{"title":"Efficient SPH-PD FSI model for blast-induced crack initiation and propagation in rocks","authors":"Jin-lu Ba, Jun-xiang Wang, Xin-chen Liu, Gang Sun, Hai-yue Yu, Jie-ru Tian","doi":"10.1007/s10704-026-00927-w","DOIUrl":"10.1007/s10704-026-00927-w","url":null,"abstract":"<div><p>In tunnel blasting engineering, drilling and blasting method remains a widely adopted and efficient technique for excavating hard rock masses. Precise control of blast-induced dynamic responses is crucial for both project safety and construction efficiency. Smoothed particle hydrodynamics (SPH) and peridynamics (PD) are widely used to simulate fluid-structure interactions (FSI). This study proposes an SPH-PD FSI model to investigate gas-rock interactions under blast loading. An index-acceleration algorithm is proposed to optimize computational efficiency during the preprocessing stage. The proposed model offers advantages in algorithmic simplicity, computational efficiency, and adaptability to significant particle spacing differences. The model was validated through representative cases. The displacement trend line (DTL) analysis and the quantitative relative displacement method were applied to elucidate the blast-induced crack initiation and propagation mechanisms. Numerical results reveal the influence of prefabricated crack angles on cracking patterns. This study offers theoretical insights into the damage evolution of rocks with prefabricated cracks under blast loading, advancing understanding of crack propagation mechanisms.</p></div>","PeriodicalId":590,"journal":{"name":"International Journal of Fracture","volume":"250 2","pages":""},"PeriodicalIF":2.5,"publicationDate":"2026-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147829832","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pierrick François, Tom Petit, Quentin Auzoux, David Le Boulch, Jacques Besson
{"title":"Experimentally-based model for delayed hydride cracking (DHC): hydrogen diffusion, hydride nucleation, growth, dissolution and crack propagation","authors":"Pierrick François, Tom Petit, Quentin Auzoux, David Le Boulch, Jacques Besson","doi":"10.1007/s10704-026-00920-3","DOIUrl":"10.1007/s10704-026-00920-3","url":null,"abstract":"<div><p>Delayed Hydride Cracking (DHC) is a hydrogen embrittlement phenomenon that may affect Zircaloy-4 fuel claddings. An experimental procedure was previously developed to measure the fracture toughness of this material using notched C-ring specimens with a precrack, for both in presence of DHC (<span>(K_{I_text {DHC}})</span>) and without (<span>(K_{I_text {C}})</span>) (François et al. 2024). Based on these experiments, and on additional experimental results on notched C-ring specimens without a precrack, a finite element model was developed to numerically reproduce the DHC phenomenon. This model couples the mechanical behavior of the material with the presence of hydrogen in solid solution and hydrides, considering the kinetics of hydrogen diffusion, and the nucleation, growth and dissolution of hydrides (HNGD model). A cohesive zone model was used for crack propagation. The numerical model successfully reproduces the experimental results and is consistent with the experimental values of <span>(K_{I_text {DHC}})</span>, crack propagation rate and incubation time at 150, and 200 <span>( ^{circ }hbox {C},)</span> for precracked specimens and 250 <span>( ^{circ }hbox {C},)</span> for both precracked and notched specimens. In addition, this study highlights the great influence of the swelling induced by the presence of hydrogen in solid solution and precipitated hydrides on the fracture of the material in case of DHC, and the importance to take it into account to model this phenomenon.</p></div>","PeriodicalId":590,"journal":{"name":"International Journal of Fracture","volume":"250 2","pages":""},"PeriodicalIF":2.5,"publicationDate":"2026-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147830038","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Fatigue life prediction of 4130 alloy based on Kriging method","authors":"Wang Weijin, Miao Xinlin, Tan Wei","doi":"10.1007/s10704-026-00921-2","DOIUrl":"10.1007/s10704-026-00921-2","url":null,"abstract":"<div><p>Microcracks are prevalent defects in mechanical structures, and their propagation behavior under cyclic loading dominates structural integrity and service life. Conventional numerical methods for three-dimensional fatigue crack growth analysis suffer from high computational complexity and poor convergence, limiting their engineering applicability. To address this challenge, this study proposes a Kriging-based surrogate model for high-efficiency prediction of microcrack propagation behavior, validated by the consistency between experimental fatigue data and finite element analysis (FEA) results. A five-dimensional feature space is constructed to map the nonlinear relationship among fatigue parameters, stress ratio, residual stress, load amplitude, and crack growth rate, enabling direct mathematical characterization of crack evolution. Numerical verification shows that the model achieves a prediction error of less than 5% compared with high-fidelity FEA results, while reducing the time cost of a single fatigue life assessment by three orders of magnitude. Meanwhile, the model circumvents the complex remeshing and convergence control procedures required by traditional FEA methods. This work provides a highly efficient and accurate tool for fatigue life evaluation of engineering structures, which is of great significance for improving the reliability of damage tolerance design.</p></div>","PeriodicalId":590,"journal":{"name":"International Journal of Fracture","volume":"250 2","pages":""},"PeriodicalIF":2.5,"publicationDate":"2026-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147829141","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Intersonic crack propagation in fiber-reinforced composites with an improved peridynamic model","authors":"Yenan Wang, Florin Bobaru","doi":"10.1007/s10704-026-00908-z","DOIUrl":"10.1007/s10704-026-00908-z","url":null,"abstract":"<div><p>We introduce an improved peridynamic (PD) model for dynamic fracture in fiber reinforced composites (FRCs). We verify it on elastodynamic and elastostatic problems and test it against the intersonic crack propagation experiment by Coker and Rosakis (2001). When a notched unidirectional FRC lamina is loaded by asymmetric impact, cracks can reach intersonic speeds of propagation. Using the PD model we explain the mechanism of crack initiation and propagation. We predict experimentally observed crack patterns, the crack propagation speed behavior, and the shockwaves generated by the propagating crack. When the PD horizon size is of a similar scale with the actual notch size used in the experiments, the match between computed and experimental results becomes quantitative. This is related to the crack nucleation process and is strength driven. The new PD composite model is calibrated with a homogenized classical model but maintains the sharp distinction between longitudinal and transverse bonds (jump discontinuity in their elastic stiffness), preserving this microstructure information (anisotropy) of the composite. We show that PD models for FRCs in which the micro-scale variation of PD bonds moduli mimics the continuous tension surface of homogenized composite cannot capture the observed failure behavior. Preservation of some essential features pertaining to failure initiation/behavior from the micro-scale, which the present PD model does, appears to be critical in predicting dynamic failure in FRCs using homogenized models.</p></div>","PeriodicalId":590,"journal":{"name":"International Journal of Fracture","volume":"250 2","pages":""},"PeriodicalIF":2.5,"publicationDate":"2026-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147829140","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Alma Brambilla, Laura De Lorenzis, Lorenza Petrini
{"title":"Variational phase-field modeling of fracture and fatigue in shape memory alloys: a one-dimensional study","authors":"Alma Brambilla, Laura De Lorenzis, Lorenza Petrini","doi":"10.1007/s10704-026-00925-y","DOIUrl":"10.1007/s10704-026-00925-y","url":null,"abstract":"<div><p>We propose a novel variational phase-field model for fracture and fatigue in pseudoelastic shape memory alloys (SMAs). The model, developed in a one-dimensional setting, builds upon the Auricchio–Petrini constitutive formulation for SMAs and couples damage evolution with phase transformation. We study analytically and numerically the homogeneous and localization responses of a bar under both monotonic and cyclic loading, and we investigate various macroscopic behaviors by tuning the constitutive parameters. A key feature of the model is the introduction of a transformation strain limit, beyond which the material is fully martensitic and behaves elastically. This leads to a distinctive behavior in which the region of localized damage widens, yielding a delay of fracture. The capability of the model to predict the fatigue performance is assessed by simulating the uniaxial response of Ni-Ti multi-wire samples under different loading conditions. The results show that the model discriminates between safe and critical loading scenarios, capturing the experimental trend of increased fatigue resistance with higher mean strain at a fixed strain amplitude. Ongoing efforts are aimed at further evaluating its reliability for quantitative fatigue life prediction.</p></div>","PeriodicalId":590,"journal":{"name":"International Journal of Fracture","volume":"250 2","pages":""},"PeriodicalIF":2.5,"publicationDate":"2026-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147829541","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A review on fracture of hydrogel coatings","authors":"Junjie Liu, Yuhong Li, Shaoxing Qu","doi":"10.1007/s10704-026-00923-0","DOIUrl":"10.1007/s10704-026-00923-0","url":null,"abstract":"<div><p>Hydrogel coatings integrate the high water content and softness of hydrogels with engineered surface functionalities, enabling diverse applications in soft robotics, stretchable electronics, and biomedical devices. However, their high water content and softness, thin-film geometry, and substrate confinement make them susceptible to delamination, cracking, fatigue, and wear, which compromise long-term reliability. This review summarizes the current understanding of fracture in hydrogel coatings. We first overview the experimental methods commonly used to characterize adhesion toughness, adhesion fatigue threshold, and adhesion strength. We then discuss fracture phenomena that are particularly relevant to coating geometries, including thickness-dependent adhesion, swelling- or stimulus-induced debonding, sliding-induced wear, and fatigue fracture under cyclic loading. Finally, we review emerging toughening and fatigue-resistant strategies for robust hydrogel coatings, including double-network designs, hierarchical architectures, nanocrystalline domains, and phase-separated structures. We conclude by outlining key challenges and opportunities for translating laboratory concepts into durable hydrogel coatings for practical applications.</p></div>","PeriodicalId":590,"journal":{"name":"International Journal of Fracture","volume":"250 2","pages":""},"PeriodicalIF":2.5,"publicationDate":"2026-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147738336","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Vasiliy Mishakin, Alexander Gonchar, Vyacheslav Klyushnikov, Konstantin Kurashkin, Alexander Solovyov
{"title":"Investigation of microdamage and failure of metastable austenitic steel AISI 321 by changes in elastic moduli and content of strain-induced martensite","authors":"Vasiliy Mishakin, Alexander Gonchar, Vyacheslav Klyushnikov, Konstantin Kurashkin, Alexander Solovyov","doi":"10.1007/s10704-026-00924-z","DOIUrl":"10.1007/s10704-026-00924-z","url":null,"abstract":"<div><p>This paper proposes a method for calculating microdamage in metastable austenitic steel based on changes in elastic moduli associated with the formation of micropores, microcracks, and an increase in the volume fraction of strain-induced martensite under fatigue. The crack shape factor for low- and high-cycle fatigue is calculated using a micromechanical model of the relationship between microdamage and Young’s modulus. Three stages of elastic moduli change, corresponding to the rate of strain-induced martensitic transformation, are identified. It is shown that the change in the rate of elastic moduli can be used to identify the transition from the low-cycle to the high-cycle region. It was found that the relationship between microdamage and cycle ratio can be described by power-law dependence similar to the expression in the nonlinear Marco–Starkey damage accumulation model, which makes it possible to predict fatigue failure.</p></div>","PeriodicalId":590,"journal":{"name":"International Journal of Fracture","volume":"250 2","pages":""},"PeriodicalIF":2.5,"publicationDate":"2026-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147737361","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Wei He, Quan Zhang, Jiaqiang Li, Xing Sun, Bin Kuang, Bo Liu, Qihong Fang, Huimin Xie, Yanhuai Ding, Shijie Liu, Xin Li
{"title":"Investigation of hydrogen-accelerated fatigue crack growth in laser repaired GH4169 superalloy using BSL 3D DIC","authors":"Wei He, Quan Zhang, Jiaqiang Li, Xing Sun, Bin Kuang, Bo Liu, Qihong Fang, Huimin Xie, Yanhuai Ding, Shijie Liu, Xin Li","doi":"10.1007/s10704-026-00922-1","DOIUrl":"10.1007/s10704-026-00922-1","url":null,"abstract":"<div><p>Laser Repair (LR) via Directed Energy Deposition (DED) is a key additive manufacturing technology for high-value applications. However, LR introduces microstructural heterogeneity and interfaces that complicate fatigue assessment, especially in hydrogen-rich environments which exacerbate fatigue damage. This study employs the crack tip localization method and Crack Opening Rate (COR) parameter via BSL 3D DIC to investigate hydrogen-accelerated fatigue crack propagation in laser-repaired (LR) GH4169 superalloy. The fatigue lives and crack closure levels of pure substrate (PS), pure deposited (PD), and LR specimens were compared. Hydrogen charging significantly accelerated crack growth, reducing fatigue life by 23%, 9.6%, and 29.2% in PS, LR, and PD specimens, respectively. Electron Backscatter Diffraction (EBSD) analysis shows hydrogen charging induces distinct cracking behaviors: the LR specimen exhibits crack deflection from the repair zone into the substrate via the heat-affected zone, while the PD specimen shifts from transgranular to intergranular fracture, exhibiting brittle characteristics with minimal plasticity.</p></div>","PeriodicalId":590,"journal":{"name":"International Journal of Fracture","volume":"250 2","pages":""},"PeriodicalIF":2.5,"publicationDate":"2026-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147737360","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Exact fundamental solutions for a Mode-I external circular crack in an infinite one-dimensional hexagonal piezoelectric quasicrystal","authors":"Jiaqi Zhang, Guozheng Kang, Xiangyu Li","doi":"10.1007/s10704-026-00914-1","DOIUrl":"10.1007/s10704-026-00914-1","url":null,"abstract":"<div><p>The unconventional behavior of quasiperiodic structures has become a focal point in condensed matter physics. This paper is devoted to the study of the Mode-I external circular crack lying in a one-dimensional hexagonal piezoelectric quasicrystal. The original problem is transformed into a mixed boundary value problem, which is solved by the generalized potential theory method. The exact full-field fundamental solutions of the problem are obtained in terms of elementary functions. For both electrically impermeable and permeable boundary conditions, important parameters in fracture mechanics are obtained in response to generalized concentrated loads and annular uniformly distributed loads. From the generalized stress intensity factors, a phonon/phason-electric coupling parameter is proposed to quantify the multiphysical interactions. The influence of the phonon-phason-electric coupling effect on the generalized crack surface displacement is characterized. The present study provides a basis for fracture behaviors of piezoelectric quasicrystals.</p></div>","PeriodicalId":590,"journal":{"name":"International Journal of Fracture","volume":"250 2","pages":""},"PeriodicalIF":2.5,"publicationDate":"2026-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147642743","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"An analytical evaluation of T-stress influence in the process zone modelling for the interface crack kinking","authors":"A. A. Kaminsky, M. V. Dudyk, Y. O. Chornoivan","doi":"10.1007/s10704-026-00916-z","DOIUrl":"10.1007/s10704-026-00916-z","url":null,"abstract":"<div><p>This study presents an analysis of the influence of <i>T</i>-stresses on the stress field near the tip of an interfacial crack under plane strain conditions, specifically examining the initial stage of crack kinking from the interface. The analysis focuses on the formation of a small-scale process zone within the less crack-resistant elastic material of a bimaterial joint. The process zone is modeled as a discontinuity line of normal displacement, where the normal stress is assumed to be equal to the failure stress of the respective material. <i>T</i>-stresses are incorporated into the model by including their contribution to the asymptotic stress field near the crack tip. This asymptotic field is subsequently used to formulate the condition at infinity for the corresponding boundary value problem within the theory of elasticity. The parameters of the process zone (its length and angle of inclination) are calculated by solving the boundary value problem using the Wiener-Hopf method. From the derived solution, an equation is obtained for calculating the length and angle of inclination of the process zone. This calculation is based on the criterion of maximum potential energy accumulated within the zone. Furthermore, the energy release rate and crack opening displacement are also determined, providing essential metrics for formulating crack initiation conditions based on energy or deformation criteria. A numerical analysis was conducted to investigate the dependence of the zone’s parameters on the applied load and to specifically study the effect of <i>T</i>-stresses on its orientation. Finally, a comparative analysis of the model’s predictions for the kinking angles was performed against values reported in existing theoretical and experimental literature.</p></div>","PeriodicalId":590,"journal":{"name":"International Journal of Fracture","volume":"250 2","pages":""},"PeriodicalIF":2.5,"publicationDate":"2026-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147642685","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}