Pub Date : 2026-05-02Epub Date: 2026-03-04DOI: 10.1016/j.engfracmech.2026.111993
Junqi Feng , Dasheng Wei , Xiyuan Zhang , Tonghui Wang , Xiang Liu , Shun Yang
Engineering components are often subjected to complex loading paths and high stress ratios. However, most existing multiaxial fatigue life prediction models are based on symmetrical loading tests. Their research is relatively limited on multiaxial fatigue under high stress ratios and complex loading paths. This study investigates the multiaxial fatigue behavior of forged Ti-6Al-4V alloy through a series of tension–torsion fatigue tests under high-stress ratios and complex paths. Digital Image Correlation (DIC) was employed to measure strain fields during the testing process. The results indicate that both tensile and shear mean stresses reduce fatigue life significantly. The fracture analysis showed obvious fatigue stripes on the fracture surface using Field Emission Scanning Electron Microscope (FESEM). Furthermore, this paper proposes a novel multiaxial fatigue life model that considers the different contributions of tensile and shear strain energy densities to fatigue damage. The comparison between the proposed model and commonly used models (SWT, FS, and CCB) shows that the accuracy and superiority of the new model in life prediction have been improved.
{"title":"Multiaxial fatigue behavior and life prediction of forged Ti-6Al-4V under complex paths with mean stress","authors":"Junqi Feng , Dasheng Wei , Xiyuan Zhang , Tonghui Wang , Xiang Liu , Shun Yang","doi":"10.1016/j.engfracmech.2026.111993","DOIUrl":"10.1016/j.engfracmech.2026.111993","url":null,"abstract":"<div><div>Engineering components are often subjected to complex loading paths and high stress ratios. However, most existing multiaxial fatigue life prediction models are based on symmetrical loading tests. Their research is relatively limited on multiaxial fatigue under high stress ratios and complex loading paths. This study investigates the multiaxial fatigue behavior of forged Ti-6Al-4V alloy through a series of tension–torsion fatigue tests under high-stress ratios and complex paths. Digital Image Correlation (DIC) was employed to measure strain fields during the testing process. The results indicate that both tensile and shear mean stresses reduce fatigue life significantly. The fracture analysis showed obvious fatigue stripes on the fracture surface using Field Emission Scanning Electron Microscope (FESEM). Furthermore, this paper proposes a novel multiaxial fatigue life model that considers the different contributions of tensile and shear strain energy densities to fatigue damage. The comparison between the proposed model and commonly used models (SWT, FS, and CCB) shows that the accuracy and superiority of the new model in life prediction have been improved.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"337 ","pages":"Article 111993"},"PeriodicalIF":5.3,"publicationDate":"2026-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147387337","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 : 2026-05-02Epub Date: 2026-03-01DOI: 10.1016/j.engfracmech.2026.111989
Yutong Hao , Lingtao Mao , Haizhou Liu , Yang Ju , François Hild
A meshless approach is proposed for Integrated Digital Image Correlation (I-DIC) and Integrated Digital Volume Correlation (I-DVC) to measure stress intensity factors (SIFs), which is validated through synthetic experiments. Combined with double cleavage drilled compression (DCDC) experiments on gypsum and in-situ X-ray computed tomography, meshless I-DIC quantifies SIFs and their variations along the surface crack path, while meshless I-DVC resolves SIF distributions along internal crack fronts. SIFs are inferred directly from images, thereby eliminating error accumulation from displacement projection and avoiding meshing challenges near tortuous crack surfaces. In a virtual crack test, a comparative analysis of meshless I–DVC, a post-processing method and mesh-based I-DVC reveals errors of 0.7%, 2.0%, and 1.2% for the three approaches, respectively, highlighting the effectiveness of the proposed method. In DCDC uniaxial compression, I-DIC results indicate that the mode I SIF component dominated along the surface crack path, while the mode II SIF increased markedly as the crack propagated, consistent with mixed mode I-II propagation. I-DVC further revealed that the mode I SIF remained predominant along internal fronts, while the KII and KIII components in local areas gradually emerged as the crack propagated, evidencing opening accompanied by shear and tearing effects. The energy release rate profiles exhibited pronounced spatial non-uniformity and support an inside-out growth mechanism originating from internal flaws.
{"title":"Evaluation of stress intensity factors using meshless integrated digital image / volume correlation","authors":"Yutong Hao , Lingtao Mao , Haizhou Liu , Yang Ju , François Hild","doi":"10.1016/j.engfracmech.2026.111989","DOIUrl":"10.1016/j.engfracmech.2026.111989","url":null,"abstract":"<div><div>A meshless approach is proposed for Integrated Digital Image Correlation (I-DIC) and Integrated Digital Volume Correlation (I-DVC) to measure stress intensity factors (SIFs), which is validated through synthetic experiments. Combined with double cleavage drilled compression (DCDC) experiments on gypsum and in-situ X-ray computed tomography, meshless I-DIC quantifies SIFs and their variations along the surface crack path, while meshless I-DVC resolves SIF distributions along internal crack fronts. SIFs are inferred directly from images, thereby eliminating error accumulation from displacement projection and avoiding meshing challenges near tortuous crack surfaces. In a virtual crack test, a comparative analysis of meshless I–DVC, a post-processing method and mesh-based I-DVC reveals errors of 0.7%, 2.0%, and 1.2% for the three approaches, respectively, highlighting the effectiveness of the proposed method. In DCDC uniaxial compression, I-DIC results indicate that the mode I SIF component dominated along the surface crack path, while the mode II SIF increased markedly as the crack propagated, consistent with mixed mode I-II propagation. I-DVC further revealed that the mode I SIF remained predominant along internal fronts, while the <em>K</em><sub>II</sub> and <em>K</em><sub>III</sub> components in local areas gradually emerged as the crack propagated, evidencing opening accompanied by shear and tearing effects. The energy release rate profiles exhibited pronounced spatial non-uniformity and support an inside-out growth mechanism originating from internal flaws.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"337 ","pages":"Article 111989"},"PeriodicalIF":5.3,"publicationDate":"2026-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147387342","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}
Most existing strain-based engineering critical assessment approaches are developed for materials exhibiting smooth stress–strain responses, leaving the influence of the Lüders plateau on ductile fracture behavior largely unexplored. In this work, the effect of the Lüders plateau on mode I ductile crack growth is investigated using the Modified Boundary Layer (MBL) model under plane strain conditions. The “up-down-up” constitutive model is implemented to capture the characteristic plateau behavior, while crack propagation is simulated through the Gurson damage model. Key factors—including the plateau length and softening modulus in the “up-down-up” model, the strain hardening behavior of the matrix material, and the initial void volume fraction—are systematically analyzed. Numerical results demonstrate that the Lüders plateau alters the crack-tip constraint and governs the evolution of damage near the crack front. Among the investigated parameters, the plateau length exerts a dominant influence on the ductile crack growth behavior in the presence of the Lüders plateau.
{"title":"Micromechanical analysis of ductile crack growth in steels with Lüders plateau behavior","authors":"Shengwen Tu , Chenxi Wu , Yanfang Hou , Yinhui Zhang","doi":"10.1016/j.engfracmech.2026.112013","DOIUrl":"10.1016/j.engfracmech.2026.112013","url":null,"abstract":"<div><div>Most existing strain-based engineering critical assessment approaches are developed for materials exhibiting smooth stress–strain responses, leaving the influence of the Lüders plateau on ductile fracture behavior largely unexplored. In this work, the effect of the Lüders plateau on mode I ductile crack growth is investigated using the Modified Boundary Layer (MBL) model under plane strain conditions. The “up-down-up” constitutive model is implemented to capture the characteristic plateau behavior, while crack propagation is simulated through the Gurson damage model. Key factors—including the plateau length and softening modulus in the “up-down-up” model, the strain hardening behavior of the matrix material, and the initial void volume fraction—are systematically analyzed. Numerical results demonstrate that the Lüders plateau alters the crack-tip constraint and governs the evolution of damage near the crack front. Among the investigated parameters, the plateau length exerts a dominant influence on the ductile crack growth behavior in the presence of the Lüders plateau.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"337 ","pages":"Article 112013"},"PeriodicalIF":5.3,"publicationDate":"2026-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147387349","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 : 2026-05-02Epub Date: 2026-02-23DOI: 10.1016/j.engfracmech.2026.111981
Xiaopeng Wang , Huile Li
Owing to their superior strength and flexibility, high-strength steel wires (HSSWs) are extensively used in critical infrastructures including bridges, cableways, and lifting equipment. Nevertheless, under the combined effects of cyclic loading and corrosive environment, HSSWs are susceptible to fatigue failure, posing serious threats to structural safety. Conventional fatigue analysis approaches such as the S-N curve method, linear elastic fracture mechanics (LEFM), and continuum damage mechanics (CDM) are limited by one or more constraints in fatigue crack growth simulation, e.g., the inability to capture damage evolution, the reliance on predefined cracks, difficulties in modeling multiple cracks, and complex fracture criteria. Peridynamics (PD), formulated in a nonlocal integral form, can naturally simulate crack initiation and growth, thereby overcoming the shortcomings of traditional methods in discontinuous damage simulation. This paper proposes a 3D finite element (FE) method with PD for fatigue analysis of HSSWs. The PD theory is incorporated into the FE framework to develop a 3D PD element on the ANSYS platform. The PD-FE model able to account for initial cracks and 3D corrosion pits is subsequently established with reduced computational cost and enhanced adaptability to complex configurations, boundaries, and load conditions. The bond strains obtained using the PD-FE model are integrated with the two-stage fatigue model. A user-defined subroutine is implemented to enable full-process simulation of crack initiation and growth, along with fatigue life prediction. The proposed method is validated against experimental data from compact tension (CT) specimen and HSSWs, demonstrating high predictive accuracy and broad applicability. Furthermore, parametric analysis is conducted to quantify the effects of multiple factors including fatigue stress amplitude, initial crack depth, crack shape factor, and pit size and distribution on the fatigue damage behavior of HSSWs. This work provides an effective framework for fatigue analysis of HSSWs and other engineering components.
{"title":"A 3D finite element method with peridynamics for fatigue analysis of high-strength steel wires","authors":"Xiaopeng Wang , Huile Li","doi":"10.1016/j.engfracmech.2026.111981","DOIUrl":"10.1016/j.engfracmech.2026.111981","url":null,"abstract":"<div><div>Owing to their superior strength and flexibility, high-strength steel wires (HSSWs) are extensively used in critical infrastructures including bridges, cableways, and lifting equipment. Nevertheless, under the combined effects of cyclic loading and corrosive environment, HSSWs are susceptible to fatigue failure, posing serious threats to structural safety. Conventional fatigue analysis approaches such as the S-N curve method, linear elastic fracture mechanics (LEFM), and continuum damage mechanics (CDM) are limited by one or more constraints in fatigue crack growth simulation, e.g., the inability to capture damage evolution, the reliance on predefined cracks, difficulties in modeling multiple cracks, and complex fracture criteria. Peridynamics (PD), formulated in a nonlocal integral form, can naturally simulate crack initiation and growth, thereby overcoming the shortcomings of traditional methods in discontinuous damage simulation. This paper proposes a 3D finite element (FE) method with PD for fatigue analysis of HSSWs. The PD theory is incorporated into the FE framework to develop a 3D PD element on the ANSYS platform. The PD-FE model able to account for initial cracks and 3D corrosion pits is subsequently established with reduced computational cost and enhanced adaptability to complex configurations, boundaries, and load conditions. The bond strains obtained using the PD-FE model are integrated with the two-stage fatigue model. A user-defined subroutine is implemented to enable full-process simulation of crack initiation and growth, along with fatigue life prediction. The proposed method is validated against experimental data from compact tension (CT) specimen and HSSWs, demonstrating high predictive accuracy and broad applicability. Furthermore, parametric analysis is conducted to quantify the effects of multiple factors including fatigue stress amplitude, initial crack depth, crack shape factor, and pit size and distribution on the fatigue damage behavior of HSSWs. This work provides an effective framework for fatigue analysis of HSSWs and other engineering components.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"337 ","pages":"Article 111981"},"PeriodicalIF":5.3,"publicationDate":"2026-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147387379","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}
To investigate the hydrogen embrittlement susceptibility and hydrogen permeation behavior of 90 mm extra-thick Q690DR steel plate in the thickness direction, samples were taken from three regions: Subsurface layer, 1/4 Thickness layer (1/4T), and 1/2 Thickness layer (1/2T). The results showed that the matrix structure in each region was mainly tempered martensite, and the grain size gradually increased from the Subsurface to 1/2T; a discontinuous banded structure existed in the Subsurface region. In-situ hydrogen permeation and mechanical testing under 6 MPa hydrogen revealed that hydrogen embrittlement susceptibility: Subsurface > 1/2T > 1/4T. The Subsurface region was significantly affected by rolling deformation, with grains elongated along the rolling direction (RD) and forming a banded structure, providing a rapid channel for hydrogen diffusion and making hydrogen more likely to permeate the material interior, resulting in the formation of fine elongated cracks during fracture. Therefore, it exhibited the highest hydrogen embrittlement susceptibility. The 1/2T region formed coarse martensite structure due to a slower cooling rate, and a large number of secondary cracks were generated during fracture. In contrast, the 1/4T region had a homogeneous distribution of tempered martensite and fine grains, with a stronger hindrance effect on hydrogen diffusion, and thus had the best hydrogen embrittlement resistance. In summary, the degree of deformation during the rolling process and the cooling rate during the cooling process are the key factors that cause the microstructure to show a gradient distribution and thereby affect hydrogen embrittlement susceptibility.
{"title":"The influence of gradient difference in microstructure on hydrogen embrittlement susceptibility of extra-thick Q690DR steel plate","authors":"Jinrong Wu , Kaiyu Zhang , Xin Liu , Wanliang Zhang , Kehan Wu , Chengshuang Zhou , Jinyang Zheng , Lin Zhang","doi":"10.1016/j.engfracmech.2026.111997","DOIUrl":"10.1016/j.engfracmech.2026.111997","url":null,"abstract":"<div><div>To investigate the hydrogen embrittlement susceptibility and hydrogen permeation behavior of 90 mm extra-thick Q690DR steel plate in the thickness direction, samples were taken from three regions: Subsurface layer, 1/4 Thickness layer (1/4T), and 1/2 Thickness layer (1/2T). The results showed that the matrix structure in each region was mainly tempered martensite, and the grain size gradually increased from the Subsurface to 1/2T; a discontinuous banded structure existed in the Subsurface region. In-situ hydrogen permeation and mechanical testing under 6 MPa hydrogen revealed that hydrogen embrittlement susceptibility: Subsurface > 1/2T > 1/4T. The Subsurface region was significantly affected by rolling deformation, with grains elongated along the rolling direction (RD) and forming a banded structure, providing a rapid channel for hydrogen diffusion and making hydrogen more likely to permeate the material interior, resulting in the formation of fine elongated cracks during fracture. Therefore, it exhibited the highest hydrogen embrittlement susceptibility. The 1/2T region formed coarse martensite structure due to a slower cooling rate, and a large number of secondary cracks were generated during fracture. In contrast, the 1/4T region had a homogeneous distribution of tempered martensite and fine grains, with a stronger hindrance effect on hydrogen diffusion, and thus had the best hydrogen embrittlement resistance. In summary, the degree of deformation during the rolling process and the cooling rate during the cooling process are the key factors that cause the microstructure to show a gradient distribution and thereby affect hydrogen embrittlement susceptibility.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"337 ","pages":"Article 111997"},"PeriodicalIF":5.3,"publicationDate":"2026-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147387387","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}
Hot cracks are irreversible defects that mainly originate when the material undergoes cooling from liquidus to solidus temperature. The occurrence of hot cracks is severe in the casting of aluminium alloys such as AA7xxx. The semi-solid plate quenching experiment using an array of water jets is designed to study secondary cooling characteristics of Direct Chill (DC) casting. Horizontal cracks are formed ahead of the impingement region where the temperature ranges are above the solidus temperature. In this study, a 2D ordinary state-based peridynamic thermo-mechanical model is used to find the deformation in the semi-solid plate quenching process. The stiffness matrix and thermal force vector are analytically derived for the 2D plane problems. A temperature and fracture mechanics based critical stretch criterion is proposed to predict the evolution of hot cracks in the plate quenching experiment. The Peridynamics approach is proposed for the first time to simulate the origination and propagation of hot cracks. The identified critical stretch criterion could predict the occurrence of multiple crack formations in the plate at different timelines, as observed in the experiment.
{"title":"Ordinary state based peridynamic thermomechanical simulation of hot crack occurrence during Semi-Solid plate quenching experiment","authors":"Jijoprasad Jayaprasad Remani, Ashok Kumar Nallathambi","doi":"10.1016/j.engfracmech.2026.111963","DOIUrl":"10.1016/j.engfracmech.2026.111963","url":null,"abstract":"<div><div>Hot cracks are irreversible defects that mainly originate when the material undergoes cooling from liquidus to solidus temperature. The occurrence of hot cracks is severe in the casting of aluminium alloys such as AA7xxx. The semi-solid plate quenching experiment using an array of water jets is designed to study secondary cooling characteristics of Direct Chill (DC) casting. Horizontal cracks are formed ahead of the impingement region where the temperature ranges are above the solidus temperature. In this study, a 2D ordinary state-based peridynamic thermo-mechanical model is used to find the deformation in the semi-solid plate quenching process. The stiffness matrix and thermal force vector are analytically derived for the 2D plane problems. A temperature and fracture mechanics based critical stretch criterion is proposed to predict the evolution of hot cracks in the plate quenching experiment. The Peridynamics approach is proposed for the first time to simulate the origination and propagation of hot cracks. The identified critical stretch criterion could predict the occurrence of multiple crack formations in the plate at different timelines, as observed in the experiment.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"337 ","pages":"Article 111963"},"PeriodicalIF":5.3,"publicationDate":"2026-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147387400","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 : 2026-05-02Epub Date: 2026-03-02DOI: 10.1016/j.engfracmech.2026.112006
Jianping Wei , Mengyuan Wang , Yong Liu , Huidong Zhang , Changjiang Chen , Xiangyu Xu , Xing Li
Particle-impact rock breaking is a feasible technology for fracturing deep, high-strength rock under high confining pressure. However, its effective fragmentation extent in hard rock is limited and the breaking efficiency remains low, which restricts engineering application. To address this issue, an auxiliary pre-grooving approach is proposed to enlarge the fragmentation extent and improve rock-breaking efficiency. Particle-impact tests were conducted on pre-cut-grooved rock specimens. The particle velocity was determined using a high-speed imaging system, and the post-impact failure morphology was quantified in combination with 3D scanning. Based on these measurements, a quantitative evaluation model for particle-impact rock breaking under grooved conditions was established, and the effects of groove parameters on impact-induced fracture behavior were systematically investigated. The results show that grooves, acting as prefabricated defect planes, markedly guide crack propagation during particle impact. Groove depth primarily controls the fracture depth, whereas groove spacing governs whether cracks can effectively extend to the grooves and coalesce into through-going fractures. When high-velocity particles vertically impact the center of double-grooved specimens, the failure mode evolves with increasing groove spacing from wedge-splitting to conjugate, unilateral, and crushing, among which the conjugate mode is the most representative. To efficiently evaluate rock-breaking performance and identify the optimal grooving scheme, a conjugate-product model was developed using the endpoint depth, midpoint depth, and fracture length of the deepest fracture section. Under the present test conditions, the optimal parameters are a groove spacing of 35 mm and a groove depth of 40 mm, corresponding to a fragmented volume of 32,043.62 mm3.
{"title":"Study on the fracture characteristics of pre-grooved rock under particle impact","authors":"Jianping Wei , Mengyuan Wang , Yong Liu , Huidong Zhang , Changjiang Chen , Xiangyu Xu , Xing Li","doi":"10.1016/j.engfracmech.2026.112006","DOIUrl":"10.1016/j.engfracmech.2026.112006","url":null,"abstract":"<div><div>Particle-impact rock breaking is a feasible technology for fracturing deep, high-strength rock under high confining pressure. However, its effective fragmentation extent in hard rock is limited and the breaking efficiency remains low, which restricts engineering application. To address this issue, an auxiliary pre-grooving approach is proposed to enlarge the fragmentation extent and improve rock-breaking efficiency. Particle-impact tests were conducted on pre-cut-grooved rock specimens. The particle velocity was determined using a high-speed imaging system, and the post-impact failure morphology was quantified in combination with 3D scanning. Based on these measurements, a quantitative evaluation model for particle-impact rock breaking under grooved conditions was established, and the effects of groove parameters on impact-induced fracture behavior were systematically investigated. The results show that grooves, acting as prefabricated defect planes, markedly guide crack propagation during particle impact. Groove depth primarily controls the fracture depth, whereas groove spacing governs whether cracks can effectively extend to the grooves and coalesce into through-going fractures. When high-velocity particles vertically impact the center of double-grooved specimens, the failure mode evolves with increasing groove spacing from wedge-splitting to conjugate, unilateral, and crushing, among which the conjugate mode is the most representative. To efficiently evaluate rock-breaking performance and identify the optimal grooving scheme, a conjugate-product model was developed using the endpoint depth, midpoint depth, and fracture length of the deepest fracture section. Under the present test conditions, the optimal parameters are a groove spacing of 35 mm and a groove depth of 40 mm, corresponding to a fragmented volume of 32,043.62 mm<sup>3</sup>.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"337 ","pages":"Article 112006"},"PeriodicalIF":5.3,"publicationDate":"2026-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147387401","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 : 2026-05-02Epub Date: 2026-02-26DOI: 10.1016/j.engfracmech.2026.111960
Shihao Lv , Jian Hua , Yan Shi , Cun-Fa Gao
Flexible piezoelectric composites are increasingly used in wearable and adaptive structures. However, their geometric nonlinearity and pronounced anisotropy pose significant challenges for reliable prediction of fracture and fatigue under electromechanical loading. This work develops an anisotropic phase-field fracture model for flexible piezoelectric composites at finite strains, in which distinct softening laws are assigned to the isotropic matrix and anisotropic fibers. To eliminate unphysical fracture modes, the energy density is decomposed using the volumetric-stretch tension–compression scheme. This model is further extended to fatigue by introducing a cumulative history variable that captures the progressive degradation of fracture toughness under cyclic loading. Numerical results demonstrate that, with a large penalty parameter in anisotropic crack surface density function, the predicted crack path aligns with the fiber orientation, and the global responses are consistent with available experimental observations. For flexible piezoelectric composites, the fracture behavior is influenced by fiber orientation and applied electric fields. For composites with symmetric fiber families, enhanced mechanical performance and stabilized crack trajectories are observed. The proposed framework provides theoretical flexibility and computational robustness for predicting fracture and fatigue failure in flexible piezoelectric composites, enabling reliability-driven design of next-generation flexible piezoelectric devices.
{"title":"An anisotropic phase-field framework for finite-deformation fracture and fatigue in flexible piezoelectric composites","authors":"Shihao Lv , Jian Hua , Yan Shi , Cun-Fa Gao","doi":"10.1016/j.engfracmech.2026.111960","DOIUrl":"10.1016/j.engfracmech.2026.111960","url":null,"abstract":"<div><div>Flexible piezoelectric composites are increasingly used in wearable and adaptive structures. However, their geometric nonlinearity and pronounced anisotropy pose significant challenges for reliable prediction of fracture and fatigue under electromechanical loading. This work develops an anisotropic phase-field fracture model for flexible piezoelectric composites at finite strains, in which distinct softening laws are assigned to the isotropic matrix and anisotropic fibers. To eliminate unphysical fracture modes, the energy density is decomposed using the volumetric-stretch tension–compression scheme. This model is further extended to fatigue by introducing a cumulative history variable that captures the progressive degradation of fracture toughness under cyclic loading. Numerical results demonstrate that, with a large penalty parameter in anisotropic crack surface density function, the predicted crack path aligns with the fiber orientation, and the global responses are consistent with available experimental observations. For flexible piezoelectric composites, the fracture behavior is influenced by fiber orientation and applied electric fields. For composites with symmetric fiber families, enhanced mechanical performance and stabilized crack trajectories are observed. The proposed framework provides theoretical flexibility and computational robustness for predicting fracture and fatigue failure in flexible piezoelectric composites, enabling reliability-driven design of next-generation flexible piezoelectric devices.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"337 ","pages":"Article 111960"},"PeriodicalIF":5.3,"publicationDate":"2026-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147387296","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 : 2026-05-02Epub Date: 2026-02-28DOI: 10.1016/j.engfracmech.2026.111999
Di Wang , Pengpeng Shi , Dongming An , Xiaofan Gou
The construction and service performance of concrete are highly influenced by environmental conditions. These conditions often result in defects such as holes and cracks, which reduce the strength and durability of the material. Defect identification and localization is critical for evaluating the safety and quality of concrete structures. This paper first presents the problem description, where defect geometries are characterized using super-shape parameters, and an ERT forward model is established to obtain electrical signal responses under varying parameter conditions. To address the multi-defect parameter optimization problem in concrete structures, a three-stage strategy for multi-defect parameters evaluation in concrete is proposed based on electrical signals. First, the Electrical resistance tomography (ERT) imaging of the structure to be detected is conducted via the FEM to establish the sensitivity matrix and reference electrical signals for defect-free condition. By analyzing deviations between the measured electrical signals and reference electrical signals, the conjugate gradient method is utilized to obtain the conductivity distribution image of the structure to be detected; After that, the conductivity distribution image is segmented and initial boundary information of defects is obtained using K-means algorithm. Finally, the parameter quantification begins by applying nonlinear least squares fitting to the initial defect boundaries, extracting super-shape equation parameters. These parameters are then used as initial inputs for the particle swarm optimization (PSO) algorithm, which optimizes the defect parameters within the defined defect domain. Numerical studies demonstrate that the proposed method accurately quantifies defect locations, sizes, and shapes in single-defect, double-defect, and multi-defect cases.
{"title":"Evaluating multi-defect parameters in concrete via electrical signals: A three-stage strategy of ERT imaging, image segmentation, parameter quantification","authors":"Di Wang , Pengpeng Shi , Dongming An , Xiaofan Gou","doi":"10.1016/j.engfracmech.2026.111999","DOIUrl":"10.1016/j.engfracmech.2026.111999","url":null,"abstract":"<div><div>The construction and service performance of concrete are highly influenced by environmental conditions. These conditions often result in defects such as holes and cracks, which reduce the strength and durability of the material. Defect identification and localization is critical for evaluating the safety and quality of concrete structures. This paper first presents the problem description, where defect geometries are characterized using super-shape parameters, and an ERT forward model is established to obtain electrical signal responses under varying parameter conditions. To address the multi-defect parameter optimization problem in concrete structures, a three-stage strategy for multi-defect parameters evaluation in concrete is proposed based on electrical signals. First, the Electrical resistance tomography (ERT) imaging of the structure to be detected is conducted via the FEM to establish the sensitivity matrix and reference electrical signals for defect-free condition. By analyzing deviations between the measured electrical signals and reference electrical signals, the conjugate gradient method is utilized to obtain the conductivity distribution image of the structure to be detected; After that, the conductivity distribution image is segmented and initial boundary information of defects is obtained using K-means algorithm. Finally, the parameter quantification begins by applying nonlinear least squares fitting to the initial defect boundaries, extracting super-shape equation parameters. These parameters are then used as initial inputs for the particle swarm optimization (PSO) algorithm, which optimizes the defect parameters within the defined defect domain. Numerical studies demonstrate that the proposed method accurately quantifies defect locations, sizes, and shapes in single-defect, double-defect, and multi-defect cases.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"337 ","pages":"Article 111999"},"PeriodicalIF":5.3,"publicationDate":"2026-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147387348","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}
Concrete demonstrates pronounced nonlinear failure behavior under multiaxial loading. However, conventional failure criteria, constrained by predefined functional forms, are inadequate for representing the complex and path-dependent failure mechanisms observed in experiments. To overcome these limitations, this study develops a hybrid modeling framework that couples the Egret Swarm Optimization Algorithm (ESOA) with a back propagation (BP) neural network to improve the representation of concrete failure behavior. The proposed framework exploits the strong capability of neural networks to approximate high-dimensional nonlinear mappings and extract the essential geometric features of the failure surface in stress space. Meanwhile, ESOA improves convergence robustness and global optimization efficiency, resulting in more reliable predictions under diverse multiaxial loading scenarios. The model is evaluated using several benchmark datasets from multiaxial strength tests. The results demonstrate that the ESOA-BP model consistently surpasses both the conventional BP network and the classical Ottosen criterion in terms of prediction accuracy, generalization capacity, and computational stability. The resulting failure surface exhibits smooth and physically consistent deviatoric sections that closely match the experimental observations. Both the tensile and compressive meridians reproduce the overall experimental trends, and the curvature evolution in the tension–compression transition zone is captured with high fidelity. Overall, the findings offer a high-accuracy, robust, and practically applicable modeling strategy for developing multiaxial failure criteria for concrete.
{"title":"A failure criterion model for concrete integrating egret swarm optimization algorithm and back propagation neural networks","authors":"Junwei Xin, Jianguo Ning, Huilan Ren, Haitao Zhao, Xiangzhao Xu","doi":"10.1016/j.engfracmech.2026.111985","DOIUrl":"10.1016/j.engfracmech.2026.111985","url":null,"abstract":"<div><div>Concrete demonstrates pronounced nonlinear failure behavior under multiaxial loading. However, conventional failure criteria, constrained by predefined functional forms, are inadequate for representing the complex and path-dependent failure mechanisms observed in experiments. To overcome these limitations, this study develops a hybrid modeling framework that couples the Egret Swarm Optimization Algorithm (ESOA) with a back propagation (BP) neural network to improve the representation of concrete failure behavior. The proposed framework exploits the strong capability of neural networks to approximate high-dimensional nonlinear mappings and extract the essential geometric features of the failure surface in stress space. Meanwhile, ESOA improves convergence robustness and global optimization efficiency, resulting in more reliable predictions under diverse multiaxial loading scenarios. The model is evaluated using several benchmark datasets from multiaxial strength tests. The results demonstrate that the ESOA-BP model consistently surpasses both the conventional BP network and the classical Ottosen criterion in terms of prediction accuracy, generalization capacity, and computational stability. The resulting failure surface exhibits smooth and physically consistent deviatoric sections that closely match the experimental observations. Both the tensile and compressive meridians reproduce the overall experimental trends, and the curvature evolution in the tension–compression transition zone is captured with high fidelity. Overall, the findings offer a high-accuracy, robust, and practically applicable modeling strategy for developing multiaxial failure criteria for concrete.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"337 ","pages":"Article 111985"},"PeriodicalIF":5.3,"publicationDate":"2026-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147387380","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}
扫码关注我们
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号