Relevant bibliographies by topics / Ductile crack

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Ductile crack'

Author: Grafiati
Published: 4 June 2021
Last updated: 30 January 2023

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Journal articles on the topic "Ductile crack"

1

Yang, Zheng, Wan Lin Guo, Chun Yong Huo, and Yi Wang. "Fracture Appearance Evaluation of High Performance Pipeline Steel DWTT Specimen with Delamination Cracks." Key Engineering Materials 324-325 (November 2006): 59–62. http://dx.doi.org/10.4028/www.scientific.net/kem.324-325.59.

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The delamination cracks and its effects on the fracture of pipeline steel are investigated experimentally by using of Drop-Weight Tear Test (DWTT). The delamination cracks are produced by the stress perpendicular to the weak interfaces before main crack beginning or accelerating, no new delamination crack is produced during the stabile propagation of fracture. The quantity, splay degree of delamination crack and the space between two delamination cracks are influenced by the stress state of the crack tip at beginning or accelerating point of main crack and the length of delamination crack is i
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Herrmann, Christoph, Daniel Schneider, Ephraim Schoof, Felix Schwab, and Britta Nestler. "Phase-Field Model for the Simulation of Brittle-Anisotropic and Ductile Crack Propagation in Composite Materials." Materials 14, no. 17 (2021): 4956. http://dx.doi.org/10.3390/ma14174956.

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In this work, a small-strain phase-field model is presented, which is able to predict crack propagation in systems with anisotropic brittle and ductile constituents. To model the anisotropic brittle crack propagation, an anisotropic critical energy release rate is used. The brittle constituents behave linear-elastically in a transversely isotropic manner. Ductile crack growth is realised by a special crack degradation function, depending on the accumulated plastic strain, which is calculated by following the J2-plasticity theory. The mechanical jump conditions are applied in solid-solid phase
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Huo, Feng Wei, Zhu Ji Jin, Fu Ling Zhao, Ren Ke Kang, and Dong Ming Guo. "Experimental Investigation of Brittle to Ductile Transition of Single Crystal Silicon by Single Grain Grinding." Key Engineering Materials 329 (January 2007): 433–38. http://dx.doi.org/10.4028/www.scientific.net/kem.329.433.

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Grinding of single crystal silicon may be achieved by two modes of material removal: ductile mode and brittle mode. Knowing of the brittle to ductile transition point at which the grinding process changes from the brittle mode to ductile mode is critically important for the realization of ductile mode grinding. This paper uses a new single grain diamond grinding method developed recently by the authors to investigate the brittle to ductile transition during grinding of single crystal silicon in all around. The results indicate that there exist four stages of brittle to ductile transition as th
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Ohata, Mitsuru, Takuya Fukahori, and Fumiyoshi Minami. "Prediction of Ductile Crack Growth from Ductility of Steel." Materials Science Forum 539-543 (March 2007): 2186–91. http://dx.doi.org/10.4028/www.scientific.net/msf.539-543.2186.

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This study pays attention to reveal the material properties that control resistance curve for ductile crack growth (CTOD-R curve) on the basis of the mechanism for ductile crack growth, so that the R-curve could be numerically predicted only from those properties. The crack growth tests using 3-point bend specimens with fatigue pre-crack were conducted for two steels that have different ductile crack growth resistance with almost the same CTOD level for crack initiation, whereas both steels have the same “Mechanical properties” in terms of strength and work hardenability. The observation of cr
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Barnby, J. T., S. L. Creswell, A. S. Nadkarni, and B. S. Spencer. "Ductile Fracture Micromechanisms in A508 CL3 Structural Steel." Journal of Pressure Vessel Technology 108, no. 4 (1986): 479–84. http://dx.doi.org/10.1115/1.3264816.

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Studies of the critical void volumes ahead of cracks at the initiation of fracture at 100° C in the ductile regime show that the void volume has a maximum at a distance of about one to two crack tip opening displacements ahead of the original crack tip. The critical void volume maximum is approximately the same for prefatigue cracked notched bend bars and cusp-shaped cracks (formed by spark machining) at initiation in A508 CL3 steel. The maximum in void volume tends to have a lower value and to be closer to the crack tip for lower values of constraint stresses (that is for lower triaxiality).
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Ayatollahi, Majid R., David John Smith, and M. J. Pavier. "Effect of Constraint on the Initiation of Ductile Fracture in Shear Loading." Key Engineering Materials 261-263 (April 2004): 183–88. http://dx.doi.org/10.4028/www.scientific.net/kem.261-263.183.

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Research studies for mode I cracks have shown that fracture toughness or the critical value of J for fracture initiation, Jcrit is not merely a material property but depends also on the geometry and loading configurations. The geometry dependency of fracture toughness can be attributed to the effect of the crack tip constraint. In this paper, the constraint effect is studies for the initiation stage in mode II ductile crack growth. Two major mechanisms of ductile fracture: 'void growth and coalescence' and 'shear band localization and de-cohesion' are considered. A boundary layer model is simu
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Azinpour, Erfan, Jose Cesar de Sa, and Abel Dias dos Santos. "Micromechanically-motivated phase field approach to ductile fracture." International Journal of Damage Mechanics 30, no. 1 (2020): 46–76. http://dx.doi.org/10.1177/1056789520948933.

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Utilization of the phase-field diffusive crack approach in prediction of crack evolution in materials containing voids is investigated herein. It has been established that the ductile failure occurs predominantly due to nucleation, growth and coalescence of micro-voids and micro-cavities, which lead to initiation and propagation of cracks till final material collapse. This study is an attempt to model the material internal degradation with the Rousselier pressure-dependent plasticity law, assisted with the phase field diffusive crack approach for the first time, in order to account for the pos
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Flinn, B. D. "Fractographic study of an Al2O3/Al composite." Proceedings, annual meeting, Electron Microscopy Society of America 46 (1988): 744–45. http://dx.doi.org/10.1017/s0424820100105783.

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Ceramics have limited engineering applications due mainly to inherent brittleness and catastrophic failure. However the fracture toughness of ceramics has been increased significantly by incorporating ductile second phases into the ceramic matrix. The exact toughening mechanism(s) have not been clearly determined, although several likely models have been proposed. In particular, the ductile phase is thought to contribute to the toughness of the composite if intact particles remain in the crack wake. The intact particles deform plastically and exert tractions on the crack surfaces which inhibit
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Lim, Bokkyu, and Young Woo Choi. "Effect of Semi Austempering Treatment on the Fatigue Properties of Ductile Cast Iron." Key Engineering Materials 345-346 (August 2007): 295–98. http://dx.doi.org/10.4028/www.scientific.net/kem.345-346.295.

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Single phase bainite structure which is obtained by the conventional austempering treatment reduces the ductility of ductile cast iron. Because of the reduction of ductility it is possible to worsen the fatigue properties. Therefore, semi austempered ductile iron which is treated from +ϒ is prepared to investigate the static strength and fatigue properties in comparison with fully austempered ductile iron (is treated from ϒ). In spite of semi austempered ductile iron shows the 86% increase of ductility. Also, semi austempered ductile iron shows the higher fatigue limit and lower fatigue crack
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Leung, D. K., N. T. Zhang, R. M. McMeeking, and A. G. Evans. "Crack progression and interface debonding in brittle/ductile nanoscale multilayers." Journal of Materials Research 10, no. 8 (1995): 1958–68. http://dx.doi.org/10.1557/jmr.1995.1958.

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Crack initiation and progression have been studied in nanoscale brittle/ductile multilayers of Cu and Si. Variations in the interface debond energy on the cracking behavior have been examined by using thin interlayers comprising either Cr (strong interface) or Au (weak interface). For strongly bonded Cr interfaces, it has been found that cracks forming in the Si invariably extend through the Cu layers, despite the ductile rupture characteristics of the Cu. This behavior occurs even when the Cu layers comprise more than 70% of the multilayer volume. It also contrasts with the crack arrest capab
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Dissertations / Theses on the topic "Ductile crack"

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Medina, Velarde Jose Luis. "Fast ductile crack growth in panels." Thesis, University of Oxford, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.343563.

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Lam, Paul W. "Crack curving in a ductile pressurized fuselage /." Thesis, Connect to this title online; UW restricted, 2000. http://hdl.handle.net/1773/7143.

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Bao, Yingbin 1972. "Prediction of ductile crack formation in uncracked bodies." Thesis, Massachusetts Institute of Technology, 2003. http://hdl.handle.net/1721.1/17634.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Ocean Engineering, 2003.<br>Includes bibliographical references (p. 233-247).<br>One of the important challenges facing the scientific and engineering community is the development of a reliable computational tool for predicting failure of structures under extreme and/or accidental loads. Considered in the present thesis is the process of formation of ductile cracks, which may be responsible for a catastrophic structural failure. Experimental, numerical and analytical studies are carried out on the prediction of ductile crack form
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Vishal, Vaibhaw 1978. "Computational aspects of ductile crack growth in three dimensions." Thesis, Massachusetts Institute of Technology, 2003. http://hdl.handle.net/1721.1/89925.

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Bezenšek, Boštjan. "Elastic-plastic crack problems in the ductile-brittle transition." Thesis, University of Glasgow, 2003. http://theses.gla.ac.uk/6946/.

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Margins in defect assessment procedures such as BS 7910 and R6/4 have been examined for cleavage and ductile tearing from complex and re-characterised defects. A range of crack profiles with re-entrant sectors developed from two co-planar surface breaking defects by fatigue has been examined experimentally and numerically. Both studies show enhanced crack driving forces in the re-entrant sector combined with a loss of crack tip constraint. Cleavage failures from complex and re-characterised defects demonstrated that the re-characterisation procedure is not conservative when cleavage occurs at
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Gibson, Gregory Paul. "Characterisation of ductile crack initiation and growth in mild steel." Thesis, Imperial College London, 1986. http://hdl.handle.net/10044/1/38013.

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Lee, Jonghee. "Fracture analysis of a propagating crack in a ductile material /." Thesis, Connect to this title online; UW restricted, 1996. http://hdl.handle.net/1773/7081.

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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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WATANABE, Katsuhiko, Hideyuki AZEGAMI, and Yasuo HIRANO. "An Evaluation of the Fracture Resistance of a Stably Growing Crack by Crack Energy Density (2nd Report, Application to a Ductile Crack in Thin Plate)." 日本機械学会, 1986. http://hdl.handle.net/2237/12160.

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Daily, Jeremy S. "Plastic Dissipation Energy in Mixed-Mode Fatigue Crack Growth on Ductile Bimaterial Interfaces." Wright State University / OhioLINK, 2003. http://rave.ohiolink.edu/etdc/view?acc_num=wright1074880923.

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Books on the topic "Ductile crack"

1

Clark, A. V. Ductile tearing stability analysis of a ship structure containing a crack arrester strake. U.S. Dept. of Commerce, National Bureau of Standards, 1986.

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2

Dickson, T. L. Inclusion of unstable ductile tearing and extrapolated crack-arrest toughness data in PWR vessel integrity assessment. Division of Engineering, Office of Nuclear Regulatory Research, U.S. Nuclear Regulatory Commission, 1990.

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United States. National Aeronautics and Space Administration., ed. Prediction and verification of ductile crack growth from simulated defects in strength overmatched butt welds: A thesis ... National Aeronautics and Space Administration, 1997.

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Zahoor, A. Ductile Fracture Handbook: Circumferential Throughwall Cracks. 3rd ed. Novetechnology, 1989.

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Book chapters on the topic "Ductile crack"

1

Radhakrishnan, V. M. "Creep Crack Growth in Ductile Materials." In Time-Dependent Fracture. Springer Netherlands, 1985. http://dx.doi.org/10.1007/978-94-009-5085-6_18.

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Rice, J. R., D. E. Hawk, and R. J. Asaro. "Crack tip fields in ductile crystals." In Non-Linear Fracture. Springer Netherlands, 1990. http://dx.doi.org/10.1007/978-94-017-2444-9_20.

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Jia, Liang-Jiu, and Hanbin Ge. "Ductile Crack Propagation under Monotonic Loading." In Ultra-low-Cycle Fatigue Failure of Metal Structures under Strong Earthquakes. Springer Singapore, 2018. http://dx.doi.org/10.1007/978-981-13-2661-5_5.

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Schmidt, Ingo, Christoph Richter, and Dietmar Gross. "Ductile Crack Growth in Metallic Foams." In Deformation and Failure in Metallic Materials. Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-540-36564-8_15.

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Dahan, M., and M. Predeleanu. "A ductile crack in an anisotropic solid." In Progress and Trends in Rheology II. Steinkopff, 1988. http://dx.doi.org/10.1007/978-3-642-49337-9_31.

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Ritchie, Robert O., and Maximilien E. Launey. "Crack Growth in Brittle and Ductile Solids." In Encyclopedia of Tribology. Springer US, 2013. http://dx.doi.org/10.1007/978-0-387-92897-5_271.

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Méïté, Mamadou, Noé Brice Nkoumbou Kaptchouang, Yann Monerie, Frédéric Perales, and Pierre-Guy Vincent. "Ductile Crack Growth Using Cohesive GTN Model." In Handbook of Damage Mechanics. Springer New York, 2021. http://dx.doi.org/10.1007/978-1-4614-8968-9_70-1.

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Méïté, Mamadou, Noé Brice Nkoumbou Kaptchouang, Yann Monerie, Frédéric Perales, and Pierre-Guy Vincent. "Ductile Crack Growth Using Cohesive GTN Model." In Handbook of Damage Mechanics. Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-60242-0_70.

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Kozák, Vladislav. "Ductile Crack Growth Modelling Using Cohesive Zone Approach." In Composites with Micro- and Nano-Structure. Springer Netherlands, 2008. http://dx.doi.org/10.1007/978-1-4020-6975-8_11.

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Kayamori, Yoichi, S. Hillmansen, P. S. J. Crofton, and Roderick A. Smith. "Ductile Crack Propagation Characteristics in Thin Steel Tubes." In Key Engineering Materials. Trans Tech Publications Ltd., 2007. http://dx.doi.org/10.4028/0-87849-456-1.248.

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Conference papers on the topic "Ductile crack"

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Sherry, A. H., M. R. Goldthorpe, J. Fonseca, and K. Taylor. "Residual Stress Effects on Ductile Tearing." In ASME 2006 Pressure Vessels and Piping/ICPVT-11 Conference. ASMEDC, 2006. http://dx.doi.org/10.1115/pvp2006-icpvt-11-93677.

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Residual stresses are internal stresses generated during the fabrication and/or operation of engineering structures. Such stresses can provide the major element of the driving force for crack initiation and growth. Structural integrity assessment procedures, provide guidance for the assessment of defects located within regions of high residual stress. However, such guidance may be conservative where the defect develops progressively during service. This paper describes recent experimental and numerical work aimed at quantifying such conservatisms and providing improved guidance for undertaking
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Kikuchi, Masanori, Kazuhiro Suga, and Shota Kawasaki. "Simulation of Ductile Fracture for Multiple Flaws." In ASME 2010 Pressure Vessels and Piping Division/K-PVP Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/pvp2010-25453.

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Interaction effect of multiple flaws on ductile fracture is studied numerically by using Gurson’s constitutive equation. Based on experiments, 2 parallel cracks problems and 3 parallel cracks problems are simulated. In some problems, crack coalescence does not occur, and it occurs in other cases. In all cases, ductile fracture processes are obtained, and results are compared with experimental ones. Fracture pattern and load-displacement curves agree well with experiments. It is shown that void growth term is dominant for the coalescence of cracks. Slanted crack problem and non-uniform length c
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Gao, Xiaosheng, and Jinkook Kim. "Modeling of Crack Growth in Ductile Solids." In ASME 2005 International Mechanical Engineering Congress and Exposition. ASMEDC, 2005. http://dx.doi.org/10.1115/imece2005-80225.

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In this study, two types of approaches are considered to model material failure process and crack propagation in ductile solids. In the first approach, voids are considered explicitly and modeled using refined finite elements. A distinct advantage of this approach is the exact implementation of the void growth behavior. In order to establish crack advance, a failure criterion for the ligament between a void and the crack tip is required, which can be obtained by conducting systematic finite element analyses of the void-containing, representative material volume subjected to different macroscop
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Yamada, Takehisa, and Yoichi Yamashita. "Ductile Crack Initiation Behavior of Prestrained Steels." In ASME 2011 Pressure Vessels and Piping Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/pvp2011-57294.

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Ductile crack initiation behaviors were experimentally and analytically investigated using compressively prestrained notched round bar specimen (lower stress triaxiality condition) and four point bend specimen (higher stress triaxiality condition). The materials used were SM400B and HT780. It was observed that ductile crack initiation of notched round bar specimen occurred at the center of specimen and was caused by coalescence of micro voids. Ductile limit curves, which are the relationships between equivalent plastic strain and stress triaxiality factor at ductile crack initiation, were obta
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Fan, Jing-Long, and Xi-Wei Lyu. "Analysis of crankshaft crack of ductile iron." In The 2015 International Conference on Mechanics and Mechanical Engineering (MME 2015). WORLD SCIENTIFIC, 2016. http://dx.doi.org/10.1142/9789813145603_0062.

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Aihara, Shuji, Kazuki Shibanuma, Yasuhito Imai, Taishi Fujishiro, and Takuya Hara. "Evaluation on Dependence of Ductile Crack Propagation Resistance on Crack Velocity." In 2012 9th International Pipeline Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/ipc2012-90637.

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Plastic strains were measured near a propagating ductile crack in drop-weight tear tests (DWTT). Plastic work evaluated from the plastic strains agreed with crack propagation energy evaluated from dynamic load versus displacement curve. Furthermore, plastic strains were measured near a propagating ductile crack in a full-scale burst tested pipes. Plastic work of the burst pipe was found to be much larger than that of the DWTT. Values of the plastic work of the DWTT and the burst pipe were plotted against crack velocity to construct crack resistance curve. Reason to the increased crack resistan
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Ancelet, O., Ph Gilles, P. Le Delliou, and G. Perez. "Ductile Tearing and Plastic Collapse Competition." In ASME 2020 Pressure Vessels & Piping Conference. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/pvp2020-21853.

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Abstract Structures containing large cracks and made in ductile materials may experience two types of failure mechanisms: ductile tearing or plastic collapse. Under displacement controlled loading ductile tearing is a stable crack growth mechanism. Plastic collapse leads to a much faster damage evolution. Ductile tearing is the result of void growth and coalescence ahead of the crack front under the high strain concentration. This mechanism is slowed down by a high material hardening and under a high constraint. The global deformation of the structure is limited. Plastic collapse is induced by
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Imad, A., and M. Naït Abdelaziz. "Crack Extension Modelling of a Ductile Fracture Damage." In ASME 2002 Pressure Vessels and Piping Conference. ASME, 2002. http://dx.doi.org/10.1115/pvp2002-1492.

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Maes, Marc A., Ruben Van Coile, Robby Caspeele, Ming Gao, and Markus R. Dann. "Probabilistic FAD and Ductile Tearing Assessment." In ASME 2013 32nd International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/omae2013-10046.

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The assessment of cracks in pipelines is one of the key elements for the integrity verification and the remaining lifetime evaluation of pipelines. This crack assessment is commonly performed through Failure Assessment Diagram (FAD) methods in which two failure criteria are combined, i.e. brittle fracture and plastic collapse. FAD assessments are, however, highly deterministic and do not take into account the various uncertainties that affect cracking. A probabilistic FAD tool is developed that accounts for these uncertainties and determines the probability of failure as a function of the crac
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Xue, Liang. "Alternating Slant Mode of the Crack Propagation in Ductile Flat Plates." In ASME 2011 Pressure Vessels and Piping Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/pvp2011-57744.

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Cracks in flat plates are often found to be about 45° to the plate plane for some metals and alloys. There are two identical 45° directions to the plate plane and the choice of crack direction seems to be random. Experiments have shown that, for large flat panels, the long ductile crack propagation exhibits a regular alternating pattern, i.e. the crack switches to the other direction after propagates some distance regularly. In this paper, a numerical examination of the details of the formation of the alternating crack pattern is presented. Relevant material parameters and their influencing fa
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Reports on the topic "Ductile crack"

1

Clark, A. V., and D. T. Read. Ductile tearing stability analysis of a ship structure containing a crack arrester strake. National Bureau of Standards, 1986. http://dx.doi.org/10.6028/nbs.ir.85-3038.

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Dickson, T., R. Cheverton, and D. Shum. Inclusion of unstable ductile tearing and extrapolated crack-arrest toughness data in PWR vessel integrity assessment. Office of Scientific and Technical Information (OSTI), 1990. http://dx.doi.org/10.2172/6909430.

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3

Keeney, J. A. Fracture assessment of ductile crack growth in weld material from a full-thickness clad RPV shell segment. Office of Scientific and Technical Information (OSTI), 1997. http://dx.doi.org/10.2172/459421.

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Narasimhan, R., and A. J. Rosakis. Three Dimensional Effects Near a Crack Tip in a Ductile Three Point Bend Specimen. Part 1. A Numerical Investigation. Defense Technical Information Center, 1988. http://dx.doi.org/10.21236/ada202636.

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Shih, C. F., L. Xia, and J. W. Hutchinson. Validity limits in J-resistance curve determination: A computational approach to ductile crack growth under large-scale yielding conditions. Volume 2. Office of Scientific and Technical Information (OSTI), 1995. http://dx.doi.org/10.2172/10123471.

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Zehnder, Alan T., and Ares J. Rosakis. Three Dimensional Effects Near a Crack Tip in a Ductile Three Point Bend Specimen. Part 2. An Experimental Investigation Using Interferometry and Caustics. Defense Technical Information Center, 1988. http://dx.doi.org/10.21236/ada202637.

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Cheng, Weili, and I. Finnie. A study of crack initiation threshold in the ductile micro-machining and grinding of glass: Final report covering the period June 21, 1988--October 31, 1988. Office of Scientific and Technical Information (OSTI), 1988. http://dx.doi.org/10.2172/5916951.

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Snyder, Victor A., Dani Or, Amos Hadas, and S. Assouline. Characterization of Post-Tillage Soil Fragmentation and Rejoining Affecting Soil Pore Space Evolution and Transport Properties. United States Department of Agriculture, 2002. http://dx.doi.org/10.32747/2002.7580670.bard.

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Tillage modifies soil structure, altering conditions for plant growth and transport processes through the soil. However, the resulting loose structure is unstable and susceptible to collapse due to aggregate fragmentation during wetting and drying cycles, and coalescense of moist aggregates by internal capillary forces and external compactive stresses. Presently, limited understanding of these complex processes often leads to consideration of the soil plow layer as a static porous medium. With the purpose of filling some of this knowledge gap, the objectives of this Project were to: 1) Identif
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THE SEISMIC PERFORMANCE OF DOUBLE TUBE BUCKLING RESTRAINED BRACE WITH CAST STEEL CONNECTORS. The Hong Kong Institute of Steel Construction, 2022. http://dx.doi.org/10.18057/ijasc.2022.18.1.2.

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The special concentrically braced frame (SCBF) is an aseismic structure, but its bracing system exhibits brittle failure and premature buckling connected with the weld fracture of the gusset plate and the post-buckling of the braces; thus, maximizing the role of energy dissipation is difficult. Here, this paper proposes a system of double-tube buckling-restrained brace with cast steel connectors for steel SCBFs. The large inelastic deformation of the bracing system is mainly concentrated in the ductile cast connectors under the earthquake, and the degree of buckling and post-buckling of braces
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