Theoretical and Applied Fracture Mechanics最新文献

{"title":"Fracture mechanical properties of ultra-high performance concrete under mode I/II mixed fracture: A study on the coupling effect of steel Fiber content and crack-to-depth ratio","authors":"Zhiqing Zhao,&nbsp;Xiangfei Cheng,&nbsp;Guoqing Li,&nbsp;Xingqing Gu,&nbsp;Chen Wu,&nbsp;Peiwei Gao","doi":"10.1016/j.tafmec.2026.105451","DOIUrl":"10.1016/j.tafmec.2026.105451","url":null,"abstract":"<div><div>Ultra-high performance concrete (UHPC) is a widely used material in long-span structures, and its service performance and failure process are often governed by Mode I/II mixed fracture. To reveal the mixed-mode fracture mechanism of UHPC beams under the coupling effect of steel fiber content (referring to volume fraction V_<em>f</em>) and Crack-to-depth Ratio (CDR), a three-point bending experiment for UHPC specimens with inclined prefabricated cracks was designed in this study by considering the V_<em>f</em> range of 0%–3% and the CDR range of 0.15–0.80. Specifically, the data of load, displacement, and crack propagation path evolution throughout the entire fracture process were obtained via the load-crack mouth opening displacement (<em>P</em>-CMOD) curves by employing the digital image correlation (DIC) technology. The Mode I/II components of the crack initiation toughness and unstable fracture toughness were derived using the single-specimen η-method combined with linear elastic finite element analysis. The results indicate that increasing the steel fiber content can significantly enhance the unstable load, whereas a higher CDR weakens the fiber strengthening efficacy and reduces the unstable load of the material. Both Mode I and Mode II components of the crack initiation toughness reached their threshold values at a CDR of 0.45. As the fiber content and CDR increased further, the unstable fracture gradually transitioned from being Mode I-dominated to Mode II-dominated. DIC analysis shows that when CDR &lt; 0.60, steel fibers primarily retarded crack propagation by inhibiting the equivalent crack opening displacement (COD_eff); when CDR ranged from 0.60 to 0.80, steel fibers achieved energy dissipation at the crack tip by restricting the equivalent crack sliding displacement (CSD_eff). By revealing the coupling mechanism between geometric constraints and fiber bridging, this study quantified the dynamic correlations among displacement, load, and crack propagation under Mode I/II mixed fracture, providing important theoretical support for the crack resistance design and performance evaluation of UHPC structures.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"143 ","pages":"Article 105451"},"PeriodicalIF":5.6,"publicationDate":"2026-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145978845","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":"Determination and evolution of mode-I dynamic fracture toughness in granite under coupled water pressure and static stress","authors":"Jiefang Jin,&nbsp;Xiaowang Peng,&nbsp;Daoxue Yang,&nbsp;Youfeng Xiao,&nbsp;Huiying Xiong,&nbsp;Shuang Hao,&nbsp;Lixing Fang,&nbsp;Wei Yuan","doi":"10.1016/j.tafmec.2026.105459","DOIUrl":"10.1016/j.tafmec.2026.105459","url":null,"abstract":"<div><div>Disasters such as water inrush induced by blasting and excavation frequently occur in deep rock engineering. These are closely associated with microcrack formation and expansion in rock. Their prevention requires a thorough understanding of the dynamic fracture behavior of rocks under coupled static stress and water pressure conditions. To address this issue, a testing method for determining the mode-I dynamic fracture toughness of rocks under such coupled conditions was developed using a self-designed rock dynamics system capable of applying static stress and water pressure. Dynamic fracture experiments were conducted on granite specimens to investigate the effects of dynamic loading rate and water pressure on mode-I dynamic fracture toughness. An evolution model was then established. The evolution mechanism was further elucidated through combined macroscopic and microscopic fracture analyses. Results indicate that, under a constant water pressure, the mode-I dynamic fracture toughness follows a power-function increase with increasing loading rate, although the enhancement becomes less pronounced at high loading rates. Under a fixed loading rate, the toughness rises linearly with water pressure. Macroscopically, higher water pressure and loading rate reduce both fracture expansion contour roughness and fractal dimension. Microscopically, the fracture mechanism transitions from intergranular to transgranular failure. These findings provide theoretical guidance for preventing water inrush disasters induced by blasting and excavation.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"143 ","pages":"Article 105459"},"PeriodicalIF":5.6,"publicationDate":"2026-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145978849","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 the mechanical properties and fracture behavior of coal gangue aggregate concrete modified by physical-chemical composite","authors":"Xiangdong Zhang ,&nbsp;Yao Dong ,&nbsp;Wenliang Li ,&nbsp;Yu Zhang ,&nbsp;Lijuan Su ,&nbsp;Guanjun Cai ,&nbsp;Qiong Wu","doi":"10.1016/j.tafmec.2026.105452","DOIUrl":"10.1016/j.tafmec.2026.105452","url":null,"abstract":"<div><div>The accumulation of coal gangue (CG) as an industrial solid waste has become increasingly severe, and its resource utilization is of great significance for promoting low-carbon development in the construction industry. To enhance the utilization of coal gangue (CG), this study introduces for the first time a composite modification technique combining “physical coating and chemical immersion” for coal gangue aggregate (CGA), which was used to fabricate coal gangue aggregate concrete (CGAC). Through multi-scale experiments and characterization techniques, the synergistic modification mechanisms of the composite method on the properties of coal gangue aggregate (CGA) and concrete are systematically investigated, with a focus on analyzing the mechanical characteristics and fracture behavior of CGAC. Experimental results indicate that the composite modification significantly improves the fundamental physical and mechanical properties of CGA, optimizing its morphological characteristics, including sphericity, elongation, flatness, and angularity. The mechanical properties of the modified CGAC are notably enhanced, with 28d compressive strength, splitting tensile strength, and flexural strength increasing by 39.7%, 45.1%, and 42.5%, respectively, compared to the control group. Based on three-point bending fracture tests combined with digital image correlation (DIC) technology, it is found that the cracking load, ultimate load, fracture toughness, and fracture energy of the composite-modified CGAC are significantly improved, demonstrating superior crack resistance. Microscopic tests reveal that sodium silicate and silane coupling agents chemically strengthen the interfacial bonding between the cement matrix and CGA, forming a dense interfacial transition zone (ITZ), which further enhances the overall performance of CGAC. By leveraging the synergistic mechanism of “physical coating to address structural defects + chemical immersion to enhance interfacial chemistry,” this approach achieves dual reinforcement of the interfacial transition zone (ITZ). Compared to single modification methods, it leads to significant improvements in key properties such as aggregate mechanical strength and concrete fracture toughness. This study provides a solid theoretical foundation and practical technical support for the research on the fracture mechanical properties of CGAC.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"143 ","pages":"Article 105452"},"PeriodicalIF":5.6,"publicationDate":"2026-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145978848","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":"Effect of testing temperatures on the toughness properties of Q355 steel welded at ambient and low temperatures","authors":"Tong Sun ,&nbsp;Jianlei Zou ,&nbsp;Yuanqing Wang ,&nbsp;Yongjiu Shi","doi":"10.1016/j.tafmec.2026.105457","DOIUrl":"10.1016/j.tafmec.2026.105457","url":null,"abstract":"<div><div>This study systematically investigates the coupled influence of welding environmental temperature and testing temperature on the fracture behavior and ductile-to-brittle transition characteristics of Q355 steel welded joints. Charpy impact and fracture toughness tests were performed on the weld metal (WM) and heat-affected zone (HAZ) over a testing temperature range from 23 °C to −100 °C under two welding conditions: room-temperature welding (23 °C) and low-temperature welding (−10 °C). The transition behavior was evaluated using the Master Curve methodology and Boltzmann fitting from both impact- and fracture-mechanics-based perspectives. The results demonstrate that low-temperature welding significantly enhances low-temperature fracture toughness and reduces data scatter in both WM and HAZ. Both the reference temperature <em>T</em>₀ and the ductile-to-brittle transition temperature <em>T</em>_t are shifted to lower values under low-temperature welding, reflecting reduced embrittlement sensitivity. While the WM consistently exhibits higher fracture toughness than the HAZ, the HAZ remains more sensitive to low temperatures. Moreover, discrepancies between impact-based and fracture-mechanics-based transition temperatures are minor in the WM but pronounced in the HAZ, highlighting the different sensitivities of the two methods to fracture mechanisms. These findings provide mechanistic insight into low-temperature embrittlement of welded joints and offer practical guidance for optimizing welding procedures and fracture safety assessment of Q355 steel structures operating in cold environments.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"143 ","pages":"Article 105457"},"PeriodicalIF":5.6,"publicationDate":"2026-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145978847","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":"Physics-informed learning of fatigue crack growth in corroded steel: A Paris-law extension with corrosion degree and stress ratio optimized by Bayesian tuning","authors":"Yiwei Wang ,&nbsp;Yong Zeng ,&nbsp;Jinrui Tang ,&nbsp;Hongmei Tan ,&nbsp;Tuoying Sun ,&nbsp;Chao Wu","doi":"10.1016/j.tafmec.2026.105456","DOIUrl":"10.1016/j.tafmec.2026.105456","url":null,"abstract":"<div><div>Fatigue degradation of corroded steels presents complex interactions between mechanical loading, stress ratio, and corrosion-induced defects, which are difficult to capture using empirical models. A Physics-Informed Neural Network (PINN) framework is developed, that embeds the residual form of Paris law into its loss function, enabling the prediction of fatigue crack growth rates in chloride-corroded Q690 steel. Then, A dimensionally consistent extension of the Paris equation is proposed by incorporating the corrosion degree (<em>P</em>) and stress ratio (<em>R</em>), calibrated through single-edge notched tension (SENT) tests. Furthermore, Bayesian Optimization (BO) is employed to automatically tune key hyperparameters of the PINN, improving convergence stability and predictive accuracy. The proposed model achieves superior agreement with experimental data compared with conventional Paris-type formulations and data-driven baselines, demonstrating the feasibility of combining physics-informed learning with corrosion-aware modeling for reliable fatigue life prediction in structural steels.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"143 ","pages":"Article 105456"},"PeriodicalIF":5.6,"publicationDate":"2026-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145978846","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 elasto-plastic phase field framework for hydrogen-assisted failure with a stress-state-dependent critical fracture energy","authors":"Sarnath Thoudam ,&nbsp;Daniel C.F. Ferreira ,&nbsp;Claudio Ruggieri ,&nbsp;Diego F.B. Sarzosa","doi":"10.1016/j.tafmec.2026.105455","DOIUrl":"10.1016/j.tafmec.2026.105455","url":null,"abstract":"<div><div>A coupled mechanical-diffusion-damage model has been developed to simulate hydrogen-assisted failure. The adopted framework is codified in Abaqus/Standard routines, including a UMAT for updating the mechanical constitutive response and a UEL for solving the hydrogen diffusion and phase-field damage evolution. A new feature is the implementation of a critical fracture energy <span><math><msub><mrow><mi>G</mi></mrow><mrow><mi>c</mi></mrow></msub></math></span>, which depends on the Lode angle <span><math><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></math></span> and the stress triaxility <span><math><mrow><mo>(</mo><mi>η</mi><mo>)</mo></mrow></math></span>. Likewise, an energy-based damage threshold parameter is also obtained in terms of the stress invariants. A numerical study is conducted to demonstrate the capabilities of the proposed model. The model is subsequently calibrated and verified using notched specimens of high-strength AISI 4135 steel. After calibration using specimens having a notch radius of <span><math><mi>R</mi></math></span>=0.1 mm, the simulated fracture strengths match the experimental results. For specimens with <span><math><mi>R</mi></math></span>=0.8 mm, which exhibit a different constraint level than the hydrogen-charged specimens used for calibration, the model yields conservative predictions of fracture strength, with an average deviation of 26%. The FORTRAN subroutines are freely available for teaching and research from the following link <span><span>https://sites.usp.br/namef/vumat-umat/</span><svg><path></path></svg></span>.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"143 ","pages":"Article 105455"},"PeriodicalIF":5.6,"publicationDate":"2026-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145978850","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":"Investigation of mixed mode I-II damage and fracture properties of concrete subjected to sulfate corrosion and freeze-thaw cycles","authors":"Bing Fan ,&nbsp;Li Song ,&nbsp;Bowen Guo ,&nbsp;Guojie Luo ,&nbsp;Zhimeng Gao ,&nbsp;Weiping Wu ,&nbsp;Hongliang Fang ,&nbsp;Tong Li ,&nbsp;Zhong Liu","doi":"10.1016/j.tafmec.2026.105453","DOIUrl":"10.1016/j.tafmec.2026.105453","url":null,"abstract":"<div><div>This study investigates the influence of sulfate corrosion and freeze-thaw cycles on the mixed mode I-II damage and fracture behavior of concrete. First, the mass loss and dynamic elastic modulus of concrete beams after different freeze-thaw cycles were measured, and the internal pore structure and mineral composition were analyzed using NMR and XRD. Subsequently, fracture tests under quasi-static loading were conducted on concrete beams in combination with the acoustic emission technique. The evolution patterns of the AE energy, AF-RA parameters, and b-value under sulfate corrosion and freeze-thaw cycles were systematically analyzed. Finally, the finite element method was employed to explore the mixed mode I-II damage scale and double-K fracture parameters. Results indicate that: (1) the coupling effect of freeze-thaw cycles and sulfate erosion exhibits a dual-mechanism behavior, characterized by initial matrix micro-densification followed by accelerated damage propagation, which ultimately culminates in significant deterioration of the fracture bearing capacity of the material. (2) with an increase in freeze-thaw cycles, the accumulated AE energy at peak load, the shear failure ratio, the critical damage scale, and the double-K fracture toughness for both mode I and mixed mode I-II cracks exhibit a consistent pattern of an initial increase followed by a subsequent decrease. (3) compared with mode I fracture, mixed mode I-II fracture exerts effects on the proportion of shear failure, critical damage scale, and cumulative AE energy, whereas it exerts a relatively minor effect on the double-K fracture parameters. (4) in contrast to water freeze-thaw environment, sulfate solution freeze-thaw induces significantly different evolutionary patterns in cumulative AE energy, AF, RA, and b-value</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"143 ","pages":"Article 105453"},"PeriodicalIF":5.6,"publicationDate":"2026-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145978844","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 peridynamic physics-informed U-net transfer learning framework for progressive crack prediction of fiber reinforced composites","authors":"Xihong Zhang ,&nbsp;Kunpang Kou ,&nbsp;Chichiu Lam ,&nbsp;Yang Yang","doi":"10.1016/j.tafmec.2026.105448","DOIUrl":"10.1016/j.tafmec.2026.105448","url":null,"abstract":"<div><div>In this paper, a peridynamic physics-informed U-net transfer learning framework is specifically designed for predicting the progressive crack in fiber reinforced composites (FRC). This framework addresses the challenges associated with undefined differentiation at displacement discontinuities that are often encountered in traditional physics-informed neural networks (PINNs). It also tackles the stiffness ill-conditioning that arises from significant differences in material properties between the fiber and the matrix. In the U-net-PINN model, a non-local convolution kernel has been developed based on the non-local characteristics of peridynamics. The introduction of a wavelet activation function further improves the network's convergence efficiency. A specially designed loss function combines the current boundary conditions and the minimum potential energy increment for FRC and fiber bonds derived from bond-based peridynamic with stretch and rotation. By applying the transfer learning technique, the U-net-PINN models are enhanced to predict the crack propagation in the FRC for various fiber directions. Several numerical results demonstrate that the nonlocal U-net-PINN can more accurately identify the crack initiation and propagation in FRC with high accuracy, efficiency, and ease of implementation. Its data-free characteristic enables the nonlocal U-net-PINN framework to predict the crack propagation in FRC, where the traditional numerical method may fall short.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"143 ","pages":"Article 105448"},"PeriodicalIF":5.6,"publicationDate":"2026-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145940359","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":"Cross-scale crack evolution in pre-flawed sandstone under high temperature: Insights from a composition-aware thermal-mechanical grain-based model","authors":"Shi Liu ,&nbsp;Zhipeng Zhang ,&nbsp;Qixing Wu ,&nbsp;Chun Feng ,&nbsp;Chen Chen ,&nbsp;Xiasong Hu","doi":"10.1016/j.tafmec.2026.105450","DOIUrl":"10.1016/j.tafmec.2026.105450","url":null,"abstract":"<div><div>In deep energy extraction, thermal damage induced by high temperatures critically degrades the mechanical integrity of rock, posing substantial risks to engineering safety. To systematically clarify the damage mechanisms under coupled thermal-mechanical-fracture conditions, this study develops a novel Composition-Aware Thermal-Mechanical Grain-Based Model (CATM-GBM).This model explicitly integrates the rock's quantitative mineralogical composition and spatial heterogeneity, implementing a temperature-dependent thermal expansion function to capture differential mineral degradation and employing parallel bond model and smooth joint model to simulate intergranular tensile and intragranular shear failure modes. Results demonstrate pronounced mechanical degradation under high-temperature exposure, characterized by marked reductions in uniaxial compressive strength and elastic modulus, significant increases in peak axial strain, and a coherent transition from brittle to ductile post-peak behavior. Crack analysis reveals tensile-dominated failure throughout loading and identifies a critical transition near 500 °C: intergranular cracking prevails below this threshold, while intragranular cracking dominates above it due to intensified thermal mismatch stresses and micro-damage within mineral grains. Pre-existing flaws control macroscopic failure patterns, promoting through-going “X”-shaped conjugate shear bands in flawed specimens, in contrast to localized “V”-shaped failures in intact ones. Microscopically, deviatoric loading induces particle-scale anisotropy, triggering progressive grain rotation, slip, and contact network destabilization. Macroscopically, cracks initiate predominantly at flaw tips and propagate to form specimen-scale through-fractures. This research provides a systematic, multi-scale decoupling of thermal cracking evolution in fractured sandstone, establishing a robust predictive numerical framework for assessing thermomechanical stability in critical deep geological engineering applications, including enhanced geothermal systems and deep geological repositories for nuclear waste.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"143 ","pages":"Article 105450"},"PeriodicalIF":5.6,"publicationDate":"2026-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145940287","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":"Integrity conditions of К-220-44-2М and К-325-23.5 turbine shafts at a short circuit on a turbogenerator in the presence of crack","authors":"A. Bovsunovsky ,&nbsp;M. Borodii ,&nbsp;O. Bovsunovsky","doi":"10.1016/j.tafmec.2026.105447","DOIUrl":"10.1016/j.tafmec.2026.105447","url":null,"abstract":"<div><div>Catastrophic failures of steam turbines, which occurred in the history of thermal power engineering, were caused by the long-term accumulation of fatigue damage and sudden application of dynamic torque. The dynamic torque is the result of abnormal operating modes of a turbogenerator at the connection of turbogenerator to the power network with an inaccurate synchronization, as well as at short circuit on a turbogenerator. So, this a real engineering problem. Under certain conditions, such a load causes intense torsional vibrations of the turbine shaft, sufficient for its disintegration in condition of crack presence. Given the problem, the method to estimate the critically dangerous sizes of circular, transverse and longitudinal crack, at which a short circuit on a turbogenerator will lead to the disintegration of the turbine shaft, has been created. The method was applied to estimate the critically dangerous size of crack in K-220-44-2 M and K-325-23.5 turbine shafts. It was based on the dynamic torques in the most stressed sections of the turbine shafts because of a short circuit. The crack for which the stress intensity factor reaches the fracture toughness of the rotor steel is considered as critically dangerous. It is assumed that such a crack will lead to disintegration of the shaft because of a short circuit. Using the method, the critical size of circular, transverse and longitudinal crack in K-220-44-2 M and K-325-23.5 turbine shafts were determined in a certain range of the rotor steel fracture toughness.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"143 ","pages":"Article 105447"},"PeriodicalIF":5.6,"publicationDate":"2026-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145940289","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}