length of the fracture process zone in sandstone, followed by a comparative analysis with the theoretical value. Meanwhile, by combining the theoretical values and the DIC measurement data, the fracture initiation angle of the sandstone specimens was effectively predicted, and the GMTS criterion was adopted to improve the prediction accuracy. Through X-ray diffraction (XRD) analysis, the mineral composition of sandstone was revealed, and the possible chemical reactions and their deterioration mechanisms were discussed. Further, the deterioration degree of sandstone was analyzed in detail from a microscopic perspective using nuclear magnetic resonance (NMR) technology. The research results show that white substances formed on the surface of sandstone, and its peak load and fracture toughness significantly decreased; under different treatment conditions, there are differences in the length of the fracture process zone of sandstone; the GMTS criterion calculated using the Schmidt model can predict the fracture initiation angle of sandstone well; the internal pore structure of sandstone changed, with the proportion of macropores increasing, and the total porosity showing an upward trend.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"139 ","pages":"Article 105005"},"PeriodicalIF":5.0,"publicationDate":"2025-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144106805","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 the fatigue crack growth under variable amplitude loading using an improved strip-yield model considering variable constraint and plastic shrinkage","authors":"Tian Xu,&nbsp;Saisai He,&nbsp;Dongfang Zeng,&nbsp;Liantao Lu","doi":"10.1016/j.tafmec.2025.104996","DOIUrl":"10.1016/j.tafmec.2025.104996","url":null,"abstract":"<div><div>The object of this study was to develop a quantitative fatigue crack growth (FCG) prediction model for general crack configurations under variable amplitude (VA) loading conditions. To achieve this, an improved strip-yield model (SYM) considering variable constraint and plastic shrinkage was developed to evaluate the plasticity-induced crack closure (PICC) behavior in an infinitely wide center-cracked plate. Based on the <em>K</em>-Analogy method, this model was employed to predict the FCG life of compact tension (CT) specimens made from 16MnDR steel under various loading conditions. The results indicate that, in comparison to the original SYM, which employed a constant constraint and without considering plastic shrinkage, the improved SYM yields results that more closely with experimental findings. This emphasizes the importrance of considering variable constraint and plastic shrinkage in predicting the FCG life under VA loading.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"139 ","pages":"Article 104996"},"PeriodicalIF":5.0,"publicationDate":"2025-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144106803","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":"An accelerated phase-field model for high-cycle fatigue behaviour in quasi-brittle materials","authors":"Zhihua Xiong ,&nbsp;Xuyao Liu ,&nbsp;Jiaqi Li ,&nbsp;Abedulgader Baktheer ,&nbsp;Kevin Wolters ,&nbsp;Markus Feldmann","doi":"10.1016/j.tafmec.2025.105003","DOIUrl":"10.1016/j.tafmec.2025.105003","url":null,"abstract":"<div><div>This paper presents an accelerated phase-field method combining an adaptive cycle increment adjustment algorithm and Phase-Field Cohesive Zone Model (PF-CZM) to simulate High-Cycle Fatigue (HCF) of quasi-brittle materials. Based on an asymptotic fatigue degradation function extended to fatigue behaviour, the analogy between accumulated history variables and damage variables is used. Acceleration is achieved by deeming the accumulated history variable in the fatigue degradation function as a damage variable. The cycle increment is associated with the increment of the accumulated history variable based on experimental data. In order to improve computational efficiency, the entire fatigue simulation process is divided into three stages, and different cycle increments are applied to each stage. In order to demonstrate the effectiveness of the proposed accelerated phase-field scheme, comprehensive verification is conducted with experimental results and previous cycle-by-cycle numerical results, including mode I crack propagation and mixed mode I + II crack propagation, highlighting the efficiency and robustness of the proposed method. In addition, the influence of phase-field length scale on the crack pattern of concrete is studied. The fatigue behaviour of both 2D and 3D structures are showcased by applying the proposed model.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"139 ","pages":"Article 105003"},"PeriodicalIF":5.0,"publicationDate":"2025-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144123482","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":"A unified threshold model for physically small and long crack based on CTOD","authors":"Lindong Chai ,&nbsp;Lu Han ,&nbsp;Luping Ren ,&nbsp;Yihai He ,&nbsp;Wei Zhang","doi":"10.1016/j.tafmec.2025.105002","DOIUrl":"10.1016/j.tafmec.2025.105002","url":null,"abstract":"<div><div>In this paper, a physically small crack threshold model based on crack tip opening displacement (CTOD) is proposed. Firstly, an in-situ SEM crack growth testing and a unified physically small crack (PSC) and long crack (LC) growth model are briefly reviewed to demonstrate that CTOD serves as a unified driving parameter for PSC and LC. Subsequently, considering the crack closure and microstructural dissimilitude, the threshold CTOD model is established. Thus, the threshold stress and corresponding non-propagating crack length can be calculated. Finally, several datasets for various materials and loading conditions are used to verify the proposed model. The model prediction has a good agreement with the experimental data. Additionally, a comparison between the proposed model and main small crack threshold models is conducted. The relationship between the transition crack length from PSC to LC and the El Haddad parameter is also discussed.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"139 ","pages":"Article 105002"},"PeriodicalIF":5.0,"publicationDate":"2025-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144106804","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 behavior and failure mechanisms of concrete-rock interfaces with interfacial grouting","authors":"Xiaojiang Deng,&nbsp;Mingxuan Shen,&nbsp;Yu Zhao,&nbsp;Jing Bi,&nbsp;Chaolin Wang,&nbsp;Yongfa Zhang,&nbsp;Yang Li,&nbsp;Lin Ning","doi":"10.1016/j.tafmec.2025.105001","DOIUrl":"10.1016/j.tafmec.2025.105001","url":null,"abstract":"<div><div>The fracture of the concrete-rock interface poses a significant challenge in practical engineering applications, often leading to structural failure. Grouting reinforcement has been demonstrated to enhance the mechanical properties of this interface. This study systematically investigates the fracture behavior and mechanisms of defective concrete-rock interfaces under various loading angles (0°, 30°, 45°, 60°, and 90°). Gypsum- and epoxy resin-based grouting materials were utilized to fill defects in concrete-sandstone composite specimens, with subsequent Brazilian splitting tests conducted on both ungrouted and grouted samples. Real-time monitoring of micro-crack initiation and propagation in the concrete-sandstone composite Brazilian disks was achieved through synchronized acoustic emission (AE) and digital image correlation (DIC) techniques. The experimental results reveal that the peak loads for ungrouted specimens at respective loading angles are 3.4 kN, 3.7 kN, 3.9 kN, 4.4 kN, and 4.9 kN. Gypsum-grouted specimens exhibited load increases of 0.7 kN, 2.1 kN, 2.3 kN, 2.1 kN, and 2.7 kN, whereas epoxy resin-grouted specimens demonstrated significantly greater enhancements of 3.5 kN, 4.7 kN, 4.8 kN, 4.9 kN, and 4.9 kN. Notably, epoxy resin grouting substantially improves both mechanical properties and interfacial adhesion in defective concrete-sandstone composites. Three key patterns emerge in AE amplitude entropy prior to failure: Low frequency and minor variations in amplitude, low frequency and large variations in amplitude, and high-frequency and significant variation in amplitude. These findings provide critical insights for optimizing grouting reinforcement strategies and enhancing risk assessment in composite structural engineering.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"139 ","pages":"Article 105001"},"PeriodicalIF":5.0,"publicationDate":"2025-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143948486","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":"Simulation of delamination propagation in laminated composites under Mode-I and Mixed-Mode bending with LCZ-Based R-curve cohesive zone modeling","authors":"H.C. Chetan,&nbsp;Subhaschandra Kattimani,&nbsp;S.M. Murigendrappa","doi":"10.1016/j.tafmec.2025.104995","DOIUrl":"10.1016/j.tafmec.2025.104995","url":null,"abstract":"<div><div>For accurate prediction of the delamination behavior in the case of composite structures, toughening mechanisms like fiber bridging occurring in the fracture process zone (FPZ) must be considered. In this study, the relationship between the fiber bridging (R-curve) and the corresponding FPZ was investigated. Structural size, stacking sequence, and loading were considered in the study of the fiber-bridging behavior of composites. We propose an R-curve expression to estimate the<!--> <!-->variation of fracture toughness along the FPZ for structures of any configuration under mode-I and mixed-mode loading. These expressions are incorporated into simple bilinear softening laws to model the<!--> <!-->delamination behavior of any structural configuration under different loading conditions. The proposed methodology is computationally efficient, requiring simple measurements from experiments, such as initial and steady-state fracture toughness values. This eliminates the challenges of the<!--> <!-->conventional cohesive zone model in modeling large-scale bridging behavior in laminated composite structures. The proposed method was validated for different specimen configurations with variable thickness and<!--> <!-->cross-ply under mode-I loading. The effect of loading was investigated by subjecting a mixed-mode bending specimen to different mode ratios. The results indicated that the predicted values are in reasonable agreement with the measured values.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"139 ","pages":"Article 104995"},"PeriodicalIF":5.0,"publicationDate":"2025-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143941912","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 loads of ISRM-suggested notched semi-circular bend rock specimens using finite fracture mechanics","authors":"Junyang Pan,&nbsp;Zhiqian Zhang,&nbsp;Wei Liu,&nbsp;Mengru Pi,&nbsp;Bowen Liu","doi":"10.1016/j.tafmec.2025.104997","DOIUrl":"10.1016/j.tafmec.2025.104997","url":null,"abstract":"<div><div>The International Society for Rock Mechanics (ISRM) recommends notched Brazilian semi-circular bend specimen (NSCB) to measure fracture parameters of rocks. However, the testing accuracy is limited by the mechanical processing precision of the specimen, especially the notch tip, thus the testing results of fracture parameter is often strongly affected by the curvature radius of the notch tip. Moreover, traditional fracture mechanics methods find it challenging to quantify the effect of notch geometry on fracture properties. This paper proposes a semi-analytical method based on finite fracture mechanics (FFM) to predict the effects of geometric parameters of the notch and specimen on the critical load of U-notched semi-circular bend specimen (U-NSCB). First, the stress fields at the notch tip of U-NSCB specimen and the stress intensity factor (SIF) at the virtual crack tip ahead of the U-notch were determined using finite element simulations combined with the contour integral method, and a relationship between the mechanical properties of U-NSCB specimen and the geometry of the U-notch was established to characterize the effects caused by changes in notch geometry. Second, a semi-analytical solution was developed using the coupled FFM criterion to predict the critical load at crack initiation for U-NSCB specimens. Finally, three-point bending tests were conducted on U-NSCB specimens made of Fangshan marble (FM) with different notch lengths and curvature radii to validate the effectiveness and accuracy of the semi-analytical method. The inherent fracture toughness of the marble was also inversely obtained based on the FFM prediction results. The research findings showed that the predictions from the FFM with point stress criterion were more accurate than those from the FFM with line stress criterion, with a maximum deviation of 6.81% from the experimental results. The proposed FFM semi-analytical method helps to improve testing accuracy of the NSCB method and offers a new approach for predicting the critical load of other specimens with finite size.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"139 ","pages":"Article 104997"},"PeriodicalIF":5.0,"publicationDate":"2025-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143937335","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":"A failure criterion developed for crack of polyurethane adhesive bonding structures under hygrothermal aging environment","authors":"Feng Li ,&nbsp;Tian Lv ,&nbsp;Qianhui Xu ,&nbsp;Jundong Ji ,&nbsp;Xiaoying Li ,&nbsp;Jingxin Na","doi":"10.1016/j.tafmec.2025.104998","DOIUrl":"10.1016/j.tafmec.2025.104998","url":null,"abstract":"<div><div>In the service process of vehicles, the performance of adhesive components is usually affected by hygrothermal aging and complex stress states for a long time. Therefore, the failure criterion of adhesive structure with practical environmental applicability is very important for fracture prevention and adhesive performance optimization. In this study, polyurethane adhesive (ISR-7008)/aluminium alloy joints were selected as the study object, and −40 ∼ 85 °C/30 ∼ 95 % RH was selected as the cyclic hygrothermal aging environment. The joints were subjected to cyclic hygrothermal aging for 0 ∼ 720 h. The quasi-static tensile tests of joints with different loading angles (0 ∼ 90°) were carried out by the improved Arcan fixture to simulate the complex stress states. The stress–strain curve, initial failure load and area of the joint were obtained, and the stress distribution of the adhesive layer was further obtained by combining the finite element method. Then, based on the ratio method, the stress components with a dimension of MPa are selected, and the equivalent stress is calculated by linear combination. The equivalent stress that is not affected by the complex stress states is selected as the failure criterion of the adhesive layer by iteration. By comparing the failure mode and the initial failure load, it is found that the ratio of 3rd invariants of the deviatoric stress <em>J</em>*₃ and 2nd invariants of the deviatoric stress <em>J</em>*₂ can predict the failure strength of the joint after hygrothermal aging. The results show that the maximal relative errors between the predicted results and the experimental results under complex stress states are 14.44 % (unaged) and 17.35 % (hygrothermal aging for 720 h). The validity of the failure criterion and the applicability of different structural joints are verified by the tensile test of single lap joints. This failure criterion provides a new idea for the failure prediction of vehicle body adhesive structure.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"139 ","pages":"Article 104998"},"PeriodicalIF":5.0,"publicationDate":"2025-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144071342","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":"Modeling structure-dependent fracture behaviors of anisotropic cracked chevron notched Brazilian disc shale samples: Laboratory scale testing","authors":"Xianhui Feng ,&nbsp;Huilin Liu ,&nbsp;Zhenyu Yin ,&nbsp;Tianzheng Li ,&nbsp;Jiliang Pan ,&nbsp;Pei Wang ,&nbsp;Tianqi Zhai ,&nbsp;Peng Li","doi":"10.1016/j.tafmec.2025.104994","DOIUrl":"10.1016/j.tafmec.2025.104994","url":null,"abstract":"<div><div>The anisotropic fracture behaviors of layered shales affect the exploration and development of shale gas resources. Extensive investigations have been devoted to revealing the anisotropic geomechanically behaviors of intact or flawed shale under various loading paths. However, the structure-dependent fracture behavior and fracture toughness of layered shale were not well understood. The presented studies aim to conduct static fracture mechanical testing on cracked chevron notched Brazilian disc shale samples with different bedding inclinations (<em>θ</em>) and different crack angles (<em>β</em>), to reveal the influence of layer angle and crack angle on its fracture behaviors. The mechanical properties, energy conversion, fracture toughness and macro-meson fracture characteristics are studied, as well as the applicability of the conventional and generalized fracture criterion in layered rock mass is discussed. The results show that (i) The peak loads and fracture energy both increase with the increase of <em>θ</em>, but they increase first and then decrease with the increase of <em>β</em>. (ii) All samples exhibit six different failure modes corresponding to different morphological characteristics at crack surfaces. (iii) The fracture toughness of the samples increases with the increase of <em>θ</em>, and the mode Ⅱ fracture toughness (<em>K</em>_Ⅱ<em>_C</em>) is about twice that of the mode Ⅰ fracture toughness (<em>K</em>_Ⅰ<em>_C</em>) under the same <em>θ</em>. The traditional maximum tangential stress (MTS) criterion predicts pure mode II fracture initiation angle (<em>φ</em>_0Ⅱ) and <em>K</em>_Ⅱ<em>_C</em> of the samples with a large error, but the generalized MTS criterion, which considers the T-stresses, has an error in predicting <em>φ</em>_0Ⅱ, but it can accurately predict <em>K</em>_Ⅱ<em>_C</em>.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"139 ","pages":"Article 104994"},"PeriodicalIF":5.0,"publicationDate":"2025-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143937263","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}