Pub Date : 2025-02-06DOI: 10.1016/j.tafmec.2025.104862
Mingchao Ding , Shuguang Bian , Pengkuo Lei , Jiaxing Huang , Gengliang Liu , Lipo Yang , Liming Wang
The stress–strain curve at the notch root can be an essential basis for studying the elastic–plastic deformation behavior of notched structure. However, current notch stress–strain studies rarely consider the effect of a finite residual size at the notch root. The blunt side-notched specimens with finite residual width are designed in this work. The material of side-notched specimen is the TC4 titanium alloy. The notch-root strain is measured using the 3D-DIC and an elastic–plastic finite element analysis is performed. It is found that the notch constraints of the finite residual width side-notched specimens are plane stress, which may not be affected by the notch-root radius of curvature. Experiment verification shows that both Neuber’s rule and ESED would underestimate the notch root strain in the plastic stage, and the main reason is that the stress concentration caused by the finite residual width is not considered. To compensate for the deficiency of the traditional method of describing stress concentrations using only Kt, a geometric concentration factor Kg is proposed. Kg can simultaneously reflect the effect of both Kt and the finite residual width on plastic deformation. By introducing the Kg, the accuracy of Neuber’s rule and ESED in describing notch stress–strain has been significantly improved.
{"title":"Study on notch stress–strain response of blunt side-notched specimen with finite residual width","authors":"Mingchao Ding , Shuguang Bian , Pengkuo Lei , Jiaxing Huang , Gengliang Liu , Lipo Yang , Liming Wang","doi":"10.1016/j.tafmec.2025.104862","DOIUrl":"10.1016/j.tafmec.2025.104862","url":null,"abstract":"<div><div>The stress–strain curve at the notch root can be an essential basis for studying the elastic–plastic deformation behavior of notched structure. However, current notch stress–strain studies rarely consider the effect of a finite residual size at the notch root. The blunt side-notched specimens with finite residual width are designed in this work. The material of side-notched specimen is the TC4 titanium alloy. The notch-root strain is measured using the 3D-DIC and an elastic–plastic finite element analysis is performed. It is found that the notch constraints of the finite residual width side-notched specimens are plane stress, which may not be affected by the notch-root radius of curvature. Experiment verification shows that both Neuber’s rule and ESED would underestimate the notch root strain in the plastic stage, and the main reason is that the stress concentration caused by the finite residual width is not considered. To compensate for the deficiency of the traditional method of describing stress concentrations using only <em>K</em><sub>t</sub>, a geometric concentration factor <em>K</em><sub>g</sub> is proposed. <em>K</em><sub>g</sub> can simultaneously reflect the effect of both <em>K</em><sub>t</sub> and the finite residual width on plastic deformation. By introducing the <em>K</em><sub>g</sub>, the accuracy of Neuber’s rule and ESED in describing notch stress–strain has been significantly improved.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"136 ","pages":"Article 104862"},"PeriodicalIF":5.0,"publicationDate":"2025-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143372474","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 : 2025-02-06DOI: 10.1016/j.tafmec.2025.104868
Jamal Bidadi, Hamed Saeidi Googarchin
Structural adhesive joints are effective strategy for constructing lightweight, cost-efficient components. Evaluating their long-term performance is crucial for designing durable and robust bonded systems. Understanding time-dependent phenomena like creep and its impact on the mechanical and fracture behavior of adhesives provides valuable insights for improved design. Creep loading significantly influences the strength, deformation, and fracture response of bonded structures over their service life. This study investigates the creep behavior and mode I fracture response of modified double-cantilever beam (MDCB) adhesive joints subjected to sustained tensile loads, focusing on two primary factors: creep stress level and creep duration. Creep tests were conducted on MDCB specimens at stress levels of 20 %, 30 %, 40 %, 50 %, and 60 % of the adhesive’s maximum tensile strength () for durations of 12, 48, and 72 h. The aim was to assess how sustained creep affects the residual fracture properties of adhesive joints. Creep behavior was characterized by analyzing strain vs. time curves, identifying elastic, primary, and secondary creep stages. Results showed that joints tolerated 20–40 % of for a maximum creep duration of 72 h. Subsequently, mode I fracture after creep (FAC) tests were performed on MDCB joints exposed to 20–40 % at a crosshead speed of 0.5 mm/min. FAC tests revealed a significant reduction in fracture load and fracture energy with increasing creep stress levels and durations compared to control specimens without creep exposure. Fracture surface analysis indicated a transition from cohesive failure to a combination of adhesive and cohesive failure with longer creep durations. Finally, a semi-empirical model was developed using response surface methodology (RSM) to predict the residual mode I fracture energy of adhesive joints, enabling future numerical simulations of creep behavior.
{"title":"Experimental study on mode I fracture response of adhesive joints subjected to systematic creep damage","authors":"Jamal Bidadi, Hamed Saeidi Googarchin","doi":"10.1016/j.tafmec.2025.104868","DOIUrl":"10.1016/j.tafmec.2025.104868","url":null,"abstract":"<div><div>Structural adhesive joints are effective strategy for constructing lightweight, cost-efficient components. Evaluating their long-term performance is crucial for designing durable and robust bonded systems. Understanding time-dependent phenomena like creep and its impact on the mechanical and fracture behavior of adhesives provides valuable insights for improved design. Creep loading significantly influences the strength, deformation, and fracture response of bonded structures over their service life. This study investigates the creep behavior and mode I fracture response of modified double-cantilever beam (MDCB) adhesive joints subjected to sustained tensile loads, focusing on two primary factors: creep stress level and creep duration. Creep tests were conducted on MDCB specimens at stress levels of 20 %, 30 %, 40 %, 50 %, and 60 % of the adhesive’s maximum tensile strength (<span><math><msub><mi>S</mi><mrow><mi>max</mi></mrow></msub></math></span>) for durations of 12, 48, and 72 h. The aim was to assess how sustained creep affects the residual fracture properties of adhesive joints. Creep behavior was characterized by analyzing strain vs. time curves, identifying elastic, primary, and secondary creep stages. Results showed that joints tolerated 20–40 % of <span><math><msub><mi>S</mi><mrow><mi>max</mi></mrow></msub></math></span> for a maximum creep duration of 72 h. Subsequently, mode I fracture after creep (FAC) tests were performed on MDCB joints exposed to 20–40 % <span><math><msub><mi>S</mi><mrow><mi>max</mi></mrow></msub></math></span> at a crosshead speed of 0.5 mm/min. FAC tests revealed a significant reduction in fracture load and fracture energy with increasing creep stress levels and durations compared to control specimens without creep exposure. Fracture surface analysis indicated a transition from cohesive failure to a combination of adhesive and cohesive failure with longer creep durations. Finally, a semi-empirical model was developed using response surface methodology (RSM) to predict the residual mode I fracture energy of adhesive joints, enabling future numerical simulations of creep behavior.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"136 ","pages":"Article 104868"},"PeriodicalIF":5.0,"publicationDate":"2025-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143375848","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 : 2025-02-04DOI: 10.1016/j.tafmec.2025.104866
Tengfei Guo , Kewei Liu , Houqiang Wang , Xuefeng Si , Yichao Rui , Chengzhi Pu , Yi Zhang , Congxiang Yuan
The crack propagation and coalescence behavior of rock-concrete composite structures with parallel double flaws is crucial for stability evaluation of rock-based concrete engineering projects. A uniaxial compression experiment was performed on rock-concrete composite (RCC) specimen in this study, and the crack extension process of RCC specimens was recorded with digital image correlation (DIC) equipment and acoustic emission (AE) equipment. The impacts of the inclination angles for flaws and rock-concrete interface planes on mechanical behavior and fracture process of RCC specimens were studied. The results reveal that fracture modes of specimens under compressive loading can be categorized into the following types: crack coalescing modes in different materials, crack extension modes in one material and crack extension modes in different materials. The initiation of cracks does not occur synchronously in different materials. Cracks in rock and concrete penetrate the interface and merge at low interface inclination angle, whereas interface cracks are generally formed at higher interface inclination angle, which inhibits crack coalescing in different materials. The coalescing of cracks between varying material is controlled by strength ratio. Increased concrete strength intensifies crack failure in rocks, facilitating crack penetration at the interface, while also strengthening the composite specimen and widening the peak strength differences across various flaw inclination angles. The peak strength is greatly affected by interface inclination angle. Furthermore, interface inclination angle and flaw inclination angle play an essential part in energy evolution. When interface inclination angle enlarges, the peak elastic strain energy first descends and subsequently ascends. The energy storage limit rises with enlarging the flaw inclination angle.
{"title":"Mechanical characteristics and fracturing behavior of rock-concrete composite specimens with two pre-existing parallel flaws under uniaxial compression based on AE and DIC systems","authors":"Tengfei Guo , Kewei Liu , Houqiang Wang , Xuefeng Si , Yichao Rui , Chengzhi Pu , Yi Zhang , Congxiang Yuan","doi":"10.1016/j.tafmec.2025.104866","DOIUrl":"10.1016/j.tafmec.2025.104866","url":null,"abstract":"<div><div>The crack propagation and coalescence behavior of rock-concrete composite structures with parallel double flaws is crucial for stability evaluation of rock-based concrete engineering projects. A uniaxial compression experiment was performed on rock-concrete composite (RCC) specimen in this study, and the crack extension process of RCC specimens was recorded with digital image correlation (DIC) equipment and acoustic emission (AE) equipment. The impacts of the inclination angles for flaws and rock-concrete interface planes on mechanical behavior and fracture process of RCC specimens were studied. The results reveal that fracture modes of specimens under compressive loading can be categorized into the following types: crack coalescing modes in different materials, crack extension modes in one material and crack extension modes in different materials. The initiation of cracks does not occur synchronously in different materials. Cracks in rock and concrete penetrate the interface and merge at low interface inclination angle, whereas interface cracks are generally formed at higher interface inclination angle, which inhibits crack coalescing in different materials. The coalescing of cracks between varying material is controlled by strength ratio. Increased concrete strength intensifies crack failure in rocks, facilitating crack penetration at the interface, while also strengthening the composite specimen and widening the peak strength differences across various flaw inclination angles. The peak strength is greatly affected by interface inclination angle. Furthermore, interface inclination angle and flaw inclination angle play an essential part in energy evolution. When interface inclination angle enlarges, the peak elastic strain energy first descends and subsequently ascends. The energy storage limit rises with enlarging the flaw inclination angle.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"136 ","pages":"Article 104866"},"PeriodicalIF":5.0,"publicationDate":"2025-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143348898","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 : 2025-02-04DOI: 10.1016/j.tafmec.2025.104865
Hossein Soroush, Amir Nourani, Gholamhossein Farrahi
Predicting the fracture load and energy in solder joints is crucial for enhancing their reliability and preventing failure in electronic systems. This study introduced a novel framework by combining experimental data, machine learning (ML) models, and multi-objective optimization to predict and optimize the fracture behavior of solder joints. For this purpose, double cantilever beam (DCB) samples were fabricated and tested under displacement-control conditions and mode I crack propagation loading with a strain rate of 0.03 , incorporating environmental factors (i.e., storage temperature and humidity) and geometrical constraints (i.e., adherend thickness, adherend width, and solder thickness). The one-way analysis of variance (ANOVA) test results revealed that while all studied factors affected the fracture load of the joints, only storage temperature, humidity, and adherend thickness meaningfully influenced the samples’ fracture energy. Next, using various machine learning (ML) techniques such as artificial neural network (ANN) and random forest (RF), the solder joint’s fracture load and energy were forecasted with 86 % and 80.5 % accuracy, respectively. According to the results, the ANN and RF models predicted the joint fracture load and energy more accurately than other ML algorithms. Finally, a multi-objective optimization was employed to achieve fracture load and energy optimal values in DCB specimens by implementing the NSGA-II algorithm. This integrated approach can minimize the need for experimental testing and enable accurate prediction of solder joint fracture behavior by employing various ML models and optimization algorithms considering different working conditions.
{"title":"A Machine learning model to predict fracture of solder joints considering geometrical and environmental factors","authors":"Hossein Soroush, Amir Nourani, Gholamhossein Farrahi","doi":"10.1016/j.tafmec.2025.104865","DOIUrl":"10.1016/j.tafmec.2025.104865","url":null,"abstract":"<div><div>Predicting the fracture load and energy in solder joints is crucial for enhancing their reliability and preventing failure in electronic systems. This study introduced a novel framework by combining experimental data, machine learning (ML) models, and multi-objective optimization to predict and optimize the fracture behavior of solder joints. For this purpose, double cantilever beam (DCB) samples were fabricated and tested under displacement-control conditions and mode I crack propagation loading with a strain rate of 0.03 <span><math><mrow><msup><mrow><mi>s</mi></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup></mrow></math></span>, incorporating environmental factors (i.e., storage temperature and humidity) and geometrical constraints (i.e., adherend thickness, adherend width, and solder thickness). The one-way analysis of variance (ANOVA) test results revealed that while all studied factors affected the fracture load of the joints, only storage temperature, humidity, and adherend thickness meaningfully influenced the samples’ fracture energy. Next, using various machine learning (ML) techniques such as artificial neural network (ANN) and random forest (RF), the solder joint’s fracture load and energy were forecasted with 86 % and 80.5 % accuracy, respectively. According to the results, the ANN and RF models predicted the joint fracture load and energy more accurately than other ML algorithms. Finally, a multi-objective optimization was employed to achieve fracture load and energy optimal values in DCB specimens by implementing the NSGA-II algorithm. This integrated approach can minimize the need for experimental testing and enable accurate prediction of solder joint fracture behavior by employing various ML models and optimization algorithms considering different working conditions.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"136 ","pages":"Article 104865"},"PeriodicalIF":5.0,"publicationDate":"2025-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143351384","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 : 2025-02-01DOI: 10.1016/j.tafmec.2024.104776
Ángel De La Rosa , Gonzalo Ruiz , Rodrigo Moreno
This study investigates the mixed-mode fracture behavior of self-compacting concrete specimens reinforced with longitudinal steel bars and steel fibers. The experimental program involved three-point bending tests on asymmetrically notched prismatic specimens designed to induce and propagate mixed-mode cracks. The influence of different steel fiber dosages on crack initiation, propagation, and final failure was evaluated. Key findings reveal that the addition of steel fibers significantly enhances energy absorption and ductility under combined mode I and mode II fracture conditions. The results demonstrate the effectiveness of steel fibers in delaying brittle failure and improving the overall structural performance. Novelty lies in the combined use of self-compacting concrete and steel fibers to explore mixed-mode fracture mechanisms in reinforced elements.
{"title":"Experimental study on quasi-static mixed mode fracture in self-compacting concrete with longitudinal reinforcement and steel fibers","authors":"Ángel De La Rosa , Gonzalo Ruiz , Rodrigo Moreno","doi":"10.1016/j.tafmec.2024.104776","DOIUrl":"10.1016/j.tafmec.2024.104776","url":null,"abstract":"<div><div>This study investigates the mixed-mode fracture behavior of self-compacting concrete specimens reinforced with longitudinal steel bars and steel fibers. The experimental program involved three-point bending tests on asymmetrically notched prismatic specimens designed to induce and propagate mixed-mode cracks. The influence of different steel fiber dosages on crack initiation, propagation, and final failure was evaluated. Key findings reveal that the addition of steel fibers significantly enhances energy absorption and ductility under combined mode I and mode II fracture conditions. The results demonstrate the effectiveness of steel fibers in delaying brittle failure and improving the overall structural performance. Novelty lies in the combined use of self-compacting concrete and steel fibers to explore mixed-mode fracture mechanisms in reinforced elements.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"135 ","pages":"Article 104776"},"PeriodicalIF":5.0,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143098664","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-01DOI: 10.1016/j.tafmec.2025.104861
Cheng Chen, Xudong Qian
This paper proposes a novel approach to quantify the crack size from strain fields measured from digital image correlation (DIC), by extrapolating the positions at peak strain or peak strain increments identified along paths parallel to the crack plane. The proposed approach does not require data in the immediate vicinity of the crack tip, where DIC measurement is usually less accurate. This study utilizes the modified boundary layer model to demonstrate the strain pattern underpinning the crack size from HRR theory and the single edge notched bend model to verify the crack sizing accuracy from the strain fields. The experimental study further validates the proposed method in plane-sided and side-grooved specimens and evaluates the plastic wake effects on the crack-sizing accuracy for propagating cracks under elasto-plastic conditions. The proposed method identifies the crack tip location directly without measuring the elastic compliance, which enables fast and convenient crack sizing under challenging conditions such as the impact tests. This study demonstrates enhanced fracture resistance of the S550 material under increasing loading rates using the proposed crack sizing method.
{"title":"A direct crack sizing approach from DIC strain analyses under elasto-plastic and dynamic conditions","authors":"Cheng Chen, Xudong Qian","doi":"10.1016/j.tafmec.2025.104861","DOIUrl":"10.1016/j.tafmec.2025.104861","url":null,"abstract":"<div><div>This paper proposes a novel approach to quantify the crack size from strain fields measured from digital image correlation (DIC), by extrapolating the positions at peak strain or peak strain increments identified along paths parallel to the crack plane. The proposed approach does not require data in the immediate vicinity of the crack tip, where DIC measurement is usually less accurate. This study utilizes the modified boundary layer model to demonstrate the strain pattern underpinning the crack size from HRR theory and the single edge notched bend model to verify the crack sizing accuracy from the strain fields. The experimental study further validates the proposed method in plane-sided and side-grooved specimens and evaluates the plastic wake effects on the crack-sizing accuracy for propagating cracks under elasto-plastic conditions. The proposed method identifies the crack tip location directly without measuring the elastic compliance, which enables fast and convenient crack sizing under challenging conditions such as the impact tests. This study demonstrates enhanced fracture resistance of the S550 material under increasing loading rates using the proposed crack sizing method.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"136 ","pages":"Article 104861"},"PeriodicalIF":5.0,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143197088","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-01DOI: 10.1016/j.tafmec.2024.104768
Chanh Dinh Vuong , Thanh-Trung Vo , Tinh Quoc Bui
Accurately modeling mixed-mode crack propagation in rock-like materials remains challenging due to the complexity of the deformation states and mechanism of fracture throughout the loading history. The objective of this paper is to analyze the damage process in rock-like materials using an enhanced smeared damage model. The mixed-mode failure in rocks is captured using our recently developed smoothing gradient damage model in conjunction with a novel equivalent strain formulation, which is developed by combining both the bi-energy norm equivalent strain and the four-parameter equivalent strain. To validate the accuracy of the developed method, several commonly reported rock fracture examples are considered in which complex crack paths and responses are reproduced and compared with the available experimental data.
{"title":"Mixed-mode crack growth simulation in rock-like materials with the smoothing gradient-enhanced damage model associated with a novel equivalent strain","authors":"Chanh Dinh Vuong , Thanh-Trung Vo , Tinh Quoc Bui","doi":"10.1016/j.tafmec.2024.104768","DOIUrl":"10.1016/j.tafmec.2024.104768","url":null,"abstract":"<div><div>Accurately modeling mixed-mode crack propagation in rock-like materials remains challenging due to the complexity of the deformation states and mechanism of fracture throughout the loading history. The objective of this paper is to analyze the damage process in rock-like materials using an enhanced smeared damage model. The mixed-mode failure in rocks is captured using our recently developed smoothing gradient damage model in conjunction with a novel equivalent strain formulation, which is developed by combining both the bi-energy norm equivalent strain and the four-parameter equivalent strain. To validate the accuracy of the developed method, several commonly reported rock fracture examples are considered in which complex crack paths and responses are reproduced and compared with the available experimental data.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"135 ","pages":"Article 104768"},"PeriodicalIF":5.0,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143098665","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 : 2025-01-31DOI: 10.1016/j.tafmec.2025.104856
Longfei Chang , Lu Chen , Mingyuan Zhang , Bo Hu , Weichen Li , Dejian Li , Yingjun Li
The instability and failure mechanisms of engineering rock masses are significantly influenced by fissures, increasing their uncertainty. Under the action of a lateral constraint load, the bearing characteristics and deformation behavior of rock masses become more complex. To investigate the impact of the ligament angle on failure mechanisms and provide precursor information for rock instability, this study conducted biaxial compression experiments on pre-cracked sandstones with varying ligament angles. Infrared thermal imaging (ITI), acoustic emission (AE), and digital image correlation (DIC) were employed. The results indicate the following: First, pre-cracked sandstone samples with different ligament angles exhibited variations in elastic modulus and strength. However, under lateral load constraints, these variations were minimal, and the failure mode demonstrated ductile characteristics. As the ligament angle increases, the crack coalescence mode transitions from the shear crack coalescence mode to the tension-dominated tensile-shear mixed mode. Second, a predictive infrared radiation-based index, the difference in average infrared radiation temperature (DIRT), was proposed to monitor the evolution of rock damage. The rate of change in the DIRT can be divided into three phases: the “steady phase–accelerated growth phase–rapid growth phase,” corresponding to different stages of damage development during rock loading. Finally, a damage variable was defined on the basis of the DIRT, and a damage constitutive model for rock was established. The model’s computational results closely match the experimental curves, validating the rationality of the defined damage variable.
{"title":"Analysis of failure characteristics and constitutive model development for sandstone with different ligament angles under biaxial loading based on infrared radiation","authors":"Longfei Chang , Lu Chen , Mingyuan Zhang , Bo Hu , Weichen Li , Dejian Li , Yingjun Li","doi":"10.1016/j.tafmec.2025.104856","DOIUrl":"10.1016/j.tafmec.2025.104856","url":null,"abstract":"<div><div>The instability and failure mechanisms of engineering rock masses are significantly influenced by fissures, increasing their uncertainty. Under the action of a lateral constraint load, the bearing characteristics and deformation behavior of rock masses become more complex. To investigate the impact of the ligament angle on failure mechanisms and provide precursor information for rock instability, this study conducted biaxial compression experiments on pre-cracked sandstones with varying ligament angles. Infrared thermal imaging (ITI), acoustic emission (AE), and digital image correlation (DIC) were employed. The results indicate the following: First, pre-cracked sandstone samples with different ligament angles exhibited variations in elastic modulus and strength. However, under lateral load constraints, these variations were minimal, and the failure mode demonstrated ductile characteristics. As the ligament angle increases, the crack coalescence mode transitions from the shear crack coalescence mode to the tension-dominated tensile-shear mixed mode. Second, a predictive infrared radiation-based index, the difference in average infrared radiation temperature (<em>DIRT</em>), was proposed to monitor the evolution of rock damage. The rate of change in the <em>DIRT</em> can be divided into three phases: the “steady phase–accelerated growth phase–rapid growth phase,” corresponding to different stages of damage development during rock loading. Finally, a damage variable was defined on the basis of the <em>DIRT</em>, and a damage constitutive model for rock was established. The model’s computational results closely match the experimental curves, validating the rationality of the defined damage variable.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"136 ","pages":"Article 104856"},"PeriodicalIF":5.0,"publicationDate":"2025-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143130756","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 : 2025-01-31DOI: 10.1016/j.tafmec.2025.104857
Yuezong Yang , Yujie Wang
The mechanical characteristics of rocks are substantially influenced by their strain rate, and the intricacy of rock dynamic failure is compounded by the presence of flaws within the rock structure. In this study, a rate-dependent Stillinger-Weber (SW) potential based discretized virtual internal bond (DVIB) model is proposed and integrated with the element partition method (EPM) to simulate the dynamic fracture of flawed rocks under varying loading rates. The rate-dependent SW potential, which is an improvement of the conventional trilinear damage potential, is produced by altering material properties to account for strain rate effects. A series of Split Hopkinson Pressure Bar (SHPB) experiments were simulated on various flawed specimens, including single-flawed, parallel-flawed and cross-flawed specimens, to validate the accuracy of our model for simulating rock dynamic fracture. The simulated findings demonstrate that all specimens’ dynamic strengths increase as the strain rate increases. For single-flawed and parallel-flawed specimens, the dynamic strength initially decreases and then increases as the flaw angle increases. Asymmetric cross-flawed specimens exhibit higher dynamic strengths compared to their symmetric counterparts. An increase in strain rate can exacerbate the dynamic failure characteristics and failure degree of different kinds of flawed specimens. The single-flawed and parallel-flawed specimens’ tensile failure characteristics deteriorate and their shear failure characteristics rise with an increase in flaw angle. The failure pattern of parallel-flawed specimens is more sensitive to changes in flaw angle than to variations in flaw spacing. Under the same strain rate conditions, the failure pattern of asymmetric cross-flawed specimen is more complex than that of symmetric cross-flawed specimen. The comparison between the simulated and experimental results confirms that the developed rate-dependent SW-DVIB model combined with EPM proves to be an effective tool for simulating the dynamic fracture behavior of flawed rocks under varying loading rates.
{"title":"Dynamic fracture simulation of flawed rocks under varying loading rates by the rate-dependent SW-DVIB model combined with EPM","authors":"Yuezong Yang , Yujie Wang","doi":"10.1016/j.tafmec.2025.104857","DOIUrl":"10.1016/j.tafmec.2025.104857","url":null,"abstract":"<div><div>The mechanical characteristics of rocks are substantially influenced by their strain rate, and the intricacy of rock dynamic failure is compounded by the presence of flaws within the rock structure. In this study, a rate-dependent Stillinger-Weber (SW) potential based discretized virtual internal bond (DVIB) model is proposed and integrated with the element partition method (EPM) to simulate the dynamic fracture of flawed rocks under varying loading rates. The rate-dependent SW potential, which is an improvement of the conventional trilinear damage potential, is produced by altering material properties to account for strain rate effects. A series of Split Hopkinson Pressure Bar (SHPB) experiments were simulated on various flawed specimens, including single-flawed, parallel-flawed and cross-flawed specimens, to validate the accuracy of our model for simulating rock dynamic fracture. The simulated findings demonstrate that all specimens’ dynamic strengths increase as the strain rate increases. For single-flawed and parallel-flawed specimens, the dynamic strength initially decreases and then increases as the flaw angle increases. Asymmetric cross-flawed specimens exhibit higher dynamic strengths compared to their symmetric counterparts. An increase in strain rate can exacerbate the dynamic failure characteristics and failure degree of different kinds of flawed specimens. The single-flawed and parallel-flawed specimens’ tensile failure characteristics deteriorate and their shear failure characteristics rise with an increase in flaw angle. The failure pattern of parallel-flawed specimens is more sensitive to changes in flaw angle than to variations in flaw spacing. Under the same strain rate conditions, the failure pattern of asymmetric cross-flawed specimen is more complex than that of symmetric cross-flawed specimen. The comparison between the simulated and experimental results confirms that the developed rate-dependent SW-DVIB model combined with EPM proves to be an effective tool for simulating the dynamic fracture behavior of flawed rocks under varying loading rates.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"136 ","pages":"Article 104857"},"PeriodicalIF":5.0,"publicationDate":"2025-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143130759","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 : 2025-01-30DOI: 10.1016/j.tafmec.2025.104858
Yue Li , Sheng-Qi Yang , De-An Zheng , Yu Song , Xiang-Xi Meng , Ke-Sheng Li
Fissures with various inclination angles are present in engineering rocky slopes, a structural geological product, profoundly influence the long-term stability of rock engineering; whereas, exploration on its macroscopic failure mechanisms and fatigue mechanical characteristics of pre-flawed granite specimens are insufficient. Therefore, this study investigated the fatigue mechanical responses and meso-macro fracture mechanisms of pre-flawed granites with different pre-flaw spaces under monotonic and multilevel fatigue loadings using the CT imaging and three-dimensional crack reconstruction technology. Results showed that the strength of granites with short, medium and long flaw-spacing and intact specimens increased sequentially. Under multilevel fatigue loading, the stiffness of pre-flawed granite produced a significant hardening and a staged increase, similar variation pattern was also reflected by the input energy density and elastic strain energy. Meanwhile, In the last fatigue stage, the damage factor of granites appeared a ‘’ − shaped upward trend, the damage deterioration rate of the specimens was the fastest during this stage. Finally, the type of pre-flaw spacing controlled the macroscopic failure patterns and crack network of granite. The non-uniform stresses at tips of pre-flawed flaws were responsible for inhibiting cracks development. The smaller the non-uniform stress was, crack network had the more possible properties to develop. Consequently, the crack network was more developed in granite with longer pre-flaw spacing.
{"title":"Fatigue behaviors of pre-flawed orthoclase granite under monotonic and multi-level cyclic loadings","authors":"Yue Li , Sheng-Qi Yang , De-An Zheng , Yu Song , Xiang-Xi Meng , Ke-Sheng Li","doi":"10.1016/j.tafmec.2025.104858","DOIUrl":"10.1016/j.tafmec.2025.104858","url":null,"abstract":"<div><div>Fissures with various inclination angles are present in engineering rocky slopes, a structural geological product, profoundly influence the long-term stability of rock engineering; whereas, exploration on its macroscopic failure mechanisms and fatigue mechanical characteristics of pre-flawed granite specimens are insufficient. Therefore, this study investigated the fatigue mechanical responses and meso-macro fracture mechanisms of pre-flawed granites with different pre-flaw spaces under monotonic and multilevel fatigue loadings using the CT imaging and three-dimensional crack reconstruction technology. Results showed that the strength of granites with short, medium and long flaw-spacing and intact specimens increased sequentially. Under multilevel fatigue loading, the stiffness of pre-flawed granite produced a significant hardening and a staged increase, similar variation pattern was also reflected by the input energy density and elastic strain energy. Meanwhile, In the last fatigue stage, the damage factor of granites appeared a ‘<span><math><mrow><mfenced><mrow><munder><mrow><mspace></mspace><mspace></mspace><mspace></mspace></mrow><mo>̲</mo></munder><mspace></mspace></mrow></mfenced></mrow></math></span>’ − shaped upward trend, the damage deterioration rate of the specimens was the fastest during this stage. Finally, the type of pre-flaw spacing controlled the macroscopic failure patterns and crack network of granite. The non-uniform stresses at tips of pre-flawed flaws were responsible for inhibiting cracks development. The smaller the non-uniform stress was, crack network had the more possible properties to develop. Consequently, the crack network was more developed in granite with longer pre-flaw spacing.</div></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":"136 ","pages":"Article 104858"},"PeriodicalIF":5.0,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143130761","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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