Pub 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":"2026-01-21","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 : 2026-01-20DOI: 10.1016/j.engfracmech.2026.111874
S.I. Okocha , M.T. Hendry , P.Y.B. Jar
This study investigates the fracture toughness (KJC) and hardness of heat-treated, cold-drawn AISI 4140 alloy (“e.t.d” 150) alongside three representative rail steels (JP, EV, and CZ) to comparatively evaluate their mechanical performance. Importance is placed on “e.t.d” 150 to assess its potentiality as a viable alternative material for rail steel applications based on current insights to rail steel material recycling and substitution. Fracture toughness (KJC) was assessed using a chamfered cylindrical flat-end and spherical indenter based on a novel virtual J-integral approach that minimizes the plastic J-integral component based on Irwin’s elastic solution, while hardness was obtained using only spherical indentation. A comparison between the KJC outcomes of both indenters are presented and discussed, showing preference to spherical indentation. The virtual J-integral approach with limit load analysis applied for estimating KJC in both indenters, incorporated stress triaxiality to account for pressure sensitivity and the hydrostatic pressure component in indentation testing. Results show that “e.t.d” 150 achieves fracture toughness and Brinell hardness values comparable to rail steels, particularly suitable for curved track sections where wear resistance and durability are critical. Fatigue analysis was also conducted for “e.t.d” 150, which confirms moderate-to-good resistance to rolling contact fatigue. These findings suggest that “e.t.d” 150 offers a reliable alternative for substituting conventional rail steels, with potential benefits for railway performance, safety, and maintenance cost reduction.
{"title":"Comprehensive mechanical evaluation of heat-treated AISI 4140 (ETD 150): fatigue behavior and novel indentation-based characterization of fracture toughness and hardness with relevance to rail steels","authors":"S.I. Okocha , M.T. Hendry , P.Y.B. Jar","doi":"10.1016/j.engfracmech.2026.111874","DOIUrl":"10.1016/j.engfracmech.2026.111874","url":null,"abstract":"<div><div>This study investigates the fracture toughness (K<sub>JC</sub>) and hardness of heat-treated, cold-drawn AISI 4140 alloy (“e.t.d” 150) alongside three representative rail steels (JP, EV, and CZ) to comparatively evaluate their mechanical performance. Importance is placed on “e.t.d” 150 to assess its potentiality as a viable alternative material for rail steel applications based on current insights to rail steel material recycling and substitution. Fracture toughness (K<sub>JC</sub>) was assessed using a chamfered cylindrical flat-end and spherical indenter based on a novel virtual J-integral approach that minimizes the plastic J-integral component based on Irwin’s elastic solution, while hardness was obtained using only spherical indentation. A comparison between the K<sub>JC</sub> outcomes of both indenters are presented and discussed, showing preference to spherical indentation. The virtual J-integral approach with limit load analysis applied for estimating K<sub>JC</sub> in both indenters, incorporated stress triaxiality to account for pressure sensitivity and the hydrostatic pressure component in indentation testing. Results show that “e.t.d” 150 achieves fracture toughness and Brinell hardness values comparable to rail steels, particularly suitable for curved track sections where wear resistance and durability are critical. Fatigue analysis was also conducted for “e.t.d” 150, which confirms moderate-to-good resistance to rolling contact fatigue. These findings suggest that “e.t.d” 150 offers a reliable alternative for substituting conventional rail steels, with potential benefits for railway performance, safety, and maintenance cost reduction.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"334 ","pages":"Article 111874"},"PeriodicalIF":5.3,"publicationDate":"2026-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146015860","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 : 2026-01-20DOI: 10.1016/j.engfracmech.2026.111870
Boya Wu , Meichen Liu , Shangyi Dai , Junwan Li , Xiaochun Wu
This study reveals the cyclic softening mechanisms of AISI H13 steel under isothermal fatigue at 600°C through experimental characterization and dislocation density-based crystal plasticity finite element method. Experiments demonstrate that AISI H13 steel exhibits three distinct softening stages within the strain amplitude range of 0.5–1.1%, namely rapid softening, transitional softening, and steady softening. Microstructural analysis reveals that with increasing cycles, the softening phenomenon intensifies, with dislocation density continuously decreasing from rapid to slow rates, accompanied by the coarsening of carbides. Accordingly, a dislocation density-based crystal plasticity model coupling realistic martensitic lath block structures and damage evolution was developed to reveal cyclic softening mechanisms, achieving hysteresis loop predictions with errors below 5%. The model reveals the dominant role of statistically stored dislocations (SSD) in cyclic softening, with SSD density decreasing from 1.68 × 103 to 1.53 × 103 μm−2 within the first five cycles. This non-uniform recovery process generates stress concentration in high SSD regions and strain localization in low SSD regions, leading to strong coupling between damage and plastic strain that drives progressive steel degradation. Simulation results further demonstrate that increasing strain amplitude from 0.5% to 1.1% significantly enhances strain localization, with accumulated plastic strain in localized regions reaching 0.5 at the 5th cycle under high amplitude compared to merely 0.002 under low amplitude. This heterogeneity accelerates damage evolution, with damage variables exceeding 0.15 in critical regions at 1.1% strain amplitude while remaining zero at 0.5%, ultimately reducing fatigue life from 650 to 214 cycles and promoting secondary crack formation near primary crack tips.
{"title":"A dislocation density-based crystal plasticity finite element analysis of cyclic softening behavior of AISI H13 steel under isothermal fatigue","authors":"Boya Wu , Meichen Liu , Shangyi Dai , Junwan Li , Xiaochun Wu","doi":"10.1016/j.engfracmech.2026.111870","DOIUrl":"10.1016/j.engfracmech.2026.111870","url":null,"abstract":"<div><div>This study reveals the cyclic softening mechanisms of AISI H13 steel under isothermal fatigue at 600°C through experimental characterization and dislocation density-based crystal plasticity finite element method. Experiments demonstrate that AISI H13 steel exhibits three distinct softening stages within the strain amplitude range of 0.5–1.1%, namely rapid softening, transitional softening, and steady softening. Microstructural analysis reveals that with increasing cycles, the softening phenomenon intensifies, with dislocation density continuously decreasing from rapid to slow rates, accompanied by the coarsening of carbides. Accordingly, a dislocation density-based crystal plasticity model coupling realistic martensitic lath block structures and damage evolution was developed to reveal cyclic softening mechanisms, achieving hysteresis loop predictions with errors below 5%. The model reveals the dominant role of statistically stored dislocations (SSD) in cyclic softening, with SSD density decreasing from 1.68 × 10<sup>3</sup> to 1.53 × 10<sup>3</sup> μm<sup>−2</sup> within the first five cycles. This non-uniform recovery process generates stress concentration in high SSD regions and strain localization in low SSD regions, leading to strong coupling between damage and plastic strain that drives progressive steel degradation. Simulation results further demonstrate that increasing strain amplitude from 0.5% to 1.1% significantly enhances strain localization, with accumulated plastic strain in localized regions reaching 0.5 at the 5th cycle under high amplitude compared to merely 0.002 under low amplitude. This heterogeneity accelerates damage evolution, with damage variables exceeding 0.15 in critical regions at 1.1% strain amplitude while remaining zero at 0.5%, ultimately reducing fatigue life from 650 to 214 cycles and promoting secondary crack formation near primary crack tips.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"334 ","pages":"Article 111870"},"PeriodicalIF":5.3,"publicationDate":"2026-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146026300","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 : 2026-01-20DOI: 10.1016/j.engfracmech.2026.111875
Weidong Liu , Ya Xu , Yu Liu , Chi Zhang , Qiushi Zhang , Jiyuan Cui
Conventional fatigue crack growth rate (FCGR) testing is constrained by limited specimen geometries and digital image correlation (DIC) technical restrictions, hindering its application to multiaxial loading conditions. This study proposes a novel ring specimen (RS) for FCGR testing. By establishing an analytical relationship between its unique equivalent force arm and crack length, and analyzing the sensitivity boundaries of this mapping mechanism regarding crack angle and tensile strain, a force/torque-sensor-based method for full-cycle crack monitoring was achieved. The results demonstrate that the RS maintains mechanical equivalence to standard specimens while extending the effective testing zone 6.5-fold. The equivalent force arm-crack length mapping model shows high robustness, with the gradient relative error remaining below 2% within reasonable variations in crack angle and strain. The RS method yields FCGRs within factor-of-two scatter bands of the standard DIC method, with Paris law parameter errors below 3% without compromising testing efficiency. This research overcomes limitations in DIC and specimen geometry to achieve full-cycle crack monitoring, offering a novel strategy for in situ monitoring of rubber crack propagation under multiaxial loading conditions.
{"title":"A novel ring specimen for fatigue crack growth rate testing of rubber with full-cycle crack length monitoring","authors":"Weidong Liu , Ya Xu , Yu Liu , Chi Zhang , Qiushi Zhang , Jiyuan Cui","doi":"10.1016/j.engfracmech.2026.111875","DOIUrl":"10.1016/j.engfracmech.2026.111875","url":null,"abstract":"<div><div>Conventional fatigue crack growth rate (FCGR) testing is constrained by limited specimen geometries and digital image correlation (DIC) technical restrictions, hindering its application to multiaxial loading conditions. This study proposes a novel ring specimen (RS) for FCGR testing. By establishing an analytical relationship between its unique equivalent force arm and crack length, and analyzing the sensitivity boundaries of this mapping mechanism regarding crack angle and tensile strain, a force/torque-sensor-based method for full-cycle crack monitoring was achieved. The results demonstrate that the RS maintains mechanical equivalence to standard specimens while extending the effective testing zone 6.5-fold. The equivalent force arm-crack length mapping model shows high robustness, with the gradient relative error remaining below 2% within reasonable variations in crack angle and strain. The RS method yields FCGRs within factor-of-two scatter bands of the standard DIC method, with Paris law parameter errors below 3% without compromising testing efficiency. This research overcomes limitations in DIC and specimen geometry to achieve full-cycle crack monitoring, offering a novel strategy for in situ monitoring of rubber crack propagation under multiaxial loading conditions.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"333 ","pages":"Article 111875"},"PeriodicalIF":5.3,"publicationDate":"2026-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146034509","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 : 2026-01-20DOI: 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":"2026-01-20","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}
To address the challenges of accurately and efficiently predicting crack propagation in tubular joints of offshore jacket platforms, this study proposes a hybrid physics-informed neural network method that integrates data -driven modeling with physical laws. First, stress analysis of the structure under extreme storm loads is performed using ANSYS to extract the maximum principal stress in critical areas. Subsequently, Franc3D simulations are conducted to obtain corresponding data on stress intensity factors and crack lengths. This data is used to construct a multilayer perceptron surrogate model, which predicts the SIF from the maximum principal stress and crack length. Next, the Paris law is discretized via the forward Euler method and embedded into a recurrent neural network to create a PINN for modeling temporal crack growth. Furthermore, a hybrid PINN model is established by replacing the parameters in the Paris law with the developed surrogate model. The model’s performance is enhanced through hyperparameter optimization using random and grid search. Comparative studies with standalone MLP and LSTM models demonstrate the superiority of the proposed hybrid PINN, achieving a MAPE of only 2.27%, which represents improvements of 31.38% and 25.33% over the MLP and LSTM models, respectively. Additional evaluation using a test set assessed the model’s safety warning capability in critical crack fracture failure scenarios. The results indicate that the remaining life estimates and safety warnings fall within the 95% confidence interval, verifying the model’s robustness and reliability. This work presents a novel solution for assessing fatigue cracks in marine engineering structures.
{"title":"Online crack propagation prediction for tubular joints of offshore jacket platforms using a hybrid physics-informed neural network","authors":"Jiancheng Leng , Zitong Chen , Zikai Jia , Haolong Wu , Hangze Guo","doi":"10.1016/j.engfracmech.2026.111868","DOIUrl":"10.1016/j.engfracmech.2026.111868","url":null,"abstract":"<div><div>To address the challenges of accurately and efficiently predicting crack propagation in tubular joints of offshore jacket platforms, this study proposes a hybrid physics-informed neural network method that integrates data -driven modeling with physical laws. First, stress analysis of the structure under extreme storm loads is performed using ANSYS to extract the maximum principal stress in critical areas. Subsequently, Franc3D simulations are conducted to obtain corresponding data on stress intensity factors and crack lengths. This data is used to construct a multilayer perceptron surrogate model, which predicts the SIF from the maximum principal stress and crack length. Next, the Paris law is discretized via the forward Euler method and embedded into a recurrent neural network to create a PINN for modeling temporal crack growth. Furthermore, a hybrid PINN model is established by replacing the parameters in the Paris law with the developed surrogate model. The model’s performance is enhanced through hyperparameter optimization using random and grid search. Comparative studies with standalone MLP and LSTM models demonstrate the superiority of the proposed hybrid PINN, achieving a MAPE of only 2.27%, which represents improvements of 31.38% and 25.33% over the MLP and LSTM models, respectively. Additional evaluation using a test set assessed the model’s safety warning capability in critical crack fracture failure scenarios. The results indicate that the remaining life estimates and safety warnings fall within the 95% confidence interval, verifying the model’s robustness and reliability. This work presents a novel solution for assessing fatigue cracks in marine engineering structures.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"333 ","pages":"Article 111868"},"PeriodicalIF":5.3,"publicationDate":"2026-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146034511","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 : 2026-01-19DOI: 10.1016/j.engfracmech.2026.111869
Xiaolong Liu , Kelian Luo , Qiang Chen , Dunxin Wang , Haibo Xiang , Rubing Guo , Xi Wang
Interior crack initiation prevails in the failure mode of railway bearings. Three characteristic regions, i.e., Inclusion, Fish-eye, and zig-zag cracks, were first defined on the fracture surface of interior crack initiation, indicating the interior crack initiation and propagation mechanism. The inclusion clusters are primarily Al2O3, with the diameters ranging from approximately 5–15 µm. Fish-eye formed during the crack initiation stage. No grain refinement was observed during this stage, suggesting that no white etching cracks developed. Zig-zag cracks exhibited larger dimensions along the major axis and smaller, denser structures along the minor axis. The crack path deflects during the propagation of mixed Mode II-III cracks, resulting in the characteristic zig-zag morphology. Based on these results, a mechanism for interior crack initiation and propagation in the outer raceway of railway bearings was proposed. These findings advance the understanding of very-high-cycle fatigue under rolling contact loading, offering critical insights for optimizing bearing design and lifespan prediction in rail transport systems.
{"title":"Characteristic regions for the fracture surface of interior crack initiation in the outer ring raceway of railway bearing","authors":"Xiaolong Liu , Kelian Luo , Qiang Chen , Dunxin Wang , Haibo Xiang , Rubing Guo , Xi Wang","doi":"10.1016/j.engfracmech.2026.111869","DOIUrl":"10.1016/j.engfracmech.2026.111869","url":null,"abstract":"<div><div>Interior crack initiation prevails in the failure mode of railway bearings. Three characteristic regions, i.e., Inclusion, Fish-eye, and zig-zag cracks, were first defined on the fracture surface of interior crack initiation, indicating the interior crack initiation and propagation mechanism. The inclusion clusters are primarily Al<sub>2</sub>O<sub>3</sub>, with the diameters ranging from approximately 5–15 µm. Fish-eye formed during the crack initiation stage. No grain refinement was observed during this stage, suggesting that no white etching cracks developed. Zig-zag cracks exhibited larger dimensions along the major axis and smaller, denser structures along the minor axis. The crack path deflects during the propagation of mixed Mode II-III cracks, resulting in the characteristic zig-zag morphology. Based on these results, a mechanism for interior crack initiation and propagation in the outer raceway of railway bearings was proposed. These findings advance the understanding of very-high-cycle fatigue under rolling contact loading, offering critical insights for optimizing bearing design and lifespan prediction in rail transport systems.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"333 ","pages":"Article 111869"},"PeriodicalIF":5.3,"publicationDate":"2026-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146034510","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 : 2026-01-16DOI: 10.1016/j.engfracmech.2026.111845
Yan Li , Pengpeng Shi , Xiaofan Gou , Wenshuai Wang , Xing Li
The interaction among multiple cracks plays a crucial role in the elastoplastic fracture behavior of materials. Although numerous studies have been devoted to elastic analyses of doubly periodic crack problems, the elastoplastic response of complex configurations such as doubly periodic cracks with diamond-shaped-interleaving arrays remains insufficiently explored. This paper investigates the plastic zone size (PZS) and crack tip opening displacement (CTOD) of doubly periodic cracks with diamond-shaped-interleaving arrays (DPC-DSIA) under longitudinal shear. Based on the Dugdale plastic zone model and the continuously distributed dislocation model, the mixed-boundary-value problem of elastoplastic behavior for DPC-DSIA configurations is transformed into a system of singular integral equations, where the semi-analytical solution is achieved using the Lobatto-Chebyshev numerical quadrature method. The accuracy of the proposed solution is verified against existing results for two typical periodic cracks with rectangular arrays and diamond-shaped arrays and the complex periodic cracks with diamond-shaped-interleaving small arrays. Furthermore, the influence of periodic parameters on key fracture quantities, including the PZS, CTOD, and stress intensity factor (SIF), are systematically examined. The results reveal the interaction mechanism between vertically and horizontally oriented cracks and highlight the complex effects of doubly periodic crack arrangements on the system’s elastoplastic behavior.
{"title":"Plastic zone size and crack tip opening displacement of doubly periodic Dugdale cracks with diamond-shaped-interleaving arrays under longitudinal shear","authors":"Yan Li , Pengpeng Shi , Xiaofan Gou , Wenshuai Wang , Xing Li","doi":"10.1016/j.engfracmech.2026.111845","DOIUrl":"10.1016/j.engfracmech.2026.111845","url":null,"abstract":"<div><div>The interaction among multiple cracks plays a crucial role in the elastoplastic fracture behavior of materials. Although numerous studies have been devoted to elastic analyses of doubly periodic crack problems, the elastoplastic response of complex configurations such as doubly periodic cracks with diamond-shaped-interleaving arrays remains insufficiently explored. This paper investigates the plastic zone size (PZS) and crack tip opening displacement (CTOD) of doubly periodic cracks with diamond-shaped-interleaving arrays (DPC-DSIA) under longitudinal shear. Based on the Dugdale plastic zone model and the continuously distributed dislocation model, the mixed-boundary-value problem of elastoplastic behavior for DPC-DSIA configurations is transformed into a system of singular integral equations, where the semi-analytical solution is achieved using the Lobatto-Chebyshev numerical quadrature method. The accuracy of the proposed solution is verified against existing results for two typical periodic cracks with rectangular arrays and diamond-shaped arrays and the complex periodic cracks with diamond-shaped-interleaving small arrays. Furthermore, the influence of periodic parameters on key fracture quantities, including the PZS, CTOD, and stress intensity factor (SIF), are systematically examined. The results reveal the interaction mechanism between vertically and horizontally oriented cracks and highlight the complex effects of doubly periodic crack arrangements on the system’s elastoplastic behavior.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"335 ","pages":"Article 111845"},"PeriodicalIF":5.3,"publicationDate":"2026-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146102466","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 : 2026-01-15DOI: 10.1016/j.engfracmech.2026.111846
Andres F. Galvis
This work presents a robust phase-field formulation for brittle fracture, combining a quasi-monolithic solution strategy with a frozen history field, Houbolt time integration for dynamic/transient regimes, and adaptive remeshing in FreeFEM++. This approach enhances numerical robustness, simplifies parameter calibration, and facilitates extensions to multi-physics fracture problems. Despite widespread interest, building on this framework, a key contribution is the first open serial implementation of this framework in FreeFEM++, offering advantages in mesh adaptivity, solver flexibility, and concise variational syntax. The mesh adaptivity feature concentrates resolution near evolving crack tips to efficiently capture fracture evolution. The implementation is validated on standard benchmarks, showing close agreement with reference crack paths, load–displacement, and dissipated energy responses. By releasing a concise, well-documented FreeFEM++ code, this work bridges a reproducibility gap and establishes a methodological foundation for future developments.
{"title":"Phase-field modelling of quasi-static and dynamic brittle fracture: A FreeFEM++ implementation","authors":"Andres F. Galvis","doi":"10.1016/j.engfracmech.2026.111846","DOIUrl":"10.1016/j.engfracmech.2026.111846","url":null,"abstract":"<div><div>This work presents a robust phase-field formulation for brittle fracture, combining a quasi-monolithic solution strategy with a frozen history field, Houbolt time integration for dynamic/transient regimes, and adaptive remeshing in <span>FreeFEM++</span>. This approach enhances numerical robustness, simplifies parameter calibration, and facilitates extensions to multi-physics fracture problems. Despite widespread interest, building on this framework, a key contribution is the first open serial implementation of this framework in <span>FreeFEM++</span>, offering advantages in mesh adaptivity, solver flexibility, and concise variational syntax. The mesh adaptivity feature concentrates resolution near evolving crack tips to efficiently capture fracture evolution. The implementation is validated on standard benchmarks, showing close agreement with reference crack paths, load–displacement, and dissipated energy responses. By releasing a concise, well-documented <span>FreeFEM++</span> code, this work bridges a reproducibility gap and establishes a methodological foundation for future developments.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"333 ","pages":"Article 111846"},"PeriodicalIF":5.3,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146034508","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 : 2026-01-13DOI: 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.
{"title":"The Capriccio method as a versatile tool for quantifying the fracture properties of glassy materials under complex loading conditions with chemical specificity","authors":"Felix Weber , Maxime Vassaux , Lukas Laubert , Sebastian Pfaller","doi":"10.1016/j.engfracmech.2026.111841","DOIUrl":"10.1016/j.engfracmech.2026.111841","url":null,"abstract":"<div><div>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 <span><math><msub><mrow><mi>K</mi></mrow><mrow><mi>Ic</mi></mrow></msub></math></span>, <span><math><msub><mrow><mi>K</mi></mrow><mrow><mi>IIc</mi></mrow></msub></math></span>, and <span><math><msub><mrow><mi>K</mi></mrow><mrow><mi>IIIc</mi></mrow></msub></math></span>. 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.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"333 ","pages":"Article 111841"},"PeriodicalIF":5.3,"publicationDate":"2026-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145973636","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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