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Benoit Tanguy - One of the best experts on this subject based on the ideXlab platform.
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ductile fracture characterization of an x70 steel re interpretation of classical Tests using the finite element technique
2008 7th International Pipeline Conference Volume 3, 2008Co-Authors: Philippe Thibaux, Benoit Tanguy, Sebastien Muller, Filip Van Den AbeeleAbstract:The crack arrest capacity of a linepipe is one of the most important material parameter for such components. In current design codes, it is expressed as the energy absorbed by a CVN impact Test. This prescribed impact energy for a given pipeline is typically between 50 and 120J, depending on the grade of the material, the pressure and the dimensions of the pipe. The continuous improvement of steel production has lead to the situation that the impact values achieved in standard pipeline steel production are much larger than 200J for the base material. The question of the significance of these high impact energies can be raised, particularly considering that no correlation has been found between CVN values and crack arrest properties of very high strength materials (X100–X120). In this investigation, instrumented Charpy Tests and notched tensile Tests were performed on an X70 material. The same Tests were also simulated using the finite element method and the Gurson-Tvergaard-Needleman damage model. The combination of supplementary experimental information coming from the instrumentation of the Charpy Test and finite element simulations delivers a different insight about the Test. It is observed that the crack does not break the sample in 2 parts in ductile mode. After 6–7mm of propagation, the crack deviates and stops. The propagation stops when the crack meets the part of the sample becoming wider due to bending. Finite element simulations proved that it results in a quasi constant force during a displacement of the hammer of almost 10mm. The consequence is that more than 25% of the energy is dissipated in a different fracture mode at the end of the Test. Finite element simulations proved also that damage is already occurring at the maximum of the load, but that damage has almost no influence on the load for two-thirds of the displacement at the maximum. In the case of the investigated steel, it means that more than 27J, as often mentioned in standards for avoidance of brittle failure, are dissipated by plastic bending before the initiation of the crack. From the findings of this study, one can conclude that the results of the Charpy Test are very sensitive to crack initiation and that only a limited part of the Test is meaningful to describe crack propagation. Therefore, it is questionable if the Charpy Test is adapted to predict the crack arrest capacity of steels with high crack initiation energy.Copyright © 2008 by ASME
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Local approach to fracture based prediction of the ΔT56J and ΔTKIc 100 shifts due to irradiation for an A508 pressure vessel steel
Engineering Fracture Mechanics, 2006Co-Authors: Benoit Tanguy, Charlotte Bouchet, Stéphane Bugat, Jacques BessonAbstract:Nuclear pressure vessel steels are subjected to irradiation embrittlement which is monitored using Charpy Tests. Reference index temperatures, such as the temperature for which the mean Charpy rupture energy is equal to 56 J (T56J), are used as embrittlement indicators. The safety integrity evaluation is performed assuming that the shift of the nil-ductility reference temperature RTNDT due to irradiation is equal to the shift of T56J. A material model integrating a description of viscoplasticity, ductile damage and cleavage brittle fracture is used to simulate both the Charpy Test and the fracture toughness Test (CT geometry). The model is calibrated on the Charpy data obtained on an unirradiated A508 Cl.3 steel. It is then applied to irradiated materials assuming that irradiation affects solely hardening. Comparison with Charpy energy data for different amounts of irradiation shows that irradiation possibly also affects brittle fracture. The model is then applied to predict the fracture toughness shifts (ΔTKIc,100) for different levels of irradiation.
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ductile to brittle transition of an a508 steel characterized by Charpy impact Test part ii modeling of the Charpy transition curve
Engineering Fracture Mechanics, 2005Co-Authors: Benoit Tanguy, Roland Piques, Jacques Besson, A PineauAbstract:Abstract A finite element simulation of the Charpy Test is developed in order to model the ductile to brittle transition curve of a pressure vessel steel. The material (an A508 steel) and the experimental results are presented in a companion paper (Part I [Engng. Fract. Mech.]). The proposed simulation includes a detailed description of the material viscoplastic behavior over a wide temperature range. Ductile behavior is modeled using modified Rousselier model. The Beremin model is used to describe brittle fracture. The Charpy Test is simulated using a full 3D mesh and accounting for adiabatic heating and contact between the specimen, the striker and the anvil. The developed model is well suited to represent ductile tearing. Using brittle failure parameters identified below −150 °C, it is possible to represent the transition curve up to −80 °C assuming that the Beremin stress parameter σu is independent of temperature. Above this temperature, a temperature dependent Beremin stress parameter, σu, must be used to correctly simulate the transition curve. Quasi-static and dynamic Tests can then be consistently modeled.
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Ductile to brittle transition of an A508 steel characterized by Charpy impact Test: Part II: modeling of the Charpy transition curve
Engineering Fracture Mechanics, 2005Co-Authors: Benoit Tanguy, Jacques Besson, R. Piques, A PineauAbstract:Abstract A finite element simulation of the Charpy Test is developed in order to model the ductile to brittle transition curve of a pressure vessel steel. The material (an A508 steel) and the experimental results are presented in a companion paper (Part I [Engng. Fract. Mech.]). The proposed simulation includes a detailed description of the material viscoplastic behavior over a wide temperature range. Ductile behavior is modeled using modified Rousselier model. The Beremin model is used to describe brittle fracture. The Charpy Test is simulated using a full 3D mesh and accounting for adiabatic heating and contact between the specimen, the striker and the anvil. The developed model is well suited to represent ductile tearing. Using brittle failure parameters identified below −150 °C, it is possible to represent the transition curve up to −80 °C assuming that the Beremin stress parameter σu is independent of temperature. Above this temperature, a temperature dependent Beremin stress parameter, σu, must be used to correctly simulate the transition curve. Quasi-static and dynamic Tests can then be consistently modeled.
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Prediction of the effects of neutron irradiation on the Charpy ductile to brittle transition curve of an A508 pressure vessel steel
Computational Materials Science, 2005Co-Authors: Charlotte Bouchet, Benoit Tanguy, Jacques Besson, Stéphane BugatAbstract:Nuclear pressure vessel steels are subjected to irradiation embrittlement which is monitored using Charpy Tests. Reference index temperatures, such as the temperature for which the mean Charpy rupture energy is equal to 56 J (T56 J), are used as embrittlement indicators. In this work a material model integrating a description of viscoplasticity, ductile damage and brittle fracture is used to simulate the Charpy Test. The model is adjusted on an unirradiated material. It is then applied to irradiated materials assuming that irradiation affects hardening. It is shown that irradiation probably also affects brittle failure. The decrease of the Charpy upper shelf energy is also interpreted.
Jacques Besson - One of the best experts on this subject based on the ideXlab platform.
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Local approach to fracture based prediction of the ΔT56J and ΔTKIc 100 shifts due to irradiation for an A508 pressure vessel steel
Engineering Fracture Mechanics, 2006Co-Authors: Benoit Tanguy, Charlotte Bouchet, Stéphane Bugat, Jacques BessonAbstract:Nuclear pressure vessel steels are subjected to irradiation embrittlement which is monitored using Charpy Tests. Reference index temperatures, such as the temperature for which the mean Charpy rupture energy is equal to 56 J (T56J), are used as embrittlement indicators. The safety integrity evaluation is performed assuming that the shift of the nil-ductility reference temperature RTNDT due to irradiation is equal to the shift of T56J. A material model integrating a description of viscoplasticity, ductile damage and cleavage brittle fracture is used to simulate both the Charpy Test and the fracture toughness Test (CT geometry). The model is calibrated on the Charpy data obtained on an unirradiated A508 Cl.3 steel. It is then applied to irradiated materials assuming that irradiation affects solely hardening. Comparison with Charpy energy data for different amounts of irradiation shows that irradiation possibly also affects brittle fracture. The model is then applied to predict the fracture toughness shifts (ΔTKIc,100) for different levels of irradiation.
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ductile to brittle transition of an a508 steel characterized by Charpy impact Test part ii modeling of the Charpy transition curve
Engineering Fracture Mechanics, 2005Co-Authors: Benoit Tanguy, Roland Piques, Jacques Besson, A PineauAbstract:Abstract A finite element simulation of the Charpy Test is developed in order to model the ductile to brittle transition curve of a pressure vessel steel. The material (an A508 steel) and the experimental results are presented in a companion paper (Part I [Engng. Fract. Mech.]). The proposed simulation includes a detailed description of the material viscoplastic behavior over a wide temperature range. Ductile behavior is modeled using modified Rousselier model. The Beremin model is used to describe brittle fracture. The Charpy Test is simulated using a full 3D mesh and accounting for adiabatic heating and contact between the specimen, the striker and the anvil. The developed model is well suited to represent ductile tearing. Using brittle failure parameters identified below −150 °C, it is possible to represent the transition curve up to −80 °C assuming that the Beremin stress parameter σu is independent of temperature. Above this temperature, a temperature dependent Beremin stress parameter, σu, must be used to correctly simulate the transition curve. Quasi-static and dynamic Tests can then be consistently modeled.
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Ductile to brittle transition of an A508 steel characterized by Charpy impact Test: Part II: modeling of the Charpy transition curve
Engineering Fracture Mechanics, 2005Co-Authors: Benoit Tanguy, Jacques Besson, R. Piques, A PineauAbstract:Abstract A finite element simulation of the Charpy Test is developed in order to model the ductile to brittle transition curve of a pressure vessel steel. The material (an A508 steel) and the experimental results are presented in a companion paper (Part I [Engng. Fract. Mech.]). The proposed simulation includes a detailed description of the material viscoplastic behavior over a wide temperature range. Ductile behavior is modeled using modified Rousselier model. The Beremin model is used to describe brittle fracture. The Charpy Test is simulated using a full 3D mesh and accounting for adiabatic heating and contact between the specimen, the striker and the anvil. The developed model is well suited to represent ductile tearing. Using brittle failure parameters identified below −150 °C, it is possible to represent the transition curve up to −80 °C assuming that the Beremin stress parameter σu is independent of temperature. Above this temperature, a temperature dependent Beremin stress parameter, σu, must be used to correctly simulate the transition curve. Quasi-static and dynamic Tests can then be consistently modeled.
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Prediction of the effects of neutron irradiation on the Charpy ductile to brittle transition curve of an A508 pressure vessel steel
Computational Materials Science, 2005Co-Authors: Charlotte Bouchet, Benoit Tanguy, Jacques Besson, Stéphane BugatAbstract:Nuclear pressure vessel steels are subjected to irradiation embrittlement which is monitored using Charpy Tests. Reference index temperatures, such as the temperature for which the mean Charpy rupture energy is equal to 56 J (T56 J), are used as embrittlement indicators. In this work a material model integrating a description of viscoplasticity, ductile damage and brittle fracture is used to simulate the Charpy Test. The model is adjusted on an unirradiated material. It is then applied to irradiated materials assuming that irradiation affects hardening. It is shown that irradiation probably also affects brittle failure. The decrease of the Charpy upper shelf energy is also interpreted.
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Prediction of the effects of neutron irradiation on the Charpy ductile to brittle transition curve of an A508 pressure vessel steel
Computational Materials Science, 2005Co-Authors: Charlotte Bouchet, Benoit Tanguy, Jacques Besson, Stéphane BugatAbstract:International audienceNuclear pressure vessel steels are subjected to irradiation embrittlement which is monitored using Charpy Tests. Reference index temperatures, such as the temperature for which the mean Charpy rupture energy is equal to 56 J (T56 J), are used as embrittlement indicators. In this work a material model integrating a description of viscoplasticity, ductile damage and brittle fracture is used to simulate the Charpy Test. The model is adjusted on an unirradiated material. It is then applied to irradiated materials assuming that irradiation affects hardening. It is shown that irradiation probably also affects brittle failure. The decrease of the Charpy upper shelf energy is also interpreted
Stéphane Bugat - One of the best experts on this subject based on the ideXlab platform.
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Local approach to fracture based prediction of the ΔT56J and ΔTKIc 100 shifts due to irradiation for an A508 pressure vessel steel
Engineering Fracture Mechanics, 2006Co-Authors: Benoit Tanguy, Charlotte Bouchet, Stéphane Bugat, Jacques BessonAbstract:Nuclear pressure vessel steels are subjected to irradiation embrittlement which is monitored using Charpy Tests. Reference index temperatures, such as the temperature for which the mean Charpy rupture energy is equal to 56 J (T56J), are used as embrittlement indicators. The safety integrity evaluation is performed assuming that the shift of the nil-ductility reference temperature RTNDT due to irradiation is equal to the shift of T56J. A material model integrating a description of viscoplasticity, ductile damage and cleavage brittle fracture is used to simulate both the Charpy Test and the fracture toughness Test (CT geometry). The model is calibrated on the Charpy data obtained on an unirradiated A508 Cl.3 steel. It is then applied to irradiated materials assuming that irradiation affects solely hardening. Comparison with Charpy energy data for different amounts of irradiation shows that irradiation possibly also affects brittle fracture. The model is then applied to predict the fracture toughness shifts (ΔTKIc,100) for different levels of irradiation.
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Prediction of the effects of neutron irradiation on the Charpy ductile to brittle transition curve of an A508 pressure vessel steel
Computational Materials Science, 2005Co-Authors: Charlotte Bouchet, Benoit Tanguy, Jacques Besson, Stéphane BugatAbstract:International audienceNuclear pressure vessel steels are subjected to irradiation embrittlement which is monitored using Charpy Tests. Reference index temperatures, such as the temperature for which the mean Charpy rupture energy is equal to 56 J (T56 J), are used as embrittlement indicators. In this work a material model integrating a description of viscoplasticity, ductile damage and brittle fracture is used to simulate the Charpy Test. The model is adjusted on an unirradiated material. It is then applied to irradiated materials assuming that irradiation affects hardening. It is shown that irradiation probably also affects brittle failure. The decrease of the Charpy upper shelf energy is also interpreted
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Prediction of the effects of neutron irradiation on the Charpy ductile to brittle transition curve of an A508 pressure vessel steel
Computational Materials Science, 2005Co-Authors: Charlotte Bouchet, Benoit Tanguy, Jacques Besson, Stéphane BugatAbstract:Nuclear pressure vessel steels are subjected to irradiation embrittlement which is monitored using Charpy Tests. Reference index temperatures, such as the temperature for which the mean Charpy rupture energy is equal to 56 J (T56 J), are used as embrittlement indicators. In this work a material model integrating a description of viscoplasticity, ductile damage and brittle fracture is used to simulate the Charpy Test. The model is adjusted on an unirradiated material. It is then applied to irradiated materials assuming that irradiation affects hardening. It is shown that irradiation probably also affects brittle failure. The decrease of the Charpy upper shelf energy is also interpreted.
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Local approach to fracture based prediction of the ∆T56J and ∆T K1C100 shifts due to irradiation for an A508 pressure vessel steel
2004Co-Authors: Charlotte Bouchet, Benoit Tanguy, Jacques Besson, Stéphane BugatAbstract:A material model integrating a description of viscoplasticity, ductile damage and brittle fracture is used to simulate both the impact (Charpy) Test and the toughness (CT) fracture Test. The model is calibrated on the Charpy data obtained on an unirradiated A508 Cl.3 steel. It is then applied to irradiated material assuming that irradiation affects solely hardening. Comparison with Charpy energy data for different amounts of irradiation shows that irradiation probably also affects brittle fracture. The model is then used to predict the DTKIc100 shifts for different levels of irradiation.
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Comparison of Predicted Transition Temperature Shifts Between Static Fracture Toughness and Charpy-V Impact Properties Due to Irradiation for an A508 Pressure Vessel Steel
RPV Integrity and Fracture Mechanics, 2004Co-Authors: Benoit Tanguy, Jacques Besson, Charlotte Bouchet, Stéphane BugatAbstract:Nuclear pressure vessel steels are subjected to irradiation embrittlement which is monitored using Charpy Tests. Reference index temperatures, such as the temperature for which the mean Charpy rupture energy is equal to 56 J (T56J ), are used as embrittlement indicators. The safety integrity evaluation is performed assuming that the shift of RTNDT due to irradiation is equal to the shift of T56J . In this work a material model integrating a description of viscoplasticity, ductile damage and brittle fracture is used to simulate both the Charpy Test and the fracture toughness Test (CT geometry). The model is adjusted on an unirradiated material. It is then applied to irradiated materials assuming that irradiation affects hardening. It is shown that irradiation probably also affects brittle failure. The shift of RTNDT and the predicted shift of T100MPam are then compared for a given level of irradiation.Copyright © 2004 by ASME
Enrico Lucon - One of the best experts on this subject based on the ideXlab platform.
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Influence of Machine Anvil Wear on Charpy Test Results
Journal of Research of the National Institute of Standards and Technology, 2020Co-Authors: Enrico Lucon, Raymond L. SantoyoAbstract:We investigated the influence of the state of wear of Charpy machine anvils on Test results byperforming impact Tests on NIST specimens of three energy levels with a machine equipped with new anvils (compliant with both ASTM E23 [1] and ISO 148-2 [2]) and worn anvils (anvil corner radii and distance outside ASTM tolerances, but within ISO tolerances). The results obtained, statistically analyzed, unequivocally show that worn anvils tend to increase absorbed energy at all energy levels. On the other hand, data variability does not appear to be significantly affected by anvil wear. This study represents NIST contribution to an international effort spearheaded by the Japan Iron and Steel Federation Standardization Center (Tokyo, Japan).
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Experimental Assessment of the Equivalent Strain Rate for an Instrumented Charpy Test
Journal of Research of the National Institute of Standards and Technology, 2016Co-Authors: Enrico LuconAbstract:Instrumented Charpy Test data can be used to obtain estimates of dynamic yield strength, by means of a well-established relationship published by W. Server in 1978. A fundamental issue in comparing measured dynamic tensile properties and Charpy-based estimations is establishing the equivalent uniaxial strain rate for an instrumented Charpy Test, typically conducted at ≈ 5.5 m/s. In this investigation, by performing tensile Tests at various strain rates and instrumented Charpy Tests for 10 different materials, we compared values of dynamic yield strength both measured from tensile Tests and estimated by means of Server’s equation. The obtained equivalent Charpy strain rates were found to vary significantly from material to material, and to correlate reasonably with specific values of absorbed energy measured during the impact Tests.
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Estimating dynamic ultimate tensile strength from instrumented Charpy data
Materials & Design, 2016Co-Authors: Enrico LuconAbstract:Abstract Instrumented Charpy Test data have often been used to obtain estimates of various mechanical properties under elevated loading rates, such as dynamic yield properties. A widely used relationship between Charpy general yield force and dynamic yield strength was originally proposed by Server in 1978. This same relationship, however, cannot be used for estimating the dynamic (ultimate) tensile strength from the Charpy maximum force, since it relies on the ratio between shear and tensile stress, which at general yield is different than at maximum force. In the study described in this paper, we modified Server's relationship in order to obtain reliable, and possibly conservative, estimates of dynamic ultimate tensile strength from the maximum force measured in an instrumented Charpy Test. Once more experimental data has been accumulated, the results of this investigation might have significant implications for the revision of fracture mechanics Test standards which utilize dynamic ultimate tensile properties for the qualification/validation of fracture toughness Tests conducted at elevated loading rates.
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Effect of Electrical Discharge Machining (EDM) on Charpy Test Results from Miniaturized Steel Specimens
Journal of Testing and Evaluation, 2012Co-Authors: Enrico LuconAbstract:Electrical discharge machining (EDM) is a manufacturing process whereby a desired shape is obtained through electrical discharges between an electrode and a workpiece, which are separated by a dielectric fluid. EDM produces a recast layer on the surface of the workpiece, which in carbon steels is typically harder and more brittle than the base metal, and is often characterized by microcracks. This type of damage, particularly in the notch region of a steel specimen, can adversely affect impact Test results. The objective of this investigation is to assess the possible influence of EDM on miniaturized Charpy Test results. We Tested Kleinstprobe (KLST)-type Charpy specimens of two reactor pressure vessel (RPV) steels, machined with different combinations of two machining processes (EDM and milling). Comparison of the impact results, combined with metallographic observations and microhardness measurements on the recast layers and the base metals, indicated no detrimental effect of EDM on the impact toughness of the materials investigated. The maximum thickness of the recast layer was about 16 μm, and the magnitude of the EDM-induced hardening varied between 34 % and 84 % with respect to the hardness of the base material, depending on the carbon content of the steel. No microcracks were observed.
Charlotte Bouchet - One of the best experts on this subject based on the ideXlab platform.
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Local approach to fracture based prediction of the ΔT56J and ΔTKIc 100 shifts due to irradiation for an A508 pressure vessel steel
Engineering Fracture Mechanics, 2006Co-Authors: Benoit Tanguy, Charlotte Bouchet, Stéphane Bugat, Jacques BessonAbstract:Nuclear pressure vessel steels are subjected to irradiation embrittlement which is monitored using Charpy Tests. Reference index temperatures, such as the temperature for which the mean Charpy rupture energy is equal to 56 J (T56J), are used as embrittlement indicators. The safety integrity evaluation is performed assuming that the shift of the nil-ductility reference temperature RTNDT due to irradiation is equal to the shift of T56J. A material model integrating a description of viscoplasticity, ductile damage and cleavage brittle fracture is used to simulate both the Charpy Test and the fracture toughness Test (CT geometry). The model is calibrated on the Charpy data obtained on an unirradiated A508 Cl.3 steel. It is then applied to irradiated materials assuming that irradiation affects solely hardening. Comparison with Charpy energy data for different amounts of irradiation shows that irradiation possibly also affects brittle fracture. The model is then applied to predict the fracture toughness shifts (ΔTKIc,100) for different levels of irradiation.
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Prediction of the effects of neutron irradiation on the Charpy ductile to brittle transition curve of an A508 pressure vessel steel
Computational Materials Science, 2005Co-Authors: Charlotte Bouchet, Benoit Tanguy, Jacques Besson, Stéphane BugatAbstract:International audienceNuclear pressure vessel steels are subjected to irradiation embrittlement which is monitored using Charpy Tests. Reference index temperatures, such as the temperature for which the mean Charpy rupture energy is equal to 56 J (T56 J), are used as embrittlement indicators. In this work a material model integrating a description of viscoplasticity, ductile damage and brittle fracture is used to simulate the Charpy Test. The model is adjusted on an unirradiated material. It is then applied to irradiated materials assuming that irradiation affects hardening. It is shown that irradiation probably also affects brittle failure. The decrease of the Charpy upper shelf energy is also interpreted
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Prediction of the effects of neutron irradiation on the Charpy ductile to brittle transition curve of an A508 pressure vessel steel
Computational Materials Science, 2005Co-Authors: Charlotte Bouchet, Benoit Tanguy, Jacques Besson, Stéphane BugatAbstract:Nuclear pressure vessel steels are subjected to irradiation embrittlement which is monitored using Charpy Tests. Reference index temperatures, such as the temperature for which the mean Charpy rupture energy is equal to 56 J (T56 J), are used as embrittlement indicators. In this work a material model integrating a description of viscoplasticity, ductile damage and brittle fracture is used to simulate the Charpy Test. The model is adjusted on an unirradiated material. It is then applied to irradiated materials assuming that irradiation affects hardening. It is shown that irradiation probably also affects brittle failure. The decrease of the Charpy upper shelf energy is also interpreted.
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Local approach to fracture based prediction of the ∆T56J and ∆T K1C100 shifts due to irradiation for an A508 pressure vessel steel
2004Co-Authors: Charlotte Bouchet, Benoit Tanguy, Jacques Besson, Stéphane BugatAbstract:A material model integrating a description of viscoplasticity, ductile damage and brittle fracture is used to simulate both the impact (Charpy) Test and the toughness (CT) fracture Test. The model is calibrated on the Charpy data obtained on an unirradiated A508 Cl.3 steel. It is then applied to irradiated material assuming that irradiation affects solely hardening. Comparison with Charpy energy data for different amounts of irradiation shows that irradiation probably also affects brittle fracture. The model is then used to predict the DTKIc100 shifts for different levels of irradiation.
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Comparison of Predicted Transition Temperature Shifts Between Static Fracture Toughness and Charpy-V Impact Properties Due to Irradiation for an A508 Pressure Vessel Steel
RPV Integrity and Fracture Mechanics, 2004Co-Authors: Benoit Tanguy, Jacques Besson, Charlotte Bouchet, Stéphane BugatAbstract:Nuclear pressure vessel steels are subjected to irradiation embrittlement which is monitored using Charpy Tests. Reference index temperatures, such as the temperature for which the mean Charpy rupture energy is equal to 56 J (T56J ), are used as embrittlement indicators. The safety integrity evaluation is performed assuming that the shift of RTNDT due to irradiation is equal to the shift of T56J . In this work a material model integrating a description of viscoplasticity, ductile damage and brittle fracture is used to simulate both the Charpy Test and the fracture toughness Test (CT geometry). The model is adjusted on an unirradiated material. It is then applied to irradiated materials assuming that irradiation affects hardening. It is shown that irradiation probably also affects brittle failure. The shift of RTNDT and the predicted shift of T100MPam are then compared for a given level of irradiation.Copyright © 2004 by ASME