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Mehmet Erdi Korkmaz - One of the best experts on this subject based on the ideXlab platform.
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Investigation of tensile Johnson-Cook model parameters for Nimonic 80A superalloy
Journal of Alloys and Compounds, 2019Co-Authors: Mehmet Erdi Korkmaz, Mustafa Günay, Patricia VerleysenAbstract:Abstract Developing high temperature technology increases the need for high temperature resistant materials. Nimonic 80A alloy is generally preferred due to its high creep resistance, oxidation resistance and high resistance to high temperature corrosion. The study determines the tensile constitutive equation (JC parameters) of Nimonic 80 A superalloys. Johnson Cook (JC) model is preferred amongst the various material constitutive equations (Zerille Armstrong, Bordner Partom, JC model). Three different kinds of tensile experiment were performed to identify the model parameters. These are quasi-static tensile experiments applied at room temperatures. These experiments were carried out at 0.001, 0.01 and 0.1 s−1 Strain Rates. Therefore, the Reference Strain Rate for all experiments was selected to be 10−3. As a second test, tensile experiments were conducted at room temperature at high Strain Rates (102–103 s−1) using the Split Hopkinson pressure bar (SHPB). Lastly, tensile experiments were conducted at high temperatures (300–900 °C) at 0.001 s−1. It was observed whether all tests are compatible with each other or not, and so five Johnson-Cook (JC) parameters of Nimonic 80 A alloy were identified via the data found from the experiments. After determination of parameters, tensile test simulations by finite element method (FEM) were performed in ANSYS Workbench. As a result, the accuracy of the JC parameters is verified since there is a deviation of %2.84 between the experimental and the simulation results.
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Confirmation of Johnson-Cook Model Parameters for Nimonic 80A alloy by Finite Element Method
Journal of Polytechnic, 2019Co-Authors: Mehmet Erdi Korkmaz, Mustafa GünayAbstract:Nimonic 80A superalloy is frequently used due to its high creep resistance, oxidation resistance and high resistance to high temperature corrosion. On the other hand, due to compatibility of simulation of plastic deformation processes, Johnson-Cook model is chosen among the materials models such as Zerille Armstrong, Bordner Partom, Steinberg-Guinan etc. In this study, primarily, quasi-static compression tests were performed for 10-3, 10-2 and 10-1 s-1 Strain Rates at room temperature. Secondly, dynamic compression tests were secondly conducted at high Strain Rates ranging from 370 to 954 s-1 using the Split Hopkinson Pressure Bar (SHPB) apparatus. Then, the compression tests were conducted at a temperature level from 24~200 °C at the Reference Strain Rate. Johnson-Cook model parameters of Nimonic 80A were determined by analyzing the data obtained from the tests. Lastly, the compression simulations with finite element method (FEM) were performed in ANSYS Workbench to confirm the accuracy of the parameters. In the light of the results, it was determined that there is an average of %3.23 deviation between the experimental and the simulation values. The result showed that accuracy of the Johnson-Cook parameters for Nimonic 80A superalloy was verified with FEM.
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Determination and Verification of Johnson–Cook Parameters for 430 Ferritic Steels via Different Gage Lengths
Transactions of The Indian Institute of Metals, 2019Co-Authors: Mehmet Erdi KorkmazAbstract:Stainless steels, especially ferritic ones, are used in heat-resistant devices, home appliances, construction materials due to their high corrosion resistance, high and low temperature availability, mechanical strength and long-time durability. In this study, it was aimed to identify the Johnson–Cook (JC) parameters of the AISI 430 ferritic stainless steel depending on the gage length variation. After preparing tensile samples with seven different gage lengths (0.5, 1, 2, 5, 10, 20 and 50 mm), the samples were subjected to tensile tests at the same deformation speed (2 mm/s). Here, the variation of the yield stress depending on the Strain Rate was investigated because the deformation speed was kept constant and the gage length was changed. The tensile tests at different Strain Rates were conducted on the same setup. The materials were also subjected to the tensile tests at different temperatures on Reference Strain Rate to perceive the change of the yield stresses at elevated temperatures. As a result of these tests, the JC parameters of the material were determined. Finally, by using these parameters, the tensile test simulations of the material were performed in the finite element simulation package. When the obtained experimental and numerical data were compared, it was determined that there was a deviation of 3.17% between them and the validity of the JC parameters of the material was proved.
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Identification of Constitutive Model Parameters for Nimonic 80A Superalloy
Transactions of the Indian Institute of Metals, 2018Co-Authors: Mehmet Erdi Korkmaz, Patricia Verleysen, Mustafa GünayAbstract:Nimonic 80A is a nickel-chrome superalloy, commonly used due to its high resistance against creep, oxidation, and temperature corrosion. This paper presents the material constitutive models of Nimonic 80A superalloy. Johnson–Cook (JC) and modified JC model is preferred among the different material constitutive equations (Zerill Armstrong, Bodner Partom, Arrhenius type) due to its accuracy in the literature. Three different types of compression tests were applied to determine the equation parameters. Firstly, quasi-static tests were performed at room temperature. These tests were conducted at 10^−3, 10^−2, and 10^−1 s^−1 Strain Rates. Secondly, compression tests were performed at room temperature at high Strain Rates (370–954 s^−1) using the Split-Hopkinson pressure bar. Finally, compression tests were performed at a temperature level from 24 to 200 °C at the Reference Strain Rate (10^−3 s^−1). Johnson–Cook and modified JC model parameters of Nimonic 80A were determined with the data obtained from these tests, and they were finally verified statistically.
A D Sahasrabudhe - One of the best experts on this subject based on the ideXlab platform.
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maxwell fluid model for generation of stress Strain curves of viscoelastic solid rocket propellants
Propellants Explosives Pyrotechnics, 2010Co-Authors: Himanshu Shekhar, A D SahasrabudheAbstract:Solid rocket propellants are modeled as Maxwell Fluid with single spring and single dashpot in series. Complete stress–Strain curve is geneRated for case-bonded composite propellant formulations by taking suitable values of spring constant and damping coefficient. Propellants from same lot are tested at different Strain Rate. It is observed that change in spring constant, representing elastic part is very small with Strain Rate but damping constant varies significantly with variation in Strain Rate. For a typical propellant formulation, when Strain Rate is varied from 0.00037 to 0.185 per second, spring constant (K) changed from 5.5 to 7.9 MPa, but damping coefficient (D) varied from 1400 to 4 MPas. For all Strain Rates, stress–Strain curve is geneRated using developed Maxwell model and close matching with actual test curve is observed. This indicates validity of Maxwell fluid model for case-bonded solid propellant formulations. It is observed that with increases in Strain Rate, spring constant increases but damping coefficient decreases representing solid rocket propellant as a true viscoelastic material. It is also established that at higher Strain Rate, damping coefficient becomes negligible as compared to spring constant. It is also observed that variation of spring constant is logarithmic with Strain Rate and that of damping coefficient follows a power law. The correlation coefficients are introduced to ascertain spring constants and damping coefficients at any Strain Rate from that at a Reference Strain Rate. Correlation for spring constant needs a coefficient “H,” which is function of propellant formulation alone and not of test conditions and the equation developed is K2=(K1-H)×{ln(de2/dt)/ln(de1/dt)}+H. Similarly for damping coefficient (D) also another constant “S” is introduced and prediction formula is given by D2=D1×{(de2/dt)/(de1/dt)}S. Evaluating constants “H” and “S” at different Strain Rates validate this mathematical formulation for different propellant formulations. Close matching of test and predicted stress–Strain curve indicates propellant behavior as viscoelastic Maxwell Fluid. Uniqueness of approach is to predict complete stress–Strain curves, which are not attempted by any other researchers.
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Viscoelastic Modelling of Solid Rocket Propellants using Maxwell Fluid Model
Defence Science Journal, 2010Co-Authors: Himanshu Shekhar, A D SahasrabudheAbstract:Maxwell fluid model consisting of a spring and a dashpot in series is applied for viscoelastic characterisation of solid rocket propellants. Suitable values of spring constant and damping coefficient wereemployed by least square variation of errors for generation of complete stress-Strain curve in uniaxial tensile mode for case-bonded solid propellant formulations. Propellants from the same lot were tested at different Strain Rates. It was observed that change in spring constant, representing elastic part was very small with Strain Rate but damping constant varies significantly with variation in Strain Rate. For a typical propellant formulation, when Strain Rate was raised from 0.00037/s to 0.185/s, spring constant K changed from 5.5 MPato 7.9 MPa, but damping coefficient D was reduced from 1400 MPa-s to 4 MPa-s. For all Strain Rates, stress-Strain curve was geneRated using Maxwell model and close matching with actual test curve was observed.This indicates validity of Maxwell fluid model for uniaxial tensile testing curves of case-bonded solid propellant formulations. It was established that at higher Strain Rate, damping coefficient becomes negligible as compared to spring constant. It was also observed that variation of spring constant is logarithmic with Strain Rate and that of damping coefficient follows power law. The correlation coefficients were introduced to ascertain spring constants and damping coefficients at any Strain Rate from that at a Reference Strain Rate. Correlationfor spring constant needs a coefficient H, which is function of propellant formulation alone and not of test conditions and the equation developeds K2 = K1 + H ´ ln{(de2/dt)/(de1/dt)}. Similarly for damping coefficient D also another constant S is introduced and prediction formula is given by D2 = D1 ´ {(de2/dt)/(de1/dt)}S.Evaluating constants H and S at different Strain Rates validate this mathematical formulation for differentpropellant formulations. Stress-Strain curves for solid propellants can be geneRated at those Strain Rates atwhich actual testing is not possible. Close matching of test and predicted stress-Strain curve indicates propellantbehavior as visco-elastic Maxwell fluid. Defence Science Journal, 2010, 60(4), pp.423-427 , DOI:http://dx.doi.org/10.14429/dsj.60.488
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Maxwell Fluid Model for Generation of Stress–Strain Curves of Viscoelastic Solid Rocket Propellants
Propellants Explosives Pyrotechnics, 2010Co-Authors: Himanshu Shekhar, A D SahasrabudheAbstract:Solid rocket propellants are modeled as Maxwell Fluid with single spring and single dashpot in series. Complete stress–Strain curve is geneRated for case-bonded composite propellant formulations by taking suitable values of spring constant and damping coefficient. Propellants from same lot are tested at different Strain Rate. It is observed that change in spring constant, representing elastic part is very small with Strain Rate but damping constant varies significantly with variation in Strain Rate. For a typical propellant formulation, when Strain Rate is varied from 0.00037 to 0.185 per second, spring constant (K) changed from 5.5 to 7.9 MPa, but damping coefficient (D) varied from 1400 to 4 MPas. For all Strain Rates, stress–Strain curve is geneRated using developed Maxwell model and close matching with actual test curve is observed. This indicates validity of Maxwell fluid model for case-bonded solid propellant formulations. It is observed that with increases in Strain Rate, spring constant increases but damping coefficient decreases representing solid rocket propellant as a true viscoelastic material. It is also established that at higher Strain Rate, damping coefficient becomes negligible as compared to spring constant. It is also observed that variation of spring constant is logarithmic with Strain Rate and that of damping coefficient follows a power law. The correlation coefficients are introduced to ascertain spring constants and damping coefficients at any Strain Rate from that at a Reference Strain Rate. Correlation for spring constant needs a coefficient “H,” which is function of propellant formulation alone and not of test conditions and the equation developed is K2=(K1-H)×{ln(de2/dt)/ln(de1/dt)}+H. Similarly for damping coefficient (D) also another constant “S” is introduced and prediction formula is given by D2=D1×{(de2/dt)/(de1/dt)}S. Evaluating constants “H” and “S” at different Strain Rates validate this mathematical formulation for different propellant formulations. Close matching of test and predicted stress–Strain curve indicates propellant behavior as viscoelastic Maxwell Fluid. Uniqueness of approach is to predict complete stress–Strain curves, which are not attempted by any other researchers.
Mustafa Günay - One of the best experts on this subject based on the ideXlab platform.
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Investigation of tensile Johnson-Cook model parameters for Nimonic 80A superalloy
Journal of Alloys and Compounds, 2019Co-Authors: Mehmet Erdi Korkmaz, Mustafa Günay, Patricia VerleysenAbstract:Abstract Developing high temperature technology increases the need for high temperature resistant materials. Nimonic 80A alloy is generally preferred due to its high creep resistance, oxidation resistance and high resistance to high temperature corrosion. The study determines the tensile constitutive equation (JC parameters) of Nimonic 80 A superalloys. Johnson Cook (JC) model is preferred amongst the various material constitutive equations (Zerille Armstrong, Bordner Partom, JC model). Three different kinds of tensile experiment were performed to identify the model parameters. These are quasi-static tensile experiments applied at room temperatures. These experiments were carried out at 0.001, 0.01 and 0.1 s−1 Strain Rates. Therefore, the Reference Strain Rate for all experiments was selected to be 10−3. As a second test, tensile experiments were conducted at room temperature at high Strain Rates (102–103 s−1) using the Split Hopkinson pressure bar (SHPB). Lastly, tensile experiments were conducted at high temperatures (300–900 °C) at 0.001 s−1. It was observed whether all tests are compatible with each other or not, and so five Johnson-Cook (JC) parameters of Nimonic 80 A alloy were identified via the data found from the experiments. After determination of parameters, tensile test simulations by finite element method (FEM) were performed in ANSYS Workbench. As a result, the accuracy of the JC parameters is verified since there is a deviation of %2.84 between the experimental and the simulation results.
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Confirmation of Johnson-Cook Model Parameters for Nimonic 80A alloy by Finite Element Method
Journal of Polytechnic, 2019Co-Authors: Mehmet Erdi Korkmaz, Mustafa GünayAbstract:Nimonic 80A superalloy is frequently used due to its high creep resistance, oxidation resistance and high resistance to high temperature corrosion. On the other hand, due to compatibility of simulation of plastic deformation processes, Johnson-Cook model is chosen among the materials models such as Zerille Armstrong, Bordner Partom, Steinberg-Guinan etc. In this study, primarily, quasi-static compression tests were performed for 10-3, 10-2 and 10-1 s-1 Strain Rates at room temperature. Secondly, dynamic compression tests were secondly conducted at high Strain Rates ranging from 370 to 954 s-1 using the Split Hopkinson Pressure Bar (SHPB) apparatus. Then, the compression tests were conducted at a temperature level from 24~200 °C at the Reference Strain Rate. Johnson-Cook model parameters of Nimonic 80A were determined by analyzing the data obtained from the tests. Lastly, the compression simulations with finite element method (FEM) were performed in ANSYS Workbench to confirm the accuracy of the parameters. In the light of the results, it was determined that there is an average of %3.23 deviation between the experimental and the simulation values. The result showed that accuracy of the Johnson-Cook parameters for Nimonic 80A superalloy was verified with FEM.
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Identification of Constitutive Model Parameters for Nimonic 80A Superalloy
Transactions of the Indian Institute of Metals, 2018Co-Authors: Mehmet Erdi Korkmaz, Patricia Verleysen, Mustafa GünayAbstract:Nimonic 80A is a nickel-chrome superalloy, commonly used due to its high resistance against creep, oxidation, and temperature corrosion. This paper presents the material constitutive models of Nimonic 80A superalloy. Johnson–Cook (JC) and modified JC model is preferred among the different material constitutive equations (Zerill Armstrong, Bodner Partom, Arrhenius type) due to its accuracy in the literature. Three different types of compression tests were applied to determine the equation parameters. Firstly, quasi-static tests were performed at room temperature. These tests were conducted at 10^−3, 10^−2, and 10^−1 s^−1 Strain Rates. Secondly, compression tests were performed at room temperature at high Strain Rates (370–954 s^−1) using the Split-Hopkinson pressure bar. Finally, compression tests were performed at a temperature level from 24 to 200 °C at the Reference Strain Rate (10^−3 s^−1). Johnson–Cook and modified JC model parameters of Nimonic 80A were determined with the data obtained from these tests, and they were finally verified statistically.
Himanshu Shekhar - One of the best experts on this subject based on the ideXlab platform.
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maxwell fluid model for generation of stress Strain curves of viscoelastic solid rocket propellants
Propellants Explosives Pyrotechnics, 2010Co-Authors: Himanshu Shekhar, A D SahasrabudheAbstract:Solid rocket propellants are modeled as Maxwell Fluid with single spring and single dashpot in series. Complete stress–Strain curve is geneRated for case-bonded composite propellant formulations by taking suitable values of spring constant and damping coefficient. Propellants from same lot are tested at different Strain Rate. It is observed that change in spring constant, representing elastic part is very small with Strain Rate but damping constant varies significantly with variation in Strain Rate. For a typical propellant formulation, when Strain Rate is varied from 0.00037 to 0.185 per second, spring constant (K) changed from 5.5 to 7.9 MPa, but damping coefficient (D) varied from 1400 to 4 MPas. For all Strain Rates, stress–Strain curve is geneRated using developed Maxwell model and close matching with actual test curve is observed. This indicates validity of Maxwell fluid model for case-bonded solid propellant formulations. It is observed that with increases in Strain Rate, spring constant increases but damping coefficient decreases representing solid rocket propellant as a true viscoelastic material. It is also established that at higher Strain Rate, damping coefficient becomes negligible as compared to spring constant. It is also observed that variation of spring constant is logarithmic with Strain Rate and that of damping coefficient follows a power law. The correlation coefficients are introduced to ascertain spring constants and damping coefficients at any Strain Rate from that at a Reference Strain Rate. Correlation for spring constant needs a coefficient “H,” which is function of propellant formulation alone and not of test conditions and the equation developed is K2=(K1-H)×{ln(de2/dt)/ln(de1/dt)}+H. Similarly for damping coefficient (D) also another constant “S” is introduced and prediction formula is given by D2=D1×{(de2/dt)/(de1/dt)}S. Evaluating constants “H” and “S” at different Strain Rates validate this mathematical formulation for different propellant formulations. Close matching of test and predicted stress–Strain curve indicates propellant behavior as viscoelastic Maxwell Fluid. Uniqueness of approach is to predict complete stress–Strain curves, which are not attempted by any other researchers.
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Viscoelastic Modelling of Solid Rocket Propellants using Maxwell Fluid Model
Defence Science Journal, 2010Co-Authors: Himanshu Shekhar, A D SahasrabudheAbstract:Maxwell fluid model consisting of a spring and a dashpot in series is applied for viscoelastic characterisation of solid rocket propellants. Suitable values of spring constant and damping coefficient wereemployed by least square variation of errors for generation of complete stress-Strain curve in uniaxial tensile mode for case-bonded solid propellant formulations. Propellants from the same lot were tested at different Strain Rates. It was observed that change in spring constant, representing elastic part was very small with Strain Rate but damping constant varies significantly with variation in Strain Rate. For a typical propellant formulation, when Strain Rate was raised from 0.00037/s to 0.185/s, spring constant K changed from 5.5 MPato 7.9 MPa, but damping coefficient D was reduced from 1400 MPa-s to 4 MPa-s. For all Strain Rates, stress-Strain curve was geneRated using Maxwell model and close matching with actual test curve was observed.This indicates validity of Maxwell fluid model for uniaxial tensile testing curves of case-bonded solid propellant formulations. It was established that at higher Strain Rate, damping coefficient becomes negligible as compared to spring constant. It was also observed that variation of spring constant is logarithmic with Strain Rate and that of damping coefficient follows power law. The correlation coefficients were introduced to ascertain spring constants and damping coefficients at any Strain Rate from that at a Reference Strain Rate. Correlationfor spring constant needs a coefficient H, which is function of propellant formulation alone and not of test conditions and the equation developeds K2 = K1 + H ´ ln{(de2/dt)/(de1/dt)}. Similarly for damping coefficient D also another constant S is introduced and prediction formula is given by D2 = D1 ´ {(de2/dt)/(de1/dt)}S.Evaluating constants H and S at different Strain Rates validate this mathematical formulation for differentpropellant formulations. Stress-Strain curves for solid propellants can be geneRated at those Strain Rates atwhich actual testing is not possible. Close matching of test and predicted stress-Strain curve indicates propellantbehavior as visco-elastic Maxwell fluid. Defence Science Journal, 2010, 60(4), pp.423-427 , DOI:http://dx.doi.org/10.14429/dsj.60.488
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Maxwell Fluid Model for Generation of Stress–Strain Curves of Viscoelastic Solid Rocket Propellants
Propellants Explosives Pyrotechnics, 2010Co-Authors: Himanshu Shekhar, A D SahasrabudheAbstract:Solid rocket propellants are modeled as Maxwell Fluid with single spring and single dashpot in series. Complete stress–Strain curve is geneRated for case-bonded composite propellant formulations by taking suitable values of spring constant and damping coefficient. Propellants from same lot are tested at different Strain Rate. It is observed that change in spring constant, representing elastic part is very small with Strain Rate but damping constant varies significantly with variation in Strain Rate. For a typical propellant formulation, when Strain Rate is varied from 0.00037 to 0.185 per second, spring constant (K) changed from 5.5 to 7.9 MPa, but damping coefficient (D) varied from 1400 to 4 MPas. For all Strain Rates, stress–Strain curve is geneRated using developed Maxwell model and close matching with actual test curve is observed. This indicates validity of Maxwell fluid model for case-bonded solid propellant formulations. It is observed that with increases in Strain Rate, spring constant increases but damping coefficient decreases representing solid rocket propellant as a true viscoelastic material. It is also established that at higher Strain Rate, damping coefficient becomes negligible as compared to spring constant. It is also observed that variation of spring constant is logarithmic with Strain Rate and that of damping coefficient follows a power law. The correlation coefficients are introduced to ascertain spring constants and damping coefficients at any Strain Rate from that at a Reference Strain Rate. Correlation for spring constant needs a coefficient “H,” which is function of propellant formulation alone and not of test conditions and the equation developed is K2=(K1-H)×{ln(de2/dt)/ln(de1/dt)}+H. Similarly for damping coefficient (D) also another constant “S” is introduced and prediction formula is given by D2=D1×{(de2/dt)/(de1/dt)}S. Evaluating constants “H” and “S” at different Strain Rates validate this mathematical formulation for different propellant formulations. Close matching of test and predicted stress–Strain curve indicates propellant behavior as viscoelastic Maxwell Fluid. Uniqueness of approach is to predict complete stress–Strain curves, which are not attempted by any other researchers.
Patricia Verleysen - One of the best experts on this subject based on the ideXlab platform.
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Investigation of tensile Johnson-Cook model parameters for Nimonic 80A superalloy
Journal of Alloys and Compounds, 2019Co-Authors: Mehmet Erdi Korkmaz, Mustafa Günay, Patricia VerleysenAbstract:Abstract Developing high temperature technology increases the need for high temperature resistant materials. Nimonic 80A alloy is generally preferred due to its high creep resistance, oxidation resistance and high resistance to high temperature corrosion. The study determines the tensile constitutive equation (JC parameters) of Nimonic 80 A superalloys. Johnson Cook (JC) model is preferred amongst the various material constitutive equations (Zerille Armstrong, Bordner Partom, JC model). Three different kinds of tensile experiment were performed to identify the model parameters. These are quasi-static tensile experiments applied at room temperatures. These experiments were carried out at 0.001, 0.01 and 0.1 s−1 Strain Rates. Therefore, the Reference Strain Rate for all experiments was selected to be 10−3. As a second test, tensile experiments were conducted at room temperature at high Strain Rates (102–103 s−1) using the Split Hopkinson pressure bar (SHPB). Lastly, tensile experiments were conducted at high temperatures (300–900 °C) at 0.001 s−1. It was observed whether all tests are compatible with each other or not, and so five Johnson-Cook (JC) parameters of Nimonic 80 A alloy were identified via the data found from the experiments. After determination of parameters, tensile test simulations by finite element method (FEM) were performed in ANSYS Workbench. As a result, the accuracy of the JC parameters is verified since there is a deviation of %2.84 between the experimental and the simulation results.
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Identification of Constitutive Model Parameters for Nimonic 80A Superalloy
Transactions of the Indian Institute of Metals, 2018Co-Authors: Mehmet Erdi Korkmaz, Patricia Verleysen, Mustafa GünayAbstract:Nimonic 80A is a nickel-chrome superalloy, commonly used due to its high resistance against creep, oxidation, and temperature corrosion. This paper presents the material constitutive models of Nimonic 80A superalloy. Johnson–Cook (JC) and modified JC model is preferred among the different material constitutive equations (Zerill Armstrong, Bodner Partom, Arrhenius type) due to its accuracy in the literature. Three different types of compression tests were applied to determine the equation parameters. Firstly, quasi-static tests were performed at room temperature. These tests were conducted at 10^−3, 10^−2, and 10^−1 s^−1 Strain Rates. Secondly, compression tests were performed at room temperature at high Strain Rates (370–954 s^−1) using the Split-Hopkinson pressure bar. Finally, compression tests were performed at a temperature level from 24 to 200 °C at the Reference Strain Rate (10^−3 s^−1). Johnson–Cook and modified JC model parameters of Nimonic 80A were determined with the data obtained from these tests, and they were finally verified statistically.