Relevant bibliographies by topics / Non-Linear strain path (NLSP)

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Non-Linear strain path (NLSP)'

Author: Grafiati
Published: 2 July 2021
Last updated: 1 February 2022

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Journal articles on the topic "Non-Linear strain path (NLSP)"

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Lee, W. B., and K. C. Chan. "A Theoretical Analysis of Equibiaxial Deformation Texture Under Non-prescribed Strain Path." Textures and Microstructures 13, no. 1 (January 1, 1990): 31–40. http://dx.doi.org/10.1155/tsm.13.31.

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A model is presented to calculate the rotation path of crystals under equibiaxial tension when the strain ratio is fixed (prescribed strain path) or when the strain ratio is allowed to adjust itself according to the external constraint and the current state of the plastic anisotropy of the material (nonprescribed strain path). It is found that the stability of grain orientation is related to the curvature of the strain path. There is a difference in the predicted equibiaxial deformation texture for the two types of strain paths. Grain orientations which are unstable under a linear strain path may become stable under a non-linear or varying strain path.
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Wi, M. S., S. Y. Lee, and F. Barlat. "Non-linear strain path experiment and modeling for very high strength material." IOP Conference Series: Materials Science and Engineering 651 (November 25, 2019): 012005. http://dx.doi.org/10.1088/1757-899x/651/1/012005.

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Lee, Shin-Yeong, Ji-Min Kim, Jin-Hwan Kim, and Frédéric Barlat. "Validation of homogeneous anisotropic hardening model using non-linear strain path experiments." International Journal of Mechanical Sciences 183 (October 2020): 105769. http://dx.doi.org/10.1016/j.ijmecsci.2020.105769.

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Ha, Jinjin, Myoung-Gyu Lee, and Frédéric Barlat. "Strain hardening response and modeling of EDDQ and DP780 steel sheet under non-linear strain path." Mechanics of Materials 64 (September 2013): 11–26. http://dx.doi.org/10.1016/j.mechmat.2013.04.004.

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Feng, Xiao Jiu, Li Fu Liang, and Si Yuan Wang. "Study the Non-Linear Heat-Elasto-Plastic Constitutive Relation." Advanced Materials Research 415-417 (December 2011): 2130–33. http://dx.doi.org/10.4028/www.scientific.net/amr.415-417.2130.

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This paper adopts Macroscopic Phenomenological Method to establish constitutive relation. In order to maintain better approximation, it adopts testing data of typical stress path, testing data of uniaxial tension and torsion test. Applying multidimensional incremental theory under general loading law, on the base of certain loading function of stress space and loading function of strain space, this essay drives heat-elasto-plastic constitutive relation of heated isotropic hardening material under the condition of elasto-plastic decoupling. Meanwhile, this constitutive relation also suits for kinematic hardening material and elastic-perfectly plastic material. This paper builds a means of driving constitutive relation of multidimensional incremental theory under general loading law in strain space.
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Li, Hongzhou, Guangyao Li, Guoqiang Gao, Wusheng Zhang, and Xin Wu. "A formability evaluation method for sheet metal forming with non-linear strain path change." International Journal of Material Forming 11, no. 2 (February 28, 2017): 199–211. http://dx.doi.org/10.1007/s12289-017-1342-y.

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Laokor, Korkiat, Bunyong Chongthairungruang, and Sansot Panich. "Influence of Pre-Stretching Levels on the Forming Limit Strain and Stress Curves of High Strength Steel Sheet." Key Engineering Materials 798 (April 2019): 25–31. http://dx.doi.org/10.4028/www.scientific.net/kem.798.25.

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In this work, Forming Limit Curves (FLCs) of the conventional and pre-stretched High Strength Steel (HSS) sheet grade 440 (SCGA440-45) were investigated. The conventional forming limit curve was experimentally determined by using the Nakajima stretching test. Subsequently, the non-linear strain path FLCs were precisely developed through the Nakajima stretching test after the specimens were pre-stretched in biaxial direction up to several levels on the Marciniak In-plane stretching test. The gained non-linear strain path FLCs were compared with the conventional FLC.Additionally, the experimental Forming Limit Stress Curve (FLSCs) were calculated using the experimental FLC and non-linear strain path FLCs data from investigated steel sheet. The yield criterion Hill’48 was employed in combination with the Swift strain hardening law to describe anisotropic deformation and plastic flow behavior of the HSS sheet, respectively. Hereby, the influence of pre-stretching levels on the experimentally determined the FLCs and FLSCs were examined. The results prove a significant influence of the pre-stretching levels on the both FLCs and FLSCs of the investigated HSS sheet. For a low pre-stretching in biaxial loading the FLCs demonstrated a reduced formability and the FLSCs exhibited the limited stress levels depending on the experimental FLC data.
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Merklein, Marion, and Sebastian Suttner. "Evolution of Yield Loci for Aluminum Alloy AA6016 and Deep Drawing Steel DC06 under the Influence of Non-Linear Strain Paths." Key Engineering Materials 549 (April 2013): 21–28. http://dx.doi.org/10.4028/www.scientific.net/kem.549.21.

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The application of modern materials plays an important role directly under the aspect of lightweight potential. To exploit these options effectively a numerical accurate reproduction of the material behavior is indispensable. Especially in the case of large deformations a directional and strain rate dependent hardening behavior can be observed. By disregarding this effect significant failure in the computed stress state can arise, which can conduct to a corruption of the spring-back forecast. Within this contribution a new test method for analyzing the evolution of subsequent yield loci under strain path changes for the aluminum alloy AA6016 and the deep drawing steel DC06 is presented. In the first stage of the experimental investigations, yield loci with linear strain paths were considered to characterize the material behavior for the initial condition. On further experiments with several stress states the strain path dependent hardening behavior of the material is determined. The non-linear strain paths are realized through uniaxial prestrained primary specimens with following extraction of secondary samples for following stress states, e.g. a modified ASTM simple shear test specimen. Subsequent yield loci are investigated and compared to the yield surfaces Hill48 and Barlat 2000 (Yld2000-2d) with an isotropic hardening behavior. With this study the evolution of the yield locus for prestrained specimens is evaluated. The research of the subsequent yield loci for strain path changes serves as basis for further scientific investigations with a view to assess different approaches of isotropic-kinematic hardening models in consideration of the analyzed steel and aluminum sheet metals.
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Apriadi, Dedi, Suched Likitlersuang, and Thirapong Pipatpongsa. "Loading path dependence and non-linear stiffness at small strain using rate-dependent multisurface hyperplasticity model." Computers and Geotechnics 49 (April 2013): 100–110. http://dx.doi.org/10.1016/j.compgeo.2012.11.007.

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Rizov, V. "Non-Linear Fatigue Fracture Analysis of Composite Laminates." Polymers and Polymer Composites 17, no. 6 (July 2009): 371–77. http://dx.doi.org/10.1177/096739110901700605.

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In this paper, results of an experimental and numerical investigation of the effects of non-linear deformation on the fatigue crack growth in composite laminates are presented and discussed. Mode I fatigue fracture experiments are carried out on extended compact tension specimens under sinusoidal load control at a frequency of 4 Hz. The fatigue fracture test data are analysed using a power law relationship between the crack growth rates and the range of the path-independent J-integral. A two- dimensional finite element model of the extended compact tension specimen is set up in order to compute the J-integral values. The model is coupled with damage analysis in order to study the effect of non-linear deformation on the fatigue fracture performance. The damage analysis is based on the Tsai-Wu failure criterion. The non-linear model is verified by carrying out comparisons between the simulated mechanical behaviour of the extended compact tension specimen and the measured one. The damage distribution within the specimen is analyzed. The J-integral is computed over paths surrounding the crack tip and not crossing the damage zone. It is shown that taking into account the damage behaviour improves the fatigue fracture resistance, which is attributed to increased strain energy dissipation as a result of non-linear deformation.
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Dissertations / Theses on the topic "Non-Linear strain path (NLSP)"

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Eriksson, Anton. "Non-Linear strain paths in Sheet Metal Forming." Thesis, Blekinge Tekniska Högskola, Institutionen för maskinteknik, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:bth-21906.

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Today's automotive requirements have resulted in complex Sheet Metal Forming (SMF) processes of Sheet Metal (SM) with reduced formability, and thus it is crucial to be able to predict formability accurately to prevent material failure during SMF. Formability predictions today utilize Forming Limit Curves (FLC)s in Finite Element Analysis (FEA), but  FLCs are not valid for the Non-Linear Strain Paths (NLSP)s generated during SMF. One purpose of this thesis is thus to increase the knowledge on FP handling NLSP,  which was obtained through providing suggestions of failure models for handling NLSP effects, based upon literature on the subject. Generating NLSP experimentally is both time and material costly with the conventional method, thus the second purpose of this thesis was to increase the knowledge on test procedures for generating NLSP in SM. Based upon the findings of Chandramohan \cite{chandramohan_study_2021} five test procedures for generating NLSP were put forward, and the Nakajima test with modified punch geometry was chosen for further study.   In this thesis, the NLSP characteristics of two modified punch geometries were evaluated by FEA performed using LS-DYNA. For the FEA three specimens with blank width of 50, 100 and 200 mm was used, and the anisotropic Barlat yld2000  was used as the material model. This material model was calibrated to material data of Mild steel CR4, Aluminium alloy AA6016, and Dual-phase steel DP800. The results for all materials showcased similar reacquiring general NLSP characteristics at the corners of the punch features, which are unfavorable positions when failure by necking is evaluated, and thus it was concluded that the tested punch geometries are not favorable and more development of the punch geometry is needed.
Dagens fordonskrav, har lett till komplexa plåtformnings processer av plåtmaterial med reducerad formbarhet, och det är därför väsenligt att kunna förutsäga formbarhet noggrant för att förhindra materialbrott under plåtformning. Försträckning och brott förutses idag genom Formgränskurvor (FGK) i finita element analyser (FEA), men dessa gäller inte för icke-linjära töjningsvägar som uppkommer under plåtformning. Ett syfte av denna avhandling är därför att öka kunskapen kring modeller för att förutsäga formbarhet under icke-linjära töjningsbanors effekter, vilket uppnådes genom att  presenteras  förslag på brott modeller för att hantera de icke-linjära töjningsvägar baserade på  literatur inom området. Att generera icke-linjära töjningsvägar experimentellt är både tids och materialkrävande med den konventionella metoden, således är det andra syftet av denna avhandling att öka kunskapen kring test metoder för att generera icke-linjär töjningsbvägar i plåt. Baserat på Chandramohans \cite{chandramohan_study_2021} resultat diskuteras fem test procedurer för att generera icke-linjära töjningsvägar, och Nakajima test med modifierad stämpelgeometri valdes för vidare studie.  I denna avhandling studerades töjningsignaturen av två stämpelgeometrier med FEA i LS-DYNA. Till FEA:n användes tre ämnen med bredd av 50, 100 och 200mm, och anisotropiska Barlat yld2000 användes som materialmodell. Denna materialmodell kalibrerades mot experimentella mätvärden för mjukt stål CR4, Aluminiumlegering AA6016 och Stål DP800. Resultaten visade för alla material återkommande generella icke-linjära töjningsbanor enbart för hörnorna på stansgeometrierna, vilket är icke önskvärda positioner då brott pga. midjebildning utvärderas, och således drogs slutsatsen att nuvarande stansgeometri inte är gynnsam och ytterligare utveckling behövs.
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Book chapters on the topic "Non-Linear strain path (NLSP)"

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Skorohod, V., M. Shtern, and S. Kudela. "Strain Path Effect on Debonding and Non-Linear Constitutive Model for Rigid Particles Reinforced Metal/Ceramic Matrix Composite." In Advanced Multilayered and Fibre-Reinforced Composites, 85–98. Dordrecht: Springer Netherlands, 1998. http://dx.doi.org/10.1007/978-94-007-0868-6_4.

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Conference papers on the topic "Non-Linear strain path (NLSP)"

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Bressan, José Divo, Mathias Liewald, and Klaus Drotleff. "Forming limit strains for non-linear strain path of AA6014 aluminium sheet deformed at room temperature." In PROCEEDINGS OF THE INTERNATIONAL CONFERENCE OF GLOBAL NETWORK FOR INNOVATIVE TECHNOLOGY AND AWAM INTERNATIONAL CONFERENCE IN CIVIL ENGINEERING (IGNITE-AICCE’17): Sustainable Technology And Practice For Infrastructure and Community Resilience. Author(s), 2017. http://dx.doi.org/10.1063/1.5007984.

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Li, Yajing, Dunji Yu, and Xu Chen. "Effects of Strain Amplitude and Loading Path on Cyclic Behavior and Martensitic Transformation of 304 Stainless Steel." In ASME 2018 Pressure Vessels and Piping Conference. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/pvp2018-84888.

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Effects of strain amplitude and loading path on cyclic deformation behavior and martensitic transformation of 304 stainless steel were experimentally investigated at room temperature. Series of symmetrical strain-control low cycle fatigue tests with strain amplitude ranging from 0.4% to 1.0% and various loading paths (uniaxial, torsional, proportional, rhombus, square and circular) with the same equivalent strain amplitude of 0.5% were carried out. Three-stage cyclic deformation behavior containing initial hardening, cyclic softening or saturation, and secondary hardening as well as near-linear relationship between α’-martensite content and number of cycles was observed during the whole life regime as for each test. Besides, a nearly linear relation between peak stress and α’-martensite content was found during secondary hardening stage. Furthermore, higher strain amplitude or non-proportionality of loading path resulted in higher cyclic stress response and α’-martensite content growth rate, defined by the slope of curves of α’-martensite content versus number of cycles.
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Yang, Xiaoyu, Stéphane Marie, and Clémentine Jacquemoud. "Cleavage Crack Path Prediction in a PWR Vessel Steel." In ASME 2014 Pressure Vessels and Piping Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/pvp2014-28418.

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Cleavage crack propagation has been tested for three different geometries of Compact Tensile (CT) specimens: CT25, CT50 and extended CT25 (CT25 with CT50 width) (Figure 3). The experimental results show that the crack paths are straight for CT25 and CT50, but they are unstable and curved for extended CT specimens (Figure 5 to 7). Numerical computation had been performed by extended finite element method (XFEM) in CAST3M software. 2D modeling was used in order to predict the crack path. The analysis was based on a local non-linear dynamic approach with a RKR fracture stress criterion depending on temperature and strain rate. In order to simulate the curvature of the cracks path, a statistical effect was introduced in the model to take into account the spatial distribution of cleavage initiators, which is the characteristic of cleavage fracture. At each step of propagation during the modeling, the direction was randomly chosen, according to a uniform defects distribution. The numerical results show a good agreement with experience. The different crack paths were curved in extended CT25, but remained almost straight in CT25 and CT50 specimens, despite of the instability introduced in the modeling in the propagation direction. These results show that the statistics of micro-defects can induce, jointly with the geometry of specimen, a large scatter of crack propagation paths.
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Korkolis, Yannis P., Nengxiu Deng, and Toshihiko Kuwabara. "Experimental Study of Biaxial Load-Unload Behavior of DP590 Steel Sheets." In ASME 2013 International Manufacturing Science and Engineering Conference collocated with the 41st North American Manufacturing Research Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/msec2013-1171.

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Biaxial load-unload tests under radial paths in the true stress space were carried out for DP590 steel sheets using specially-designed cruciform specimens. Depending on the specific path, over 15% equivalent logarithmic plastic strain was achieved so that the load-unload behavior was successfully probed at relatively high strain levels. It was found that the stress-strain response at the initial load/unload follows the predicted linearly elastic response very well and that subsequently the slope decays. Following this initial phase, a second linear response is observed, which ultimately leads to the non-linear plastic response. The biaxial non-linear strain recovery components εxnl and εynl were measured to be on average approximately 11% of the elastic strains εxe and εye, respectively. At higher strains, this ratio is approximately 25%, indicating the inaccuracy of springback simulations when a linearly elastic unloading response is assumed. For each load-unload cycle, the dissipated energy density tends to increase with the progression of prestrain. The plastic work contours covering the first quadrant of the stress space were successfully constructed and the directions of the plastic strain rates were then calculated. A good agreement with the experimental facts was found by adopting the anisotropic yield function Yld2000-2D.
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Bousquet, Amaury, Stéphane Marie, and Philippe Bompard. "Cleavage Crack Propagation and Arrest in a Nuclear Pressure Vessel Steel." In ASME 2012 Pressure Vessels and Piping Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/pvp2012-78174.

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The integrity assessment of Reactor Pressure Vessels, mainly based on crack initiation, can be completed by studying crack propagation and arrest. Whereas engineering approaches do not take into account dynamic effects, these effects are important in unstable cleavage crack propagation, arrest and possible propagation re-initiation events. This study deals with physical mechanisms of cleavage crack propagation and numerical computations related to brittle fracture in the framework of local approach to fracture. Experiments were carried out on thin CT 25 specimens made of 16MND5 PWR vessel steel at five temperatures (−150°C, −125°C, −100°C, −75°C, −50°C). Two kinds of crack path, straight or branching path, were observed. Branching cracks appear for the highest critical loadings at initiation, that increase the elastic stored energy and the effect of plasticity. The elastic-viscoplastic behavior of the ferritic steel was studied up to a strain rate of 104 s−1 and taken into account in the numerical simulations. The eXtended Finite Element Method (X-FEM) was used in CAST3M FE software to model crack propagation. Numerical computations combine a local non linear dynamic approach with a RKR type fracture stress criterion. The different physical micro-mechanisms, involved in cleavage fracture, were examined by the means of SEM fracture surface analyses at different temperatures and strain rates for the two kinds of crack path. The links of the critical fracture stress with both temperature and strain rate for straight crack path as well as analyses of branching crack phenomena were considered by the means of Scanning Electron Microscopy (SEM) fracture surface analyses, 3D quantitative optical microscopy and FE computations in order to aim at a robust physical justification of the propagation model which has already been developed at CEA in the frame of the B. Prabel PhD.
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Martindale, Hugh, Steven Rossiter, Terence Sheldrake, and Richard Langdon. "Improved Dynamic Structural Modelling for Subsea Power Cables With Bitumen Coated Armour Wires." In ASME 2017 36th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/omae2017-61848.

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This paper presents improved dynamic modelling of subsea power cables using new models for the determination of non-linear cable mechanical properties. The modelling has been developed for cables typically used in offshore wind and for interconnectors, as well as dynamic power umbilicals. The results provide a better simulation of the dynamic response and allow better integration of local and global modelling for determination of stress and fatigue in offshore power cables. Cable response due to bending is modelled by including non-linear adhesion induced stresses due to a yielding bond between armour wire and neighbouring layers, which captures the effects of temperature and strain rate and provides better representation than purely friction-based modelling especially at low tension. Local armour bending stiffness is included by using average wire strain energy after slip along the strained helical path to determine the armour layer bending stiffness contribution. Mathematical modelling for mechanical properties is verified by sample testing and FEA, to provide a robust method for predicting cable response. Although dynamic subsea power cables are essentially non-bonded structures there is a certain amount of adhesion within the structure. Previous work has focused on friction-tension based modelling of armour wire-core interaction, that is not appropriate as critical slip curvatures at low tension are understated and full-slip stress distributions do not account for work done against friction during further bending. The principal result of this new approach is the improved determination of lifetime stresses for critical components within the cable structure. Non-linear bend stiffness modelling produces characteristic moment-curvature relations including hysteresis on reversal of bending. These curves provide an improved representation of the onset of slip in the armour wires and allow for the influence of temperature and strain rate on the cable bending stiffness to be included. The bend-stiffness model has been validated against test data both of complete bundles and individual components. The overall result is a methodology that typically results in increased fatigue life and can reduce the requirement for ancillary products such as ballast/buoyancy and bend stiffeners/restrictors. Additionally, the non-linear, hysteretic response of a cable significantly reduces certain phenomena that are often associated with numerical modelling of cables using a linear bend stiffness. Specifically, a cable catenary attached to a vessel and modelled with a linear bend stiffness will often experience ‘compression waves’ when the vessel is moving in response to wave loading. Use of a non-linear, hysteretic bend stiffness minimises the compression wave phenomenon, giving a much more realistic response and often greatly improving operability windows for offshore operations.
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Seipp, Trevor G., Mark Stonehouse, and Charles Ormsbee. "Considerations in Using FEA for Layered Vessel Construction." In ASME 2010 Pressure Vessels and Piping Division/K-PVP Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/pvp2010-26127.

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This paper will examine some of the considerations for using finite element analysis when evaluating pressure vessels constructed using the layered-shell construction. Since the layers of the shell interact through contact and at the circumferential welds, these particular aspects are discussed. Special attention is paid to the proper selection of the initial gap between the layers. The use of an elastic-plastic stress-strain curve is also discussed. Since the material model is non-linear, the path-dependency of the loading sequence is demonstrated, including the inclusion of the initial hydrostatic test. The techniques presented will be demonstrated using an example of a typical layered shell pressure vessel. Since the evaluation of this type of vessel is usually undertaken in a fitness-for-service sense, and fatigue is often the primary damage mechanism, the remaining fatigue life of this typical pressure vessel is calculated.
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Rossillon, Fre´de´rique, and Yves Me´zie`re. "Analysis of Fracture Specimen Failure of Inconel 600: Elastic-Plastic Calculations and Thermo-Plastic Energy Fracture Parameter." In ASME 2010 Pressure Vessels and Piping Division/K-PVP Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/pvp2010-25323.

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The integrity of structures exhibiting flaws in nuclear power plants, and in particular for class 1 components (pipes, vessels, internals), has to be assessed to meet safety criteria. Technical rules along with simplified assessment methods are available in various standards: ASME, RSE-M, RCC-MR, R6 etc…. They rely on conservative hypotheses and parameters (loading, material properties, failure diagram). They are developed using analytical or numerical approaches and are validated with adequate demonstrative experimental testing. In particular, RSE-M and RCC-MR codes include a large set of compendia for the calculation of the fracture parameter J, depending on component and defect geometries, loading and material characteristics. However, it is essential first to consider the type of failure that the structure is likely to undergo and then to apply the proper assessment methods with the criteria required by the safety rules. For structures made of a material with a high strain-hardening behavior combined with a large enough value of ductile tearing resistance, it is not so easy to identify properly the failure mode between ductile failure or plastic collapse. This paper deals with the fracture mechanical test on a specimen made on Inconel 600 up to the ultimate failure of the sample. Due to the high mechanical properties of this material, the determination of ductile fracture initiation and propagation is quite difficult. Nonetheless the tests were carried out on a Center Cracked specimen under Tension (CCT). A numerical analysis of this experiment is provided using Finite Element (FE) calculations. In this case, the small-scale-yielding hypothesis is not verified and a complex load path is observed. The classical fracture mechanics parameter J-integral is not relevant anymore. The use of an energy fracture parameter in thermo-plasticity, called GTP, seems to be a more adequate parameter to describe correctly the effect of the crack growth. Different models are evaluated and a comparison with more classical parameters in a Non-Linear Elastic (NLE) behavior is done.
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Prabel, B., S. Marie, and A. Combescure. "Mixed Mode Brittle Crack Propagation Modelling in a PWR Vessel Steel." In ASME 2008 Pressure Vessels and Piping Conference. ASMEDC, 2008. http://dx.doi.org/10.1115/pvp2008-61234.

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R&D activities and some development are performed at CEA on the brittle crack propagation and arrest. Phenomena occurring after the initiation of a brittle crack are not yet well understood. Absence of model able to predict the rapid growth of a brittle crack motivates this study. Due to the rapid growth of the crack, inertial effects and dynamic fracture should be considered. Assumption of a linear elastic solid are often preferred, but when plasticity of the material become non negligible (which is the case in the vicinity of the transition zone), these models become more limited. That’s why the paper presented here deals with dynamic crack propagation in elastic-viscoplastic material and aims at proposing a model able to predict the brittle crack propagation and arrest. To this end, experimental work is carried out for different geometries made of french RPV ferritic steel. Compact Tension specimens with different thickness, isothermal rings under compression with different positions of the initial defect to study also a mixed mode configuration. The test conditions and mains results (crack initiation, crack velocity measurements, ...) are collected and presented in a first part of the paper. To model efficiently the crack propagation in the Finite Element calculation, the eXtended Finite Element Method (X-FEM) implemented in the CEA F.E. software CAST3M is described in the second part of the paper. Thanks to this numerical technique, the crack path does not need to follow the element edges and the crack progress is directly incorporated in the degrees of freedom of the elements crossed by the crack. A two-steps methodology is presented in the third and fourth parts of this paper. The first step consider only the CT specimen, experimental crack speed evolution with time is imposed in numerical simulations. Energy terms and stress field at the crack tip are evaluated and discussed to build up a criterion. Then, the criterion identified on CT specimen is used in a second step as a predictive model to simulate crack propagation for each geometry studied (CT, ring in both mode I and mixed mode). In particular, crack propagation models based on the stress field evaluated at the crack tip and on a critical cleavage stress dependent on the strain rate, exhibit very good agreement with experimental data in term of crack speed, crack path and crack length at arrest. The mixed mode case is discussed in detail because to be pertinent, a model of brittle crack propagation should not only give the crack speed, but also its preferred direction of evolution.
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