PSI - Issue 14

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Procedia Structural Integrity 14 (2019) 798–805

2nd International Conference on Structural Integrity and Exhibition 2018 Implementation of Internal-State-Variable Based Model into Finite Element Code and its Applicability to Study the Tensile Behaviour of Type 316LN SS With Different Notch Radii C. Praveen a, *, J. Christopher a , V. Ganesan a , Vani Shankar a , G.V. Prasad Reddy a , B.K. Choudhary a a Materials Development and Technology Division Indira Gandhi Centre for Atomic Research, HBNI, Kalpakkam – 603 102, Tamil Nadu, India Abstract An attempt has been made towards the implementation of two-internal-variable model based on the evolution of forest dislocation density and mean free path with the plastic strain into finite element code via user-defined material subroutine using implicit Euler backward algorithm with radial-return scheme. The rate independent two-internal-variable model considers isotropic hardening and the parameters associated with the model are optimised by fitting uniaxial true stress-true plastic strain data. Applicability of the implemented scheme has been examined by simulating the tensile behaviour of type 316LN austenitic stainless steel with different U-notch radii as 1.25, 2.5 and 5 mm at 300 K. Good agreement between the predicted and experimental data has been observed. Detailed analysis showed notch-strengthening effect increases with decrease in notch radius at 300 K. 1. Introduction Constitutive models available in the commercial finite element softwares to describe the flow and work hardening behaviour of metals and alloys are usually of empirical relationships. In common, flow stress is described as a function of external variable i.e. plastic strain in empirical power law based models. These constitutive descriptions are lacking in interpretation of physical processes during deformation. Hor et al., (2013) mentioned that constitutive models should be capable of accounting for the evolving internal microstructural features during inelastic deformation irrespective of variations in imposed conditions such as strain, strain rate and temperature. It was reported that models based on internal-state-variables (I-S-Vs) not only provide better description of inelastic deformation but also capture the evolution of internal microstructural features during deformation (Kocks et al., 1976). In general, several models based on the evolution of internal state-variable i.e. dislocation density were proposed to describe the tensile flow behavior of materials (Mecking and Kocks, 1981; Estrin and Mecking, 1984; Estrin and Kubin, 1986). In these models, the concept of two competitive rate processes i.e. dislocation storage against obstacles and thermally activated dynamic recovery 2nd International Conference on Structural Integrity and Exhibition 2018 Implementation of Internal-State-Variable Based Model into Finite Element Code and its Applicability to Study the Tensile Behaviour of Type 316LN SS With Different Notch Radii C. Praveen a, *, J. Christopher a , V. Ganesan a , Vani Shankar a , G.V. Prasad Reddy a , B.K. Choudhary a a Materials Development and Technology Division Indira Gandhi Centre for Atomic Research, HBNI, Kalpakkam – 603 102, Tamil Nadu, India Abstract An attempt has been made towards the implementation of two-internal-variable model based on the evolution of forest dislocation density and mean free path with the plastic strain into finite element code via user-defined material subroutine using implicit Euler backward algorithm with radial-return scheme. The rate independent two-internal-variable model considers isotropic hardening and the parameters associated with the model are optimised by fitting uniaxial true stress-true plastic strain data. Applicability of the implemented scheme has been examined by simulating the tensile behaviour of type 316LN austenitic stainless steel with different U-notch radii as 1.25, 2.5 and 5 mm at 300 K. Good agreement between the predicted and experimental data has been observed. Detailed analysis showed notch-strengthening effect increases with decrease in notch radius at 300 K. Keywords: Two-internal-variable model; Type 316LN SS; U-notch; Euler backward algorithm 1. Introduction Constitutive models available in the commercial finite element softwares to describe the flow and work hardening behaviour of metals and alloys are usually of empirical relationships. In common, flow stress is described as a function of external variable i.e. plastic strain in empirical power law based models. These constitutive descriptions are lacking in interpretation of physical processes during deformation. Hor et al., (2013) mentioned that constitutive models should be capable of accounting for the evolving internal microstructural features during inelastic deformation irrespective of variations in imposed conditions such as strain, strain rate and temperature. It was reported that models based on internal-state-variables (I-S-Vs) not only provide better description of inelastic deformation but also capture the evolution of internal microstructural features during deformation (Kocks et al., 1976). In general, several models based on the evolution of internal state-variable i.e. dislocation density were proposed to describe the tensile flow behavior of materials (Mecking and Kocks, 1981; Estrin and Mecking, 1984; Estrin and Kubin, 1986). In these models, the concept of two competitive rate processes i.e. dislocation storage against obstacles and thermally activated dynamic recovery 2nd International Conference on Structural Integrity and Exhibition 2018 Implementation of Internal-State-Variable Based Model into Finite Element Code and its Applicability to Study the Tensile Behaviour of Type 316LN SS With Different Notch Radii C. Praveen a, *, J. Christopher a , V. Ganesan a , Vani Shankar a , G.V. Prasad Reddy a , B.K. Choudhary a a Materials Development and Technology Division Indira Gandhi Centre for Atomic Research, HBNI, Kalpakkam – 603 102, Tamil Nadu, India Abstract An attempt has been made towards the implementation of two-internal-variable model based on the evolution of forest dislocation density and mean free path with the plastic strain into finite element code via user-defined material subroutine using implicit Euler backward algorithm with radial-return scheme. The rate independent two-internal-variable model considers isotropic hardening and the parameters associated with the model are optimised by fitting uniaxial true stress-true plastic strain d ta. Applicability of the implemented scheme has been examine by simulating the tensile behaviour of type 316LN austenitic stainless steel with different U-notch radii as 1.25, 2.5 a 5 mm at 300 K. Good agreement between he predicted and experiment l data has been observed. Detailed analysis showed notch-strengthening eff ct increase with decrease in notch radius at 300 K. Keywords: Two-int r al-variable mo el; Type 316LN SS; U-notch; Euler backward algorithm 1. Introduction Constitutive models available in the commercial finite element softwares to describe the flow and work hardening behaviour of metals and alloys are usually of empirical relationships. In common, flow stress is described as a function of external variable i.e. plastic strain in empirical power law based models. These constitutive descr ptions are lacking in interpretation of physical processes during deformation. Hor et al., (2013) mentioned that constitutive models should be capable of accounting for the evolving internal microstructural features during inelastic deformation irrespective of variations in imposed conditions suc as strain, strain rate and temperature. It was reported that models based on internal-state-variables (I-S-Vs) not only provide b tter d scription of inelastic deformation but also capture the evolution of internal microstructur features during d formation (Kocks et al., 1976). In general, several models based on the evolution of internal state-variable i.e. dislocation density ere roposed to describe the te sile flow behavior of materials (Mecking and Kocks, 1981; Estrin and Mecking, 1984; Estrin and Kubin, 1986). In these models, the concep of two competitive rate processes i.e. dislocation storage agai st ob tacles and thermally activated dynamic recovery * Corresponding author. Tel: +91 9444640519 E-mail address: cpraveen@igcar.gov.in 2nd International onference on Structural Integrity and Exhibition 2018 I l t ti f I t r l- t - ri l s l i t i it l t its li ilit t t t Te sil B i r f it iff r t t ii C. Praveen a, *, J. Christopher a , V. Ganesan a , Vani Shankar a , G.V. Prasad Reddy a , B.K. Choudhary a a Materials Development and Technology Division Indira Gandhi Centre for Atomic Rese rch, HBNI, Kalpakkam – 603 102, Tamil Nadu, India Abstract An attempt has been made towards the implementation of two-internal-variable model based on the evolution of forest dislocation density and mean free path with the plastic strain into finite element code via user-defined material subroutine using implicit Euler backward algorithm with radial-return scheme. The rate independent two-internal-variable model considers isotropic hardening and the para eters associated with the model are optimised by fitting uniaxial true stress-true plastic strain data. Applicability of the implemented scheme has been examined by simulating the tensile behaviour of type 316LN austenitic stainless steel with different U-notch radii as 1.25, 2.5 and 5 mm at 300 K. Good agreement between the predicted and experimental data has been observed. Detailed analysis showed notch-strengthening effect increases with decrease in notch radius at 300 K. Keywords: Two-internal-variable model; Type 316LN SS; U-notch; Euler backward algorithm 1. Introduction Constitutive odels available in the commercial finite element softwares to describe the flow and work hardening behaviour of etals and alloys are usually of e pirical relationships. In co on, flo stress is described as a function of external variable i.e. plastic strain in e pirical power law based m dels. These constitutive descriptions are lacking in interpretation of physical processes during defor ation. Hor et al., (2013) mentioned that constitutive models should be capable of accounting for the evolving internal microstructural features during inelastic deformation irrespective of variations in i posed conditions such as strain, strain rate and temperature. It was reported that models based on internal-state-variables (I-S-Vs) not only provide better description of inelastic defor ation but also capture the evolution of internal icrostructural features during defor ation (Kocks et al., 1976). In general, several models based on the evolution of internal state-variable i.e. dislocation density were proposed to describe the tensile flow behavior of aterials ( ecking and Kocks, 1981; Estrin and Mecking, 1984; Estrin and Kubin, 1986). In these models, the c cept of two co petitive rate processes i.e. dislocation storage against obstacles and thermally activated dynamic recovery * Corresponding author. Tel: +91 9444640519 E-mail address: cpraveen@igcar.gov.in 2nd International Conference on Structural Integrity and Exhibition 2018 Implementation of Internal-State-Variable Based Model into Finite El ment C de and its Applicability to Stu y the Tensile Behaviour of Type 316LN SS With Different Notch Radii C. Praveen a, *, J. Christopher a , V. Ganesan a , Vani Shankar a , G.V. Prasad Reddy a , B.K. Choudhary a a Materials Development and Technology Division Indira Gandhi Centre for Atomic Research, HBNI, Kalpakkam – 603 102, Tamil Nadu, India Abstract An attempt has been ade towards the mplementa on of two-inter al-variable m el based on the evolution of forest dislocation density and mean free path with the plastic strai into finite lem nt cod via user-defined material subroutine using mplicit Euler backwar algorith with radial-return scheme. Th r t independent two-internal-variabl model considers iso opic hardening and the parameters associated with the model are optimised by fitting uniaxial true stress-tr e plastic strain data. Applicability of the implemented scheme has been examined by simulating the tensile behaviour of typ 316LN aust nitic stainless stee with different U-notch radii as 1.25, 2.5 and 5 mm at 300 K. Good agr ement between th predicted and experimental data has been observed. Detailed analysis showed notch-strengthening effect increases with decrease in notch radius at 300 K. Keywords: Two-internal-variable model; Type 316LN SS; U-notch; Euler backward algorithm 1. Introduction Constitutive models available in the commercial inite element softwares to describe the flo and work hardening behaviour f metals and alloys are usually of empirical relationships. In common, flow stress is described as a function of external variable i. . plastic strain in mpirical power law based m dels. These constitutive descriptions are lacking in interpretation f phys cal processes during defor ati n. Hor et al., (2013) mentioned that constitutive models should b capable of accounting for the volving internal microstructural features during inelast c deformation irrespective of variations in imposed conditions such as strain, strain rate and temperature. It was reported that models b sed on internal-state-variables (I-S-Vs) not o ly provide better description of inelastic deformation but also capture the evolution of internal micro tr tural feature during deformation (Kocks et al., 1976). In general, several mod ls based on the evolution of internal state-variable i.e. dislocation density wer p oposed to describe the tensile flow behavior of materials (Mecking and Kocks, 1981; Estrin and Mecking, 1984; Estrin and Kubin, 1986). In these models, the c cept of two competitive rate processes i.e. di location st rage against obstacl s a d thermally ctivated dynamic recovery 2nd International Conference on Structural Integrity and Exhibition 2018 I plementation of Internal-State-Variable ased odel into Finite Ele ent ode and its pplicability to Study the Tensile ehaviour of Typ 316L SS ith Different Notch Radii C. Praveen a, *, J. Christopher a , V. Ganesan a , Vani Shankar a , G.V. Prasad Reddy a , B.K. Choudhary a a Materials Development and Technology Division Indira Gandhi Centre for Atomic Research, HBNI, Kalpakkam – 603 102, Tamil Nadu, India Abstract An attempt has been made towards the implementation of two-internal-variable model based on the evolution of forest dislocation density and mean free path with the plastic strain into finite element code via user-defined material subroutine using implicit Euler backw rd alg rith with radial-return scheme. Th rat independent two internal-variable model considers sotropic hardening and the para eters associat d with the model are optimised by fitting uniaxial true stress-true plastic strain data. Applicability of the implemented scheme has been examined by simulating the tensil behavio r of type 316LN auste itic st inless steel with different U-notch r dii as 1.25, 2.5 and 5 mm at 300 K. Good agreement betwe n the predict d and experimenta data has be observed. Detailed analysis showed notch-strengthening effect increases with decrease in notch radius at 300 K. Keywords: Two-internal-variable model; Type 316LN SS; U-notch; Euler backward algorithm 1. Introduction Constitutive models available in the commercial finite element softwares to describe the flow and work hardening behaviour of metals and alloys are usually of empirical relationships. In common, flow stress is described as a functi n of external variable i.e. plastic strain in empirical power law based model . These constitutive descripti s are lacking in interpretation of physical processes during deformation. Hor et al., (2013) m ntioned that constitut ve models should be capable of accounting for the evolving internal microstructural features during inelastic deformation irr spective of variations in imposed conditions such as strain, strain r te and temperature. It was reported that models based on internal-state-variables (I-S-Vs) not only provide better description of inelastic deformation but also capture the evolution of internal microstructural features during deformation (Kock et al., 1976). In general, several models based on the evolution of internal st e-variable i.e. dislocation density were proposed to describe the tensile flow behavior of materials (Mecking and Kocks, 1981; Estrin and Mecking, 1984; Estrin and Kubin, 1986). In these models, the concept of two competitive rate processes i.e. dislocation storage agai st obstacles and thermally activated dynamic recovery © 2019 The Authors. Publish d by Elsevier B.V. This is an op n access article under he CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of Peer-review und responsibility of the SICE 2018 organizers. Keywords: Two-internal-variable model; Type 316LN SS; U-notch; Euler backward algorithm

* Corresponding author. Tel: +91 9444640519 E-mail address: cpraveen@igcar.gov.in * Corresponding author. Tel: +91 9444640519 E-mail address: cpraveen@igcar.gov.in * Corresponding author. Tel: +91 9444640519 E-mail address: cpraveen@igcar.gov.in * Corresponding author. Tel: +91 9444640519 E-mail address: cpraveen@igcar.gov.in

2452-3216  2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of Peer-review under responsibility of the SICE 2018 organizers. 10.1016/j.prostr.2019.07.058 2452-3216 © 2018 Th Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://crea ivecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of Peer-review under responsibility of the SICE 2018 organizers. 2452-3216 © 2018 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of Peer-review under responsibility of the SICE 2018 organizers. 2452-3216 © 2018 Th Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of Peer-review under responsibility of the SICE 2018 organizers. 2452-3216 © 2018 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of Peer-review under responsibility of the SICE 2018 organizers. 2452-3216 © 2018 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creat vecommons.org/licenses/by- c-nd/4.0/) Selection and peer-review under responsibility of Peer-review under responsibility of the SICE 2018 organizers. 2452-3216 © 2018 The Authors. Published by Elsevier B.V. This is an open ac ess article under the CC BY-NC-ND license (https://creativecommon .org/licenses by-nc-nd/4.0/) Selection and peer-review under responsibility of P er-revi w under responsibility of the SICE 2018 organizers.