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}
Pub Date : 2026-01-01DOI: 10.1016/j.engfracmech.2025.111838
Yaohui Deng , Peisheng Liu , Zhao Zhang , Jiajie Jin , Feiyu Qiang
A unified energy-based framework is developed to predict fatigue life and interpret damage evolution in viscoplastic joints under combined thermal cycling and broadband random vibration. The methodology integrates the Anand constitutive model for nonlinear time-dependent deformation, Darveaux’s strain energy density method for low-cycle thermal fatigue, and a Basquin-type strain life relation for vibration-induced high-cycle fatigue. Using strain energy density as a physically grounded surrogate for the fracture driving force, we propose a coupling law with an explicit interaction term that links thermal and vibrational damage channels. We further derive an analytical lifetime bound showing that the coupled lifetime is upper-bounded by the harmonic mean of the single-mode lives. Dimensionless similarity groups are introduced to generalize the predictions across materials and geometries and to support rapid design screening. Finite-element case studies on micro-interconnects demonstrate nonlinear degradation under coupled loading. The predicted hot-spot locations qualitatively follow experimentally reported corner-joint and upper-interface initiation trends. The proposed framework provides quantitative life estimation, spatial localization of fracture-prone regions without explicit crack tracking, and mechanism-informed design guidance for layered structures containing viscoplastic interfaces in thermo-vibrational environments.
{"title":"Energy-based coupling law and lifetime bounds for nonlinear fatigue of viscoplastic joints under thermo-vibrational loading","authors":"Yaohui Deng , Peisheng Liu , Zhao Zhang , Jiajie Jin , Feiyu Qiang","doi":"10.1016/j.engfracmech.2025.111838","DOIUrl":"10.1016/j.engfracmech.2025.111838","url":null,"abstract":"<div><div>A unified energy-based framework is developed to predict fatigue life and interpret damage evolution in viscoplastic joints under combined thermal cycling and broadband random vibration. The methodology integrates the Anand constitutive model for nonlinear time-dependent deformation, Darveaux’s strain energy density method for low-cycle thermal fatigue, and a Basquin-type strain life relation for vibration-induced high-cycle fatigue. Using strain energy density as a physically grounded surrogate for the fracture driving force, we propose a coupling law with an explicit interaction term that links thermal and vibrational damage channels. We further derive an analytical lifetime bound showing that the coupled lifetime is upper-bounded by the harmonic mean of the single-mode lives. Dimensionless similarity groups are introduced to generalize the predictions across materials and geometries and to support rapid design screening. Finite-element case studies on micro-interconnects demonstrate nonlinear degradation under coupled loading. The predicted hot-spot locations qualitatively follow experimentally reported corner-joint and upper-interface initiation trends. The proposed framework provides quantitative life estimation, spatial localization of fracture-prone regions without explicit crack tracking, and mechanism-informed design guidance for layered structures containing viscoplastic interfaces in thermo-vibrational environments.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"333 ","pages":"Article 111838"},"PeriodicalIF":5.3,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145881613","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-31DOI: 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":"2025-12-31","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 : 2025-12-31DOI: 10.1016/j.engfracmech.2025.111836
Tong Cui, Xiaofang Zhang, Yanan Yuan
The variable wing requires a flexible skin composite that combines high strength, high toughness, and flexibility. Inspired by the layered arrangements found in biological structures such as fish scales, a novel gradient overlapped structural design strategy based on the span direction using thin ply has been proposed. Under three-point bending tests, experimental results demonstrate that the gradient overlapped laminates with thin ply can effectively mitigates the inherent brittle fracture of continuous fiber composite. Compared to continuous fiber designs, the bio-inspired overlapped design exhibits superior structural performance in terms of flexibility and damage tolerance. Particularly, the four-gradient overlap structure achieves an excellent balance between strength and toughness by integrating the advantages of continuous and short overlap configurations. Finite element simulations further reveal the significant advantages of “S-C type” special joints designs in enhancing the comprehensive mechanical performance of composites. The optimized special joint configurations demonstrate exceptional superiority in terms of toughness and flexibility. This study provides new insights and methodologies for the structural design of composite laminates, offering important guidance for engineering applications such as aircraft skin structures that require a balance between high strength and high toughness.
{"title":"Design strategy of overlapped composite joint integrating strength, flexibility and toughness","authors":"Tong Cui, Xiaofang Zhang, Yanan Yuan","doi":"10.1016/j.engfracmech.2025.111836","DOIUrl":"10.1016/j.engfracmech.2025.111836","url":null,"abstract":"<div><div>The variable wing requires a flexible skin composite that combines high strength, high toughness, and flexibility. Inspired by the layered arrangements found in biological structures such as fish scales, a novel gradient overlapped structural design strategy based on the span direction using thin ply has been proposed. Under three-point bending tests, experimental results demonstrate that the gradient overlapped laminates with thin ply can effectively mitigates the inherent brittle fracture of continuous fiber composite. Compared to continuous fiber designs, the bio-inspired overlapped design exhibits superior structural performance in terms of flexibility and damage tolerance. Particularly, the four-gradient overlap structure achieves an excellent balance between strength and toughness by integrating the advantages of continuous and short overlap configurations. Finite element simulations further reveal the significant advantages of “S-C type” special joints designs in enhancing the comprehensive mechanical performance of composites. The optimized special joint configurations demonstrate exceptional superiority in terms of toughness and flexibility. This study provides new insights and methodologies for the structural design of composite laminates, offering important guidance for engineering applications such as aircraft skin structures that require a balance between high strength and high toughness.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"333 ","pages":"Article 111836"},"PeriodicalIF":5.3,"publicationDate":"2025-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145882175","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-31DOI: 10.1016/j.engfracmech.2025.111821
Zhen Yue , Chi Zhan , Hanming Yang , Yifang Qin , Ningge Fan , Shunhua Chen
Fiber-reinforced thermoplastic laminated composites are highly sensitive to low-velocity impacts, which induces barely visible damage and accelerates fatigue failure under cyclic loading, thereby reducing structural service life. Conventional approaches for predicting post-impact fatigue behavior rely heavily on experimental testing and numerical simulations, which are often time-consuming and costly. Moreover, existing machine learning studies pay limited attention to the effects of initial impact-induced damage. To address these limitations, this study combines experimental and machine learning-based approaches for accurate fatigue life prediction of laminated composites after low-velocity impacts. Low-velocity impact tests are performed on composite specimens, and their impact responses are recorded. The induced damage is characterized using non-destructive techniques. The impacted specimens are then subjected to tensile–tensile fatigue tests to determine residual fatigue life and construct the corresponding S–N curves. The experimental results show that higher energy impacts significantly reduce the fatigue life of laminated composites. To improve model robustness, a fatigue knowledge-based data augmentation strategy via S–N curves is presented to expand the fatigue life dataset. Multiple machine learning algorithms, including Support Vector Machines (SVM), Random Forests (RF), Back-Propagation Neural Networks (BPNN), and Bayesian Neural Networks (BNNs), are introduced, trained, and optimized through hyperparameter tuning. The predictive results indicate that all employed models estimate post-impact fatigue life with reasonable accuracy, with BPNN and BNNs achieving the best overall performance.
{"title":"Experimental study and machine learning-based fatigue life prediction of thermoplastic laminated composites after low-velocity impact","authors":"Zhen Yue , Chi Zhan , Hanming Yang , Yifang Qin , Ningge Fan , Shunhua Chen","doi":"10.1016/j.engfracmech.2025.111821","DOIUrl":"10.1016/j.engfracmech.2025.111821","url":null,"abstract":"<div><div>Fiber-reinforced thermoplastic laminated composites are highly sensitive to low-velocity impacts, which induces barely visible damage and accelerates fatigue failure under cyclic loading, thereby reducing structural service life. Conventional approaches for predicting post-impact fatigue behavior rely heavily on experimental testing and numerical simulations, which are often time-consuming and costly. Moreover, existing machine learning studies pay limited attention to the effects of initial impact-induced damage. To address these limitations, this study combines experimental and machine learning-based approaches for accurate fatigue life prediction of laminated composites after low-velocity impacts. Low-velocity impact tests are performed on composite specimens, and their impact responses are recorded. The induced damage is characterized using non-destructive techniques. The impacted specimens are then subjected to tensile–tensile fatigue tests to determine residual fatigue life and construct the corresponding S–N curves. The experimental results show that higher energy impacts significantly reduce the fatigue life of laminated composites. To improve model robustness, a fatigue knowledge-based data augmentation strategy via S–N curves is presented to expand the fatigue life dataset. Multiple machine learning algorithms, including Support Vector Machines (SVM), Random Forests (RF), Back-Propagation Neural Networks (BPNN), and Bayesian Neural Networks (BNNs), are introduced, trained, and optimized through hyperparameter tuning. The predictive results indicate that all employed models estimate post-impact fatigue life with reasonable accuracy, with BPNN and BNNs achieving the best overall performance.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"333 ","pages":"Article 111821"},"PeriodicalIF":5.3,"publicationDate":"2025-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145881615","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-31DOI: 10.1016/j.engfracmech.2025.111829
Zhongpan Li , Yan Li , Boumediene Nedjar , Ling Tao , Huijian Chen , Zhiqiang Feng
This paper presents a semi-explicit algorithm for modeling dynamic damage and fracture in ductile materials under finite deformation. The algorithm combines the efficiency of explicit methods with the stability of implicit schemes, enabling robust simulations in large deformation and contact scenarios. To further enhance numerical stability, a rotational stress update scheme based on Kirchhoff stress is implemented, which effectively handles rigid-body rotations and mitigates artificial stress artifacts. Frictional contact is addressed using an implicit algorithm based on the bi-potential method, ensuring stable and efficient contact resolution. The damage model is formulated within the continuum damage mechanics (CDM) framework, following the damage evolution theory of Chaboche and Lemaitre. Material nonlinearity is captured using an isotropic von Mises yield criterion. The proposed method is implemented in the plastic finite element program CCMPF and verified through a series of numerical examples. Two quasi-static simulations are first conducted to evaluate the mesh sensitivity of the local damage model and to verify the accuracy of the constitutive integration scheme. A dynamic Taylor impact, including both 2D and 3D cases, is performed to validate the algorithm under high strain-rate conditions. The results demonstrate the method’s accuracy, efficiency, and robustness in simulating dynamic failure in ductile materials.
{"title":"Dynamic damage evolution and fracture initiation in finite deformation ductile materials","authors":"Zhongpan Li , Yan Li , Boumediene Nedjar , Ling Tao , Huijian Chen , Zhiqiang Feng","doi":"10.1016/j.engfracmech.2025.111829","DOIUrl":"10.1016/j.engfracmech.2025.111829","url":null,"abstract":"<div><div>This paper presents a semi-explicit algorithm for modeling dynamic damage and fracture in ductile materials under finite deformation. The algorithm combines the efficiency of explicit methods with the stability of implicit schemes, enabling robust simulations in large deformation and contact scenarios. To further enhance numerical stability, a rotational stress update scheme based on Kirchhoff stress is implemented, which effectively handles rigid-body rotations and mitigates artificial stress artifacts. Frictional contact is addressed using an implicit algorithm based on the bi-potential method, ensuring stable and efficient contact resolution. The damage model is formulated within the continuum damage mechanics (CDM) framework, following the damage evolution theory of Chaboche and Lemaitre. Material nonlinearity is captured using an isotropic von Mises yield criterion. The proposed method is implemented in the plastic finite element program CCMPF and verified through a series of numerical examples. Two quasi-static simulations are first conducted to evaluate the mesh sensitivity of the local damage model and to verify the accuracy of the constitutive integration scheme. A dynamic Taylor impact, including both 2D and 3D cases, is performed to validate the algorithm under high strain-rate conditions. The results demonstrate the method’s accuracy, efficiency, and robustness in simulating dynamic failure in ductile materials.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"333 ","pages":"Article 111829"},"PeriodicalIF":5.3,"publicationDate":"2025-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145922262","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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