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Effect of Triaxial State of Stress on Tensile Behavior of Modified 9Cr-1Mo Steel

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Abstract

In this investigation, effect of triaxial state of stress on tensile behavior of modified 9Cr-1Mo steel has been studied. In order to introduce different triaxial states of stresses, circumferential notches of different notch root radii were incorporated in the smooth specimens. The tensile tests were conducted at room temperature and at a strain rate of 3 × 10−4 s−1 in air environment. The tensile strength increased, and the ductility (% reduction in area) decreased with a decrease in notch root radius. The curve fitting of tensile data of smooth specimen was carried out using various constitutive equations. The Voce constitutive equation was found to represent the tensile data of the smooth specimen up to the point of necking. An approach consisting of Voce equation for pre-necking and an exponential equation for post-necking behavior of the material was used as input material model which could predict the complete tensile response of the material. The tensile data obtained from the analysis were used as input for the estimation of tensile response of the notched specimens. The load–displacement curves of the notched specimens could be predicted well using finite element analysis. The comparison of stress and strain obtained from finite element analysis was also carried out with the Bridgman equations for the notched specimens. Significant difference in stress distribution was observed as compared to the distribution obtained by finite element analysis for relatively sharper notches.

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References

  1. L. Niu, H. Takaku, and M. Kobayashi, Tensile Fracture Behaviours in Double-Notched Thin Plates of a Ductile Steel, ISIJ Int., 2005, 45, p 281–287

    Article  CAS  Google Scholar 

  2. A. Wormsen, F. Kirkemo, and, T. Hagner, Tensile Testing and Analysis of Notched Low Alloy Steel Specimens, Proceedings of the ASME 2016 Pressure Vessels and Piping Conference PVP2016, July 17–21, 2016, Vancouver, British Columbia, Canada

  3. W. Wang, X. Qian, R. Su, and X. Wang, Tensile Tests and Analyses of Notched Specimens Fabricated from High Strength Steels Using a Generalized Yield Model, Fatigue Fract. Eng. Mater. Struct., 2010, 33, p 310–319

    CAS  Google Scholar 

  4. S. Goyal, K. Laha, C.R. Das, S. Panneer Selvi, and M.D. Mathew, Finite Element Analysis of State of Triaxial State of Stress on Creep Cavitation and Rupture Behaviour of 2.25Cr-1Mo Steel, Int. J. Mech. Sci., 2013, 75, p 233–243

    Article  Google Scholar 

  5. S. Goyal, K. Laha, C.R. Das, S. Panneer Selvi, and M.D. Mathew, Finite Element Analysis of Uniaxial and Multiaxial State of Stress on Creep Rupture Behaviour of 2.25Cr-1Mo Steel, Mater. Sci. Eng., A, 2013, 563, p 68–77

    Article  CAS  Google Scholar 

  6. S. Goyal and K. Laha, Creep Life Prediction of 9Cr-1Mo Steel Under Multiaxial State of Stress, Mater. Sci. Eng., A, 2014, 615, p 348–360

    Article  CAS  Google Scholar 

  7. K.S. Zhang and Z.H. Li, Numerical Analysis of the Stress–Strain Curve and Fracture Initiation for Ductile Material, Eng. Fract. Mech., 1994, 49, p 235–241

    Article  Google Scholar 

  8. Y. Bao, Dependence of Ductile Crack Formation in Tensile Tests on Stress Triaxiality, Stress and Strain Ratios, Eng. Fract. Mech., 2005, 72, p 505–522

    Article  Google Scholar 

  9. P. Bridgman, Studies in Large Plastic Flow and Fracture, McGraw-Hill Book Company, New York, 1952

    Google Scholar 

  10. B. Wattrisse, A. Chrysochoos, J.-M. Muracciole, and M. Némoz-Gaillard, Analysis of Strain Localization During Tensile Tests by Digital Image Correlation, Exp. Mech., 2001, 41, p 29–39

    Article  Google Scholar 

  11. A. Kato, Measurement of Strain Distribution in Metals for Tensile Test Using Digital Image Correlation Method and Consideration of Stress–Strain Relation, Mech. Eng. J., 2016, 3, p 16–00141

    Article  Google Scholar 

  12. L. Wang and W. Tong, Identification of Post Necking Strain Hardening Behaviour of Thin Sheet Metals from Image-Based Surface Strain Data in Uniaxial Tension Tests, Int. J. Solids Struct., 2015, 75–76, p 12–31

    Article  Google Scholar 

  13. Y. Ling, Uniaxial True Stress–Strain After Necking, AMP J. Technol., 1996, 5, p 37–48

    Google Scholar 

  14. M. Joun, J.G. Eom, and M.C. Lee, A New Method for Acquiring True Stress–Strain Curves Over a Large Range of Strains Using a Tensile Test and Finite Element Method, Mech. Mater., 2008, 40, p 586–593

    Article  Google Scholar 

  15. M. Joun, I. Choi, J. Eom, and M. Lee, Finite Element Analysis of Tensile Testing with Emphasis on Necking, Comput. Mater. Sci., 2007, 41, p 63–69

    Article  Google Scholar 

  16. S. Coppieters and T. Kuwabara, Identification of Post-Necking Hardening Phenomena in Ductile Sheet Metal, Exp. Mech., 2014, 54, p 1355–1371

    Article  CAS  Google Scholar 

  17. C.R. Das, S.K. Albert, J. Swaminathan, S. Raju, A.K. Bhaduri, and B.S. Murty, Transition of Crack from Type IV to Type II, Resulting from Improved Utilization of Boron in the Modified 9Cr-1Mo Steel Weldment, Metall. Mater. Trans. A, 2012, 43, p 3724–3741

    Article  CAS  Google Scholar 

  18. A.G. Miller, Review of Limit Loads of Structures Containing Defects, Int. J. Press. Vessels Pip., 1988, 32, p 197–327

    Article  Google Scholar 

  19. Y.-J. Kim, O. Chang-Kyun, M.-S. Myung, and J.-M. Park, Fully Plastic Analyses for Notched Bars and Plates Using Finite Element Limit Analysis, Eng. Fract. Mech., 2006, 73, p 1849–1864

    Article  Google Scholar 

  20. J.H. Hollomon, Tensile Deformation, Trans. Metall. Soc. AIME, 1945, 162, p 268–290

    Google Scholar 

  21. P. Ludwik, Elements der Technologischen Mechanik, Vol 32, Verlag Von Julius Springer, Berlin, 1909

    Book  Google Scholar 

  22. H.W. Swift, Plastic Instability Under Plane Stress, J. Mech. Phys. Solids, 1952, 1, p 1–18

    Article  Google Scholar 

  23. D.C. Ludwigson, Modified Stress–Strain Relation for FCC Metals and Alloys, Metall. Trans., 1971, 2, p 2825–2828

    Article  CAS  Google Scholar 

  24. E. Voce, The Relationship Between Stress and Strain for Homogeneous Deformation, J. Inst. Metal., 1948, 74, p 537–562

    CAS  Google Scholar 

  25. J. Vanaja, K. Laha, S. Shiju, M. Nandagopal, S. Panneer Selvi, M.D. Mathew, T. Jayakumar, and E. Rajendra Kumar, Influence of Strain Rate and Temperature on Tensile Properties and Flow Behaviour of a Reduced Activation Ferritic–Martensitic Steel, J. Nucl. Mater., 2012, 424, p 116–122

    Article  CAS  Google Scholar 

  26. C. Girish Shastry, M.D. Mathew, K.B.S. Rao, and S.L. Mannan, Analysis of Elevated Temperature Flow and Work Hardening Behaviour of Service-Exposed 2.25 Cr-1Mo Steel Using Voce Equation, Int. J. Press. Vessels Pip., 2004, 81, p 297–301

    Article  Google Scholar 

  27. V. Shiva, S. Goyal, R. Sandhya, K. Laha, and A.K. Bhaduri, Flow Behaviour of Modified 9Cr-1Mo Steel at Elevated Temperatures, Trans. Indian Inst. Metals, 2017, 70, p 589–596

    Article  CAS  Google Scholar 

  28. J. Christopher, B.K. Choudhary, E. Isaac Samuel, M.D. Mathew, and T. Jayakumar, Tensile Stress–Strain and Work Hardening Behaviour of P9 Steel for Wrapper Application in Sodium Cooled Fast Reactors, J. Nucl. Mater., 2012, 420, p 583–590

    Article  CAS  Google Scholar 

  29. M. Alves and N. Jones, Influence of Hydrostatic Stress on Failure of Axisymmetric Notched Specimens, J. Mech. Phys. Solids, 1999, 47, p 643–667

    Article  CAS  Google Scholar 

  30. J.C. Earl and D.K. Brown, Distributions of Stress and Plastic Strain in Circumferentially Notched Tension Specimens, Eng. Fract. Mech., 1976, 8, p 599–611

    Article  Google Scholar 

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Authors and Affiliations

  1. Rubber Technology Centre, Indian Institute of Technology, Kharagpur, Kharagpur, 721302, India

    Mohit Goswami & Abhay Kumar

  2. Materials Engineering Group, Indira Gandhi Centre for Atomic Research, Kalpakkam, 603102, India

    Sunil Goyal & S. K. Albert

  3. Department of Mechanical Engineering, National Institute of Technology, Srinagar, Srinagar, 190006, India

    G. A. Harmain

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  1. Mohit Goswami
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  2. Sunil Goyal
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  3. Abhay Kumar
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  4. G. A. Harmain
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Correspondence to Sunil Goyal.

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Goswami, M., Goyal, S., Kumar, A. et al. Effect of Triaxial State of Stress on Tensile Behavior of Modified 9Cr-1Mo Steel. J. of Materi Eng and Perform 29, 1579–1588 (2020). https://doi.org/10.1007/s11665-020-04670-8

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  • DOI: https://doi.org/10.1007/s11665-020-04670-8

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