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Journal of Molecular Modeling

, 25:321 | Cite as

Understanding the physics of non-linear unloading-reloading behavior of metal for springback prediction

  • Ashutosh Rajput
  • Surajit Kumar PaulEmail author
Original Paper

Abstract

Finite element simulation technique is extensively useful nowadays for die designing by optimizing the springback from the formed state of sheet metal panel. The magnitude of springback is normally calculated in finite element simulation by assuming a completely elastic recovery in non-linear kinematic hardening law. Constant values of elastic modulus and Poisson’s ratio are required to estimate the elastic recovery by non-linear kinematic hardening law. Cleveland and Ghosh (Int J Plast 18:769–785, 2002), Li and Wagoner (Int J Plast 1827:1126–1144, 2011), and many other research groups have reported that inelastic strain release during unloading is the main source of extra strain recovery and as a result poor springback prediction by commercial finite element software. In this regard, many theoretical postulates have been proposed to explain such inelastic strain release during unloading. In this work, we show from atomistic simulation that irreversible movement of dislocation, i.e., microplasticity, is the source of inelastic strain release during unloading.

Keywords

Uniaxial tensile deformation Unloading-reloading Springback Nanocrystalline gold Molecular dynamics simulation 

Notes

References

  1. 1.
    Sun L, Wagoner RH (2011) Complex unloading behavior: nature of the deformation and its consistent constitutive representation. Int. J. Plast. 1827:1126–1144CrossRefGoogle Scholar
  2. 2.
    Wagoner RH, Wang JF, Li M (2006) “Springback,” Chapter in ASM handbook. 14B: Metalworking: sheet forming, pp. 14:733–755Google Scholar
  3. 3.
    Cleveland RM, Ghosh AK (2002) Inelastic effects on springback in metals. Int. J. Plast. 18:769–785CrossRefGoogle Scholar
  4. 4.
    Pourboghrat F, Chung K, Richmond O (1998) A hybrid membrane/shell method for rapid estimation of springback in anisotropic sheet metals. J Appl Mech–T ASME 6:671–684CrossRefGoogle Scholar
  5. 5.
    Morestin F, Boivin M (1996) On the necessity of taking into account the variation in the young modulus with plastic strain in elastic-plastic software. Nucl. Eng. Des. 162:107–116CrossRefGoogle Scholar
  6. 6.
    Yoshida F, Uemori T (2002) A model of large-strain cyclic plasticity describing the Bauschinger effect and workhardening stagnation. Int. J. Plast. 18:661–686CrossRefGoogle Scholar
  7. 7.
    Eggertsen PA, Mattiasson K (2010) On constitutive modeling for springback analysis. Int. J. Mech. Sci. 52:804–818CrossRefGoogle Scholar
  8. 8.
    Fei DY, Hodgson P (2006) Experimental and numerical studies of springback in air v-bending process for cold rolled TRIP steels. Nucl Eng and Des 236:1847–1851CrossRefGoogle Scholar
  9. 9.
    Yu HY (2009) Variation of elastic modulus during plastic deformation and its influence on springback. Mater Desi 30:846–850CrossRefGoogle Scholar
  10. 10.
    Murnaghan FD (1967) Finite deformation of an elastic solid. Dover, New YorkGoogle Scholar
  11. 11.
    Ghosh AK (1980) A physically-based constitutive model for metal deformation. Acta Metall. 28:1443–1465CrossRefGoogle Scholar
  12. 12.
    Zhou H, Xian Y, Wu R, Hu G, Xia R (2017) Formation of gold composite nanowires using cold welding: a structure-based molecular dynamics simulation. CrystEngComm 19:6347CrossRefGoogle Scholar
  13. 13.
    Li J, Lu B, Zhou H, Tian C, Xian Y, Hu G, Xia R (2019) Molecular dynamics simulation of mechanical properties of nanocrystalline platinum: grain size and temperature effects. Phys. Lett. A 383:1922–1928CrossRefGoogle Scholar
  14. 14.
    Li J, Tian C, Lu B, Xian Y, Wu R, Hu G, Xia R (2019) Deformation behavior of nanoporos gold based composite in compression: a finite element analysis. Compos. Struct. 211:229–235CrossRefGoogle Scholar
  15. 15.
    Hirel P (2015)Atomsk: a tool for manipulating and converting atomic data files. Comput. Phys Commun 197:212–219CrossRefGoogle Scholar
  16. 16.
    Plimpton S (1995) Fast parallel algorithms for short-range molecular dynamics. J. Comput. Phys. 117:1–19CrossRefGoogle Scholar
  17. 17.
    Stukowski A (2010) Visualization and analysis of atomistic simulation data with OVITO-the Open Visualization Tool. Model. Simul. Mater. Sci. Eng. 18Google Scholar
  18. 18.
    Nathanson M, Kanhaiya K, Pryor A, Miao J, Heinz H (2018) Atomic-scale structure and stress release mechanism in core-shell nanoparticles. ACS Nano 12:12296–12304CrossRefGoogle Scholar
  19. 19.
    Luo LM, Ghosh AK (2003) Elastic and inelastic recovery after plastic deformation of DQSK steel sheet. J Eng Mater-T ASME 125:237–246CrossRefGoogle Scholar
  20. 20.
    Andar MO, Kuwabara T, Yonemura S, Uenishi A (2010) Elastic-plastic and inelastic characteristics of high strength steel sheets under biaxial loading and unloading. ISIJ Int. 50:613–619CrossRefGoogle Scholar
  21. 21.
    Kim H, Kim C, Barlat F, Pavlina E, Lee MG (2013) Nonlinear elastic behaviors of low and high strength steels in unloading and reloading. Mater Sci Eng-A 562:161–171CrossRefGoogle Scholar
  22. 22.
    Chen Z, Bong HJ, Li D, Wagoner RH (2016) The elasticeplastic transition of metals. Int. J. Plast. 83:178–201CrossRefGoogle Scholar
  23. 23.
    Cottrell AH (1961) Dislocations and plastic flow in crystals. Clarendon Press, OxfordGoogle Scholar
  24. 24.
    Frank FC, Read WT (1950) Multiplication processes for slow moving dislocations. Phys. Rev. 79:722CrossRefGoogle Scholar
  25. 25.
    Mott NF (1946) Atomic physics and strength of metals. J. Inst. Met. 72:367Google Scholar
  26. 26.
    Yamakov V, Wolf D, Salazar M, Phillpot SR, Gleiter H (2001) Length-scale effects in the nucleation of extended dislocations in nanocrystalline Al by molecular-dynamics simulation. Acta Mater. 49:2713–2722CrossRefGoogle Scholar
  27. 27.
    Jiang B, Tu A, Wang H, Duan H, He S, Ye H, Du K (2018) Direct observation of deformation twinning under stress gradient in body-centered cubic metals. Acta Mater. 155:56–68CrossRefGoogle Scholar
  28. 28.
    George E. Deiter (2016) Mecanical Metallurgy, pp 35–36Google Scholar
  29. 29.
    Wael A, Huseyin S (2017) Critical resolved shear stress for slip and twin nucleation in single crystalline FeNiCoCrMn high entropy alloy. Mater Charac. 129:288–299CrossRefGoogle Scholar
  30. 30.
    Aral G, Wang YJ, Ogata S, Van Duin CT (2016) A effects of oxidation on tensile deformation of iron nanowires: insights from reactive molecular dynamics simulations. J Appl Phy 135104:1–14Google Scholar
  31. 31.
    Shimizu F, Ogata S, Li J (2007) Theory of shear banding in metallic glasses and molecular dynamics calculations. Mater. Trans. 48:2923–2927CrossRefGoogle Scholar
  32. 32.
    Sha ZD, Pei QX, Liu ZS, Zhang YW, Wang TJ (2015) Necking and notch strengthening in metallic glass with symmetric sharp-and-deep notches. Sci. Rep. 5:1–7Google Scholar
  33. 33.
    Rajut A, Ghosal P, Kumar A, Paul SK (2019) Monotonic and cyclic plastic deformation behavior of nanocrystalline gold: atomistic simulations. J. Mol. Model. 25:153CrossRefGoogle Scholar
  34. 34.
    Paul SK (2018) Effect of twist boundary angle on deformation behavior of 〈1 0 0〉 FCC copper nanowires. Comput. Mater. Sci. 150:24–32CrossRefGoogle Scholar
  35. 35.
    Gianola DS, Van Petegem S, Legros M, Brandstetter S, Van SH (2006) Stress-assisted discontinuous grain growth and its effect on the deformation behavior of nanocrystalline aluminum thin films. Acta Mater. 54:2253–2263CrossRefGoogle Scholar
  36. 36.
    Rupert TJ, Gianola DS, Gan Y, Hemker KJ (2009) Experimental observations of stress- driven grain boundary migration. Sci 326:1686–1690CrossRefGoogle Scholar
  37. 37.
    Schiotz J, Di Tolla FD, Jacobsen KW (1998) Softening of nanocrystalline metals at very small grain sizes. Nature 39:561CrossRefGoogle Scholar
  38. 38.
    Schiotz J, Di Tolla FD, Jacobsen KW (1999) Atomic-scale simulations of the mechanical deformation of nanocrystalline metals. Phys. Rev. B 60:11971CrossRefGoogle Scholar
  39. 39.
    Swygenhoven HV, Spaczer M, Caro A (1999) A microscopic description of plasticity in computer generated metallic nanophase samples: a comparison between Cu and Ni. Acta Mater. 47:3117CrossRefGoogle Scholar
  40. 40.
    Keblinski P, Wolf D, Gleiter H (1998) Molecular-dynamics simulation of grain-boundary diffusion creep. Interface Sci 6:205CrossRefGoogle Scholar
  41. 41.
    Yamakov V, Phillpot S R, Wolf D, Gleiter H (2000) Computer simulations in condensed matter physics, Vol. XIII, ed. D. P. Landau, S. P. Lewis and H. -B. Schu¨ttler. Springer, New York, p. 195Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringIndian Institute of Technology PatnaBihtaIndia

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