Jiawei Li, Ni Ao, Yanan Hu, Xu Zhang, Qianhua Kan, Guozheng Kang
{"title":"Phase-field coupled crystal plasticity modeling of fatigue fracture in pearlitic microstructures","authors":"Jiawei Li, Ni Ao, Yanan Hu, Xu Zhang, Qianhua Kan, Guozheng Kang","doi":"10.1007/s10704-026-00937-8","DOIUrl":"10.1007/s10704-026-00937-8","url":null,"abstract":"<div><p>Pearlitic carbon steel, a primary material widely employed in railway engineering, frequently undergoes cyclic loading in service. Nevertheless, the intricate microstructure of pearlite complicates the understanding of its influence on fatigue crack initiation and propagation in such steels. To address this, the present study employs a modeling framework that integrates a fracture phase-field approach with a crystal plasticity model to examine the microstructure-sensitive fracture response of pearlite. Within this framework, the crystal plasticity model captures the deformation behavior of ferrite, whereas the deformation of cementite is represented by an isotropic plasticity formula. The fracture behavior of pearlite is analyzed by a fracture phase field model considering the influence of fatigue damage. Utilizing this coupled methodology, simulations are conducted to evaluate the effects of ferrite orientation, cementite lamellar angle, and interlamellar spacing on the fatigue fracture characteristics of pearlite. The findings indicate that ferrite orientation alters the distribution of cumulative plastic slip, thereby influencing both fatigue crack initiation and propagation. The lamellar angle markedly governs the accumulation rate of plastic slip, which in turn affects crack initiation. Variations in lamellar spacing are shown to significantly alter the fatigue crack propagation path in pearlite. This study advances the mechanistic understanding of fracture in pearlitic microstructures and provides insights for the design of pearlitic materials with enhanced fatigue resistance.</p></div>","PeriodicalId":590,"journal":{"name":"International Journal of Fracture","volume":"250 4","pages":""},"PeriodicalIF":2.8,"publicationDate":"2026-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148838010","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":"Cracks of narrow shapes: compliance and resistance contributions","authors":"Y. Pronina, A. Markov, M. Kachanov","doi":"10.1007/s10704-026-00936-9","DOIUrl":"10.1007/s10704-026-00936-9","url":null,"abstract":"<div><p>The work addresses quantitative characterization of cracks of certain class of “irregular” (non-elliptical) geometries. This responds to needs of applications where cracks typically have non-circular shapes. The present work focuses specifically on 3D flat cracks of narrow shapes in isotropic materials. Their contributions to the effective elastic properties are analyzed; the cross-property connection implies similar results for the effective conductive properties. A method of estimation of compliance contributions of cracks of narrow shapes is based on treating a crack as a set of 2D plane strain cross-sections. It is shown that the plane strain approximation is quite accurate for sufficiently elongated cracks, as tested on rectangular, elliptical, and curved shapes. For shorter shapes, the stiffening effect of the crack ends becomes noticeable and this effect is estimated; its incorporation into the plane strain framework provides an almost perfect accuracy. In particular, explicit expressions are given for the compliance contributions of the rectangular and annular crack geometries.</p></div>","PeriodicalId":590,"journal":{"name":"International Journal of Fracture","volume":"250 4","pages":""},"PeriodicalIF":2.8,"publicationDate":"2026-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148837420","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":"Systematic analysis of damage irreversibility enforcement in phase-field fracture models","authors":"Andrea Vigliotti, Ferdinando Auricchio","doi":"10.1007/s10704-026-00940-z","DOIUrl":"10.1007/s10704-026-00940-z","url":null,"abstract":"<div><p>Phase-field fracture models require the enforcement of damage irreversibility to prevent unphysical healing. Among the available approaches, history-field methods are widely used because of their simplicity and computational efficiency, although their relation to the original constrained variational problem depends on the specific phase-field formulation adopted. The present work examines this issue through a combined analytical and numerical study, with particular attention to the differences between threshold-based AT1 models and the smoother AT2 formulation. A one-dimensional analysis is used to clarify the origin of the discrepancy between history-field enforcement and variationally consistent constrained solutions, showing that, in AT1, the history-based treatment acts in a manner analogous to the local truncation of inadmissible damage updates and may therefore alter the regularity and spatial extent of the damage profile. In contrast, the same effect is much less pronounced in AT2, where damage evolves continuously from the undamaged state. These observations are then quantified in a series of numerical examples, including uniaxial tensile tests, compact-tension specimens, and heterogeneous composite representative volume elements under multiaxial loading. The results show that history-field approaches give results very similar to those of variationally consistent constrained enforcement for the AT2 model in the cases examined here, whereas in AT1 they may overestimate strength and alter the spatial distribution of damage. The paper is therefore intended as a systematic analysis of irreversibility enforcement in phase-field fracture, aimed at clarifying when history-field approximations remain acceptable and when a direct constrained treatment becomes more appropriate.</p></div>","PeriodicalId":590,"journal":{"name":"International Journal of Fracture","volume":"250 4","pages":""},"PeriodicalIF":2.8,"publicationDate":"2026-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148837421","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}
Kalyan Boyina, Anna Mariya Shajan, Raghu Piska, Raj Kiran, Raj Das
{"title":"Adaptive anisotropic phase field modeling of dynamic fracture in polycrystalline materials","authors":"Kalyan Boyina, Anna Mariya Shajan, Raghu Piska, Raj Kiran, Raj Das","doi":"10.1007/s10704-026-00938-7","DOIUrl":"10.1007/s10704-026-00938-7","url":null,"abstract":"<div><p>This study investigates the dynamic fracture behavior of crystalline materials using an anisotropic fracture resistance phase field framework. The phase field fracture model is reformulated to account for crystallographic anisotropy by introducing a structural tensor that governs the crack evolution along preferential cleavage planes and grain boundaries. The formulation enables a unified treatment of intergranular and transgranular fracture mechanisms within a continuum setting. The resulting coupled system of momentum balance and phase field evolution equations is solved using a finite element formulation with a staggered solution strategy. To improve computational efficiency in dynamic simulations, quadtree-based adaptive mesh refinement is integrated with polygonal finite elements, enabling localized resolution of evolving cracks while maintaining a reduced computational cost. Dynamic analysis of bicrystalline and polycrystalline configurations with varying orientations of preferential crack planes is performed. The predicted crack paths and energy dissipation characteristics are compared with the existing literature, demonstrating a good agreement. The influence of anisotropic parameters on crack path trajectories, elastic and fracture energies is also examined.</p></div>","PeriodicalId":590,"journal":{"name":"International Journal of Fracture","volume":"250 4","pages":""},"PeriodicalIF":2.8,"publicationDate":"2026-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148837422","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":"Molecular dynamics simulations of the fracture of goldene","authors":"Minh-Quy Le","doi":"10.1007/s10704-026-00941-y","DOIUrl":"10.1007/s10704-026-00941-y","url":null,"abstract":"<div><p>The present work investigates some aspects of the fracture of goldene through molecular dynamics simulations with bond order potentials at room temperature. Two central crack models are proposed, including initial cracks along and perpendicular to the bond direction. It is found that cracks prefer to propagate along the bond direction due to lower surface energy, compared to the direction perpendicular to the bond direction. Fracture stress associated with the initial crack length and crack-tip displacement field are used to study the mode-I stress intensity factor of goldene. These two methods provide very similar results, which are compared with available data for other two-dimensional materials.</p></div>","PeriodicalId":590,"journal":{"name":"International Journal of Fracture","volume":"250 4","pages":""},"PeriodicalIF":2.8,"publicationDate":"2026-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148783355","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":"Characterization of tensile and torsional fatigue behaviors of additively manufactured super duplex stainless steel SAF 2507","authors":"Maxime Piras, Anis Hor, Eric Charkaluk","doi":"10.1007/s10704-026-00935-w","DOIUrl":"10.1007/s10704-026-00935-w","url":null,"abstract":"<div><p>Super duplex stainless steels (SDSSs) are well known for their good mechanical properties and corrosion resistance inherited from the dual-phase microstructure with equivalent proportion of ferrite and austenite. The development of additive manufacturing has given rise to the use of more diversified material than usual metallic alloys such as SDSSs. Nevertheless, this material is fully ferritic in the as-built state from laser powder bed fusion process. Despite this phase ratio difference with conventional processes, literature has demonstrated that the monotonic tensile properties are higher than wrought material, and with an equivalent corrosion behavior. Given these observations, it is interesting to determine the influence of process parameters on the fatigue behavior of single phase SDSS. Hence, two batches of dense specimens were built with two different set of process parameters. The respective defect populations and microstructures were characterized by means of X-ray computed tomography, electron backscattered diffraction, X-ray diffraction, and transmission electron microscopy. Based on these features, the monotonic tensile behavior, and fully-reversed tension and torsion fatigue properties of the specimens obtained with the two batches are analyzed. Defects of equivalent size between the two batches were obtained but the difference in defect density resulted in crack initiation scatter. With defect size, in the range of the grain size, tension and torsion fatigue behavior were not similarly affected. Tension fatigue behavior and strength were different depending on crack initiation phenomena: surface defect or grain. However, behavior in torsion loading is not affected by the change of crack initiation phenomena.</p></div>","PeriodicalId":590,"journal":{"name":"International Journal of Fracture","volume":"250 4","pages":""},"PeriodicalIF":2.8,"publicationDate":"2026-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10704-026-00935-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148752408","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Sharlotte L. B. Kramer, Thomas A. Ivanoff, Edmundo Corona, Yuhao Li, Cuneyt Sakonder, Marcelo Paredes, Ahmed Mostafa, Md. Mustafa Kamal, Shashank Agarwal, Brett Davis, Behnam Ahmadikia, John P. Mersch, Paul R. Miles, David A. Najera-Flores, Robert J. Kuether, Joseph E. Bishop, Kyle N. Karlson, Adam C. Sokolow
{"title":"Sandia mechanics challenge 2023","authors":"Sharlotte L. B. Kramer, Thomas A. Ivanoff, Edmundo Corona, Yuhao Li, Cuneyt Sakonder, Marcelo Paredes, Ahmed Mostafa, Md. Mustafa Kamal, Shashank Agarwal, Brett Davis, Behnam Ahmadikia, John P. Mersch, Paul R. Miles, David A. Najera-Flores, Robert J. Kuether, Joseph E. Bishop, Kyle N. Karlson, Adam C. Sokolow","doi":"10.1007/s10704-026-00932-z","DOIUrl":"10.1007/s10704-026-00932-z","url":null,"abstract":"<div><p>The Sandia Mechanics Challenge (SMC) provides the solid-mechanics community a forum for assessing its ability to predict mechanical behavior in structures and materials through a blind, round-robin format. Computationalists are asked to predict the behavior of an unfamiliar geometry given experimental calibration data; their predictions are compared to experimental measurements of the SMC scenario, and then the participants assess and compare their approaches, documenting their findings. The SMC broadens the scope of Sandia-hosted benchmarking problems, which previously focused on ductile failure through the Sandia Fracture Challenges, enabling an enduring, community-wide self-assessment of predictive capabilities for various mechanics topics. The topic of the SMC2023 is threaded fastener joints, specifically the deformation and failure of a structure with a threaded fastener joint in a drop scenario. These analyses required modeling of several phenomena, including multi-axial joint mechanics, material deformation and failure at intermediate strain rates, and contact mechanics. The experiments of the Challenge geometry revealed two competing failure mechanisms as the drop velocity increased: material failure of a flanged cantilever and fastener failure. While all teams were able to predict aspects of the fastener failure, certain modeling choices obscured the material failure of the flanged cantilever, in some cases completely. Incorporation of shear behavior of the fasteners, not just the tensile behavior typically considered, improved the predictions of fastener behavior. This SMC called attention to these diverse and challenging analyses, rallying the solid-mechanics community to identify and address potential shortcomings.\u0000</p></div>","PeriodicalId":590,"journal":{"name":"International Journal of Fracture","volume":"250 4","pages":""},"PeriodicalIF":2.8,"publicationDate":"2026-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148752362","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":"Crack propagation analysis using a hybrid 2D finite element–peridynamics framework with a residual-based quasi-static solver","authors":"Laxman Khanal, Mijia Yang","doi":"10.1007/s10704-026-00933-y","DOIUrl":"10.1007/s10704-026-00933-y","url":null,"abstract":"<div><p>This paper presents a hybrid finite element–peridynamics (FE–PD) framework for two-dimensional fracture simulation. The framework embeds a peridynamic fracture zone within surrounding finite element domains through a modified volume-based (VL) coupling scheme, enabling accurate representation of crack initiation and propagation while retaining the computational efficiency of finite element analysis in the elastic far field. A major contribution of this work is the development of a residual-based dynamic relaxation solver (RBDR) for quasi-static analyses of hybrid FE–PD coupled systems. Unlike adaptive dynamic relaxation (ADR) methods, which rely on artificial damping and fictitious mass to suppress oscillations, the proposed solver is entirely damping-free and achieves equilibrium by directly minimizing the residual force field through a Richardson-type pseudo-time iteration. The solver is matrix-free, reaches higher accuracy, and 23 times faster in wall-clock time than the standard Adaptive Dynamic Relaxation method. The framework is validated against the classical Kirsch stress concentration problem, where the ABAQUS FE model recovers the analytical SCF of 3.0 and the hybrid FE–PD model reproduces the correct quantitative distribution, except at the hole surface. The hybrid method with both RBDR and ADR is then applied to crack propagation problems under Mode I tensile loading, reproducing the crack morphology and global kinetic energy evolution of a reference PD-only model with high accuracy. For the crack propagation case under quasi-static loading at four times the dynamic load level solved through the hybrid method with RBDR, crack branching does not occur, consistent with classical fracture mechanics theory that inertia is the driven factor for dynamic instability.</p></div>","PeriodicalId":590,"journal":{"name":"International Journal of Fracture","volume":"250 3","pages":""},"PeriodicalIF":2.8,"publicationDate":"2026-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13354626/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148417675","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Mesh variational r-adaptivity for sharp modeling of brittle fracture","authors":"Gatien Dony, Nicolas Moës, Jean-François Remacle","doi":"10.1007/s10704-026-00934-x","DOIUrl":"10.1007/s10704-026-00934-x","url":null,"abstract":"<div><h3>\u0000 <b>Purpose:</b>\u0000 </h3><p>Brittle fracture modeling is framed as a coupled evolution of spatial and material configurations. The displacement field between these configurations drives the fracture process, and the crack path alters the geometry. This interplay has been expressed in the variational formalism of Francfort and Marigo. However, numerical models based on this formalism generally introduce a regularization to circumvent the need for geometry modification. Here, we propose to combine explicit sharp crack modeling with a variational formalism.</p><h3>\u0000 <b>Methods:</b>\u0000 </h3><p>Both mesh and displacement field are tuned to minimize the functional. Consequently, the crack path appears naturally. In this work, we first present the minimization of the fracture functional in a <i>r</i>-adaptive scheme and the advantage it presents. Afterwards, we present a staggered optimization procedure to construct the spatial and material configurations of a body undergoing brittle fracture.</p><h3>\u0000 <b>Results:</b>\u0000 </h3><p>Afterwards, the method is demonstrated through several numerical examples. Namely, we recover theoretical behavior for a manufactured solution and present the crack path of single edge notch specimen.</p><h3>\u0000 <b>Conclusion:</b>\u0000 </h3><p>This method is a direct implementation of the variational formalism of fracture mechanics. Therefore, it provides a straightforward way to compute the energy release rate and crack path. Moreover, it does not require any regularization and the crack is directly represented in the geometry of the specimen. However, it is computationally expensive as the mesh needs to be optimized at each step of the loading.</p></div>","PeriodicalId":590,"journal":{"name":"International Journal of Fracture","volume":"250 3","pages":""},"PeriodicalIF":2.8,"publicationDate":"2026-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148323236","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":"Exploring the application of rigid triangular blocks in simulating the mechanics of masonry composites via DEM","authors":"Rhea Wilson, Jose V. Lemos, Bora Pulatsu","doi":"10.1007/s10704-026-00931-0","DOIUrl":"10.1007/s10704-026-00931-0","url":null,"abstract":"<div><p>Understanding the behaviour of masonry under various loading conditions is crucial for the structural design, assessment, and preservation of masonry structures. High-fidelity computational modelling offers a powerful method for investigating the complex mechanical interactions within masonry composites, complementing and reducing the need for extensive experimental programs. To this end, this research presents a numerical framework using the discrete element method (DEM), a discontinuum-based approach, to simulate the compressive behaviour of masonry prisms. The modelling approach represents masonry (i.e., brick units and cement mortar) as rigid, irregular triangular blocks, enabling explicit simulation of cracking and damage evolution. Building on previous developments, this study provides an in-depth examination of the advantages and limitations of the proposed framework. Particular attention is given to the influence of geometrical parameters such as block size and regularity and the stochastic variations associated with the block generation process. The findings indicate that incorporating block irregularity is crucial for achieving realistic compressive responses, while variations in block size have only a minor impact on the predicted capacity within the examined range. The study also demonstrates that the stochastic nature of the tessellation process leads to some variability in predicted strength, underscoring the value of analyzing multiple realizations to obtain representative trends. Overall, the framework provides reliable predictions of behaviour and fracture patterns, supporting its use in the assessment of masonry composites under compressive loading.</p></div>","PeriodicalId":590,"journal":{"name":"International Journal of Fracture","volume":"250 3","pages":""},"PeriodicalIF":2.8,"publicationDate":"2026-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148281484","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}