Engineering Fracture Mechanics最新文献

{"title":"Real-time high-temperature SHPB experimental investigation on dynamic mechanical properties and fracture characteristics of surrounding rock in tunnel fire explosion","authors":"Danqing Song ,&nbsp;Shengwen Mai ,&nbsp;Xiaoli Liu ,&nbsp;Nan Hu ,&nbsp;Wanpeng Shi ,&nbsp;Enzhi Wang ,&nbsp;Yifeng Yang","doi":"10.1016/j.engfracmech.2025.111596","DOIUrl":"10.1016/j.engfracmech.2025.111596","url":null,"abstract":"<div><div>This work utilized the SHPB test system and an intelligent box-type resistance furnace to simulate the coupling of real-time high temperature and dynamic load on surrounding rock in tunnel fire explosions. The effects of high temperature and air pressure on the dynamic mechanical properties and fracture characteristics were analyzed. The intrinsic correlation mechanism between the mineral composition and the kinetic characteristics was analyzed via high-precision XRD. The experimental results reveal that the dynamic stress‒strain curves under the coupling of high temperature and impact load can be divided into four stages, namely, the initial, elastic, plastic, and damage stage, without a compaction stage. When the real-time temperature is high, the damage mode of rock transforms from brittle to ductile. The effect of real-time temperature on the internal structure of rock is the key factor influencing its dynamic mechanical properties, macroscopic fracture characteristics, and microscopic mineral composition, and the effect can be divided into a strengthening stage (100 ∼ 300 °C) and a deterioration stage (400 ∼ 800 °C), while high-temperature treatment always results in a deterioration effect. Under real-time high temperatures, the dynamic mechanical properties of rock have obvious temperature effects, and the threshold temperature is approximately 200 °C. Under higher strain rates, the strengthening effect on the dynamic mechanical properties in the early heating process is no longer obvious, but the deterioration effect in the later heating process becomes more significant. This research can provide a certain theoretical basis for evaluating the stability of the surrounding rock in tunnel fire explosions.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"329 ","pages":"Article 111596"},"PeriodicalIF":5.3,"publicationDate":"2025-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145227511","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":"Characterization of mechanical behaviors for the dynamic shear rupture by photoelastic fringes in time series","authors":"Tingting Li ,&nbsp;Zhangyu Ren ,&nbsp;Jiansheng Liao ,&nbsp;Lingtao Mao ,&nbsp;Yang Ju","doi":"10.1016/j.engfracmech.2025.111598","DOIUrl":"10.1016/j.engfracmech.2025.111598","url":null,"abstract":"<div><div>Visualization and quantitative characterization of mechanical behaviors in shear rupture propagation along fault interfaces play a critical role in elucidating mechanism of the dynamic rupture. Recent advances in laboratory-scale fault modeling have significantly advanced the characterization of dynamic shear rupture processes through synergistic integration of optical measurement techniques, including digital image correlation, photoelasticity, and real contact zone monitoring. While time-series analyses of these methods have yielded important insights, the temporal evolution of photoelastic fringe patterns with multiple orders-a crucial diagnostic feature to characterize dynamic shear rupture behaviors − remains underexplored in dynamic rupture studies. This study firstly presents time-series photoelastic fringes with multiple orders induced by impact loads to investigate dynamic shear rupture mechanisms. Fault models were 3D-printed, and dynamic shear experiments were conducted under varying boundary conditions. High-speed imaging captured fringe evolution near fault surfaces, from which time-series fringes were extracted. Based on variations observed in these time-series fringes, rupture tip propagation characteristics, rupture velocity transitions, spatiotemporal evolution of stress fields, local fault slip distributions, and the nucleation and rupture of fault were analyzed. By offering direct insight, the technique confirms the potential of time-series photoelastic fringes for elucidating the intrinsic mechanisms of dynamic shear fracture.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"329 ","pages":"Article 111598"},"PeriodicalIF":5.3,"publicationDate":"2025-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145227512","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 surface crack growth model considering load sequence effects and application to damage tolerance evaluation of railway bogie frames","authors":"Tian Xu ,&nbsp;Youren Lai ,&nbsp;Saisai He ,&nbsp;Liantao Lu ,&nbsp;Dongfang Zeng","doi":"10.1016/j.engfracmech.2025.111587","DOIUrl":"10.1016/j.engfracmech.2025.111587","url":null,"abstract":"<div><div>This study developed a surface crack growth model that accounts for load sequence effects under variable amplitude loading. This was achieved using a three-dimensional crack growth analysis model that integrates the strip-yield model and the <em>K</em>-Analogy method. Fatigue crack growth (FCG) tests were performed on surface-cracked steel plates under various variable amplitude loadings to calibrate and validate the strip-yield model. The results demonstrate that the developed model exhibits superior predictive accuracy in estimating surface crack growth life under variable amplitude loading compared to the conventional NASGRO equation. As an application case for the damage tolerance evaluation of railway bogie frames, the developed model was then utilized to evaluate the residual life of a metro bogie frame’s gearbox suspension seat featuring a surface crack under a 12-level spectrum loading, resulting in a predicted operational distance of 430 × 10³ km for a descending-order load sequence. Stochastic analysis was conducted to explore the impact of load sequence effects and load spectrum expansion on the FCG life of bogie frames. Findings indicated that load sequence effects significantly influence FCG life predictions, with FCG life following a normal distribution. Contrary to traditional assumptions, descending-order load sequences may lead to non-conservative FCG life estimates. Additionally, load spectrum expansion increases the median FCG life and alters the scatter characteristics of life predictions. The developed model supports damage tolerance design, maintenance optimization, and the design of fatigue test spectra for railway components.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"329 ","pages":"Article 111587"},"PeriodicalIF":5.3,"publicationDate":"2025-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145227513","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 localized failure simulation and electromagnetic radiation–acoustic emission signal characteristics of roof sandstone under low-intensity impact: Based on drop-weight impact tests","authors":"Zihao Mao ,&nbsp;Enyuan Wang ,&nbsp;Dexing Li ,&nbsp;Haishan Jia ,&nbsp;Dongming Wang","doi":"10.1016/j.engfracmech.2025.111595","DOIUrl":"10.1016/j.engfracmech.2025.111595","url":null,"abstract":"<div><div>To address the limited understanding of the localized failure response characteristics of coal mine roof sandstone under low-intensity impact conditions, a drop-weight impact loading method was employed to simulate actual disturbance scenarios. The mechanical response, failure behavior, and the evolution of electromagnetic radiation (EMR) and acoustic emission (AE) signals during loading were systematically monitored. The results show that sandstone undergoes a nonlinear evolution process comprising compaction, yielding, critical fracturing, and eventual instability, with tensile failure as the predominant mode. The propagation velocity of Mode I (opening) cracks is negatively correlated with EMR frequency and positively correlated with AE energy intensity. With increasing impact velocity, the absorbed impact energy shows a slight rise, while the energy absorption rate decreases significantly. Meanwhile, the failure time shortens and the size of fragmented blocks increases. Due to differences in the sequence of energy release, EMR signals exhibit a distinct “precursor response” compared to AE signals. During crack propagation, intense dipole oscillations cause the EMR to emerge earlier and rapidly develop to its peak. In contrast, the coalescence of numerous cracks leads to the rapid release of elastic energy, resulting in the peak intensity of the AE signal. “The near-synchronous peaks” of EMR and AE signals mark the transition from localized instability to macroscopic failure. Accurate identification of these signal characteristics is of great significance for elucidating the localized failure behavior of sandstone roofs under low-intensity disturbances and for enhancing the early warning capabilities for dynamic hazards in coal mines.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"329 ","pages":"Article 111595"},"PeriodicalIF":5.3,"publicationDate":"2025-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145227510","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":"Deciphering confining pressure effects on coal failure mechanisms using acoustic emission approaches","authors":"Qican Ran ,&nbsp;Wenting Zhao ,&nbsp;Yunpei Liang ,&nbsp;Chunfeng Ye ,&nbsp;Yanhao Ning","doi":"10.1016/j.engfracmech.2025.111592","DOIUrl":"10.1016/j.engfracmech.2025.111592","url":null,"abstract":"<div><div>With the gradual transfer of coal resource mining to the deep part, the high confining pressure (CP) environment in which the coal is located puts forward higher safety and security demands on its mechanical properties and failure behavior. To reveal the deformation and failure mechanism of coal under CP and its acoustic emission (AE) evolution pattern, this study carries out compression experiments of coal samples under different CPs and combines with AE technology to monitor the crack propagation process in real time. The key to this study lies in the systematic integration of AE multi-parameter analysis and statistical fractal methods to quantitatively reveal the crack propagation mechanism of coal under varying CPs. The results showed that the increase of CP significantly enhanced the peak strength and deformation capacity of coal samples. Moreover, the strain energy analysis showed that the high CP helped to enhance the elastic energy percentage of coal and reduce the intensity of dissipative energy release. As for AE parameters, the <em>b</em>-value decreased with the increasing CP; while the <em>S</em>-value slightly increased. Meanwhile, AE energy followed a power-law trait, while the critical index declined as CP rose, reflecting a higher likelihood of large-energy events under elevated CP conditions. The AE signal also followed Hurst’s statistical law, and the increase in CP strengthened this statistical pattern with a higher Hurst’s exponent. The AE energy fractal results further revealed that the AE energy sequence exhibited stronger scale aggregation and regularity under high CP conditions. This study systematically reveals the mechanism of the influence of CP to the dynamic response and multiscale rupture characteristics of coal, which provides a theoretical basis for the prevention and control of coal-rock hazards under deep mining conditions.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"329 ","pages":"Article 111592"},"PeriodicalIF":5.3,"publicationDate":"2025-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145227538","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":"Pioneering insights into High-Temperature sandstone fracture Mechanics: Integrating damage evolution modeling with experimental validation","authors":"Tao Wang ,&nbsp;Weiwei Ye ,&nbsp;Liyuan Liu ,&nbsp;Xiaogang Liu ,&nbsp;Xiaodong Sun","doi":"10.1016/j.engfracmech.2025.111599","DOIUrl":"10.1016/j.engfracmech.2025.111599","url":null,"abstract":"<div><div>To address the high-temperature-induced damage and fracture phenomena in deep underground rock masses, this paper conducts fracture toughness tests on thermally damaged sandstone, meticulously monitoring crack morphology, surface displacement, and strain fields during the experiment. A damage evolution-focused thermo-mechanical coupling model is employed for simulations to examine the thermal damage and failure processes of sandstone under varying temperature conditions. The analytical solutions of the model are validated against experimental results, leading to the following conclusions: thermal damage in rocks is predominantly tensile, and as the temperature increases, the tensile damage intensifies. The fracture toughness <em>K_IC</em> of sandstone decreases with increasing temperature but increases to varying degrees as the prefabricated crack length decreases. As the temperature rises, the ductility of the rock improves, its deformation capacity increases, and the material gradually becomes more heterogeneous. The consistency between laboratory results and numerical simulations further demonstrates the rationality and applicability of the proposed damage evolution-focused thermo-mechanical coupling model.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"329 ","pages":"Article 111599"},"PeriodicalIF":5.3,"publicationDate":"2025-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145264092","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 multi-point constraint-based coupled PD-FEM model for high-cycle fatigue simulation: enhanced surface effect corrections","authors":"Baoyin Sun ,&nbsp;Kairui Yang ,&nbsp;Chuyan Wang ,&nbsp;Jinzhe Ye ,&nbsp;Kai Wang ,&nbsp;Jiaheng Xuan","doi":"10.1016/j.engfracmech.2025.111577","DOIUrl":"10.1016/j.engfracmech.2025.111577","url":null,"abstract":"<div><div>This study proposes a direct coupled approach integrating Bond-Based Peridynamics (BBPD) and the Finite Element Method (FEM) for high-cycle fatigue (HCF) simulations. The proposed method achieves direct coupling without shared nodes through the use of Multi-Point Constraint (MPC), incorporating surface effect correction to adjust the constitutive behavior of PD bonds near the PD-FEM interface. First, static analyses of cantilever beam models were performed both without and with three different surface effect correction methods. Comparison with FEM results confirmed the necessity of surface effect correction at the interface and demonstrated the effectiveness of the coupling strategy in two-dimensional (2D) scenarios. Among the correction methods evaluated, the Energy Density Method (EDM) proved to be the most effective. The static response of a three-dimensional (3D) bar model was also analyzed and compared with the FEM solution, further validating the coupling method’s applicability to 3D problems. Subsequently, HCF crack propagation simulations were conducted on a compact tension (CT) specimen and a T-shaped welded joint. The accuracy of the PD fatigue model was validated through comparisons with test results. Finally, the coupled PD-FEM model was applied to HCF analysis of the CT specimen and T-joint. The close correlation between the simulation and experimental outcomes confirms the model’s capability for component-level HCF simulations.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"329 ","pages":"Article 111577"},"PeriodicalIF":5.3,"publicationDate":"2025-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145183718","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":"Direct measurement of the interlaminar Mode I energy release rate in composite T-joints using digital image correlation","authors":"WeeLiam Khor ,&nbsp;Francesco Ciampa","doi":"10.1016/j.engfracmech.2025.111579","DOIUrl":"10.1016/j.engfracmech.2025.111579","url":null,"abstract":"<div><div>This study proposes a Digital Image Correlation (DIC)-enabled methodology to directly measure the delamination opening and Mode I fracture toughness of a composite T-joint. Opening stresses at the delamination tip were first derived from the opening angles of composite beam specimens made from the same material and layup of the bond line between the flange and the skin of the T-joint, which were subjected to double cantilever beam tests. These experiments produced a representative cohesive zone model (CZM) describing the opening stress-displacement relationship for progressive damage at crack interfaces. Integration of the CZM provided a direct measurement of the Mode I energy release rate, G_I, which was correlated to the G_I calculated using the standard test method, ASTM <span><span>D5528</span><svg><path></path></svg></span>-13. The CZM was then applied to delamination opening measurements from the composite T-joint to determine the corresponding opening stress. Integrating the opening stress-displacement curve enabled direct measurement of the G_I from the T-joint specimen. Results showed that as the delamination increased in the skin-flange region, the measured G_I decreased, thus suggesting a transition from pure Mode I to mixed-mode, and finally pure Mode II failure. Microscopic observations of fracture surfaces further supported these findings.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"329 ","pages":"Article 111579"},"PeriodicalIF":5.3,"publicationDate":"2025-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145227590","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":"Elastic fields of surface steps and notches and associated cracks","authors":"Bonan Wang ,&nbsp;Yangjian Si ,&nbsp;Yujie Wei","doi":"10.1016/j.engfracmech.2025.111571","DOIUrl":"10.1016/j.engfracmech.2025.111571","url":null,"abstract":"&lt;div&gt;&lt;div&gt;Surface notches or steps may induce local stress concentration. As a consequence, they play a central role in oxidation, corrosion, and fatigue cracking in engineering practice. In this paper, we supply analytic solutions of half-space steps and notches with or without cracks. Full-field displacements and stresses, general stress intensity factors (SIFs) at the root of steps and notches or the crack tips after crack initiation, as well as separation across the crack plane, are readily calculated. For a step of height &lt;span&gt;&lt;math&gt;&lt;mi&gt;h&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; on the half-space, it generates a stress field around the root in the form of &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;γ&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;K&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;∗&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;γ&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mfenced&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mfenced&gt;&lt;mrow&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;h&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;o&lt;/mi&gt;&lt;mfenced&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mfenced&gt;&lt;mrow&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;h&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, where &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; is the order of singularity given in terms of the slope angle &lt;span&gt;&lt;math&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; of the step with &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;≈&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;π&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;π&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;msqrt&gt;&lt;mrow&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mtext&gt;sinc&lt;/mtext&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;π&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;5&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mtext&gt;sinc&lt;/mtext&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;π&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/mrow&gt;&lt;/msqrt&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mtext&gt;for&lt;/mtext&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mtext&gt;sinc&lt;/mtext&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mo&gt;sin&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, and &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;K&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;γ&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; is the general SIFs associated with steps and notches. The same conclusion applies to a V-notch of depth &lt;span&gt;&lt;math&gt;&lt;mi&gt;h&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; and an opening angle of &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;π&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;. When a crack emanating from the root of the step or notch, the SIFs in terms of the newly formed crack of length &lt;span&gt;&lt;math&gt;&lt;mi","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"328 ","pages":"Article 111571"},"PeriodicalIF":5.3,"publicationDate":"2025-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145227384","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":"Progressive deterioration and fracture mechanisms of heterogeneous rocks induced by open-ended microwave irradiation: A multi-scale numerical and experimental investigation","authors":"Yueyang Li,&nbsp;Yubo Li,&nbsp;Lei He,&nbsp;Huaiguang Xiao,&nbsp;Weiqiang Zhu,&nbsp;Tienan Wang,&nbsp;Guogang Bai","doi":"10.1016/j.engfracmech.2025.111567","DOIUrl":"10.1016/j.engfracmech.2025.111567","url":null,"abstract":"<div><div>A comprehensive multi-scale spatial investigation of the time-dependent process of microwave-irradiated rock is conducive to revealing its underlying failure mechanisms. The innovation of this study lies in the systematic analysis of the progressive failure process of heterogeneous rocks induced by open-ended microwave irradiation, from temporal-spatial and multi-scale. Based on a high-fidelity heterogeneous rock model, a time-stepping iterative staggered finite element approach is proposed for solving multi-physical processes. And the process from local deterioration to global fracture of the rock under microwave irradiation is simulated. The results indicate that the failure process can be divided into three stages: Non-failure Stage (NFS), Local Deterioration Stage (LDS), and Global Fracture Stage (GFS), with the evolution characteristics significantly influenced by the rock structure and microwave conditions. The increase in microwave power and the associated thermal shock effects not only weaken the uniaxial compressive strength of the rock, but also accelerate the onset of LDS and GFS, while shortening the duration of LDS. The meso-mechanical analysis reveals that the local high tensile stress at the grain boundaries makes these regions more prone to failure than the interior of the grains, with biotite and feldspar grains being more likely to fail. Additionally, the marked crack path trajectories show that the low proportion of biotite and the high strength of quartz jointly influence the crack propagation path. This study provides a multi-scale perspective to reveal the characteristics of microwave-induced rock failure, and can offer guidance for the subsequent timing and path planning of mechanical tool penetration.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"329 ","pages":"Article 111567"},"PeriodicalIF":5.3,"publicationDate":"2025-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145227539","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}