Pub Date : 2025-12-31DOI: 10.1016/j.engfracmech.2025.111834
Tianchi Hui , Yu Tan , Zirong Guo , Xuejun Gao , Jianjun Zhao , Xiangyu Li
Magneto-electro-elastic (MEE) solids are renowned for their excellent coupling effect among electric, magnetic and elastic fields. Nevertheless, MEE solids are susceptible to failure owing to their weak fracture toughness and inherent brittleness. Fracture analyses of MEE materials are therefore of great academic importance. In this paper, a length scale insensitive phase-field fracture model for MEE materials is proposed. The corresponding analytical solutions, including the critical stress upon crack nucleation and global responses of the specimen, are derived for the first time in 1D cases. Analytical and numerical examples are carried out to verify the insensitivity of the length scale parameter and analyse the influences of the external magnetic and electric fields on the fracture behaviors of MEE solids. The fracture load may be increased under a negative magnetic or electric field, which provides strategies for enhancing the fracture resistance performance of MEE specimens. This work is of significance in assessing the reliability of MEE-based structures and devices.
{"title":"A phase-field fracture model for magneto-electro-elastic materials: Analytical and numerical results","authors":"Tianchi Hui , Yu Tan , Zirong Guo , Xuejun Gao , Jianjun Zhao , Xiangyu Li","doi":"10.1016/j.engfracmech.2025.111834","DOIUrl":"10.1016/j.engfracmech.2025.111834","url":null,"abstract":"<div><div>Magneto-electro-elastic (MEE) solids are renowned for their excellent coupling effect among electric, magnetic and elastic fields. Nevertheless, MEE solids are susceptible to failure owing to their weak fracture toughness and inherent brittleness. Fracture analyses of MEE materials are therefore of great academic importance. In this paper, a length scale insensitive phase-field fracture model for MEE materials is proposed. The corresponding analytical solutions, including the critical stress upon crack nucleation and global responses of the specimen, are derived for the first time in 1D cases. Analytical and numerical examples are carried out to verify the insensitivity of the length scale parameter and analyse the influences of the external magnetic and electric fields on the fracture behaviors of MEE solids. The fracture load may be increased under a negative magnetic or electric field, which provides strategies for enhancing the fracture resistance performance of MEE specimens. This work is of significance in assessing the reliability of MEE-based structures and devices.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"333 ","pages":"Article 111834"},"PeriodicalIF":5.3,"publicationDate":"2025-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145922263","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 : 2025-12-30DOI: 10.1016/j.engfracmech.2025.111820
Johannes Jonasson , Johan Lindström , Henrik Danielsson , Erik Serrano
The characterisation of wood’s fracture behaviour is a challenging task due to its inherently complex microstructure and natural variability. Consequently, to accurately model wood for engineering applications, deterministic input parameters are rarely sufficient in, for example, finite element models; the stochastic nature of the material must be considered. In the present work, we aim to quantify the variability in the fracture behaviour of two wood species: Norway spruce, which is commonly used for structural purposes in Europe, and birch, which could be an advantageous complement to Norway spruce, mainly thanks to its stiffer and stronger mechanical properties. The fracture behaviour is characterised through the three parameters that govern a material’s brittleness: the stiffness, the strength and the specific fracture energy. By formulating a parameter estimation problem based in probability theory, we use Bayesian optimisation to estimate statistical distributions of the fracture parameters of interest. These distributions are multi-variate distributions and thus contain information about the mean values, variability and dependence among the parameters. It is shown that by using random samples from the acquired distributions as input parameters to finite element models, variability observed in experimental testing is recovered well.
{"title":"Probabilistic parameter estimation and uncertainty quantification of mode I fracture in wood","authors":"Johannes Jonasson , Johan Lindström , Henrik Danielsson , Erik Serrano","doi":"10.1016/j.engfracmech.2025.111820","DOIUrl":"10.1016/j.engfracmech.2025.111820","url":null,"abstract":"<div><div>The characterisation of wood’s fracture behaviour is a challenging task due to its inherently complex microstructure and natural variability. Consequently, to accurately model wood for engineering applications, deterministic input parameters are rarely sufficient in, for example, finite element models; the stochastic nature of the material must be considered. In the present work, we aim to quantify the variability in the fracture behaviour of two wood species: Norway spruce, which is commonly used for structural purposes in Europe, and birch, which could be an advantageous complement to Norway spruce, mainly thanks to its stiffer and stronger mechanical properties. The fracture behaviour is characterised through the three parameters that govern a material’s brittleness: the stiffness, the strength and the specific fracture energy. By formulating a parameter estimation problem based in probability theory, we use Bayesian optimisation to estimate statistical distributions of the fracture parameters of interest. These distributions are multi-variate distributions and thus contain information about the mean values, variability and dependence among the parameters. It is shown that by using random samples from the acquired distributions as input parameters to finite element models, variability observed in experimental testing is recovered well.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"333 ","pages":"Article 111820"},"PeriodicalIF":5.3,"publicationDate":"2025-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145922250","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 : 2025-12-30DOI: 10.1016/j.engfracmech.2025.111830
Hong Zhao , Lei Peng , Guangcheng Long , Gang Ma , Wei Hou , Fan Wang
The mechanical responses of concrete are vital for the long-term stability of CRTS III slab track structure. This study employs laboratory tests and discrete element method (DEM) simulations to investigate the fracture behavior and crack propagation of steam-cured concrete (SC) and self-compacting concrete (SCC) used in CRTS III slab tracks. Results reveal that SC primarily fails due to aggregate penetration, while SCC is characterized by aggregate pullout. SC exhibits approximately 28% higher initial fracture toughness, about 30% greater unstable fracture toughness, and nearly 16% higher fracture energy than SCC, along with a modest 3% increase in ductility index. In contrast, SCC shows larger ultimate deformation, a more uniform crack-opening displacement distribution, and a slower evolution of the fracture process zone (FPZ), indicating better deformation capacity and crack dispersion. DEM simulations show that SC has a straighter crack propagation path, denser force-chain networks, and higher load-bearing capacity due to continuous stress transmission through the mortar matrix. Conversely, SCC demonstrates significant stress localization within aggregates, resulting in a more tortuous load-transfer path and a complex fracture process.
{"title":"Fracture behaviors of steam-cured concrete and self-compacting concrete under three-point bending:laboratory testing and DEM simulation","authors":"Hong Zhao , Lei Peng , Guangcheng Long , Gang Ma , Wei Hou , Fan Wang","doi":"10.1016/j.engfracmech.2025.111830","DOIUrl":"10.1016/j.engfracmech.2025.111830","url":null,"abstract":"<div><div>The mechanical responses of concrete are vital for the long-term stability of CRTS III slab track structure. This study employs laboratory tests and discrete element method (DEM) simulations to investigate the fracture behavior and crack propagation of steam-cured concrete (SC) and self-compacting concrete (SCC) used in CRTS III slab tracks. Results reveal that SC primarily fails due to aggregate penetration, while SCC is characterized by aggregate pullout. SC exhibits approximately 28% higher initial fracture toughness, about 30% greater unstable fracture toughness, and nearly 16% higher fracture energy than SCC, along with a modest 3% increase in ductility index. In contrast, SCC shows larger ultimate deformation, a more uniform crack-opening displacement distribution, and a slower evolution of the fracture process zone (FPZ), indicating better deformation capacity and crack dispersion. DEM simulations show that SC has a straighter crack propagation path, denser force-chain networks, and higher load-bearing capacity due to continuous stress transmission through the mortar matrix. Conversely, SCC demonstrates significant stress localization within aggregates, resulting in a more tortuous load-transfer path and a complex fracture process.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"333 ","pages":"Article 111830"},"PeriodicalIF":5.3,"publicationDate":"2025-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145881667","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 : 2025-12-29DOI: 10.1016/j.engfracmech.2025.111818
Peichen Chang , Yujun Xie , Lu Wang
The natural flaws in geotechnical, mining and civil engineering structures are primarily subjected to Mode II loading and confining pressure. Studying the fracture mechanisms of pre-cracked rock subjected to both Mode II loading and confining pressure holds great academic and practical significance. A double-ended cracked cylindrical specimen can be employed to generate a reliable quasi-Mode II singular stress field, as recommended by ISRM for determining the Mode II fracture toughness KIIC. Based on conservation law and elementary strength theory, a condition for iso-stress intensity factor (SIF) has been found for double-ended cracked cylinders subjected to punch-through shear (PTS) loading. The effective SIFs have been determined. Using the multiple-crack initiation model, the potential fracture behaviors, including notch tip coplanar growth, kinking, and branching, along with the corresponding fracture toughness KIIC, have been predicted for the PTS specimen. The notch effect on potential fracture behaviors has been investigated. The practical application of the present method has been demonstrated through the experimental investigation.
{"title":"A condition of iso-stress intensity factor and the potential fracture behaviors for double-ended cracked cylinder in punch-through shear test","authors":"Peichen Chang , Yujun Xie , Lu Wang","doi":"10.1016/j.engfracmech.2025.111818","DOIUrl":"10.1016/j.engfracmech.2025.111818","url":null,"abstract":"<div><div>The natural flaws in geotechnical, mining and civil engineering structures are primarily subjected to Mode II loading and confining pressure. Studying the fracture mechanisms of pre-cracked rock subjected to both Mode II loading and confining pressure holds great academic and practical significance. A double-ended cracked cylindrical specimen can be employed to generate a reliable quasi-Mode II singular stress field, as recommended by ISRM for determining the Mode II fracture toughness <em>K<sub>IIC</sub></em>. Based on conservation law and elementary strength theory, a condition for <em>iso</em>-stress intensity factor (SIF) has been found for double-ended cracked cylinders subjected to punch-through shear (PTS) loading. The effective SIFs have been determined. Using the multiple-crack initiation model, the potential fracture behaviors, including notch tip coplanar growth, kinking, and branching, along with the corresponding fracture toughness <em>K<sub>IIC</sub></em>, have been predicted for the PTS specimen. The notch effect on potential fracture behaviors has been investigated. The practical application of the present method has been demonstrated through the experimental investigation.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"333 ","pages":"Article 111818"},"PeriodicalIF":5.3,"publicationDate":"2025-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146034506","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 : 2025-12-27DOI: 10.1016/j.engfracmech.2025.111826
Yannan Lu , Yongjia Song , Deyou Yu , Wei Guan , Hengshan Hu
This paper analyzes the Mode-I stress intensity factor (SIF) of parallel cracks in a poroelastic medium. In particular, we investigate the influences of crack shielding on fluid flow which in turn can further change the frequency-dependent behaviors of SIF. Numerical results reveal that the frequency-dependent behaviors of SIF are jointly controlled by fluid flow and the shielding effect which is characterized by a spacing ratio , the ratio of crack spacing to crack length. The SIF of permeable cracks decreases with frequency, implying that in short-term responses the fluid has insufficient time to flow between cracks and surrounding micropores so that the crack deformation is inhibited. In the case of , the shielding effect is negligible so that our results reduce to that of a single crack for which the SIF decays the fastest when the wavelength of fluid diffusion roughly equals the crack length. For , the shielding effect can remarkably reduce the magnitude of the SIF over a broader frequency range and thereby enhance the effective material strength. In this case, the SIF decays the fastest at a higher characteristic frequency where the wavelength of fluid diffusion equals the crack spacing. For an intermediate value of , the characteristic frequency is influenced by both crack length and crack spacing. In contrast, the effect of fluid flow on the SIF of impermeable cracks is much weaker. Our findings show that both the crack shielding and permeability of crack surfaces strongly affect the magnitudes and frequency-dependent behaviors of the SIF.
{"title":"Effect of fluid flow on Mode-I dynamic stress intensity factor in the presence of crack shielding in a poroelastic medium","authors":"Yannan Lu , Yongjia Song , Deyou Yu , Wei Guan , Hengshan Hu","doi":"10.1016/j.engfracmech.2025.111826","DOIUrl":"10.1016/j.engfracmech.2025.111826","url":null,"abstract":"<div><div>This paper analyzes the Mode-I stress intensity factor (SIF) of parallel cracks in a poroelastic medium. In particular, we investigate the influences of crack shielding on fluid flow which in turn can further change the frequency-dependent behaviors of SIF. Numerical results reveal that the frequency-dependent behaviors of SIF are jointly controlled by fluid flow and the shielding effect which is characterized by a spacing ratio <span><math><mi>γ</mi></math></span>, the ratio of crack spacing to crack length. The SIF of permeable cracks decreases with frequency, implying that in short-term responses the fluid has insufficient time to flow between cracks and surrounding micropores so that the crack deformation is inhibited. In the case of <span><math><mrow><mi>γ</mi><mo>≥</mo><mn>10</mn></mrow></math></span>, the shielding effect is negligible so that our results reduce to that of a single crack for which the SIF decays the fastest when the wavelength of fluid diffusion roughly equals the crack length. For <span><math><mrow><mi>γ</mi><mo><</mo><mn>1</mn></mrow></math></span>, the shielding effect can remarkably reduce the magnitude of the SIF over a broader frequency range and thereby enhance the effective material strength. In this case, the SIF decays the fastest at a higher characteristic frequency where the wavelength of fluid diffusion equals the crack spacing. For an intermediate value of <span><math><mrow><mn>1</mn><mo><</mo><mi>γ</mi><mo><</mo><mn>10</mn></mrow></math></span>, the characteristic frequency is influenced by both crack length and crack spacing. In contrast, the effect of fluid flow on the SIF of impermeable cracks is much weaker. Our findings show that both the crack shielding and permeability of crack surfaces strongly affect the magnitudes and frequency-dependent behaviors of the SIF.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"333 ","pages":"Article 111826"},"PeriodicalIF":5.3,"publicationDate":"2025-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145882176","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 : 2025-12-26DOI: 10.1016/j.engfracmech.2025.111827
Dong Li, Yan Liu, Liu Jin, Xiuli Du
This study proposes an automated meso-scale numerical simulation method based on the extended self-consistent finite stress principle and the “static-dynamic unified” meso-fracture criterion, aiming to investigate the propagation behavior of concrete cracks either around or through aggregates under dynamic loads. This study mainly includes the following contributions. First, a strain rate-dependent elastic modulus subroutine is developed using Fortran, which overcomes the limitation of the Concrete Damaged Plasticity (CDP) model in characterizing the elastic modulus strengthening effect under dynamic uniaxial tension. Second, a dynamic propagation criterion for concrete cracks undergoing through-aggregate failure is established. Integrating meso-mechanical parameters and strain rate effects, this criterion can quantitatively predict whether cracks propagate through aggregates or along interfaces under dynamic loads. Further, two key improved technologies are proposed to enhance the authenticity of meso-scale simulations. One is defective aggregate modeling, i.e., presetting initial geometric defects at the aggregate-interfacial transition zone (ITZ) interface; the other is graded material property division, i.e., constructing a gradient transition layer of material properties in the mortar surrounding the ITZ to characterize the stress concentration caused by aggregate inclusions. Validation results in the single-aggregate model show that the ITZ crack length exhibits significant mesh sensitivity but is insensitive to strain rate. The constructed automated analysis framework can effectively simulate the dynamic propagation path of cracks around or through aggregates in single-aggregate systems, which is consistent with theoretical predictions. For multi-graded concrete, aggregate defects are located via image recognition technology, and the meso-scale dynamic propagation process of cracks around or through aggregates considering the stress interference effects between aggregates is successfully simulated. This study provides a theoretical framework and technical support for the multiscale predictive model of concrete dynamic fracture behavior.
{"title":"Meso-scale simulation method for dynamic propagation behavior of concrete cracks around or through aggregates","authors":"Dong Li, Yan Liu, Liu Jin, Xiuli Du","doi":"10.1016/j.engfracmech.2025.111827","DOIUrl":"10.1016/j.engfracmech.2025.111827","url":null,"abstract":"<div><div>This study proposes an automated <em>meso</em>-scale numerical simulation method based on the extended self-consistent finite stress principle and the “static-dynamic unified” <em>meso</em>-fracture criterion, aiming to investigate the propagation behavior of concrete cracks either around or through aggregates under dynamic loads. This study mainly includes the following contributions. First, a strain rate-dependent elastic modulus subroutine is developed using Fortran, which overcomes the limitation of the Concrete Damaged Plasticity (CDP) model in characterizing the elastic modulus strengthening effect under dynamic uniaxial tension. Second, a dynamic propagation criterion for concrete cracks undergoing through-aggregate failure is established. Integrating <em>meso</em>-mechanical parameters and strain rate effects, this criterion can quantitatively predict whether cracks propagate through aggregates or along interfaces under dynamic loads. Further, two key improved technologies are proposed to enhance the authenticity of <em>meso</em>-scale simulations. One is defective aggregate modeling, i.e., presetting initial geometric defects at the aggregate-interfacial transition zone (ITZ) interface; the other is graded material property division, i.e., constructing a gradient transition layer of material properties in the mortar surrounding the ITZ to characterize the stress concentration caused by aggregate inclusions. Validation results in the single-aggregate model show that the ITZ crack length exhibits significant mesh sensitivity but is insensitive to strain rate. The constructed automated analysis framework can effectively simulate the dynamic propagation path of cracks around or through aggregates in single-aggregate systems, which is consistent with theoretical predictions. For multi-graded concrete, aggregate defects are located via image recognition technology, and the <em>meso</em>-scale dynamic propagation process of cracks around or through aggregates considering the stress interference effects between aggregates is successfully simulated. This study provides a theoretical framework and technical support for the multiscale predictive model of concrete dynamic fracture behavior.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"333 ","pages":"Article 111827"},"PeriodicalIF":5.3,"publicationDate":"2025-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145882173","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 : 2025-12-26DOI: 10.1016/j.engfracmech.2025.111825
Z.Q. Chen , Y.H. Cheng , H. Wu
The conventional field reduced-scale test is a primary method for examining the blast resistance of concrete gravity dam against underwater explosion, while the inherent scaling effect prevents the extrapolation of reduced-scale test results to predict the dynamic behaviors of prototype dam. At present, a series of numerical simulations is carried out to clarify the underlying causes of scaling effect and establish a similarity relationship for concrete gravity dam against underwater explosion in the field test. Firstly, the critical influential factors of scaling effect were clarified based on the dimensional analysis, including the gravitational effect, strain rate effect and material size effect. The dimensionless horizontal displacement of dam was found to be dependent on the dimensionless damage number and gravitational characteristic number. Secondly, a finite element analysis approach incorporating the aforementioned influential factors was developed and comprehensively verified from both macroscopic and mesoscopic aspects. Subsequently, based on a 120 m-high prototype gravity dam, eight scenarios with the scaling factors ranging from 1/50 to 1 were designed and analyzed from the perspectives of both explosion loading and structural behaviors. Furthermore, the contributions of three influential factors to the scaling effect were examined. It indicates that the contribution of the strain rate effect is particularly significant in the small-scale model and sensitive to the intensity of blast wave, while the gravitational effect plays a dominant role in the large-scale model. Additionally, the influence of concrete size effect is comparable at different scales and relatively limited. Finally, the similarity relationships of horizontal dam displacement in the field test, involving the normalized displacement, displacement increase factor and the dimensionless displacement, were established, which address the limitations imposed by the scaling effect on the extrapolation of displacement data acquired from the reduced-scale test and provide a valuable reference for evaluating the blast resistance of prototype dam.
{"title":"Scaling effect of concrete gravity dam subjected to underwater explosion in the field test","authors":"Z.Q. Chen , Y.H. Cheng , H. Wu","doi":"10.1016/j.engfracmech.2025.111825","DOIUrl":"10.1016/j.engfracmech.2025.111825","url":null,"abstract":"<div><div>The conventional field reduced-scale test is a primary method for examining the blast resistance of concrete gravity dam against underwater explosion, while the inherent scaling effect prevents the extrapolation of reduced-scale test results to predict the dynamic behaviors of prototype dam. At present, a series of numerical simulations is carried out to clarify the underlying causes of scaling effect and establish a similarity relationship for concrete gravity dam against underwater explosion in the field test. Firstly, the critical influential factors of scaling effect were clarified based on the dimensional analysis, including the gravitational effect, strain rate effect and material size effect. The dimensionless horizontal displacement of dam was found to be dependent on the dimensionless damage number and gravitational characteristic number. Secondly, a finite element analysis approach incorporating the aforementioned influential factors was developed and comprehensively verified from both macroscopic and mesoscopic aspects. Subsequently, based on a 120 m-high prototype gravity dam, eight scenarios with the scaling factors ranging from 1/50 to 1 were designed and analyzed from the perspectives of both explosion loading and structural behaviors. Furthermore, the contributions of three influential factors to the scaling effect were examined. It indicates that the contribution of the strain rate effect is particularly significant in the small-scale model and sensitive to the intensity of blast wave, while the gravitational effect plays a dominant role in the large-scale model. Additionally, the influence of concrete size effect is comparable at different scales and relatively limited. Finally, the similarity relationships of horizontal dam displacement in the field test, involving the normalized displacement, displacement increase factor and the dimensionless displacement, were established, which address the limitations imposed by the scaling effect on the extrapolation of displacement data acquired from the reduced-scale test and provide a valuable reference for evaluating the blast resistance of prototype dam.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"333 ","pages":"Article 111825"},"PeriodicalIF":5.3,"publicationDate":"2025-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145882178","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}
The continuous trend towards miniaturization in electronic devices has stimulated the development of a new generation of printed circuit boards (PCBs) with embedded components. Throughout their lifespan, PCBs are subjected to thermal loads generated by heat from active components or the surrounding environment. In particular, mismatches in thermal expansion coefficients between materials are a leading cause of thermal stresses, often resulting in layer delamination, either between insulating substrates or at the copper-substrate interface. Traditionally, the peel test has been the dominant method for evaluating interfacial energy within PCBs, offering an estimate of the interface energy based on the IPC standard. During peeling, the copper layer often undergoes significant plastic deformation, complicating the precise determination of the fracture energy. Thus, achieving an accurate assessment of the mechanical response at the interface remains a challenging task. To overcome these limitations, we have designed a new specimen and adapted the Double Cantilever Beam (DCB) and End Notched Flexure (ENF) tests to the PCB context where layer thickness is significantly constrained (with copper layers ranging from 17 to ). Prior to experimentation, simulations demonstrate that, unlike the peel test, the DCB and ENF configurations exhibit minimal plastic dissipation. One of the main outcomes of the work is that a precise description of the plastic behavior of copper is not necessary to determine accurate estimations of the critical strain energy release rates in mode I and mode II. Furthermore, a notable advantage of these methods is their ability to maintain a controlled fracture mode, whereas the peel test inherently involves a mixed-mode (I and II) fracture process. The synergy between finite element analysis and experimental testing provides critical insights about the framework of application of the methods.
{"title":"Towards a new methodology to characterize the fracture energies of the woven composite/copper interface in mode I and mode II: Application to printed circuit boards","authors":"Charaf-Eddine Ziouani , Gautier Girard , Sébastien Mercier , François Lechleiter","doi":"10.1016/j.engfracmech.2025.111819","DOIUrl":"10.1016/j.engfracmech.2025.111819","url":null,"abstract":"<div><div>The continuous trend towards miniaturization in electronic devices has stimulated the development of a new generation of printed circuit boards (PCBs) with embedded components. Throughout their lifespan, PCBs are subjected to thermal loads generated by heat from active components or the surrounding environment. In particular, mismatches in thermal expansion coefficients between materials are a leading cause of thermal stresses, often resulting in layer delamination, either between insulating substrates or at the copper-substrate interface. Traditionally, the peel test has been the dominant method for evaluating interfacial energy within PCBs, offering an estimate of the interface energy based on the IPC standard. During peeling, the copper layer often undergoes significant plastic deformation, complicating the precise determination of the fracture energy. Thus, achieving an accurate assessment of the mechanical response at the interface remains a challenging task. To overcome these limitations, we have designed a new specimen and adapted the Double Cantilever Beam (DCB) and End Notched Flexure (ENF) tests to the PCB context where layer thickness is significantly constrained (with copper layers ranging from 17 to <span><math><mrow><mn>70</mn><mspace></mspace><mi>μ</mi><mi>m</mi></mrow></math></span>). Prior to experimentation, simulations demonstrate that, unlike the peel test, the DCB and ENF configurations exhibit minimal plastic dissipation. One of the main outcomes of the work is that a precise description of the plastic behavior of copper is not necessary to determine accurate estimations of the critical strain energy release rates in mode I and mode II. Furthermore, a notable advantage of these methods is their ability to maintain a controlled fracture mode, whereas the peel test inherently involves a mixed-mode (I and II) fracture process. The synergy between finite element analysis and experimental testing provides critical insights about the framework of application of the methods.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"333 ","pages":"Article 111819"},"PeriodicalIF":5.3,"publicationDate":"2025-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145882174","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 : 2025-12-26DOI: 10.1016/j.engfracmech.2025.111828
Kun Zheng , Linjian Ma , Wen Hua
Fracture toughness remains a significant research topic in solid fracture mechanics, representing the material resistance to crack propagation. The shear fracture often occurs in rock masses, especially for mines, slopes, and faults. To determine the rock shear (or true mode-II) fracture toughness, this paper develops a new fracture test method based on the Mohr-Coulomb criterion. The new method comprises a double-edge notched rectangular column (DNRC) specimen, which is substantiated by the experimental data obtained from various mode-II test methods. The designed DNRC specimens exhibit a self-planar crack propagation pattern, which conforms to the shear fracture definition. The average shear fracture toughness KIIc of DNRC sandstone specimens is 2.81 MPa•m0.5, and the average tensile fracture toughness KIc of ENDB (edge-notched disk bend) sandstone specimens is 1.03 MPa•m0.5. The ratio of KIIc to KIc is 2.73, which is consistent with published experimental results obtained from the established mode-II test methods. The Mohr-Coulomb criterion provides theoretical explanations for the newly designed DNRC specimen, and the current and previous experimental results further validate its effectiveness and reliability. This paper aims to develop a test method which can realize both mode II loading and true mode II fracturing, thereby exploring the shear fracture behaviors of brittle and quasi-brittle materials.
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Pub Date : 2025-12-26DOI: 10.1016/j.engfracmech.2025.111824
Junwei Chen , Zhi Zhao
Rock masses in engineering often experience anisotropic stress fields. To ensure the long-term integrity of rock masses, it is crucial to establish accurate three-dimensional strength criteria for analyzing and predicting the deformation and displacement of surrounding rocks. This paper extends the classical mixed-mode fracture criterion to cracks under compressive stress by incorporating the effects of friction on crack surfaces, thereby establishing a three-dimensional strength criterion. The study focuses on stress-induced initiation and subsequent propagation of pre-existing penny-shaped cracks, which form a fan-shaped damage zone. To avoid explicit modeling of the complex physics mechanism of crack propagation, this damage zone is correlated with acoustic emission experiments, bridging micro- and macro-scale strength behavior of rock samples and ultimately proposing a novel 3D strength criterion for hard rocks. The results indicate that the proposed strength criterion reliably predicts triaxial strength across a range of rock types, with strong agreement with experimental data. Furthermore, when the intermediate principal stress equals the minimum principal stress, this criterion naturally reduces to the classical Hoek-Brown strength criterion. Therefore, the proposed criterion is robust for analyzing and predicting rock strength under three-dimensional stress conditions.
{"title":"A fracture mechanics-based three‑dimensional strength criterion for hard rocks","authors":"Junwei Chen , Zhi Zhao","doi":"10.1016/j.engfracmech.2025.111824","DOIUrl":"10.1016/j.engfracmech.2025.111824","url":null,"abstract":"<div><div>Rock masses in engineering often experience anisotropic stress fields. To ensure the long-term integrity of rock masses, it is crucial to establish accurate three-dimensional strength criteria for analyzing and predicting the deformation and displacement of surrounding rocks. This paper extends the classical mixed-mode fracture criterion to cracks under compressive stress by incorporating the effects of friction on crack surfaces, thereby establishing a three-dimensional strength criterion. The study focuses on stress-induced initiation and subsequent propagation of pre-existing penny-shaped cracks, which form a fan-shaped damage zone. To avoid explicit modeling of the complex physics mechanism of crack propagation, this damage zone is correlated with acoustic emission experiments, bridging micro- and macro-scale strength behavior of rock samples and ultimately proposing a novel 3D strength criterion for hard rocks. The results indicate that the proposed strength criterion reliably predicts triaxial strength across a range of rock types, with strong agreement with experimental data. Furthermore, when the intermediate principal stress equals the minimum principal stress, this criterion naturally reduces to the classical Hoek-Brown strength criterion. Therefore, the proposed criterion is robust for analyzing and predicting rock strength under three-dimensional stress conditions.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"333 ","pages":"Article 111824"},"PeriodicalIF":5.3,"publicationDate":"2025-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145838691","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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