Pub Date : 2026-03-11Epub Date: 2026-01-29DOI: 10.1016/j.engfracmech.2026.111907
Honghao Wang , Naiwei Lu , Michael Brun , Wen Chen , Francis Praud , Yuan Luo , Yang Liu
Welding residual stress is a key factor leading to the initiation of multiple cracks in orthotropic steel decks. However, the effects of welding residual stress on evolutionary properties of multiple cracks in welded joints remain unclear. This study proposes a multiple cracks growth analysis method considering welding residual stress relaxation. Subsequently, the influence mechanism of welding residual stresses and multiple crack effects on fatigue life is investigated. Finally, the evolutionary properties of multiple cracks were revealed through experiments. The results show that fatigue life prediction result considering welding residual stress tend to yield conservative results, while incorporating its relaxation effects proves more consistent with experimental data. Welding residual stress accelerates the occurrence of multiple crack merging behavior. As crack depth increases, the effect of residual stresses on crack growth in the depth direction gradually decreases, while the merging behavior of multiple cracks becomes the critical driving force for structural fracture. Reverse analysis of beach marks indicates that the macrocracks observed on the fracture surface originate from the merging behavior of high-density microcrack clusters. The fatigue crack density at the rib-to-deck weld is severely underestimated, and numerous cracks have merged before reaching observable dimensions. This research provides a theoretical basis for comprehensively assessing the fatigue performance of orthotropic steel decks.
{"title":"Effect of weld residual stress relaxation on evolutionary properties of multiple cracks in orthotropic steel deck","authors":"Honghao Wang , Naiwei Lu , Michael Brun , Wen Chen , Francis Praud , Yuan Luo , Yang Liu","doi":"10.1016/j.engfracmech.2026.111907","DOIUrl":"10.1016/j.engfracmech.2026.111907","url":null,"abstract":"<div><div>Welding residual stress is a key factor leading to the initiation of multiple cracks in orthotropic steel decks. However, the effects of welding residual stress on evolutionary properties of multiple cracks in welded joints remain unclear. This study proposes a multiple cracks growth analysis method considering welding residual stress relaxation. Subsequently, the influence mechanism of welding residual stresses and multiple crack effects on fatigue life is investigated. Finally, the evolutionary properties of multiple cracks were revealed through experiments. The results show that fatigue life prediction result considering welding residual stress tend to yield conservative results, while incorporating its relaxation effects proves more consistent with experimental data. Welding residual stress accelerates the occurrence of multiple crack merging behavior. As crack depth increases, the effect of residual stresses on crack growth in the depth direction gradually decreases, while the merging behavior of multiple cracks becomes the critical driving force for structural fracture. Reverse analysis of beach marks indicates that the macrocracks observed on the fracture surface originate from the merging behavior of high-density microcrack clusters. The fatigue crack density at the rib-to-deck weld is severely underestimated, and numerous cracks have merged before reaching observable dimensions. This research provides a theoretical basis for comprehensively assessing the fatigue performance of orthotropic steel decks.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"334 ","pages":"Article 111907"},"PeriodicalIF":5.3,"publicationDate":"2026-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146076004","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 : 2026-03-11Epub Date: 2026-01-25DOI: 10.1016/j.engfracmech.2026.111871
Hui Huang , Yanli Wang , Jian Chen , Yongbing Li , Zhili Feng
Welding residual stresses especially the high tensile stresses are proved to have negative impacts on the fatigue and fracture behaviors of welded structures. In this study, a virtual fabrication of test specimens from welding process to specimen preparation was carried out by numerical simulation. An austenitic stainless steel multi-pass pipe welding was simulated by transient thermal–mechanical finite element analysis, the residual stresses were then mapped into the test specimen to evaluate fracture toughness. The findings in this study confirmed that, residual stress can be high in a sub-sized compact tensile specimen, which may accelerate or hinder the crack propagation during actual fatigue and fracture tests as reported in recent years. The influence of the cutting location and orientation of the specimen on fracture performance was investigated systematically to provide a fundamental understanding of welding residual stress and necessary insights into the specimen preparation procedure. Considering the limitation of measuring techniques and the complexity of the stress distribution, the developed numerical model can be a very useful tool to elucidate the stress evolution and quantify the effect of remaining welding stress on fracture toughness.
{"title":"On the roles of welding residual stresses in determination of fracture toughness in austenitic stainless steel SUS 304 pipeline girth welds","authors":"Hui Huang , Yanli Wang , Jian Chen , Yongbing Li , Zhili Feng","doi":"10.1016/j.engfracmech.2026.111871","DOIUrl":"10.1016/j.engfracmech.2026.111871","url":null,"abstract":"<div><div>Welding residual stresses especially the high tensile stresses are proved to have negative impacts on the fatigue and fracture behaviors of welded structures. In this study, a virtual fabrication of test specimens from welding process to specimen preparation was carried out by numerical simulation. An austenitic stainless steel multi-pass pipe welding was simulated by transient thermal–mechanical finite element analysis, the residual stresses were then mapped into the test specimen to evaluate fracture toughness. The findings in this study confirmed that, residual stress can be high in a sub-sized compact tensile specimen, which may accelerate or hinder the crack propagation during actual fatigue and fracture tests as reported in recent years. The influence of the cutting location and orientation of the specimen on fracture performance was investigated systematically to provide a fundamental understanding of welding residual stress and necessary insights into the specimen preparation procedure. Considering the limitation of measuring techniques and the complexity of the stress distribution, the developed numerical model can be a very useful tool to elucidate the stress evolution and quantify the effect of remaining welding stress on fracture toughness.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"334 ","pages":"Article 111871"},"PeriodicalIF":5.3,"publicationDate":"2026-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146076009","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 : 2026-03-11Epub Date: 2026-01-28DOI: 10.1016/j.engfracmech.2026.111885
Feifei Qin, Shiming Dong
Fracture is one of engineering materials’ most critical failure modes, directly threatening structural safety and stability. Accurate prediction of crack propagation behaviour is crucial for the reliable design and extended service life of engineering structures. To address the limitations of traditional numerical approaches in capturing complex crack topologies, this study develops an improved phase-field model that incorporates the critical energy release rate (CERR) derived from the weight function method for Brazilian disk specimens under non-uniform compressive loading. A staggered scheme decouples elastic deformation from fracture evolution, ensuring stability and efficiency. The model is validated by strong agreement between simulated and experimental load–displacement responses and strain energy evolution. System simulations investigated the effects of loading angle on strain energy evolution, crack initiation angle, crack propagation trajectory, and damage accumulation. Results reveal that loading angle critically influences crack morphology and structural capacity, with larger angles enhancing shear contributions and promoting mixed-mode fracture. These findings advance the theoretical understanding of fracture in brittle materials and establish a reliable predictive framework for evaluating and optimizing fracture resistance in engineering applications.
{"title":"An improved phase-field model incorporating the critical energy release rate for simulating damage evolution in cracked Brazilian disks under non-uniform compressive loading","authors":"Feifei Qin, Shiming Dong","doi":"10.1016/j.engfracmech.2026.111885","DOIUrl":"10.1016/j.engfracmech.2026.111885","url":null,"abstract":"<div><div>Fracture is one of engineering materials’ most critical failure modes, directly threatening structural safety and stability. Accurate prediction of crack propagation behaviour is crucial for the reliable design and extended service life of engineering structures. To address the limitations of traditional numerical approaches in capturing complex crack topologies, this study develops an improved phase-field model that incorporates the critical energy release rate (CERR) derived from the weight function method for Brazilian disk specimens under non-uniform compressive loading. A staggered scheme decouples elastic deformation from fracture evolution, ensuring stability and efficiency. The model is validated by strong agreement between simulated and experimental load–displacement responses and strain energy evolution. System simulations investigated the effects of loading angle on strain energy evolution, crack initiation angle, crack propagation trajectory, and damage accumulation. Results reveal that loading angle critically influences crack morphology and structural capacity, with larger angles enhancing shear contributions and promoting mixed-mode fracture. These findings advance the theoretical understanding of fracture in brittle materials and establish a reliable predictive framework for evaluating and optimizing fracture resistance in engineering applications.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"334 ","pages":"Article 111885"},"PeriodicalIF":5.3,"publicationDate":"2026-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146185545","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 : 2026-03-11Epub Date: 2026-01-20DOI: 10.1016/j.engfracmech.2026.111877
Wei-Jian Li , Yan-Liang Du , Qi-Zhi Zhu , Leong Hien Poh
Fracture in quasi-brittle materials initiates as a diffuse network of microcracks that evolve anisotropically and progressively coalesce into macroscopic cracks. To accurately represent this process, a novel nonlocal anisotropic damage model is proposed. It is based on the multidimensional quasi-bond framework enriched with both shear and transverse deformation mechanisms. The model successfully captures microcrack–matrix interactions, offering superior capability for simulating crack propagation compared to conventional bond-based models. By incorporating direction-dependent deformations evaluated over multiple interaction domains to assess bond damage, the model integrates anisotropic damage evolution with the nonlocal interaction effects of microcracks. Consequently, it effectively eliminates mesh dependence in predicting crack paths and material softening responses, while also preventing spurious damage growth often encountered in conventional nonlocal integral or gradient-enhanced models. Benchmark tests demonstrate that the proposed approach, without resorting to complex constitutive models, accurately captures combined tensile and shear fracture behaviors in quasi-brittle materials under complex loading conditions.
{"title":"Nonlocal anisotropic damage modeling enabled by the multidimensional quasi-bond approach","authors":"Wei-Jian Li , Yan-Liang Du , Qi-Zhi Zhu , Leong Hien Poh","doi":"10.1016/j.engfracmech.2026.111877","DOIUrl":"10.1016/j.engfracmech.2026.111877","url":null,"abstract":"<div><div>Fracture in quasi-brittle materials initiates as a diffuse network of microcracks that evolve anisotropically and progressively coalesce into macroscopic cracks. To accurately represent this process, a novel nonlocal anisotropic damage model is proposed. It is based on the multidimensional quasi-bond framework enriched with both shear and transverse deformation mechanisms. The model successfully captures microcrack–matrix interactions, offering superior capability for simulating crack propagation compared to conventional bond-based models. By incorporating direction-dependent deformations evaluated over multiple interaction domains to assess bond damage, the model integrates anisotropic damage evolution with the nonlocal interaction effects of microcracks. Consequently, it effectively eliminates mesh dependence in predicting crack paths and material softening responses, while also preventing spurious damage growth often encountered in conventional nonlocal integral or gradient-enhanced models. Benchmark tests demonstrate that the proposed approach, without resorting to complex constitutive models, accurately captures combined tensile and shear fracture behaviors in quasi-brittle materials under complex loading conditions.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"334 ","pages":"Article 111877"},"PeriodicalIF":5.3,"publicationDate":"2026-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146015859","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 : 2026-03-11Epub Date: 2026-01-27DOI: 10.1016/j.engfracmech.2026.111879
Yanan Zhang , Xin Cai , Xudong Chen , Xingwen Guo
To investigate the effect of different interlayer interface structures on the fracture behavior of Cemented granular materials (CGM) this study prepared three types of interlayer interface specimens untreated mortar and neat paste and conducted three-point bending fracture tests acoustic emission (AE) technology and 3D scanning technology to systematically analyze the entire fracture process of the interlayer interface in CGM. The results indicate that interlayer interface treatment significantly alters the fracture behavior of cemented granular materials with untreated interfaces exhibiting brittle failure while cement mortar and neat paste treatments enhance the bond strength and overall toughness of the interface delaying crack propagation and improving crack resistance. The neat paste-treated interface exhibits a lower initial -value, a steady increase in the -value, and a trend dominated by low-frequency main frequencies, indicating more coordinated microcrack propagation and a more stable interface structure. RA–AF parameters and Gaussian Mixture Model (GMM) clustering analysis show that, after neat paste and mortar treatments, the proportions of tensile cracks are 25.1% and 17.7%, respectively, and the consistency of crack propagation is enhanced. 3D scanning results show that the treated interface has more uniform bond strength and smoother crack propagation especially neat paste treatment effectively suppresses brittle fracture and improves fracture resistance This study provides theoretical support for optimizing interlayer interface treatment in cemented granular material dams and reveals the critical role of interface structure in the fracture process of cemented granular materials.
{"title":"Multiscale analysis of the entire fracture process of cemented granular materials Considering structural differences in the interlayer interfaces","authors":"Yanan Zhang , Xin Cai , Xudong Chen , Xingwen Guo","doi":"10.1016/j.engfracmech.2026.111879","DOIUrl":"10.1016/j.engfracmech.2026.111879","url":null,"abstract":"<div><div>To investigate the effect of different interlayer interface structures on the fracture behavior of Cemented granular materials (CGM) this study prepared three types of interlayer interface specimens untreated mortar and neat paste and conducted three-point bending fracture tests acoustic emission (AE) technology and 3D scanning technology to systematically analyze the entire fracture process of the interlayer interface in CGM. The results indicate that interlayer interface treatment significantly alters the fracture behavior of cemented granular materials with untreated interfaces exhibiting brittle failure while cement mortar and neat paste treatments enhance the bond strength and overall toughness of the interface delaying crack propagation and improving crack resistance. The neat paste-treated interface exhibits a lower initial <span><math><mi>b</mi></math></span>-value, a steady increase in the <span><math><mi>b</mi></math></span>-value, and a trend dominated by low-frequency main frequencies, indicating more coordinated microcrack propagation and a more stable interface structure. RA–AF parameters and Gaussian Mixture Model (GMM) clustering analysis show that, after neat paste and mortar treatments, the proportions of tensile cracks are 25.1% and 17.7%, respectively, and the consistency of crack propagation is enhanced. 3D scanning results show that the treated interface has more uniform bond strength and smoother crack propagation especially neat paste treatment effectively suppresses brittle fracture and improves fracture resistance This study provides theoretical support for optimizing interlayer interface treatment in cemented granular material dams and reveals the critical role of interface structure in the fracture process of cemented granular materials.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"334 ","pages":"Article 111879"},"PeriodicalIF":5.3,"publicationDate":"2026-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146076006","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 : 2026-03-11Epub Date: 2026-01-21DOI: 10.1016/j.engfracmech.2026.111866
Yuqi Yang, Haibiao Yin, Weixing Yao, Zuoting Liu
High-strength aluminum alloys manufactured by Selective Laser Melting (SLM) technology are widely used in high-performance aerospace components due to their combination of high strength, low density, and excellent corrosion resistance. This study investigates the high-cycle fatigue (HCF) behavior of SLM-manufactured TiB2-Al (FCA101Y-1) and AlMgScZr high-strength aluminum alloys under vibrational loading. A frequency-based approach is proposed for fatigue life prediction given the strong correlation between natural frequency variation and damage accumulation. The approach accounts for the influence of fracture surface defects, characterized and analyzed through Scanning Electron Microscopy (SEM) and Optical Microscopy (OM). Model calculation results indicate that crack growth and brittle fracture stages account for approximately 80% and 20% of the total fatigue life of SLM aluminum alloys, respectively. This approach has proven reliable, as the predicted fatigue lives fall within a factor-of-two scatter band and coefficient of determination is all around 0.9.
{"title":"Frequency-based approach for fatigue life analysis of SLM high-strength aluminum alloys","authors":"Yuqi Yang, Haibiao Yin, Weixing Yao, Zuoting Liu","doi":"10.1016/j.engfracmech.2026.111866","DOIUrl":"10.1016/j.engfracmech.2026.111866","url":null,"abstract":"<div><div>High-strength aluminum alloys manufactured by Selective Laser Melting (SLM) technology are widely used in high-performance aerospace components due to their combination of high strength, low density, and excellent corrosion resistance. This study investigates the high-cycle fatigue (HCF) behavior of SLM-manufactured TiB2-Al (FCA101Y-1) and AlMgScZr high-strength aluminum alloys under vibrational loading. A frequency-based approach is proposed for fatigue life prediction given the strong correlation between natural frequency variation and damage accumulation. The approach accounts for the influence of fracture surface defects, characterized and analyzed through Scanning Electron Microscopy (SEM) and Optical Microscopy (OM). Model calculation results indicate that crack growth and brittle fracture stages account for approximately 80% and 20% of the total fatigue life of SLM aluminum alloys, respectively. This approach has proven reliable, as the predicted fatigue lives fall within a factor-of-two scatter band and coefficient of determination <span><math><mrow><msup><mi>R</mi><mn>2</mn></msup></mrow></math></span> is all around 0.9.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"334 ","pages":"Article 111866"},"PeriodicalIF":5.3,"publicationDate":"2026-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146075931","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 : 2026-03-11Epub Date: 2026-01-29DOI: 10.1016/j.engfracmech.2026.111904
P. Villarroel , E.V. González , J.A. Artero-Guerrero , A. Cimadevilla , E. de Blanpre , V. Jacques
Bonded joints in composite structures are subjected to crash scenarios and their mechanical behaviour can depend on the strain rate. However, their dynamic characterization remains not fully standardized due to the difficulty of isolating the dynamic effects from the actual behaviour of the adhesive. The present study addresses this issue by developing, via finite element (FE) simulations, a slotted single-lap shear (SLS) specimen with a new set of dimensions tailored for pure mode II testing of co-bonded adhesive joints under quasi-static (QS) and dynamic conditions. This geometry is consistent with the manufacturing constraints of the Carbon-Fibre Reinforced Polymer (CFRP) adherents. The main novelty is the design of a custom metallic tooling to enhance dynamic equilibrium, reduce bending, and improve repeatability. Using Split Hopkinson Pressure Bar (SHPB) testing combined with Digital Image Correlation (DIC), results show that dynamic shear strength increases relative to the QS reference, but decreases at higher strain rates. The optimized set-up provides reliable data to support advanced modelling of composite structures under dynamic loading.
{"title":"Mode II strength of co-bonded adhesive joints at different strain rates","authors":"P. Villarroel , E.V. González , J.A. Artero-Guerrero , A. Cimadevilla , E. de Blanpre , V. Jacques","doi":"10.1016/j.engfracmech.2026.111904","DOIUrl":"10.1016/j.engfracmech.2026.111904","url":null,"abstract":"<div><div>Bonded joints in composite structures are subjected to crash scenarios and their mechanical behaviour can depend on the strain rate. However, their dynamic characterization remains not fully standardized due to the difficulty of isolating the dynamic effects from the actual behaviour of the adhesive. The present study addresses this issue by developing, via finite element (FE) simulations, a slotted single-lap shear (SLS) specimen with a new set of dimensions tailored for pure mode II testing of co-bonded adhesive joints under quasi-static (QS) and dynamic conditions. This geometry is consistent with the manufacturing constraints of the Carbon-Fibre Reinforced Polymer (CFRP) adherents. The main novelty is the design of a custom metallic tooling to enhance dynamic equilibrium, reduce bending, and improve repeatability. Using Split Hopkinson Pressure Bar (SHPB) testing combined with Digital Image Correlation (DIC), results show that dynamic shear strength increases relative to the QS reference, but decreases at higher strain rates. The optimized set-up provides reliable data to support advanced modelling of composite structures under dynamic loading.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"334 ","pages":"Article 111904"},"PeriodicalIF":5.3,"publicationDate":"2026-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146076008","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 : 2026-02-21Epub Date: 2025-12-31DOI: 10.1016/j.engfracmech.2025.111833
Tom De Vuyst , Rade Vignjevic , Nenad Djordjevic , Marius Gintalas , Kevin Hughes
<div><div>The stress intensity factors or strain energy release rate are typically used to characterise the stress field in the vicinity of a crack in fracture mechanics. One way to obtain the strain energy release rate in elastic–plastic fracture mechanics is from the stress and deformation field around the crack tip through the calculation of the J integral. The J-integral is contour independent, although the contour must start and end from a traction-free surface, such as the crack surface. Using Green’s theorem, the J-integral can be formulated as a surface or area integral, which makes it convenient for implementation in finite element method (FEM). More importantly, the J-integral calculation is insensitive to uncertainty of the exact crack tip location, can be applied for linear elastic analysis with small scale yielding and in an improved formulation for elastic–plastic fracture. In short, the J-integral is an indispensable tool in the study of fracture mechanics.</div><div>Despite the J-integral being widely used in FEM, including availability in most commercial FEM codes, there is currently no algorithm to calculate the J-integral in the Smoothed Particle Hydrodynamics (SPH) method. This is somewhat surprising since the SPH method, due to its meshless nature, has inherent advantages in dealing with cracks compared to mesh based methods such as FEM. In this paper we will therefore address this deficiency and develop an algorithm for calculation of the J integral in the SPH method. The implementation of his new alghorithm is based on a new definition of the weighting function <span><math><msub><mrow><mi>q</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>, as appropriately normalised kernel function, which inherently satisfies all the specific requirements on <span><math><msub><mrow><mi>q</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>: The function is sufficiently smooth in the J-integral area, it is equal to unit inside contour path of the integral and zero outside of the path. A further element of novelty is that in the current implementation, the gradient of this function is evaluated analytically rather than through a numerical approximation. The verification and validation of developed algorithm is based on simulation of the standard single edge notch tension test (SENT) under the plain strain conditions. The SPH results are compared to the FEM results for stress and displacement fields in the vicinity of the crack tip, as well as the J integral solutions. The SPH results demonstrated convergence and were within 2% of the converged FEM solutions. The validation also allows for the definition of simple guidelines for the definition of the J-integral area to achieve accurate results. The implementation is currently developed for linear elastic fracture mechanics applications, but its generalisation and application to elastic–plastic fracture mechanics, including the combination with elastic–plastic constitutive models is
{"title":"Fracture Mechanics in Smoothed Particle Hydrodynamics: An algorithm to calculate the J-Integral","authors":"Tom De Vuyst , Rade Vignjevic , Nenad Djordjevic , Marius Gintalas , Kevin Hughes","doi":"10.1016/j.engfracmech.2025.111833","DOIUrl":"10.1016/j.engfracmech.2025.111833","url":null,"abstract":"<div><div>The stress intensity factors or strain energy release rate are typically used to characterise the stress field in the vicinity of a crack in fracture mechanics. One way to obtain the strain energy release rate in elastic–plastic fracture mechanics is from the stress and deformation field around the crack tip through the calculation of the J integral. The J-integral is contour independent, although the contour must start and end from a traction-free surface, such as the crack surface. Using Green’s theorem, the J-integral can be formulated as a surface or area integral, which makes it convenient for implementation in finite element method (FEM). More importantly, the J-integral calculation is insensitive to uncertainty of the exact crack tip location, can be applied for linear elastic analysis with small scale yielding and in an improved formulation for elastic–plastic fracture. In short, the J-integral is an indispensable tool in the study of fracture mechanics.</div><div>Despite the J-integral being widely used in FEM, including availability in most commercial FEM codes, there is currently no algorithm to calculate the J-integral in the Smoothed Particle Hydrodynamics (SPH) method. This is somewhat surprising since the SPH method, due to its meshless nature, has inherent advantages in dealing with cracks compared to mesh based methods such as FEM. In this paper we will therefore address this deficiency and develop an algorithm for calculation of the J integral in the SPH method. The implementation of his new alghorithm is based on a new definition of the weighting function <span><math><msub><mrow><mi>q</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>, as appropriately normalised kernel function, which inherently satisfies all the specific requirements on <span><math><msub><mrow><mi>q</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>: The function is sufficiently smooth in the J-integral area, it is equal to unit inside contour path of the integral and zero outside of the path. A further element of novelty is that in the current implementation, the gradient of this function is evaluated analytically rather than through a numerical approximation. The verification and validation of developed algorithm is based on simulation of the standard single edge notch tension test (SENT) under the plain strain conditions. The SPH results are compared to the FEM results for stress and displacement fields in the vicinity of the crack tip, as well as the J integral solutions. The SPH results demonstrated convergence and were within 2% of the converged FEM solutions. The validation also allows for the definition of simple guidelines for the definition of the J-integral area to achieve accurate results. The implementation is currently developed for linear elastic fracture mechanics applications, but its generalisation and application to elastic–plastic fracture mechanics, including the combination with elastic–plastic constitutive models is ","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"333 ","pages":"Article 111833"},"PeriodicalIF":5.3,"publicationDate":"2026-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145922181","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 : 2026-02-21Epub Date: 2026-01-06DOI: 10.1016/j.engfracmech.2025.111822
Kim Wallin
The second-generation Eurocode EN1993-1-10 which covers design of steel structures with respect to brittle fracture includes two tables giving the maximum allowable thickness depending on design temperature, level of stress and steel grade and class. Table 4.2 is developed for fatigue loaded details whereas Table 4.3 is developed for statically loaded details and Here, the tables in EN1993-1-10 are expressed in a simple analytical form which simplifies and enhances the use of the tables. Furthermore, a new fatigue cycle adjustment to the tables is developed. This extends the use of EN1993-1-10 to a large variety of loading cases, without conflicting with the safety level built into the standard.
{"title":"An analytic interpretation of the new EN1993-1-10 standard","authors":"Kim Wallin","doi":"10.1016/j.engfracmech.2025.111822","DOIUrl":"10.1016/j.engfracmech.2025.111822","url":null,"abstract":"<div><div>The second-generation Eurocode EN1993-1-10 which covers design of steel structures with respect to brittle fracture includes two tables giving the maximum allowable thickness depending on design temperature, level of stress and steel grade and class. Table 4.2 is developed for fatigue loaded details whereas Table 4.3 is developed for statically loaded details and Here, the tables in EN1993-1-10 are expressed in a simple analytical form which simplifies and enhances the use of the tables. Furthermore, a new fatigue cycle adjustment to the tables is developed. This extends the use of EN1993-1-10 to a large variety of loading cases, without conflicting with the safety level built into the standard.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"333 ","pages":"Article 111822"},"PeriodicalIF":5.3,"publicationDate":"2026-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145973638","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 : 2026-02-21Epub Date: 2026-01-13DOI: 10.1016/j.engfracmech.2026.111841
Felix Weber , Maxime Vassaux , Lukas Laubert , Sebastian Pfaller
Molecular dynamics (MD) simulations are widely used to provide insights into fracture mechanisms while maintaining chemical specificity. However, particle-based techniques such as MD are limited in terms of accessible length scales and applicable boundary conditions, which restricts the investigation of fracture phenomena in typical engineering settings. In an attempt to overcome these limitations, we apply the partitioned-domain Capriccio method to couple atomistic MD samples representing silica glass with the finite element (FE) method. With this approach, we perform mode I (rectangular panel under tension, three-, and four-point bending), mode II as well as mode III (rectangular panel under in-plane or out-of-plane shear) simulations. Thereby, we investigate multiple criteria to identify the onset of crack propagation based on the virial stress, the number of pair interactions, the kinetic energy/temperature, the crack velocity, and the crack opening displacement. It becomes apparent that the maximum virial stress can actually serve as an objective and meaningful indicator for the start of crack growth, in contrast to, for example, the temperature evolution The approach presented provides quantitatively plausible results for the critical stress intensity factors , , and . This contribution shows that the Capriccio method is a flexible means of performing fracture simulations that take into account boundary conditions typical of experimental test setups with atomistic specificity near the crack tip. While also pointing out the current limitations of the Capriccio method, we demonstrate its potential to integrate atomistic insights into FE models with significantly larger overall dimensions.
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