Pub Date : 2026-01-07DOI: 10.1016/j.engfracmech.2026.111847
Chenghui Xu , Tianle Meng , Zichen Deng , Tao Wu
This study presents a Hamiltonian-based symplectic methodology for investigating swelling-induced fracture in hydrogels caused by water absorption. A constitutive model for hydrogels, incorporating chemical coupling effects, is established through perturbation analysis rooted in a physically rigorous theoretical framework. Within the Hamiltonian system, the dual equation governing plane fracture in hydrogels is directly solved using the method of separation of variables. Analytical expressions for the generalized stress/displacement fields are explicitly derived based on eigenvalues and eigensolutions, thereby obviating the need for trial functions. Moreover, critical fracture parameters (including stress intensity factors (SIFs) and J-integral), as well as the crack initiation angle are accurately quantified. Finally, the influence of chemical potential on these fracture parameters and initiation angle is systematically examined. These findings offer a robust theoretical basis for the practical engineering applications of hydrogel materials.
{"title":"A symplectic analytical method for fracture analysis of hydrogels under chemo-mechanical coupled loading","authors":"Chenghui Xu , Tianle Meng , Zichen Deng , Tao Wu","doi":"10.1016/j.engfracmech.2026.111847","DOIUrl":"10.1016/j.engfracmech.2026.111847","url":null,"abstract":"<div><div>This study presents a Hamiltonian-based symplectic methodology for investigating swelling-induced fracture in hydrogels caused by water absorption. A constitutive model for hydrogels, incorporating chemical coupling effects, is established through perturbation analysis rooted in a physically rigorous theoretical framework. Within the Hamiltonian system, the dual equation governing plane fracture in hydrogels is directly solved using the method of separation of variables. Analytical expressions for the generalized stress/displacement fields are explicitly derived based on eigenvalues and eigensolutions, thereby obviating the need for trial functions. Moreover, critical fracture parameters (including stress intensity factors (SIFs) and <em>J</em>-integral), as well as the crack initiation angle are accurately quantified. Finally, the influence of chemical potential on these fracture parameters and initiation angle is systematically examined. These findings offer a robust theoretical basis for the practical engineering applications of hydrogel materials.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"333 ","pages":"Article 111847"},"PeriodicalIF":5.3,"publicationDate":"2026-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145922256","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 : 2026-01-06DOI: 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":"2026-01-06","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 : 2026-01-06DOI: 10.1016/j.engfracmech.2026.111843
Jie Luo , Qiao Wang , Wei Zhou , Xiaolin Chang , Qiang Yue , Zhangzhen Peng , Chuqiao Feng , Anli Wang
Sulfate-induced cracking shortens the service life of concrete structures. Numerical modeling is a valuable tool for investigating the degradation process. Most previous models can assess the damage extent, but struggle to predict cracking induced by erosion. This study proposes a coupled chemical-transport-mechanical phase-field model to effectively simulate the cracking process of sulfate-eroded concrete. The diffusion–reaction process is modeled based on transport law and reaction kinetics. A simplified kinetic equation is employed to describe the calcium leaching phenomenon. By employing the phase-field model, discrete erosion cracks are converted into regularized cracks, enabling easy coupling of the cracking process with the diffusion–reaction process. The cracking driving force in the phase-field model is calculated by the expansion strain, which is derived by solving the diffusion–reaction model. A new piecewise function is used to describe the influence of cracks and pores on ion transport, achieving bidirectional coupling between the cracking and transport processes. By solving the phase-field equations, complex erosion cracks can be automatically predicted. The calculation results align well with experimental data and can reproduce the transverse cracks observed in the erosion-expansion experiment. Compared to other models, the proposed model achieves more accurate results with a larger residual error. Furthermore, the deterioration of concrete column corners under various factors is simulated, and the significance of different factors and their interactions is analyzed, providing new insights for enhancing the durability of concrete structures in sulfate environments.
{"title":"Numerical simulation of sulfate-eroded concrete structure based on a coupled chemical-transport-mechanical phase-field model","authors":"Jie Luo , Qiao Wang , Wei Zhou , Xiaolin Chang , Qiang Yue , Zhangzhen Peng , Chuqiao Feng , Anli Wang","doi":"10.1016/j.engfracmech.2026.111843","DOIUrl":"10.1016/j.engfracmech.2026.111843","url":null,"abstract":"<div><div>Sulfate-induced cracking shortens the service life of concrete structures. Numerical modeling is a valuable tool for investigating the degradation process. Most previous models can assess the damage extent, but struggle to predict cracking induced by erosion. This study proposes a coupled chemical-transport-mechanical phase-field model to effectively simulate the cracking process of sulfate-eroded concrete. The diffusion–reaction process is modeled based on transport law and reaction kinetics. A simplified kinetic equation is employed to describe the calcium leaching phenomenon. By employing the phase-field model, discrete erosion cracks are converted into regularized cracks, enabling easy coupling of the cracking process with the diffusion–reaction process. The cracking driving force in the phase-field model is calculated by the expansion strain, which is derived by solving the diffusion–reaction model. A new piecewise function is used to describe the influence of cracks and pores on ion transport, achieving bidirectional coupling between the cracking and transport processes. By solving the phase-field equations, complex erosion cracks can be automatically predicted. The calculation results align well with experimental data and can reproduce the transverse cracks observed in the erosion-expansion experiment. Compared to other models, the proposed model achieves more accurate results with a larger residual error. Furthermore, the deterioration of concrete column corners under various factors is simulated, and the significance of different factors and their interactions is analyzed, providing new insights for enhancing the durability of concrete structures in sulfate environments.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"333 ","pages":"Article 111843"},"PeriodicalIF":5.3,"publicationDate":"2026-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145922255","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}
Fracture failure is an essential concern on the design, manufacture and utilization of piezoelectric functional materials. Both traditional piezoelectric ceramics and new flexible piezoelectric materials demand objective modeling of fracture under the coupled action of electric and mechanical fields. Currently, the widely developed electromechanical fracture phase-field model (EM-PFM), which employs the mechanical energy release rate as the crack driving force, cannot sensibly predict some of the classical experimental reports. In this work, the necessity of the mechanical energy release rate as the fracture criterion is revised based on a semi-analytical demonstration on the EM-PFM, and a new crack driving force formulation is proposed. More specifically, the new crack driving force consists of the mechanical energy release rate contributed from the effective stress and a part of the electro-mechanical coupled energy release rate, where the transformation rate of the latter is controlled by an intrinsic material parameter. The proposed EM-PFM is numerically implemented in a multi-field finite element framework in the commercial software ABAQUS via a user element subroutine. A representative one-dimensional ideal numerical test demonstrates the rationality of the present model. Most importantly, for the first time, we achieved numerical reproduction of Park and Sun’s classical experiments in the EM-PFM without changing any piezoelectric coefficients. The present work contributes to a better understanding of piezoelectric materials and is beneficial in predicting the fracture of piezoelectric materials realistically.
{"title":"Phase-field fracture modeling of piezoelectric solids with a novel crack driving force incorporating an intrinsic material parameter","authors":"Xin Li , Shihao Lv , Chuwei Zhou , Chen Xing , Umberto Perego","doi":"10.1016/j.engfracmech.2026.111842","DOIUrl":"10.1016/j.engfracmech.2026.111842","url":null,"abstract":"<div><div>Fracture failure is an essential concern on the design, manufacture and utilization of piezoelectric functional materials. Both traditional piezoelectric ceramics and new flexible piezoelectric materials demand objective modeling of fracture under the coupled action of electric and mechanical fields. Currently, the widely developed electromechanical fracture phase-field model (EM-PFM), which employs the mechanical energy release rate as the crack driving force, cannot sensibly predict some of the classical experimental reports. In this work, the necessity of the mechanical energy release rate as the fracture criterion is revised based on a semi-analytical demonstration on the EM-PFM, and a new crack driving force formulation is proposed. More specifically, the new crack driving force consists of the mechanical energy release rate contributed from the effective stress and a part of the electro-mechanical coupled energy release rate, where the transformation rate of the latter is controlled by an intrinsic material parameter. The proposed EM-PFM is numerically implemented in a multi-field finite element framework in the commercial software ABAQUS via a user element subroutine. A representative one-dimensional ideal numerical test demonstrates the rationality of the present model. Most importantly, for the first time, we achieved numerical reproduction of Park and Sun’s classical experiments in the EM-PFM without changing any piezoelectric coefficients. The present work contributes to a better understanding of piezoelectric materials and is beneficial in predicting the fracture of piezoelectric materials realistically.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"333 ","pages":"Article 111842"},"PeriodicalIF":5.3,"publicationDate":"2026-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145922251","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 : 2026-01-05DOI: 10.1016/j.engfracmech.2026.111840
Xuanming Cai , Penglei Wang , Yang Hou , Zhiyong Wang , Wei Zhang , Zhongcheng Mu , Anxiao Guo , Linzhuang Han , Yunhao Yang , Yalin He , Bin Liu , Wenbo Xie
Short fiber-reinforced polymer-matrix composites (SFRPC), renowned for high specific strength, are widely employed in high strain-rate structures. Elucidating their dynamic response and failure mechanisms under high strain-rate loading is crucial for safety design and performance optimization. A three-dimensional multiscale constitutive model and failure criterion for SFRPC were developed using micro–macro mechanics, whose validity was verified by comparing quasi-static uniaxial tensile simulations of representative volume element (RVE) cells with experimental results at the macroscopic level. The RVE model extracted effective elastic constants under various loadings, acting as key dynamic parameters for high strain-rate simulations. Three types of SFRPC porous structures with different volume fractions were designed via triply periodic minimal surface (TPMS) equations and fabricated into specimens by 3D printing. Multiscale simulations and high strain-rate impact experiments investigated the dynamic response and damage evolution. Results show that the SFRPC structures exhibit strain-rate sensitivity under dynamic loading, with dynamic strength rising as strain rate increases. At similar strain rates, peak stress, specific energy absorption (SEA), and energy absorption efficiency (EAE) rise with higher volume fractions. SEA and EAE both increase with the strain rate, with EAE of higher volume fraction structures more influenced by strain rate effects. Microscopic damage analysis showed volume fraction strongly affects shear failure: 25 % and 35 % fractions show dominant fiber pull-out, while 45 % shows brittle fracture and plastic deformation. Multiscale simulations reproduced experimental damage patterns, and their multi-directional modes clarify internal damage evolution under high strain rate conditions.
{"title":"Dynamic response behavior and damage evolution mechanism of additively manufactured porous structures of composites under high strain rates","authors":"Xuanming Cai , Penglei Wang , Yang Hou , Zhiyong Wang , Wei Zhang , Zhongcheng Mu , Anxiao Guo , Linzhuang Han , Yunhao Yang , Yalin He , Bin Liu , Wenbo Xie","doi":"10.1016/j.engfracmech.2026.111840","DOIUrl":"10.1016/j.engfracmech.2026.111840","url":null,"abstract":"<div><div>Short fiber-reinforced polymer-matrix composites (SFRPC), renowned for high specific strength, are widely employed in high strain-rate structures. Elucidating their dynamic response and failure mechanisms under high strain-rate loading is crucial for safety design and performance optimization. A three-dimensional multiscale constitutive model and failure criterion for SFRPC were developed using micro–macro mechanics, whose validity was verified by comparing quasi-static uniaxial tensile simulations of representative volume element (RVE) cells with experimental results at the macroscopic level. The RVE model extracted effective elastic constants under various loadings, acting as key dynamic parameters for high strain-rate simulations. Three types of SFRPC porous structures with different volume fractions were designed via triply periodic minimal surface (TPMS) equations and fabricated into specimens by 3D printing. Multiscale simulations and high strain-rate impact experiments investigated the dynamic response and damage evolution. Results show that the SFRPC structures exhibit strain-rate sensitivity under dynamic loading, with dynamic strength rising as strain rate increases. At similar strain rates, peak stress, specific energy absorption (SEA), and energy absorption efficiency (EAE) rise with higher volume fractions. SEA and EAE both increase with the strain rate, with EAE of higher volume fraction structures more influenced by strain rate effects. Microscopic damage analysis showed volume fraction strongly affects shear failure: 25 % and 35 % fractions show dominant fiber pull-out, while 45 % shows brittle fracture and plastic deformation. Multiscale simulations reproduced experimental damage patterns, and their multi-directional modes clarify internal damage evolution under high strain rate conditions.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"333 ","pages":"Article 111840"},"PeriodicalIF":5.3,"publicationDate":"2026-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145922254","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 : 2026-01-04DOI: 10.1016/j.engfracmech.2025.111831
Szymon Dziuba , Aleksandra Królicka , Michał Smolnicki , Grzegorz Lesiuk , Dariusz Rozumek , Roman Kuziak
The present study investigates the fatigue crack growth behavior of ultra-fine bainitic steel under mixed-mode (I + II) loading conditions, relevant to the complex stress states occurring in railway track service. Experimental tests were performed using Compact Tension Shear (CTS) specimens loaded at angles of 30°, 45°, and 60°, enabling controlled combinations of tensile and shear stresses. The fatigue crack growth rate (FCGR) was analyzed and correlated with the equivalent stress intensity factor (ΔKeq) calculated according to Tanaka’s criterion. Complementary finite element method (FEM) simulations were employed to determine local fracture parameters, including KI, KII, T-stress, and J-integral values, and to model the evolution of crack paths. The experimental results demonstrated that with an increasing contribution of Mode II, the crack propagation angle (ψ0) increased, while the specimen lifetime showed a non-linear dependence on load angle. Fractographic analysis revealed a transition from predominantly transgranular fracture at lower angles toward a higher fraction of intergranular and quasi-cleavage fracture at higher angles. The proposed experimental–numerical approach provides a consistent framework for describing mixed-mode fatigue behavior and for constructing generalized FCGR diagrams. The results contribute to improving the predictive capability of fatigue life models for advanced bainitic steels applied in railway infrastructure.
{"title":"Fatigue crack growth under mixed mode I + II loading conditions of ultra-fine bainitic steel designed for railway applications","authors":"Szymon Dziuba , Aleksandra Królicka , Michał Smolnicki , Grzegorz Lesiuk , Dariusz Rozumek , Roman Kuziak","doi":"10.1016/j.engfracmech.2025.111831","DOIUrl":"10.1016/j.engfracmech.2025.111831","url":null,"abstract":"<div><div>The present study investigates the fatigue crack growth behavior of ultra-fine bainitic steel under mixed-mode (I + II) loading conditions, relevant to the complex stress states occurring in railway track service. Experimental tests were performed using Compact Tension Shear (CTS) specimens loaded at angles of 30°, 45°, and 60°, enabling controlled combinations of tensile and shear stresses. The fatigue crack growth rate (FCGR) was analyzed and correlated with the equivalent stress intensity factor (ΔK<sub>e</sub>q) calculated according to Tanaka’s criterion. Complementary finite element method (FEM) simulations were employed to determine local fracture parameters, including K<sub>I</sub>, K<sub>II</sub>, T-stress, and J-integral values, and to model the evolution of crack paths. The experimental results demonstrated that with an increasing contribution of Mode II, the crack propagation angle (ψ<sub>0</sub>) increased, while the specimen lifetime showed a non-linear dependence on load angle. Fractographic analysis revealed a transition from predominantly transgranular fracture at lower angles toward a higher fraction of intergranular and quasi-cleavage fracture at higher angles. The proposed experimental–numerical approach provides a consistent framework for describing mixed-mode fatigue behavior and for constructing generalized FCGR diagrams. The results contribute to improving the predictive capability of fatigue life models for advanced bainitic steels applied in railway infrastructure.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"333 ","pages":"Article 111831"},"PeriodicalIF":5.3,"publicationDate":"2026-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145973552","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}
In this work, we employed a phase field fracture model for understanding the crack-interface interactions in the presence of material heterogeneities under dynamic loading. The crack-interface interaction is explored for the system with a sharp interface (zero thickness) as well as a regularized interface (finite thickness) having tan-hyperbolic regularization. The interface is regularized in order to capture the realistic condition across the interface. Within this framework, the length-scale parameters of the bulk material and the interface are not treated independently. Instead, they are expressed in terms of a tuning parameter called the diffusivity parameter , as a length-scale diffusivity ratio . This enables optimization of the length-scale, balancing accuracy and computational efficiency while maintaining the physical relevance. Moreover, the existing numerical complexity in capturing interface mechanics, the need for conforming interface, and homogenization methods are no longer required, making the implementation straightforward. Crack propagation, branching/penetration, and crack arrest are readily simulated, highlighting the capability of the model to reproduce the complex dynamic fracture mechanisms. The comparison with sharp interface results confirms the accuracy of predictions. The in-depth fracture studies are carried out by considering different fracture toughness ratios between the constituent materials, varying the nature, location of the interfaces, and the inclination of the interface as well. All these factors have found to play a vital role in governing the dynamic fracture characteristics.
{"title":"A regularized phase-field model for dynamic fracture in bi-material structures: Influence of interface and geometric characteristics","authors":"Krishnendu Sivadas , Amol Vuppuluri , Chandu Parimi , Raghu Piska , Hirshikesh","doi":"10.1016/j.engfracmech.2025.111832","DOIUrl":"10.1016/j.engfracmech.2025.111832","url":null,"abstract":"<div><div>In this work, we employed a phase field fracture model for understanding the crack-interface interactions in the presence of material heterogeneities under dynamic loading. The crack-interface interaction is explored for the system with a sharp interface (zero thickness) as well as a regularized interface (finite thickness) having tan-hyperbolic regularization. The interface is regularized in order to capture the realistic condition across the interface. Within this framework, the length-scale parameters of the bulk material <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mi>s</mi></mrow></msub></math></span> and the interface <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> are not treated independently. Instead, they are expressed in terms of a tuning parameter called the diffusivity parameter <span><math><mi>k</mi></math></span>, as a length-scale diffusivity ratio <span><math><mrow><msub><mrow><mi>ℓ</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>/</mo><mi>k</mi></mrow></math></span>. This enables optimization of the length-scale, balancing accuracy and computational efficiency while maintaining the physical relevance. Moreover, the existing numerical complexity in capturing interface mechanics, the need for conforming interface, and homogenization methods are no longer required, making the implementation straightforward. Crack propagation, branching/penetration, and crack arrest are readily simulated, highlighting the capability of the model to reproduce the complex dynamic fracture mechanisms. The comparison with sharp interface results confirms the accuracy of predictions. The in-depth fracture studies are carried out by considering different fracture toughness ratios between the constituent materials, varying the nature, location of the interfaces, and the inclination of the interface as well. All these factors have found to play a vital role in governing the dynamic fracture characteristics.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"333 ","pages":"Article 111832"},"PeriodicalIF":5.3,"publicationDate":"2026-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145922252","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 : 2026-01-02DOI: 10.1016/j.engfracmech.2025.111837
Bowen Lv , Dingjun Li , Jie Mao , Chunming Deng , Changguang Deng , Min Liu , Kesong Zhou
Strain-tolerant thermal barrier coatings achieve superior thermal shock resistance by incorporating ceramic top coats with vertically cracked, segmented or columnar structures. In hydrogen-fueled gas turbines, the elevated operating temperatures intensify the sintering process, rendering the interactions among multiple cracks in these complex architectures particularly pronounced but still insufficiently understood. In this work, mechanisms underlying multi-crack competition driven by differential sintering were investigated through a combined experimental–numerical approach. Experimental characterization under both uniform/nonuniform temperature fields was conducted to capture sintering-induced structural and mechanical evolution. Based on these findings, a temperature-dependent constitutive model was developed within a variational principle framework and implemented in finite element simulations for fracture analyses. The model predictions were validated by thermal shock and sintering experiments under various thermomechanical boundary conditions. The results show that enhanced interfacial strength and differential sintering promote branching crack propagation in different regions of the ceramic top coat. Although interfacial delamination remains the dominant fracture mode, this failure mechanism can be mitigated through controlled interfacial strengthening and sintering gradients. A three-dimensional fracture mechanism map is further proposed to elucidate the relationships among sintering behavior, crack competition, and fracture modes in strain-tolerant ceramic coatings.
{"title":"Multi-crack competition induced by differential sintering in strain-tolerant thermal barrier coatings","authors":"Bowen Lv , Dingjun Li , Jie Mao , Chunming Deng , Changguang Deng , Min Liu , Kesong Zhou","doi":"10.1016/j.engfracmech.2025.111837","DOIUrl":"10.1016/j.engfracmech.2025.111837","url":null,"abstract":"<div><div>Strain-tolerant thermal barrier coatings achieve superior thermal shock resistance by incorporating ceramic top coats with vertically cracked, segmented or columnar structures. In hydrogen-fueled gas turbines, the elevated operating temperatures intensify the sintering process, rendering the interactions among multiple cracks in these complex architectures particularly pronounced but still insufficiently understood. In this work, mechanisms underlying multi-crack competition driven by differential sintering were investigated through a combined experimental–numerical approach. Experimental characterization under both uniform/nonuniform temperature fields was conducted to capture sintering-induced structural and mechanical evolution. Based on these findings, a temperature-dependent constitutive model was developed within a variational principle framework and implemented in finite element simulations for fracture analyses. The model predictions were validated by thermal shock and sintering experiments under various thermomechanical boundary conditions. The results show that enhanced interfacial strength and differential sintering promote branching crack propagation in different regions of the ceramic top coat. Although interfacial delamination remains the dominant fracture mode, this failure mechanism can be mitigated through controlled interfacial strengthening and sintering gradients. A three-dimensional fracture mechanism map is further proposed to elucidate the relationships among sintering behavior, crack competition, and fracture modes in strain-tolerant ceramic coatings.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"333 ","pages":"Article 111837"},"PeriodicalIF":5.3,"publicationDate":"2026-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145922182","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 : 2026-01-02DOI: 10.1016/j.engfracmech.2025.111835
Mario D. Barahona, Laura Carreras, Cristina Barris
Modelling the cracking behaviour of reinforced concrete (RC) elements remains a major challenge due to the inherent heterogeneity of concrete and the complex interaction with steel reinforcement. Existing finite element (FE) approaches are restricted to simplified 2D representations, depend on predefined crack paths, or do not incorporate the material heterogeneity of RC in three dimensions. This study presents a 3D FE framework in Abaqus to model the cracking behaviour of RC tie elements, combining a phase field formulation with stochastic random fields (RF) to represent spatial variability in tensile strength and fracture toughness. Parametric studies demonstrate the influence of key modelling parameters, including the phase field length scale, solution scheme, and correlation length of the RF. The numerical results are validated against experimental data from RC tie tests in the literature, and demonstrate good agreement in the global load–displacement response and localised crack patterns. The study shows that the proposed approach is a robust predictive tool able to capture the uncertainty arising from local material heterogeneity, and can simulate diverse crack initiation and propagation scenarios in RC.
{"title":"Finite element modelling of cracking behaviour of reinforced concrete tensile members using a phase field approach","authors":"Mario D. Barahona, Laura Carreras, Cristina Barris","doi":"10.1016/j.engfracmech.2025.111835","DOIUrl":"10.1016/j.engfracmech.2025.111835","url":null,"abstract":"<div><div>Modelling the cracking behaviour of reinforced concrete (RC) elements remains a major challenge due to the inherent heterogeneity of concrete and the complex interaction with steel reinforcement. Existing finite element (FE) approaches are restricted to simplified 2D representations, depend on predefined crack paths, or do not incorporate the material heterogeneity of RC in three dimensions. This study presents a 3D FE framework in Abaqus to model the cracking behaviour of RC tie elements, combining a phase field formulation with stochastic random fields (RF) to represent spatial variability in tensile strength and fracture toughness. Parametric studies demonstrate the influence of key modelling parameters, including the phase field length scale, solution scheme, and correlation length of the RF. The numerical results are validated against experimental data from RC tie tests in the literature, and demonstrate good agreement in the global load–displacement response and localised crack patterns. The study shows that the proposed approach is a robust predictive tool able to capture the uncertainty arising from local material heterogeneity, and can simulate diverse crack initiation and propagation scenarios in RC.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"333 ","pages":"Article 111835"},"PeriodicalIF":5.3,"publicationDate":"2026-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145922253","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}
Flow forming is an advanced metal forming technique that allows the production of thin-walled, axisymmetric components with high dimensional accuracy and mechanical integrity. However, because preforms are subjected to complex stress states and intense plastic deformation during forming, geometric distortions and ductile fractures can occur, especially at high reduction ratios. This study provides a detailed analysis of widely used uncoupled ductile damage models for predicting fracture behavior during the flow forming of Inconel 718 alloy. Fifteen damage criteria, including both single- and multi-parameter damage models, are calibrated using tensile tests for four different geometries representing varying stress states. The models are implemented using a user-defined subroutine (VUSDFLD) in Abaqus/Explicit. The calibrated models are applied to both tensile tests and the flow forming process, with the results validated against experimental data. The findings indicate that the Ayada model provides more accurate damage predictions across all reduction ratios compared to other models, making it particularly suitable for the flow forming process. Furthermore, the influence of process parameters such as feed rate, revolution speed, feed ratio, and roller offset on formability and fracture initiation is investigated. The results underscore the crucial importance of selecting suitable process parameters and optimizing the forming process.
{"title":"Ductile fracture prediction for flow forming of Inconel 718 with experimental validation and finite element simulations","authors":"Hande Vural , Tevfik Ozan Fenercioğlu , Tuncay Yalçinkaya","doi":"10.1016/j.engfracmech.2025.111787","DOIUrl":"10.1016/j.engfracmech.2025.111787","url":null,"abstract":"<div><div>Flow forming is an advanced metal forming technique that allows the production of thin-walled, axisymmetric components with high dimensional accuracy and mechanical integrity. However, because preforms are subjected to complex stress states and intense plastic deformation during forming, geometric distortions and ductile fractures can occur, especially at high reduction ratios. This study provides a detailed analysis of widely used uncoupled ductile damage models for predicting fracture behavior during the flow forming of Inconel 718 alloy. Fifteen damage criteria, including both single- and multi-parameter damage models, are calibrated using tensile tests for four different geometries representing varying stress states. The models are implemented using a user-defined subroutine (VUSDFLD) in Abaqus/Explicit. The calibrated models are applied to both tensile tests and the flow forming process, with the results validated against experimental data. The findings indicate that the Ayada model provides more accurate damage predictions across all reduction ratios compared to other models, making it particularly suitable for the flow forming process. Furthermore, the influence of process parameters such as feed rate, revolution speed, feed ratio, and roller offset on formability and fracture initiation is investigated. The results underscore the crucial importance of selecting suitable process parameters and optimizing the forming process.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"333 ","pages":"Article 111787"},"PeriodicalIF":5.3,"publicationDate":"2026-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145881668","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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