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Articoli di riviste sul tema "Ductile fracture simulations"

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Liu, HS, and MW Fu. "Prediction and analysis of ductile fracture in sheet metal forming—Part I: A modified Ayada criterion." International Journal of Damage Mechanics 23, no. 8 (2014): 1189–210. http://dx.doi.org/10.1177/1056789514541559.

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A modified ductile fracture criterion is proposed based on the traditional Ayada criterion and coded into the finite element simulation platform of VUMAT/ABAQUS for prediction and analysis of ductile fracture in metal plastic strain processes. In this modified ductile fracture criterion, stress triaxiality is taken into account, and more importantly, the exponential effect of the equivalent plastic strain on the damage behavior, which is generally ignored in other ductile fracture criteria, is also considered. The material related constants in the modified ductile fracture criterion are determ
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Azizi, Muhammad Azim, Mohd Faiz Mohd Ridhuan, Mohd Zakiyuddin Mohd Zahari, Sharafiz Abdul Rahim, and Muhammad Amin Azman. "Peridynamic Model for Tensile Elongation and Fracture Simulations of Polymethyl Methacrylate Notched Specimens." Applied Mechanics and Materials 909 (September 28, 2022): 11–28. http://dx.doi.org/10.4028/p-2z0841.

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This paper presents the peridynamic (PD) numerical model for simulating a tensile test until total fracture for a brittle polymeric material namely polymethyl methacrylate (PMMA). U-notched and V-notched specimens were used to investigate the effect of the notches on the elongation and fracture of PMMA. The tensile elongation of PMMA exhibits nonlinearity with respect to the applied load, while the fracture occurs when the material stress has reached the ultimate tensile stress of the material. Similar elongation and fracture properties were applied on PD simulations. Two types of elongation e
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Dzioba, Ihor, and Sebastian Lipiec. "Fracture Mechanisms of S355 Steel—Experimental Research, FEM Simulation and SEM Observation." Materials 12, no. 23 (2019): 3959. http://dx.doi.org/10.3390/ma12233959.

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In this study, the fracture mechanisms of S355 ferritic steel were analyzed. In order to obtain different mechanisms of fracture (completely brittle, mixed brittle and ductile or completely ductile), tests were carried out over a temperature range of −120 to +20 °C. Our experimental research was supplemented with scanning electron microscopy (SEM) observations of the specimens’ fracture surfaces. Modeling and load simulations of specimens were performed using the finite element method (FEM) in the ABAQUS program, and accurate calibration of the true stress–strain material dependence was made.
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Banabic, Dorel, and Abdolvahed Kami. "Applications of the Gurson’s model in sheet metal forming." MATEC Web of Conferences 190 (2018): 01002. http://dx.doi.org/10.1051/matecconf/201819001002.

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Recent advances in the modelling of metals encompass modelling of metals structural inhomogeneity, damage, porosity, twinning/untwining and non-local and second order effects. This presentation is focused on modelling the void growth in ductile fractures. The growth and coalescence of microscopic voids are the main mechanisms in ductile fracture of bulk metallic parts. In sheet metals, ductile fracture is preceded by necking during which existing voids do not have significant growth. However, necking is highly sensitive to plastic flow direction which in turn is sensitive to the presence of vo
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Watanabe, Atsuo, Kunio Hayakawa, and Shinichiro Fujikawa. "An Anisotropic Damage Model for Prediction of Ductile Fracture during Cold-Forging." Metals 12, no. 11 (2022): 1823. http://dx.doi.org/10.3390/met12111823.

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Researchers have formulated equations of ductile fracture to simulate and predict defects in cold-forged parts, e.g., the Cockcroft–Latham criterion. However, these equations are not applicable to certain cases of fracture in forged products. This study formulates a new equation for predicting ductile fractures with better prediction accuracy than the convention by which the cost for trial-and-error design can be reduced. The equation is expressed as a second-rank symmetric tensor, which is the inner product of the stress and strain-increment tensors. The theoretical efficacy of the equation i
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Tong, Ying. "The Evaluation of Ductile Fracture Criteria (DFC) of 6061-T6 Aluminum Alloy." Applied Mechanics and Materials 44-47 (December 2010): 2837–41. http://dx.doi.org/10.4028/www.scientific.net/amm.44-47.2837.

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As one of the principal failures, ductile fracturing restricts metal forming process. Cockcroft-Latham fracture criterion is suited for tenacity fracture in bulk metal-forming simulation. An innovative approach involving physical compression experiments, numerical simulations and mathematic computations provides mutual support to evaluate ductile damage cumulating process and ductile fracture criteria (DFC). The results show that the maximum cumulated damage decreases with strain rate rising, and the incremental ratios, that is damage sensitive rate, vary uniformly during the upsetting process
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Matsuno, Takashi, Jin Eguchi, Yasuhiro Kunii, et al. "Derivation of Point Plot-based Ductile Fracture Loci through Assimilation of Finite Element Simulation and Individual Actual Punched Surface Profile." MATEC Web of Conferences 408 (2025): 02001. https://doi.org/10.1051/matecconf/202540802001.

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This study demonstrated the inverse identification of the ductile fracture locus (DFL), successfully reproducing the actual punched surface profiles of DP980 steels. The primary aim was to visualize the plastic strain and residual stress distribution in the observed punching surface cross-section. First, cracks were incorporated into finite element (FE) half-punching simulations, on the basis of preliminary observations of the actual crack propagation behavior, to replicate individual punched surface profiles. Notably, ductile fracture modeling was not employed during the initial FE simulation
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Simkins, D. C., and S. Li. "Meshfree simulations of thermo-mechanical ductile fracture." Computational Mechanics 38, no. 3 (2005): 235–49. http://dx.doi.org/10.1007/s00466-005-0744-8.

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Sun, Dong Zhi, Michael Krawiec, and Hariaokto Hooputra. "Characterization and Modelling of the Damage Behavior of Extruded Aluminum Profiles for Crash Simulations." Materials Science Forum 877 (November 2016): 674–79. http://dx.doi.org/10.4028/www.scientific.net/msf.877.674.

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The damage behavior of aluminum profiles depends strongly on the stress state. Many investigations have shown that both ductile and shear fracture have to be taken into account in damage analysis. Since fracture strains of aluminum profiles are relatively low, damage modelling has to be included in component simulations. However, it is an open question, which kind of damage model can be used for crash simulations and which tests should be performed in order to calibrate the model. An extruded aluminum profile with double chambers of AA6060-T79 was characterized under different stress triaxiali
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Meng, Xianbo, Zixi Jiao, Haiyan Zhu, et al. "Study of the Brittle–Ductile Characteristics and Fracture Propagation Laws of Ultra-Deep Tight Sandy Conglomerate Reservoirs." Processes 13, no. 6 (2025): 1880. https://doi.org/10.3390/pr13061880.

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Ultra-deep tight sandy conglomerate reservoirs in the Junggar Basin are characterized by vertically alternating lithologies that include mudstone, sandy conglomerate, and sandstone. High in situ stresses and formation temperatures contribute to a brittle–ductile transition process in the reservoir rocks. However, the brittle behavior and ductile hydraulic fracture propagation mechanisms under in situ conditions remain inadequately understood. In this study, ultra-deep core samples were subjected to triaxial compression tests under varying confining pressures and temperatures to simulate differ
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Tesi sul tema "Ductile fracture simulations"

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Xenos, Sokratis. "Porous materials : constitutive modeling and computational issues." Electronic Thesis or Diss., Institut polytechnique de Paris, 2024. http://www.theses.fr/2024IPPAX040.

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Ce travail porte sur le développement, la calibration et l'implémentation numérique d'un nouveau modèle élastoplastique entièrement explicite, isotrope et indépendant du taux de déformation pour les matériaux métalliques poreux. La microstructure est supposée être constituée d'une distribution aléatoire de vides sphéroïdaux de même forme, orientés de manière aléatoire et avec une probabilité uniforme. Le modèle proposé est basé sur des estimations d'homogénéisation antérieures qui utilisent une théorie de comparaison composite linéaire (LCC). Pour évaluer l'exactitude du modèle analytique, nou
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Davaze, Valentin. "Modélisation numérique de l'amorçage et la propagation des fissures dans les tôles métalliques ductiles pour les simulations de crash." Thesis, Paris Sciences et Lettres (ComUE), 2019. http://www.theses.fr/2019PSLEM060.

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Lors d’un crash automobile, les pièces faites de tôles métalliques sont sujettes à rupture. La rupture des matériauxductiles n’est actuellement pas prédite de manière fiable dans un contexte industriel, entraînant des coûts et délaissupplémentaires sur la conception. Cette problématique est alors abordée dans cette thèse CIFRE du Groupe PSAmenée en collaboration avec l’Onera et le Centre des Matériaux. L’objectif de ces travaux est de développer et d’implanterune stratégie numérique fiable de prédiction de fissure par la méthode des Éléments Finis (EF) dans les calculs de crashautomobile. Une
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Ren, Sicong. "Mesures de champs et simulations par élément finis de l'interaction entre vieillissement dynamique et endommagement dans les alliages métalliques." Thesis, Paris Sciences et Lettres (ComUE), 2018. http://www.theses.fr/2018PSLEM001/document.

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Récemment, les observations in-situ par laminographie aux rayons X (au synchrotron) montrent que les multiples bandes de localisation sont les précurseurs de l'endommagement et éventuellement de la rupture en biseau. Ces bandes peuvent être liées aux phénomènes de vieillissement par la déformation (type effet de L"uders ou Portevin-Le Chatelier (PLC)) dont l'influence sur la rupture est encore mal compris. Ces effets sont pourtant observés dans de nombreux alliages industriels comme les aluminiums de la série 2000 ou 5000, ou par exemple, dans le cas des aciers C-Mn pour lesquels un creux de d
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Mbarek, Imen Asma. "Étude dynamique pour définition d'aciers de blindage innovants contre les explosions." Thesis, Université de Lorraine, 2017. http://www.theses.fr/2017LORR0189.

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Le travail de thèse de doctorat porte sur une étude complète du comportement dynamique de trois aciers de blindage soumis à des impacts balistiques. Dans un premier temps, afin de comprendre les phénomènes mis en jeu pendant la perforation de cibles fines, des essais de caractérisation du comportement thermo-viscoplastique et de rupture ont été réalisés. Les paramètres des lois de comportement et des critères de rupture ont été identifiés pour alimenter un modèle numérique simulant l'essai de perforation. La réponse des cibles impactées par des projectiles coniques a ensuite été évaluée à l'ai
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Bude, Jérémie. "Ductile fracture simulation using the strong discontinuity method." Thesis, Compiègne, 2015. http://www.theses.fr/2015COMP2243/document.

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Dans un contexte d’évaluation de la criticité des chargements, les travaux de thèse ont les objectifs suivants : prendre en compte les phénomènes sous-jacents à le rupture ductile : les phénomènes de dissipation volumique (plasticité et endommagement) et surfaciques (fissuration). On s'intéresse également à régulariser la solution vis-à-vis du maillage, à prédire le phénomène de transition de mode de rupture plan vers un mode de propagation oblique observé pour certains essais. La méthode utilisée est basée sur la méthode des discontinuités fortes. Un des enjeux majeurs de ces travaux est d’ét
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Emerson, Tonya Lynn. "Ductile fracture mechanics : modeling, experiments, and computational simulation /." For electronic version search Digital dissertations database. Restricted to UC campuses. Access is free to UC campus dissertations, 2002. http://uclibs.org/PID/11984.

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Wang, Li. "Ductile fracture simulation of structural steel using the local approach method." Thesis, University of the West of England, Bristol, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.271053.

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Myers, Andrew T. "Testing and probabilistic simulation of ductile fracture initiation in structural steel components and weldments /." May be available electronically:, 2009. http://proquest.umi.com/login?COPT=REJTPTU1MTUmSU5UPTAmVkVSPTI=&clientId=12498.

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Hůlka, Jiří. "Aplikace modelů tvárného porušování při výpočtové simulaci technologických operací." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2008. http://www.nusl.cz/ntk/nusl-227954.

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This diploma thesis is an introduction to the ductile fracture under large plastic deformations and is focused to numerical simulation of this type of problems. Explicit finite element method (FEM) is discussed in theoretical introduction as the most powerful tool for numerical calculations in this area. Actual state of research and possibilities of ductile fracture simulations are presented. Applicable fracture criteria are collected in a summary sheet and the most important ones are selected and commented in detail. The problem of implementation of selected criteria into commercial FEM packa
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Hütter, Geralf. "Multi-scale simulation of crack propagation in the ductile-brittle transition region." Doctoral thesis, Technische Universitaet Bergakademie Freiberg Universitaetsbibliothek "Georgius Agricola", 2013. http://nbn-resolving.de/urn:nbn:de:bsz:105-qucosa-121281.

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In the present thesis the crack propagation in the ductile-brittle transition region is studied on two scales with deterministic models. In the macroscopic model the ductile failure is described by a non-local Gurson-model whereas the discrete void microstructure is resolved around the crack tip in the microscopic model. The failure by cleavage is not evaluated by means of a post-processing criterion but is modeled equivalently using a cohesive zone model on both scales. Thus, cleavage is not a priori identified with unstable crack propagation but the transition between stable and unstable mod
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Libri sul tema "Ductile fracture simulations"

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Komori, Kazutake. Ductile Fracture in Metal Forming: Modelling and Simulation. Elsevier Science & Technology, 2019.

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Komori, Kazutake. Ductile Fracture in Metal Forming: Modeling and Simulation. Elsevier Science & Technology Books, 2019.

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Capitoli di libri sul tema "Ductile fracture simulations"

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Gerke, S., M. Schmidt, M. Dirian, and M. Brünig. "Damage and Fracture of Ductile Sheet Metals: Experiments and Numerical Simulations with New Biaxial Specimens." In Advanced Structured Materials. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-70563-7_5.

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Yoon, D. H., and J. Choung. "Collision simulations between a floating offshore wind turbine and a tanker considering ductile fracture and hydrodynamics of FOWT." In Advances in the Collision and Grounding of Ships and Offshore Structures. CRC Press, 2023. http://dx.doi.org/10.1201/9781003462170-56.

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Spaniel, M. "Numerical Simulation of Ductile Fracture." In The Latest Methods of Construction Design. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-22762-7_41.

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Kikuchi, Masanori. "Numerical Simulation of Ductile Fracture Process Including Shear-Lip Fracture." In The Mechanical Behavior of Materials X. Trans Tech Publications Ltd., 2007. http://dx.doi.org/10.4028/0-87849-440-5.839.

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Hello, Gaëtan, Hocine Kebir, and Laurent Chambon. "Numerical Simulation of the Ductile Fracture Growth Using the Boundary Element Method." In Damage and Fracture Mechanics. Springer Netherlands, 2009. http://dx.doi.org/10.1007/978-90-481-2669-9_48.

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Bora, Dipankar, Manoj Kumar, and Sachin S. Gautam. "Continuum Damage Mechanics Based Simulation of Ductile Fracture of Cylindrical Tubes." In Lecture Notes in Mechanical Engineering. Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-13-6469-3_6.

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Arfaoui, Latifa, Amel Samet, and Amna Znaidi. "Ductile Fracture Characterization of an IF Steel Tensile Test by Numerical Simulation." In Lecture Notes in Mechanical Engineering. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-27146-6_34.

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Mu, Lei, Zhe Jia, Ben Guan, and Yong Zang. "Finite Element Simulation of Edge Fracture by Mapping the Shear-Induced Ductile Damage into Hole-Expansion Simulation." In Forming the Future. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-75381-8_137.

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Urata, Shingo, and Shaofan Li. "Simulation of Ductile Fracture in Amorphous and Polycrystalline Materials by Multiscale Cohesive Zone Model." In Mathematical Analysis of Continuum Mechanics and Industrial Applications II. Springer Singapore, 2017. http://dx.doi.org/10.1007/978-981-10-6283-4_4.

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Alves, José, Hazem Eldahshan, Ugo Ripert, Richard Ducloux, Daniel Pino Munoz, and Pierre-Olivier Bouchard. "Advancements in the Simulation of 3D Ductile Damage Transition to Fracture with FORGE®." In Lecture Notes in Mechanical Engineering. Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-42093-1_27.

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Atti di convegni sul tema "Ductile fracture simulations"

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Li, J. "Meshless Analysis of Ductile Failure." In ASME 2011 Pressure Vessels and Piping Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/pvp2011-57134.

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We study ductile fracture using Reproducing Kernel Particle Interpolation and the Gurson-Tvergaard-Needleman (GTN) model. The meshless simulations are compared with the available experimental results and previous finite element simulations for crack propagation. The results agree well with experimental results, and it is confirmed that the proposed method provides a convenient and yet accurate means for simulation of ductile fracture.
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Deng, Xiaomin, and Michael A. Sutton. "Experiments, Analysis and Simulation of Mixed Mode Ductile Fracture." In ASME 2005 Pressure Vessels and Piping Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/pvp2005-71384.

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This paper provides a review of findings of a comprehensive research effort by the authors and collaborators in the area of experiments, analysis and simulation of mixed-mode ductile fracture. Topics include mixed-mode Arcan stable tearing tests, the mixed-mode CTOD fracture criterion and its basis, normalization of ductile crack tip fields, ductile failure envelope, crack tunneling and slanting, effects of stress constraint, custom 2D and 3D mixed-mode crack growth simulation codes, and simulations of mixed-mode stable tearing crack growth tests.
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Ding, Huafeng, Caichao Zhu, Zhong Zhou, and Dong Qian. "Ductile Failure in Processed Thin Sheet Metals." In ASME 2013 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/imece2013-65584.

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Ductile fracture in thin sheet metals is a common failure mechanism that governs many important industrial applications. A variety of simulation methods, ranging from the atomistic to continuum scales, have been proposed and demonstrated. To assess the capabilities of the existing simulation tools, a group of researchers presented their modeling predictions on the so-called Sandia Fracture Challenge problem at the 2012 ASME IMECE conference. The discrepancies between the simulation and experimental results, and among the experimental results themselves led to consensus that more needs to be do
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Zhu, Xueming, Zhiyang Lv, Jian Shuai, Lei Shi, Shengyang Yu, and Gang Xia. "Ductile Fracture Criterion Parameter Calibration and Analysis: X80 Pipe Steel." In ASME 2024 Pressure Vessels & Piping Conference. American Society of Mechanical Engineers, 2024. http://dx.doi.org/10.1115/pvp2024-123037.

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Abstract To investigate the ductile fracture mechanical properties of high strength pipeline steel under a series of stress states, the basic mechanical properties and fracture parameters of X80 pipeline steel were obtained from four types of tensile specimens with six different stress concentration factors and their symmetrical finite element models by an experimental-simulation hybrid method. The ductile fracture parameters of the fracture criterion were calibrated by selecting three specimen data, and the calibrated fracture criterion was imported into ABAQUS using the Vumat subroutine to p
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Nonn, Aida, Marcelo Paredes, Vincent Keim, and Tomasz Wierzbicki. "Comparison of Fracture Models to Quantify the Effects of Material Plasticity on the Ductile Fracture Propagation in Pipelines." In 2018 12th International Pipeline Conference. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/ipc2018-78366.

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Various numerical approaches have been developed in the last years aimed to simulate the ductile fracture propagation in pipelines transporting CO2 or natural gas. However, a reliable quantification of the influence of material plasticity on the fracture resistance is still missing. Therefore, more accurate description of the material plasticity on the ductile fracture propagation is required based on a suitable numerical methodology. In this study, different plasticity and fracture models are compared regarding the ductile fracture propagation in X100 pipeline steel with the objective to quan
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Fonzo, Andrea, Andrea Meleddu, Giuseppe Demofonti, Michele Tavassi, and Brian Rothwell. "Ductile Fracture Control for High Strength Steel Pipelines." In 2006 International Pipeline Conference. ASMEDC, 2006. http://dx.doi.org/10.1115/ipc2006-10331.

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The determination of the toughness values required for arresting ductile fracture propagation has been historically based on the use of models whose resulting predictions can be very unreliable when applied to new high strength linepipe materials (≥X100) and/or different operating conditions. In addition, for the modern high strength steels a methodology for determining the material fracture resistance for arresting running shear fracture starting from laboratory data is still lacking. The work here presented (developed within a PRCI sponsored project) deals with the use of CSM’s proprietary P
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Kane, Alexandre, Sigmund Ås, and Erling Østby. "3D Fracture Simulations of SENT Specimens Including Welding Residual Stresses." In ASME 2012 31st International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/omae2012-84057.

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In pipe-laying and reeling operations, high levels of plastic deformation may occur in the pipe wall. The effect of plastic deformation should be investigated and quantified in order to qualify a steel material for a given pipe-laying process. This paper presents a numerical modeling approach for realistic simulation of ductile fracture, including results from FE welding simulations. A 3D model of a SENT specimen is adopted, where crack propagation is modelled using a Gurson model. An elastic-plastic hardening model is used to capture the global deformation of the specimen. Results compare wel
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Suga, Kazuhiro, Katsumasa Miyazaki, Ryotaro Senda, and Masanori Kikuchi. "Interaction Effect Evaluation of Plural Surface Cracks in Ductile Fracture Process." In ASME 2012 Pressure Vessels and Piping Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/pvp2012-78132.

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Effect of surface flaw on ductile fracture behavior of non-aligned multiple flaws in plate is studied numerically using Gurson’s constitutive equation. Based on experiments, two parallel non-aligned crack problems are simulated. From experimental and simulation data, crack coalescence, interaction between two cracks and crack penetration was observed. In all cases, ductile fracture processes are obtained and results are compared with experimental ones. Fracture patterns agree well with experimental results. Close qualitative match was obtained by comparing each load displacement curves that ar
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Miyajima, Yuuki, Masanori Kikuchi, and Akiyuki Takahashi. "Ductile Fracture Simulation of a Pipe of Steam Generator in PWR." In ASME 2013 Pressure Vessels and Piping Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/pvp2013-97582.

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Ductile fracture of steam generator pipes may occur due to inner pressure. The final fracture process by inner pressure occurs as a burst of a pipe, and ductile high speed crack growth occurs with large deformation of the structure. For the simulation of such fracture process, Gurson’s yield function is used as a constitutive equation, and large deformation theory is employed. As the simulation is conducted by load control condition, it is difficult to simulate burst phenomenon. Final fracture condition is discussed and finally crack opening displacement is chosen as burst fracture criterion.
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Ryu, Ho-Wan, Hune-Tae Kim, Jae-Jun Han, et al. "Effects of Side Groove on Fracture Toughness." In ASME 2015 Pressure Vessels and Piping Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/pvp2015-45731.

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This paper describes ductile tearing simulation for compact tension (C(T)) specimens using FE damage analysis based on the stress-modified fracture strain model. The side groove effect on J-resistance curve was estimated by experimental and analytical ways. In this paper, SA508 Grade 1A low alloy steel pipe material was considered. Tensile and C(T) specimens are simulated to determine the failure criteria with finite element method. Then, different shapes of C(T) specimens are analysed and the results from simulations are compared with test data for verification of proposed method. Overall, th
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Rapporti di organizzazioni sul tema "Ductile fracture simulations"

1

Kanninen, M. F. L51718 Development and Validation of a Ductile Fracture Analysis Model. Pipeline Research Council International, Inc. (PRCI), 1994. http://dx.doi.org/10.55274/r0010321.

Testo completo
Abstract (sommario):
In close cooperation with the Centro Sviluppo Materiali (CSM) and SNAM of Italy, with several years of support from the PRCI NG-18 committee, the Southwest Research Institute (SwRI) has developed and validated a "first principles" predictive model for ductile fracture in a gas transmission pipeline. In particular, the coordinated SwRI and CSM projects for the PRC -supplemented by work contributed by SNAM - has established a theoretically valid methodology and an accompanying line pipe material characterization procedure for gas industry use. This progress provides a theoretically sound framewo
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