To more accurately study and analyze the fatigue crack growth (FCG) behavior of welded structures under mixed mode I + II loading, this paper proposes a relative displacement (RD) method to calculate the stress intensity factors at the crack tip. This method simplifies complex stress conditions into measurable displacement variations. It is based on changes in the local displacement field at the crack tip, combining surface node displacement principles and relative displacement techniques to derive the corresponding driving parameters. Subsequently, FCG experiments were conducted at loading angles of 0°, 30°, 45°, and 60°, with analysis performed using digital image correlation technology. The M−integral method, Sajith’s method, and the RD method were used to calculate and compare the SIFs at the crack tip of compact-tension-shear specimens. The results show that, due to the influence of residual stress, the ΔKI and ΔKeq values obtained from the RD method are larger during crack growth. The da/dN–ΔKeq curve based on this method exhibits a higher degree of fitting accuracy. The findings offer new insights into the FCG behavior of welded joints under mixed mode loading and provide theoretical support for predicting the remaining useful life of railway vehicle frames.
为了更准确地研究和分析混合模式 I + II 载荷下焊接结构的疲劳裂纹生长（FCG）行为，本文提出了一种相对位移（RD）方法来计算裂纹尖端的应力强度因子。该方法将复杂的应力条件简化为可测量的位移变化。它基于裂纹尖端局部位移场的变化，结合表面节点位移原理和相对位移技术，得出相应的驱动参数。随后，在 0°、30°、45° 和 60°加载角度下进行了 FCG 实验，并利用数字图像相关技术进行了分析。使用 M 积分法、Sajith 法和 RD 法计算和比较了紧凑拉伸剪切试样裂缝顶端的 SIF。结果表明，由于残余应力的影响，RD 方法得到的 ΔKI 和 ΔKeq 值在裂纹生长过程中较大。基于这种方法的 da/dN-ΔKeq 曲线具有更高的拟合精度。这些发现为研究混合模式加载下焊接接头的 FCG 行为提供了新的视角，并为预测铁路车辆框架的剩余使用寿命提供了理论支持。
{"title":"Mixed mode (I/II) fatigue crack growth in butt-welded joints using actual stress intensity factors","authors":"Zhe Zhang, Bing Yang, Shuancheng Wang, Mian Huang, Haoyu Zheng, Shoune Xiao","doi":"10.1016/j.tafmec.2025.104894","DOIUrl":"10.1016/j.tafmec.2025.104894","url":null,"abstract":"<div><div>To more accurately study and analyze the fatigue crack growth (FCG) behavior of welded structures under mixed mode I + II loading, this paper proposes a relative displacement (RD) method to calculate the stress intensity factors at the crack tip. This method simplifies complex stress conditions into measurable displacement variations. It is based on changes in the local displacement field at the crack tip, combining surface node displacement principles and relative displacement techniques to derive the corresponding driving parameters. Subsequently, FCG experiments were conducted at loading angles of 0°, 30°, 45°, and 60°, with analysis performed using digital image correlation technology. The M−integral method, Sajith’s method, and the RD method were used to calculate and compare the SIFs at the crack tip of compact-tension-shear specimens. The results show that, due to the influence of residual stress, the Δ<em>K<sub>I</sub></em> and Δ<em>K<sub>eq</sub></em> values obtained from the RD method are larger during crack growth. The d<em>a</em>/d<em>N</em>–Δ<em>K<sub>eq</sub></em> curve based on this method exhibits a higher degree of fitting accuracy. The findings offer new insights into the FCG behavior of welded joints under mixed mode loading and provide theoretical support for predicting the remaining useful life of railway vehicle frames.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"138 ","pages":"Article 104894"},"PeriodicalIF":5.0,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143463416","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}
Pub Date : 2025-02-19DOI: 10.1016/j.tafmec.2025.104895
Xiang Wang , Zhende Zhu , Haijun Wang , Yingjie Chen , Shu Zhu , Semaierjiang Maimaitiyusupu
Crack expansion in brittle materials due to low temperatures is a prevalent issue in engineering practices, particularly in cold regions and mining engineering. Understanding the behavior of cracks in materials subjected to thermal stress is crucial. Current research on crack extension under thermal stress primarily focuses on surface or penetrating cracks in materials, with limited studies on the expansion of three-dimensional internal cracks. This study examined the impact of thermal stress on the expansion of eccentric internal cracks within glass material, which were fabricated using laser technology to prevent surface damage. The specimens were subjected to low temperatures to observe the expansion pattern of internal cracks. Furthermore, three-dimensional (3D) numerical simulations were performed to calculate stress intensity factors (SIFs) and illustrate the crack expansion paths, thereby elucidating the expansion mechanism of eccentric internal cracks. The results revealed that thermal stress at the crack tip influences the expansion of prefabricated eccentric cracks, resulting in distinct crack morphologies such as ’S’ and ’L’ shapes. Moreover, the crack expansion within the specimen exhibited a mixed mode I-II-III crack. These findings provide valuable insights into the expansion of internal cracks in brittle materials under thermal stress.
{"title":"Characterization of eccentric internal crack expansion in brittle materials at low temperature","authors":"Xiang Wang , Zhende Zhu , Haijun Wang , Yingjie Chen , Shu Zhu , Semaierjiang Maimaitiyusupu","doi":"10.1016/j.tafmec.2025.104895","DOIUrl":"10.1016/j.tafmec.2025.104895","url":null,"abstract":"<div><div>Crack expansion in brittle materials due to low temperatures is a prevalent issue in engineering practices, particularly in cold regions and mining engineering. Understanding the behavior of cracks in materials subjected to thermal stress is crucial. Current research on crack extension under thermal stress primarily focuses on surface or penetrating cracks in materials, with limited studies on the expansion of three-dimensional internal cracks. This study examined the impact of thermal stress on the expansion of eccentric internal cracks within glass material, which were fabricated using laser technology to prevent surface damage. The specimens were subjected to low temperatures to observe the expansion pattern of internal cracks. Furthermore, three-dimensional (3D) numerical simulations were performed to calculate stress intensity factors (SIFs) and illustrate the crack expansion paths, thereby elucidating the expansion mechanism of eccentric internal cracks. The results revealed that thermal stress at the crack tip influences the expansion of prefabricated eccentric cracks, resulting in distinct crack morphologies such as ’S’ and ’L’ shapes. Moreover, the crack expansion within the specimen exhibited a mixed mode I-II-III crack. These findings provide valuable insights into the expansion of internal cracks in brittle materials under thermal stress.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"138 ","pages":"Article 104895"},"PeriodicalIF":5.0,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143471549","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}
Pub Date : 2025-02-19DOI: 10.1016/j.tafmec.2025.104893
Bin Qiang , Qiang Xie , Hongkai Qiu , Yadong Li , Xin Wang , Guozheng Kang
This study presents the application of the weight function method (WFM) for analyzing fatigue crack growth life (FCGL) in semi-elliptical cracks under complex two-dimensional welding residual stress (WRS) conditions in U-rib-to-deck joints. A novel point load weight function was proposed, accounting for various crack configurations, including weld angle (θ), aspect ratio (a/c), crack depth ratio (a/T), and deck-to-rib thickness ratio (T/t). This new weight function was validated against multiple stress distributions. It was then applied using the NASGRO fatigue crack propagation model to determine stress intensity factors (SIF) and predict the FCGL under varying WRS conditions, initial crack aspect ratios, and cyclic load scenarios. Results indicate that the proposed weight function provides high accuracy for both one- and two-dimensional stress distributions. Tensile WRS significantly increases the SIF at the weld toe, accelerating fatigue crack growth by approximately 60 % compared to cases without WRS. The initial crack aspect ratio (a/c) plays a crucial role in determining FCGL, with higher ratios leading to longer FCGL and slower crack growth, stabilizing at approximately a/c = 0.6 in the later growth stages. Additionally, increasing cyclic stress peak shortens the linear crack growth phase, accelerates propagation, and reduces FCGL, highlighting the importance of mitigating high-stress conditions and WRS in U-rib-to-deck joints to extend their FCGL in practical engineering applications. Overall, the proposed method offers a conservative yet acceptable accuracy in evaluating the FCGL of U-rib-to-deck joints.
{"title":"Determination of approximate point load weight functions and fatigue crack growth analysis for U-rib-to-deck joints","authors":"Bin Qiang , Qiang Xie , Hongkai Qiu , Yadong Li , Xin Wang , Guozheng Kang","doi":"10.1016/j.tafmec.2025.104893","DOIUrl":"10.1016/j.tafmec.2025.104893","url":null,"abstract":"<div><div>This study presents the application of the weight function method (WFM) for analyzing fatigue crack growth life (FCGL) in semi-elliptical cracks under complex two-dimensional welding residual stress (WRS) conditions in U-rib-to-deck joints. A novel point load weight function was proposed, accounting for various crack configurations, including weld angle (<em>θ</em>), aspect ratio (<em>a</em>/<em>c</em>), crack depth ratio (<em>a</em>/<em>T</em>), and deck-to-rib thickness ratio (<em>T</em>/<em>t</em>). This new weight function was validated against multiple stress distributions. It was then applied using the NASGRO fatigue crack propagation model to determine stress intensity factors (SIF) and predict the FCGL under varying WRS conditions, initial crack aspect ratios, and cyclic load scenarios. Results indicate that the proposed weight function provides high accuracy for both one- and two-dimensional stress distributions. Tensile WRS significantly increases the SIF at the weld toe, accelerating fatigue crack growth by approximately 60 % compared to cases without WRS. The initial crack aspect ratio (<em>a</em>/<em>c</em>) plays a crucial role in determining FCGL, with higher ratios leading to longer FCGL and slower crack growth, stabilizing at approximately <em>a</em>/<em>c</em> = 0.6 in the later growth stages. Additionally, increasing cyclic stress peak shortens the linear crack growth phase, accelerates propagation, and reduces FCGL, highlighting the importance of mitigating high-stress conditions and WRS in U-rib-to-deck joints to extend their FCGL in practical engineering applications. Overall, the proposed method offers a conservative yet acceptable accuracy in evaluating the FCGL of U-rib-to-deck joints.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"138 ","pages":"Article 104893"},"PeriodicalIF":5.0,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143479658","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}
Dynamic disturbances and structural planes (discontinuities) are of critical importance in influencing the damage of surrounding rock in underground engineering. To explore the rockburst process of structural planes under dynamic disturbances, true triaxial tests with coupled dynamic − static loading considering structural planes and periodic weak disturbances were carried out. Cubic specimens with circular holes and pre − fabricated cracks, simulating structural planes, were used as test objects. The damage and micro − cracking processes of the surrounding rock were monitored by a high − speed camera system and an acoustic emission system under three different disturbance frequency and amplitude conditions (Condition 1: 2 Hz, 40 KN; Condition 2: 6 Hz, 30 KN; Condition 3: 10 Hz, 15 KN). A comparative analysis was conducted on the failure processes, strength characteristics, acoustic emission features, debris fractal characteristics, and damage morphologies of specimens with and without structural planes under the three weak dynamic cyclic disturbance conditions. The main conclusions are (1) During the uniform loading stage, discontinuities change the occurrence time, location, and intensity of rockburst. During the disturbance, the damage of specimens with structural planes mainly occurs on the side without structural planes, and the damage intensity and frequency are lower than those of specimens without structural planes.(2) Both structural planes and disturbances weaken rock masses to some extent. Different disturbance conditions have different impacts on structure − controlled rockbursts. An increase in disturbance amplitude promotes new failures in rock masses, while an increase in disturbance frequency facilitates the expansion and connection of original micro − cracks.(3) The presence of structural planes changes the damage pattern of specimens. More shear cracks are observed in specimens with structural planes. The disturbance exacerbates stress concentration, leading to more severe damage to the rock mass. In practical engineering, construction should avoid discontinuities as much as possible. Grouting and support can effectively reduce the hazards of rockbursts caused by structural planes.
{"title":"Experimental study on the influence of structure plane on rockburst of hard rock tunnel under combined dynamic-static loading conditions","authors":"Shunchuan Wu, Zhenrui Zhang, Longqiang Han, Haiyong Cheng, Zhiyuan Xia","doi":"10.1016/j.tafmec.2025.104892","DOIUrl":"10.1016/j.tafmec.2025.104892","url":null,"abstract":"<div><div>Dynamic disturbances and structural planes (discontinuities) are of critical importance in influencing the damage of surrounding rock in underground engineering. To explore the rockburst process of structural planes under dynamic disturbances, true triaxial tests with coupled dynamic − static loading considering structural planes and periodic weak disturbances were carried out. Cubic specimens with circular holes and pre − fabricated cracks, simulating structural planes, were used as test objects. The damage and micro − cracking processes of the surrounding rock were monitored by a high − speed camera system and an acoustic emission system under three different disturbance frequency and amplitude conditions (Condition 1: 2 Hz, 40 KN; Condition 2: 6 Hz, 30 KN; Condition 3: 10 Hz, 15 KN). A comparative analysis was conducted on the failure processes, strength characteristics, acoustic emission features, debris fractal characteristics, and damage morphologies of specimens with and without structural planes under the three weak dynamic cyclic disturbance conditions. The main conclusions are (1) During the uniform loading stage, discontinuities change the occurrence time, location, and intensity of rockburst. During the disturbance, the damage of specimens with structural planes mainly occurs on the side without structural planes, and the damage intensity and frequency are lower than those of specimens without structural planes.(2) Both structural planes and disturbances weaken rock masses to some extent. Different disturbance conditions have different impacts on structure − controlled rockbursts. An increase in disturbance amplitude promotes new failures in rock masses, while an increase in disturbance frequency facilitates the expansion and connection of original micro − cracks.(3) The presence of structural planes changes the damage pattern of specimens. More shear cracks are observed in specimens with structural planes. The disturbance exacerbates stress concentration, leading to more severe damage to the rock mass. In practical engineering, construction should avoid discontinuities as much as possible. Grouting and support can effectively reduce the hazards of rockbursts caused by structural planes.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"137 ","pages":"Article 104892"},"PeriodicalIF":5.0,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143453946","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}
Pub Date : 2025-02-17DOI: 10.1016/j.tafmec.2025.104891
Yang-Long Diao , Wen-Jie Wang , Feng Luo , Zhi-Qi Feng
The instability of the locked segment in rock structures is a common geological hazard and has been widely studied. However, the instability of through-boundary type locked segment structures with rock bridges of the same length but different angles has not been fully reported. In this paper, three failure modes and the tensile-shear failure characteristics of the fracture surface were identified by physical experiments. Using PFC2D, the local displacement field, force field distribution, and crack evolution characteristics were studied. The results show that under different rock bridge inclinations, the rock mass penetration modes can be categorized into three types: penetration at the joint tip and upper end, penetration of the rock bridge between adjacent joint tips, and oblique straight-line penetration at the upper and lower ends. The local scratch surface exhibits three distinct distribution characteristics: the locked rock mass above the rock bridge, within the rock bridge region, and around the joint region. As the rock bridge inclination increases, the peak stress tend to decrease, with crack development becoming more concentrated (excluding 90°). The minimum local displacement field in the central part transitions from a shell shape to a core shape. In the direction of the force source, stress concentration at the ends of the rock bridge (LM1 and RM1, LM3 and RM3) becomes more pronounced, but the degree of concentration is constrained by the rock bridge inclination. The distribution range of normal contact forces increases, and the maximum tangential contact force deviates toward the axial direction.
{"title":"Macro-mesoscopic study of the deformation and failure mechanism of through-boundary type locked rock masses","authors":"Yang-Long Diao , Wen-Jie Wang , Feng Luo , Zhi-Qi Feng","doi":"10.1016/j.tafmec.2025.104891","DOIUrl":"10.1016/j.tafmec.2025.104891","url":null,"abstract":"<div><div>The instability of the locked segment in rock structures is a common geological hazard and has been widely studied. However, the instability of through-boundary type locked segment structures with rock bridges of the same length but different angles has not been fully reported. In this paper, three failure modes and the tensile-shear failure characteristics of the fracture surface were identified by physical experiments. Using PFC2D, the local displacement field, force field distribution, and crack evolution characteristics were studied. The results show that under different rock bridge inclinations, the rock mass penetration modes can be categorized into three types: penetration at the joint tip and upper end, penetration of the rock bridge between adjacent joint tips, and oblique straight-line penetration at the upper and lower ends. The local scratch surface exhibits three distinct distribution characteristics: the locked rock mass above the rock bridge, within the rock bridge region, and around the joint region. As the rock bridge inclination increases, the peak stress tend to decrease, with crack development becoming more concentrated (excluding 90°). The minimum local displacement field in the central part transitions from a shell shape to a core shape. In the direction of the force source, stress concentration at the ends of the rock bridge (LM1 and RM1, LM3 and RM3) becomes more pronounced, but the degree of concentration is constrained by the rock bridge inclination. The distribution range of normal contact forces increases, and the maximum tangential contact force deviates toward the axial direction.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"137 ","pages":"Article 104891"},"PeriodicalIF":5.0,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143445853","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}
Pub Date : 2025-02-17DOI: 10.1016/j.tafmec.2025.104889
Yunlong Wang , Peng Hou , Shanjie Su , Xin Liang , Yanan Gao , Feng Gao
Cyclic liquid nitrogen (LN2) fracturing is a promising innovative technology expected to rapidly form fracture networks in geothermal reservoirs. The fracture characteristics are crucial for estimating the effect of the artificial fracturing. Therefore, a cyclic heating-rapid cooling (CHRC) experiment is conducted on the notched semi-circular bend (NSCB) granite, where LN2 and water cooling are employed. The structural damage and fracture characteristics of the CHRC treated sample are analyzed using ultrasonic detection, three-point bending test, and acoustic emission (AE) technique. A grain-based model with thermo‑mechanical coupling is constructed to explore the micro-cracking mechanism of the CHRC treatment. The results indicate that the damage caused by the CHRC increases significantly in the first five cycles, especially under LN2 cooling. The decline of fracture toughness with cycles under different cooling methods. LN2 cooling can dramatically enhance the AE energy release and fracture surface roughness in the initial cycles. LN2 cooling can promote the generation of tensile cracks and intra-granular microcracks. The fracture behaviors of the CHRC treated granite are mainly determined by the stable thermal stress, significantly affected by mineral distribution. These results can provide a comprehensive understanding of cyclic LN2 fracturing compared to hydraulic fracturing, supporting theoretical guidance for geothermal extraction.
{"title":"Effect of cyclic heating-rapid cooling on fracture behavior of notched semi-circular bend granite","authors":"Yunlong Wang , Peng Hou , Shanjie Su , Xin Liang , Yanan Gao , Feng Gao","doi":"10.1016/j.tafmec.2025.104889","DOIUrl":"10.1016/j.tafmec.2025.104889","url":null,"abstract":"<div><div>Cyclic liquid nitrogen (LN<sub>2</sub>) fracturing is a promising innovative technology expected to rapidly form fracture networks in geothermal reservoirs. The fracture characteristics are crucial for estimating the effect of the artificial fracturing. Therefore, a cyclic heating-rapid cooling (CHRC) experiment is conducted on the notched semi-circular bend (NSCB) granite, where LN<sub>2</sub> and water cooling are employed. The structural damage and fracture characteristics of the CHRC treated sample are analyzed using ultrasonic detection, three-point bending test, and acoustic emission (AE) technique. A grain-based model with thermo‑mechanical coupling is constructed to explore the micro-cracking mechanism of the CHRC treatment. The results indicate that the damage caused by the CHRC increases significantly in the first five cycles, especially under LN<sub>2</sub> cooling. The decline of fracture toughness with cycles under different cooling methods. LN<sub>2</sub> cooling can dramatically enhance the AE energy release and fracture surface roughness in the initial cycles. LN<sub>2</sub> cooling can promote the generation of tensile cracks and intra-granular microcracks. The fracture behaviors of the CHRC treated granite are mainly determined by the stable thermal stress, significantly affected by mineral distribution. These results can provide a comprehensive understanding of cyclic LN<sub>2</sub> fracturing compared to hydraulic fracturing, supporting theoretical guidance for geothermal extraction.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"137 ","pages":"Article 104889"},"PeriodicalIF":5.0,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143453947","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}
Pub Date : 2025-02-16DOI: 10.1016/j.tafmec.2025.104890
M.J. Qadyani, B. Ameri, F. Taheri-Behrooz
To effectively integrate 3D-printed components into real-world applications, it is crucial for designers to fully understand the behavior of these constructions, particularly their fracture characteristics. This study addresses the fracture behavior of Fused Deposition Modeling (FDM) 3D-printed Double Cantilever Beam (DCB) specimens by analyzing the Mode-I strain energy release rate. The investigation encompasses two materials: (Acrylonitrile Butadiene Styrene) ABS, a brittle reference, and Polylactic acid (PLA), a ductile reference. Finite Element Analysis (FEA) is utilized to predict fracture behavior and evaluate the applicability of the model across various unidirectional raster angles (0°, 30°, 45°, 60°, and 90°) based on the Cohesive Zone Model (CZM). The study systematically explores fracture initiation, crack propagation, and critical failure points. Scanning Electron Microscopy (SEM) fractography examines the effects of different raster angles and material properties on construction behavior. The results reveal that the 60-degree raster angle yields the highest critical energy release rate, attributed to the mixed Mode-I/II interaction and significant shear deformation, with 2.3 mJ/mm2 values for ABS and 2.4 mJ/mm2 for PLA. This angle also demonstrates strand bridging, enhancing the material’s toughness. Conversely, samples with a 45-degree raster angle exhibit lower critical energy release rates, indicating reduced fracture resistance under these conditions. This comprehensive analysis provides valuable insights into optimizing 3D-printed structures for improved performance in practical applications.
{"title":"Critical strain energy release rate in additively manufactured polymers through comparative study of ABS and PLA across various raster angles","authors":"M.J. Qadyani, B. Ameri, F. Taheri-Behrooz","doi":"10.1016/j.tafmec.2025.104890","DOIUrl":"10.1016/j.tafmec.2025.104890","url":null,"abstract":"<div><div>To effectively integrate 3D-printed components into real-world applications, it is crucial for designers to fully understand the behavior of these constructions, particularly their fracture characteristics. This study addresses the fracture behavior of Fused Deposition Modeling (FDM) 3D-printed Double Cantilever Beam (DCB) specimens by analyzing the Mode-I strain energy release rate. The investigation encompasses two materials: (Acrylonitrile Butadiene Styrene) ABS, a brittle reference, and Polylactic acid (PLA), a ductile reference. Finite Element Analysis (FEA) is utilized to predict fracture behavior and evaluate the applicability of the model across various unidirectional raster angles (0°, 30°, 45°, 60°, and 90°) based on the Cohesive Zone Model (CZM). The study systematically explores fracture initiation, crack propagation, and critical failure points. Scanning Electron Microscopy (SEM) fractography examines the effects of different raster angles and material properties on construction behavior. The results reveal that the 60-degree raster angle yields the highest critical energy release rate, attributed to the mixed Mode-I/II interaction and significant shear deformation, with 2.3 mJ/mm<sup>2</sup> values for ABS and 2.4 mJ/mm2 for PLA. This angle also demonstrates strand bridging, enhancing the material’s toughness. Conversely, samples with a 45-degree raster angle exhibit lower critical energy release rates, indicating reduced fracture resistance under these conditions. This comprehensive analysis provides valuable insights into optimizing 3D-printed structures for improved performance in practical applications.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"138 ","pages":"Article 104890"},"PeriodicalIF":5.0,"publicationDate":"2025-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143453300","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}
Pub Date : 2025-02-15DOI: 10.1016/j.tafmec.2025.104884
Yating Wang , Dongyi Xing , Meilu Yu , Qing Qiao
Quantifying the internal deformation of three-dimensional (3D) fractured solids during crack propagation is crucial for understanding the failure mechanism of 3D fractured solids and quantifying fracture parameters at the embedded crack tip. At present, there are still certain difficulties in measuring the internal deformation of 3D fractured solids during the failure process through physical experimental methods. Utilizing advanced technologies, including multi-material/color 3D printing, simulated speckle algorithms, and stereo digital image correlation (stereo-DIC), this study innovatively achieves dynamic measurement of the internal displacement field in 3D solids containing parallel cracks during crack propagation. The obtained displacement field is used to analyze the deformation characteristics of embedded cracks and determine the parameters at the 3D crack tip (stress intensity factors and theoretical crack initiation angle). The influence of prefabricated crack spacing on the 3D solid failure process was quantitatively analyzed through the differences in initiation pressures, failure pressures and crack tip parameters. The experimental results indicate that as the spacing between parallel cracks decreases, the compression effect at the crack tip in the center of the model diminishes while the shear effect increases, ultimately reducing the model’s bearing capacity.
{"title":"Experimental study of internal deformation in 3D solids with embedded parallel cracks during the fracture process using multi-material 3D printing and stereo digital image correlation","authors":"Yating Wang , Dongyi Xing , Meilu Yu , Qing Qiao","doi":"10.1016/j.tafmec.2025.104884","DOIUrl":"10.1016/j.tafmec.2025.104884","url":null,"abstract":"<div><div>Quantifying the internal deformation of three-dimensional (3D) fractured solids during crack propagation is crucial for understanding the failure mechanism of 3D fractured solids and quantifying fracture parameters at the embedded crack tip. At present, there are still certain difficulties in measuring the internal deformation of 3D fractured solids during the failure process through physical experimental methods. Utilizing advanced technologies, including multi-material/color 3D printing, simulated speckle algorithms, and stereo digital image correlation (stereo-DIC), this study innovatively achieves dynamic measurement of the internal displacement field in 3D solids containing parallel cracks during crack propagation. The obtained displacement field is used to analyze the deformation characteristics of embedded cracks and determine the parameters at the 3D crack tip (stress intensity factors and theoretical crack initiation angle). The influence of prefabricated crack spacing on the 3D solid failure process was quantitatively analyzed through the differences in initiation pressures, failure pressures and crack tip parameters. The experimental results indicate that as the spacing between parallel cracks decreases, the compression effect at the crack tip in the center of the model diminishes while the shear effect increases, ultimately reducing the model’s bearing capacity.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"137 ","pages":"Article 104884"},"PeriodicalIF":5.0,"publicationDate":"2025-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143429424","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}
Pub Date : 2025-02-15DOI: 10.1016/j.tafmec.2025.104885
Shankun Zhao , Mingyuan Zhang , Guanghui He , Kun Lv , Dejian Li , Yingjun Li , Hainan Gao
The planning and construction of mine roadways inevitably involve crossing interfaces between coal and rock seams. While previous studies have extensively examined the mechanical properties of coal-rock combinations with varying coal and rock seam thicknesses, few research has focused on the fracture behavior of samples with different rock seam strengths. Three-point bending experiments were conducted on coal-rock combined samples with pre-crack and sandstone, which had uniaxial compressive strength of 34.4 MPa and 124.7 MPa, respectively, to analyze their influence on the mechanical properties of the samples. Each combination types featured coal-rock thickness ratios of 1:1, 2:1, and 5:1, respectively. The entire fracture process, from loading to failure, was captured using the ultrafast time-resolution method based on pulsed laser technology, achieving a time resolution of 15 picoseconds. The experimental results revealed distinct failure mechanisms between samples with weak versus strong sandstone seams. The macroscopic cracks in samples with weak sandstone emerged at the peak load, whereas in those with strong sandstone, macroscopic crack occurred prior to peak load. Furthermore, samples with weaker sandstone exhibited progressive failure modes at coal-rock thickness ratios of 2:1 and 5:1, whereas all other groups demonstrated brittle failure. The crack tip locations and mode I stress intensity factors (SIF) at crack initiation were determined using digital image correlation (DIC) in conjunction with the immune algorithm (IA). It is recommended that mine roadways construction account not only for the coal seam thickness-to- roadway height ratio but also for the strength of the overlying rock strata.
{"title":"Experimental study on fracture behavior of coal-rock samples with varying sandstone strength using the ultrafast time-resolution method","authors":"Shankun Zhao , Mingyuan Zhang , Guanghui He , Kun Lv , Dejian Li , Yingjun Li , Hainan Gao","doi":"10.1016/j.tafmec.2025.104885","DOIUrl":"10.1016/j.tafmec.2025.104885","url":null,"abstract":"<div><div>The planning and construction of mine roadways inevitably involve crossing interfaces between coal and rock seams. While previous studies have extensively examined the mechanical properties of coal-rock combinations with varying coal and rock seam thicknesses, few research has focused on the fracture behavior of samples with different rock seam strengths. Three-point bending experiments were conducted on coal-rock combined samples with pre-crack and sandstone, which had uniaxial compressive strength of 34.4 MPa and 124.7 MPa, respectively, to analyze their influence on the mechanical properties of the samples. Each combination types featured coal-rock thickness ratios of 1:1, 2:1, and 5:1, respectively. The entire fracture process, from loading to failure, was captured using the ultrafast time-resolution method based on pulsed laser technology, achieving a time resolution of 15 picoseconds. The experimental results revealed distinct failure mechanisms between samples with weak versus strong sandstone seams. The macroscopic cracks in samples with weak sandstone emerged at the peak load, whereas in those with strong sandstone, macroscopic crack occurred prior to peak load. Furthermore, samples with weaker sandstone exhibited progressive failure modes at coal-rock thickness ratios of 2:1 and 5:1, whereas all other groups demonstrated brittle failure. The crack tip locations and mode I stress intensity factors (SIF) at crack initiation were determined using digital image correlation (DIC) in conjunction with the immune algorithm (IA). It is recommended that mine roadways construction account not only for the coal seam thickness-to- roadway height ratio but also for the strength of the overlying rock strata.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"137 ","pages":"Article 104885"},"PeriodicalIF":5.0,"publicationDate":"2025-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143438131","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}
Pub Date : 2025-02-14DOI: 10.1016/j.tafmec.2025.104867
Tao Zhou , Yuchun Lin , Jiarong Chen
The propagation of internal cracks is a common cause of instability and failure in engineering rock masses, which can pose significant risks to their safety and operational integrity. This study systematically investigated the underlying mechanisms of crack propagation in red sandstone specimens containing a single flaw under uniaxial compressive loading. The entire cracking process including initiation, propagation, and coalescence, was recorded and analyzed from macro-meso scales scale using acoustic emission (AE) technology, high-speed photography systems, and a scanning electron microscope (SEM). Furthermore, two new parameters, the weakening parameter Rc and the brittleness parameter Ri, have been proposed for the evaluation of crack sensitivity and the assessment of crack-bearing working capacity in rock masses comprising diverse lithologies (sandstone, plaster, granite, marble, and rock-like materials) and flawed inclinations (0°, 15°, 30°, 45°, 60°, 75°, and 90°). Based on the comprehensive assessment of Rc and Ri, the study proposes a new classification system that divides the safety performance of rock masses into four distinct zones: a safe zone, a flaw sensitive zone, a dangerous zone, and a brittle zone. In terms of natural rock, approximately 60–75% of sandstone and granite specimens fall within the brittle and dangerous zones, indicating a higher tendency to rockburst. In contrast, this proportion decreases to 50% for marble specimens. The dangerous zone for natural rocks is concentrated between 0° and 45°, with the most hazardous flawed inclinations ranging from 15° to 30°. Over 60% of the specimens fall within the dangerous zone at these ranges. The incorporation of fillers has been demonstrated to significantly enhance the overall load-bearing capacity of natural rock masses, notably increasing the proportion of brittle and safe zones. In comparison to natural rocks, rock-like materials have been shown to demonstrate superior safety performance, particularly in their resistance to flaw weakening and their capacity to bear initial cracks. The present study demonstrates that 75% of concrete and 54% of plaster materials are situated within the safe zone when the flawed inclination is below 75°. This research offers a novel scientific reference point for the safety performance assessment of flawed rock masses, which is advantageous for the secure construction and operation of rock mass engineering.
{"title":"Macro-meso crack propagation characteristics and safety performance assessment of flawed rock mass","authors":"Tao Zhou , Yuchun Lin , Jiarong Chen","doi":"10.1016/j.tafmec.2025.104867","DOIUrl":"10.1016/j.tafmec.2025.104867","url":null,"abstract":"<div><div>The propagation of internal cracks is a common cause of instability and failure in engineering rock masses, which can pose significant risks to their safety and operational integrity. This study systematically investigated the underlying mechanisms of crack propagation in red sandstone specimens containing a single flaw under uniaxial compressive loading. The entire cracking process including initiation, propagation, and coalescence, was recorded and analyzed from macro-meso scales scale using acoustic emission (AE) technology, high-speed photography systems, and a scanning electron microscope (SEM). Furthermore, two new parameters, the weakening parameter <em>R<sub>c</sub></em> and the brittleness parameter <em>R</em><sub>i</sub>, have been proposed for the evaluation of crack sensitivity and the assessment of crack-bearing working capacity in rock masses comprising diverse lithologies (sandstone, plaster, granite, marble, and rock-like materials) and flawed inclinations (0°, 15°, 30°, 45°, 60°, 75°, and 90°). Based on the comprehensive assessment of <em>R</em><sub>c</sub> and <em>R</em><sub>i</sub>, the study proposes a new classification system that divides the safety performance of rock masses into four distinct zones: a safe zone, a flaw sensitive zone, a dangerous zone, and a brittle zone. In terms of natural rock, approximately 60–75% of sandstone and granite specimens fall within the brittle and dangerous zones, indicating a higher tendency to rockburst. In contrast, this proportion decreases to 50% for marble specimens. The dangerous zone for natural rocks is concentrated between 0° and 45°, with the most hazardous flawed inclinations ranging from 15° to 30°. Over 60% of the specimens fall within the dangerous zone at these ranges. The incorporation of fillers has been demonstrated to significantly enhance the overall load-bearing capacity of natural rock masses, notably increasing the proportion of brittle and safe zones. In comparison to natural rocks, rock-like materials have been shown to demonstrate superior safety performance, particularly in their resistance to flaw weakening and their capacity to bear initial cracks. The present study demonstrates that 75% of concrete and 54% of plaster materials are situated within the safe zone when the flawed inclination is below 75°. This research offers a novel scientific reference point for the safety performance assessment of flawed rock masses, which is advantageous for the secure construction and operation of rock mass engineering.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"137 ","pages":"Article 104867"},"PeriodicalIF":5.0,"publicationDate":"2025-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143418967","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}
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